Multidimensional Component Inspection Devices

Transcript

Miltiadis A. Boboulos, Ph.D. MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES ABSTRACT The evaluation of the mechanical behaviour of a sample under conditions of tension and compression can be performed to provide basic material property data that is critical for component design and service performance assessment. The requirements for tensile and compression strength values and the methods for testing these properties are specified in various standards for a wide variety of materials. Testing as explained in this book can be performed on machined material samples or on full-size or scale models of actual components. These tests are typically performed using mechanical testing instruments. Worn suspension bushings may also cause excessive side-to-side caster angle and toe angle changes during steering, braking and acceleration driving modes. The best way to inspect suspension bushings in a loaded condition is to place the vehicle on a drive-on lift. During your inspection process, it's important to visualize exactly how the chassis loads each bushing. When suspension loading is taken into account, it's easy to see why the inner and outer bushing sleeves should appear to be concentric. If the bushing doesn't appear to be concentric, the rubber inside the bushing has lost its resiliency and has taken a "set" because of suspension system loading. Many products and components are in addition subjected to torsional forces during their operation. Products such as biomedical catheter tubing, switches, fasteners, and automotive steering columns are just a few devices subject to such torsional stresses. By testing these products in torsion, manufacturers are able to simulate real life service conditions, check product quality, verify designs, and ensure proper manufacturing techniques. In this publication torsion tests have been performed and explained by applying only a rotational motion and torsional forces. Types of torsion testing such as failure, and proof are being analyzed. MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES TABLE OF CONTENTS A. INSPECTION DEVICE FOR BUSHING-TYPE COMPONENTS ___ 1 1. INTRODUCTION ________________________________________________ 1 2. REVIEW OF MULTI-DIMENSIONAL INSPECTION DEVICES FOR INSPECTING BUSHING-TYPE COMPONENTS _____________________ 3 2.1 2.2 SCHEMATIC DIAGRAMS__________________________________________ 3 DESIGN SCHEMATICS ____________________________________________ 7 3. SELECTION OF A SCHEMATIC DIAGRAM _______________________ 10 4. CONSTRUCTION CALCULATIONS_______________________________ 12 4.1 4.2 FLAT SPRINGS__________________________________________________ 12 SPRING PARALLELOGRAMS _____________________________________ 12 4.2.1 Spring parallelograms supporting intermediate elements_______ 13 4.2.2 Spring parallelogram supporting the measuring bracket _______ 13 4.3 4.4 SPRING HINGE _________________________________________________ 13 CYLINDRICAL HELICAL SPRINGS ________________________________ 15 4.4.1 SPRINGS PROVIDING MEASUREMENT PRESSURE ______ 15 4.4.2 Clamp spring _________________________________________ 16 5. MEASUREMENT ERROR ANALYSIS _____________________________ 18 5.1 KINEMATICAL AND TECHNOLOGICAL ERRORS ___________________ 19 5.1.1 Kinematical errors_____________________________________ 19 5.1.2 Technological errors ___________________________________ 19 5.2 5.3 ERRORS OF THE MEASUREMENT UNIT (INSTRUMENT ERROR) _____ 20 ERRORS IN THE MEASUREMENT DIAGRAM _______________________ 21 5.3.1 Effect of surface roughness over errors of the measurement diagram ___________________________________ 21 5.4 ERRORS DUE TO POSITIONING IN MEASUREMENT ________________ 21 5.4.1 Effect of the violation of the principle of unity of bases ________ 22 5.4.2 Errors of positioning during measurement of internal cylindrical surfaces occurring as a result of the displacement of measurement baseline in respect to the inspected diameter ______ 22 5.5 5.6 TEMPERATURE ERROR__________________________________________ 22 ERRORS DUE TO FORCES ACTING DURING MEASUREMENT ________ 24 5.6.1 Characteristics of measurement pressure ____________________ 24 5.6.2 Contact deformations ___________________________________ 25 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 5.7 ERRORS DUE TO ADJUSTMENT OPERATIONS _____________________ 25 5.7.1 Adjustment operation errors depending on the quality of the adjustment unit _______________________________________ 25 5.7.2 Adjustment operation errors depending on the selected adjustment technique____________________________________ 26 5.7.3 Adjustment operation errors related to operator’s state and qualifications_________________________________________ 26 5.8 5.9 SUBJECTIVE ERROR ____________________________________________ 27 OPERATION ERROR _____________________________________________ 27 5.9.1 Measurement shoe wear ________________________________ 27 5.9.2 Rate of distortion of the adjustment of the measuring device____ 28 6. DEVICE ADJUSTMENT TECHNIQUE_____________________________ 28 REFERENCES ____________________________________________________ 29 B. A TENSION/PRESSURE LOAD TESTING DEVICE__________ 30 1. DEVICE OPERATION PRINCIPLE________________________________ 30 2. SAFETY REGULATIONS & ENVIRONMENTAL CONSIDERATIONS _ 31 3. TENSION TESTING RIG _________________________________________ 34 4. CLAMPING THREADS CALCULATIONS FOR FASTENING PLATES 39 REFERENCES ____________________________________________________ 44 C. A TORSION TESTING DEVICE___________________________ 45 1. INTRODUCTION _______________________________________________ 45 2. STATIC TESTS _________________________________________________ 45 3. MATERIAL TORSION TEST SYSTEM (ASSEMBLY DIAGRAM) _____ 49 3.1 Torsion testing equipment specification________________________________ 51 4. DESIGN & STRENGTH CALCULATIONS _________________________ 53 REFERENCES ____________________________________________________ 76 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES A. INSPECTION DEVICE FOR BUSHING-TYPE COMPONENTS 1. INTRODUCTION One of the most important factors determining technical progress in machinebuilding production is increasing labour efficiency and product quality. One real prerequisite to accelerate production process is building of new metal processing machines and establishing new processing techniques. Likewise, quality improvement is associated with precision of both processing and post-processing operations [1]. No matter how perfect may metal-processing machines be there are still a number of technological factors which influence precision during product manufacturing and these are tool wear, and the thermal and impact distortion of the technological system [1]. Errors caused as a result of these factors have the character of accidental dimensional functions. For this reason, it is very hard to compensate them by means of prior machine adjustments. The problem of decreasing the influence of said technological factors is the concern of the so-called active (technological) inspection. When using precise connections like roller bearings, piston groups, it is a necessity for a machine or a device-building to make economically justified components that are totally interchangeable. Problems may arise with components requiring higher precision of geometry and relative position of planes and axes [2]. In such cases it is necessary to discard out of size components or sort them within tolerance groups to ensure product quality. This is the purpose of the so-called passive (post-operational) inspection [2]. Passive inspection is performed via the following means, depending on the type of the technological process: inspection devices; dimension measuring machines; inspection and sorting automated devices. Inspection and sorting automated devices have got completely automated inspection cycle. They are used to inspect the parameters of groups of similar components. Human intervention is only possible when periodic loading of components is necessary while the automated device is working fully independently [2]. Dimension measuring machines are a means of making universal measurements automatically. Three-dimensional machines are used to inspect according to a previously set programme dimensions of components, deviations in shape and relative position of planes, complicated profiles, etc. with automated data processing. The task of the operator is to initially position the component relative to the coordinate system of the machine. Page 1 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Inspection devices possess the lowest level of automation. They offer automation only in inspection and data processing. All other operations (feed-in, positioning, sorting of components) are manually performed [2]. Inspection devices can be single-dimensional (inspection of a single parameter) and multi-dimensional (simultaneous inspection of several parameters). Usage of the latter allows increase of productivity and inspection efficiency. The inspection device subject of the present work is of the same multi-dimensional type. The possibility to perform simultaneous inspection of several parameters, decrease of subjective errors in measurement and their relatively low values provide for the high economic efficiency ensured by the implementation of inspection devices. Page 2 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 2. REVIEW OF MULTI-DIMENSIONAL INSPECTION DEVICES FOR INSPECTING BUSHING-TYPE COMPONENTS Multi-dimensional inspection devices are built up on the basis of schematic diagrams of single-dimension devices for inspection of the corresponding parameters incorporated in a single construction. Therefore, a wide variety of designs are available based on the objectives laid out. The present review is a survey of several kinematical diagrams of single-dimension devices for inspection of diameters (both outer and inner) and heights. It also provides some practical implementations of several of them and also, some developments of multidimensional devices. Universal inspection and measurement devices are developed mainly for inspection of external and internal cylindrical surfaces, shaft lengths and geometry deviations. This is only a small part of inspected parameters of machine components but the complexity and specificity of inspection processes limit the possibilities for a wider normalization [3]. Moreover, the percentage of this type of inspection is too high and there are more developments made for it due to this. 2.1 SCHEMATIC DIAGRAMS Fig. 1 shows an inspection location for shaft diameters. It represents a doublecontact adjustable bracket the bottom shoe 7 of which is fixed (throughout the measurement process) to the tube 2. The upper shoe 6 is floating and supported on flat springs 5 thus transmitting measurement signal to the transducer 4. The entire bracket is floating, too. It is mounted to the body of the device by means of a spring parallelogram that in this case is a special hinge l. Clamping of the bottom shoe to the component is by means of the spring 3. The schematic diagram shown on Fig. 2 can be used for inspection of holes. A double-contact bracket having one fixed shoe 3 is also used here which is at the same time used as a stop for positioning the component l along its inner surface. The other shoe 2 is a floating type and mounted on the strip 4, which in turn is mounted on flat springs. The strip transmits via the contact tip 5 the measurement signal to the transducer 6. To achieve higher precision in positioning of the component so the measurement line coincides with the diameter, the fixed shoe can be made provided with two contact points similar to the inside dial gauge. This way, the schematic diagram of a universal unit for simultaneous inspection of inner and outer diameters was also developed, as shown in Fig. 3. The design developed is used for the measurement of bushing-type components. The device comprises a base plate l with two diametrically moving against each other measuring slides 2 and 3. One slide 2 carries four sensor elements (6, 7, 8 and 9) and the other measurement slide 3 carries two sensor elements 10 and 11. All four sensor elements are located in pairs symmetrically against the axis 12 running along the other two sensor elements 10 and 11 and in the same axis of symmetry 13 with the inspected component. The use of the contact pairs 6-7 and 8-9 is implied by the fact that when sensor elements Page 3 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES contact the wall in two points it is not always possible to achieve precise preliminary adjustment, which adversely effects measurement accuracy. The principle of action of the device shown is the following: The component to be measured 14 is positioned over the measurement plate 18, which is located above sensor elements 6 thru 11. By descending the plate the component is positioned at the height of measurement. Measuring slides 2 and 3 are moved out (or in, respectively) by means of spindle-drive nut 4 and the sensors 8, 9 and 10 (6, 7 and 11, respectively) perform threepoint contact. Thus, an independent component positioning in the measuring location is achieved. The inspection device described can easily be included in an automated production process thanks to the fact that the component is a self-positioning. Another development design for a device for measurement of inner and outer diameters is shown in Fig. 4. One significant advantage here is the possibility to work without any preliminary adjustment of a defined dimension. The basic elements of the device are the body 8 having a radial guide on which the measurement fork l is situated with several sensor elements 2 mounted on its arms 3. The device is moved by means of the driving element 5 and driving module 6. Movement is effected against the fixed receiver of measurement values 7. Fig. 4a shows measurement of an outer diameter. The measurement fork l is moving until the component 4 positioned between the arms 3 consecutively contacts the sensors 2. Thus, the values of the measuring device 7 are read and the diameter is determined in the “rest” position of the component. Page 4 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Fig. 1 Fig. 2 Page 5 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Fig. 3 Similar is the method used for the measurement of inner diameters shown on Fig. 4b. In this case the component is located on the table 9 and positioned against the stop 10. The basic difference from the measurement of outer diameters is in the fact that the sensors 2 are located on the same arm 3. To perform the measurement, it is necessary that the sensors 3 consecutively contact the component. Reading is similar to the previous measurement. Page 6 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 2.2 DESIGN SCHEMATICS A first design represents a design schematic of a universal measurement unit for the inspection of outer diameters. It is made according to the schematic diagram of Fig. 1. The unit is capable of measuring various diameters and adjustment is made by means of moving the shoe 1 and the carriage 2. Thanks to the suspension of flat springs 3 the bracket is a self-adjusting one and no arresting unit is necessary for the positioning and removal of the inspected component. Similar is the arrangement used for the present development. In a device for measuring hole diameters, the unit is used to inspect the opening for the piston pin of the piston. The principle of action is as follows: the piston is inserted over the mandrel having welded hard-alloy strips. The strip presses the piston against the upper hard-alloy support of the mandrel under the action of the springs. The dimensional deviation of the diameter is transmitted to the measurement head or sensor tip via the arm with spherical and flat tip. The present design uses a similar mandrel for positioning the component to be inspected and transmitting measurement signal via a flat and spherical tip arm. In a device for inspecting holes: Mounted on the flat springs to the body are the location pins and the measurement tips. They can be moved along T-shaped groove guides and fixed in position by means of screws 6 thus changing measuring range from φ15 to φ60 mm. The plate’s lapped surface is used for face positioning of inspected components. The arm 8 arrests measuring and location pins simultaneously. It has two end positions determined by a ball catch. A screw is used to coincide the measurement line with the diameter of the inspected component. The screw is used for the fine adjustment of the built-in inductive transducer. A cable is used to connect the inductive unit to the intermediate transducer. Page 7 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Fig. 4 a) Fig. 4 b) For the inspection of light components – bushings the adjustment for coincidence of the measurement line with the hole diameter is only performed a single time and each component is automatically positioned afterwards at a location deviation of less than ±0.2µm. A multi-dimensional inspection device is used to inspect three diameters and two Page 8 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES heights of a bushing-type component. The component is positioned on the mandrel 1, pressed into the carriage that can move in reciprocating manner with the handle via the tooth section and the rack. Thus, the component is moved into measuring position and positioned on (off) the mandrel. Diameters are inspected by means of double-contact brackets, suspended on a spring parallelogram. The electrical contact transducers are mounted on the brackets. The measuring tip of the transducer receives data for the inspected diameter via an intermediate bar suspended on flat springs and mounted to the bracket. Suspension of brackets on spring parallelogram eliminates errors resulting from eventual run-out of inspected cylindrical surfaces against the base cylindrical plane. Both heights are inspected using single-contact units comprising the intermediate transmission elements and the electric contact transducers. Recently often used are inspection and measurement devices built on modular principle. Normalized assemblies and elements used to build a universal, adjustable multidimensional device for the inspection of components like shafts and pins for diameters up to φ 100mm and lengths up to 750mm. The quantity, type and inter-positioning of assemblies and elements used to build up the device are determined by the construction of the inspected component. The set includes four basic groups: I II - Measuring brackets. - Assemblies for positioning and locating the inspected components: prisms, centers, and pin stops. III – Fastening elements: plates, pins, stands and arms for positioning and supporting above elements in a given arrangement IV - Tips and transmission assemblies – aids for suitable location of measurement devices and transducers on brackets. Layouts for multi-dimensional devices based on MPV are the vertical layout with positioning between centers and the horizontal with positioning over two pins in locating brackets. The Swiss company TESA also produces elements and assemblies for multidimensional devices. Their nomenclature allows a wider variety of layouts for measuring diameters (inner and outer) and lengths [5]. The use of multi-dimensional devices built-up of normalized elements and assemblies provides lots of advantages: Eliminates the need for many specialized attachments. This gives many organizational advantages with respect to storehouses, maintenance and necessity to discard equipment when seizing a given production. Normalized elements and assemblies are not tied up to certain products. Conditions are set out for centralized production of elements for measuring equipment. Inspection efficiency is largely improved. Expenses for universal measurement instruments are cut down. - 3. Page 9 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES SELECTION OF A SCHEMATIC DIAGRAM The device to be developed in the present work aims at inspecting all three parameters of a smooth bushing simultaneously. As mentioned earlier, multi-dimensional inspection devices can be considered as consisting of several single-dimensional ones. For our case, these are constructions for measuring inner diameters, outer diameters and heights (lengths, respectively) [5]. We selected a commonly occurring solution for the inspection of the outer diameter – the double-contact bracket. The schematic diagram for this bracket is shown on Fig. 1. There are several reasons for this particular selection. First of all is the simplicity of the construction. Another reason is the self-adjustment of the bracket. This is achieved through flat spring suspension and eliminates possible errors from radial run-out against the base plane. An advantage of this diagram is also the fact that the Abbey principle is being observed in the measurement. The schematic diagram for inspecting the inner diameter of the bushing was developed on the basis of the diagram shown on Fig. 2. Several changes were made for this particular application of the diagram. The strip 4 in Fig. 2 was exchanged for a bar supported on a spring hinge. Another change that was shared with the Fig. 3 schematic diagram is using two fixed shoes to improve positioning. We have chosen the solution for the length measurement. Its advantages are construction simplicity and observing Abbe’s principle [6]. The design diagram of the device shown on Fig.5 is a synthesis of all three diagrams considered so far. Various views show how inspection of each parameter is performed. The sections for inspection of the other dimensions are shown as a block (rectangle) in each view. The principle of action is the following: The carriage 2 is drawn out by means of the handle 1. The component 3 is positioned at inner diameter inspection position. Positioning is achieved by means of fixed shoes 15 and measuring tip 14 mounted on the bar. The carriage containing the outer diameter and length inspection sections is then returned at measurement position. When carriage is set in position the measuring tips mounted on intermediate elements 4 and 9 contacts the component. The deviations from set in adjustment dimensions are then transmitted via elements 4 and 9 to transducers 6 and 11. These are moved by means of spring parallelograms 5 and 10. Measurement pressure is ensured by springs 7 and 13. The spring parallelogram 12 is provided for the outer diameter inspection double-contact bracket and it provides self-adjustment of the bracket and avoids any errors from radial run-out against the base plane. The hole diameter inspection section is actuated immediately following component loading as it also provides positioning. When the component is loaded it rests against fixed shoes 15. The measuring tip contacts bushing inner surface and sends the signal to the transducer 17 via the bar 14 mounted on the spring hinge 16. The measurement pressure is also provided here by the spring 18. Page 10 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Fig. 5 The basic parts of the schematic diagrams are: 1 Carriage; 2 Handle; 3 Component; 4 Intermediate element; 5 Spring parallelogram; 6 Transducer; 7 Spring; 8 Fixed shoe; 9 Intermediate element; 10 Spring parallelogram; 11 Transducer; 12 Spring parallelogram; 13 Spring; 14 Bar; 15 Fixed shoes; 17 Spring hinge; 18 Transducer; 19 Spring. 4. Page 11 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES CONSTRUCTION CALCULATIONS Construction calculations for the design developed include kinematical and a strength calculation for flat and cylindrical helical springs and spring parallelograms used in the construction. These shall be considered as follows: 4.1 Positioning element flat spring 4.2 Spring parallelograms 4.2.1 Spring parallelograms supporting transmission elements 4.2.2 Spring parallelogram supporting measuring bracket 4.3 Spring hinge 4.4 Cylindrical helical springs 4.4.1 Springs providing measurement pressure 4.4.2 Clamp spring 4.1 FLAT SPRINGS The flat spring subject to the present calculation is provided to ensure holding of the component when positioned on the mandrel. This spring shall have to compensate for the action of the spring providing measurement pressure and the spring parallelogram of the outer diameter-inspecting bracket. The formulas needed for the calculations can be found in the literature [1]. The basic characteristics of the spring are: - material – 65G steel - modulus of linear elongation – E=2.10¹¹Pa - allowed bending stress – [σ bn] = 65.10 Pa - full load – F=7N - length – l=24mm We assume the necessary deflection value to be f=1.6mm. We calculated strip thickness h from the equation [6]: h = 2l2[σ bn] / 3Ef h=0.7mm We use this result to calculate strip width using the formula: b=6Fl / h2[σ bn] b=3.6mm (4.2) (4.1) 4.2 SPRING PARALLELOGRAMS Spring parallelograms represent two flat springs connected in parallel, which support an element providing some small linear displacement. When making my calculations for these springs we used the technique from Para 4.1. Spring parallelograms Page 12 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES are used in two cases in this particular design. We have chosen the same material for both – steel 65G. It has the following characteristics [7]: - modulus of linear elongation – E=2.10¹¹Pa - allowed bending stress – [σ bn] = 65.10 Pa It should be kept in mind during calculation that when connected in parallel the load is distributed proportionately between the connected springs. As is in this particular case, when using two identical springs the acting force is being equally distributed over them. 4.2.1 Spring parallelograms supporting intermediate elements There are two spring parallelograms in this particular design and these support elements having measuring tips mounted on them, which transmit the measurement signal to the inductive transducers in the length and outer diameter inspection sections. These are designed to carry identical loads as intermediate elements have very similar masses [8]. The initial data for the calculations are: - full load – F=1.8N - length –l=22mm We choose spring width of b=5mm. Calculating the strip thickness using the equation: h=√6Fl/b[σ bn] (4.3) h=0.3mm We use this result to calculate deflection using the formula: f=Fl³/3EJ where J=bh³/12 is the cross section inertia. f=2.8mm. (4.4) 4.2.2 Spring parallelogram supporting the measuring bracket The purpose of this spring parallelogram is to ensure self-adjustment of the outer diameter inspection double-contact bracket. The data for this calculation are: maximum load – F=1.6N length –l=25mm We choose spring width of b=8mm. We use the relationship (4.3) to calculate spring thickness using the data chosen. The result is: h=0.25mm. We calculated the deflection using equation (4.4) [7]: f= 4mm 4.3 SPRING HINGE The spring hinge in the present design is used to provide turning of the bar, which transmits measurement signals to the transducer at the bushing inner diameter inspection section. This hinge comprises two flat springs connected in parallel and positioned under Page 13 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES an angle against each other. The angle of rotation is small. This minimizes the error from the variable centre of rotation. We assume the bar transmitting the measurement pressure is a strut-framed beam. The reactions at the supports represent the loads on the flat springs. The force acting on the beam is the same from the spring providing the measurement pressure, i.e. F=5N. Loads can be presented as their components. Each spring is subjected to the action of one bending and one tensioning (pressure) force [8]. For this particular case the forces are: A = 30N B = 25N The angle at which hinge strips are positioned is α = 20°. The components will be presented by: A1= A cosα=28.19N B1=B cosα = 23.49N A2= A sinα = 10.26N B2=B sinα = 8.55N A1 and B1 are bending forces in above equations and A2 (B2) are tension (pressure respectively) forces. The material for the springs is steel 65G having the following characteristics [9]: - modulus of linear elongation – E=2.10¹¹Pa allowed bending stress – [σ bn] = 65.10 Pa Strip width is b = 6mm. The length is calculated from the expression: l = l / cosα = 10.6mm Thickness is calculated using the formula (4.3): bA = 0.7mm bB = 0.7mm Deflection is calculated from the expression for springs under combined loading: f max = f max1/(1±√P2/Po), (4.5) where f max1 is the bending under the action of the bending component according to formula (4.4) P2 is the other component; Po is the critical load calculated from the expression: Po = π²EJ/4l² (4.6) The type of the force P2 determines the sign in the brackets. When pressure is applied the sign is “+” and when tension is applied the sign is “-“. The values are: fmax A = fmax B = 0.3mm 4.4 Page 14 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES CYLINDRICAL HELICAL SPRINGS 4.4.1 SPRINGS PROVIDING MEASUREMENT PRESSURE We have chosen a cylindrical helical spring to provide measurement pressure because of the linearity of its characteristics. The spring is tension loaded. We have shared the calculations for similar springs from the reference literature [10]. The material chosen for the springs is steel having the following characteristics: modulus of angular deformation – G=8.10¹ºPa allowed torsion stress – [τ trs] = 6.10 Pa pre-load F o = 2N maximum load F max = 5N. The following initial parameters for the spring, can be altered later: The pre-load Fo ensures stable spring operation. It is selected within the range Fo = (0.3÷0.8) Fmax. For this particular case I have chosen a value of 0.4. In view of minimizing its size I have chosen an average spring diameter of D = 3mm. For construction considerations I have chosen wire diameter of d = 0.45mm. I used these two values to find the spring index c using the formula: c = D/d c = 0.667. With the values thus calculated I could check the spring axial load – torsion stress. It is calculated from the formula: τ trs = 8FD / πd3 (4.5) Considering the effect of the helical scan having a coefficient k 1, the check becomes τ trs = k1 (8FD / πd3) ≤ [τ trs] (4.6) The coefficient k1 depends on the value of the spring index c. This coefficient increases as c decreases and when c >10 it may be considered that k1 ≈ 1. For the rest of the cases it is determined by the expression [11]: k1 = (4c – 1)/(4c - 4) + 0.615 / c For this particular case: K1 = 1.2246. The result from the check is: τtrs = 5.13.108 Pa < [τtrs] = 6. 108 Pa The conclusion is that the parameters chosen meet our requirements. The next step is the calculation of the number of windings and the lengths at various loads. For this purpose it is necessary to know spring deflection at maximum load f. I assume that for our case f = 2mm will be sufficient. The formula for the calculation of the number of windings is: Page 15 (4.4) (4.7) MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES n = Gd / 8Fc³ n = 6.075 windings For the number of windings the closest higher number is taken i.e. n = 7. We determine the spring constant K: K – Gd / 8c³n Following the substitution with known values: K = 3037.5 N/m The total number of windings is calculated from the relation: ntl = n + (1÷2) ntl = 8 windings (4.8) (4.9) (4.10) Further calculations involve spring lengths at various loads. The following formulas are used: length of the spring occupied with windings: (4.11) L = ntl d L = 3.6mm length of unloaded spring, i.e. distance between securing points: (4.12) Lo = L +(1÷2) D Lo = 6.6mm spring length at maximum operational load: (4.13) Lm = Lo +8c³ntl(F max – Fo) Gd Lm = 8.2mm length of the wire used for spring windings: (4.14) (4.15) l = πDntl/cos α + l 1 To find the slope of the helical line α I use the expression: α = arctg (t / πD) As the pitch t of springs loaded on tension we assume the thickness of the wire as in most cases windings are touching each other. In this case t = 0.45mm and the slope angle is: α = 2°44′. We assume an additional length needed to form the securing ends of l1 = 17mm. If we substitute the values in (3.8), then l= 92.5 mm 4.4.2 Clamp spring The clamp spring is loaded on pressure. Similar to the one, which provides measurement pressure, it is calculated according to a technique developed in the reference Page 16 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES literature [1]. The differences from the calculations for springs loaded on tension are in the formulas for various lengths. We have chosen the material for the spring to be steel having the following characteristics [12]: - modulus of angular deformation – G=8.10¹ºPa allowed torsion stress – [τtrs] = 6.108 Pa The output data necessary for the calculations are: maximum load Fmax = 8 N; initial load F0 = 4 N; deflection under maximum load fmax = 1mm. For construction considerations we choose the diameter of the wire to be d = 0.7mm and an average diameter of the spring D = 4mm. When I substitute these values in equation (4.4) I find the spring index to be: c = 5.714. When we substitute this into the equation (4.7) the coefficient defining the curvature of the windings can be found: k1 = 5.714. We use the values to check spring torsion according to formula (4.6) and I find: τtrs =3.10 Pa < [τtrs] = 6. 108 Pa The result of the check shows that the spring is properly dimensioned and will carry the expected load. The next step is to determine the number of spring operational windings. In equation (4.8) we substitute the values assumed and round the result to the closest higher number: n = 5 windings. The total number of windings for a spring subjected to pressure is calculated using the relationship: ntl = n + (1.5÷2) ntl= 7 windings The calculations that follow are related to spring lengths at various loads. minimum gap between windings at maximum load: (4.17) ∆ = (0.1÷0.2) f/n ∆= 0.017mm spring pitch: (4.18) t = f/n +d+∆ t =0.86mm spring length when pressed until windings touch: (4.19) L=(ntl-0.5) d L=4.55mm Page 17 (4.16) MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES - length of unloaded spring (4.20) L0=L+n (t-d) L0=5.35 mm angle of slope of helical line: α=arctg (t/πD) α=3°55′ length of the wire used to wind the spring: l = πDntl/cos α l=63mm For springs working under pressure the following condition is observed: L0/D<3 particular case: L0/D=1.3375<3, i.e. this condition is met. (4.21) (4.22) (4.23) When this condition is kept the spring will be resistant to buckling. For our 5. MEASUREMENT ERROR ANALYSIS Automatic inspection systems, along with universal measuring devices share a common metrological base determined by the measurement process. Hence, the theory of accuracy for universal measurement means could be transferred into the automatic inspection systems observing the features of inspection processes. Unlike the inspection involving universal measurement means, which has a continuous nature, the automatic inspection is in most cases of discrete nature. The discrete feature is defined by the fact that the systems used to perform this inspection most often only react to certain values for the inspected parameter. For example, this could be a limiting size of a component in the conditions of passive inspection. A conclusion can be drawn from all said above that automatic inspection devices must have discrete features regardless of the technique used for conversion of the measurement signal in the primary inspection section. The output signal of the primary transducer in the developed design is an analogue signal. Therefore, a transition should be considered from the analogue into a discrete signal for read out. The metrological analysis for the accuracy of the automated inspection of dimensions could be made based on the accuracy analysis of the measurement process using universal measuring means. These, on the other hand are characterized by a device reading error, which represents the difference between device readings and the actual value of the inspected parameter. Adopting a similar feature for the automatic inspection systems would be contrary to their discrete character and functional application. Therefore, their accuracy should be determined based on the difference between the actual value read for the inspected parameter at which the system is actuated, and the value for Page 18 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES this parameter for the sample used for the adjustment of the device. Actually, this difference represents an accumulated error of the system, which includes the errors of all its modules: receiving, transmitting, processing, comparing and executing. Three basic groups of errors are considered to comprise the cumulative error: kinematical and technological errors of transmitting circuits; errors due to the construction of the device and measurement process; errors caused by the operation conditions and adjustment 5.1 KINEMATICAL AND TECHNOLOGICAL ERRORS 5.1.1 Kinematical errors These errors are mainly due to the selected design diagrams for the measurement units or systems regardless of the method of transforming of the measurement signal. Kinematical errors are characterized by the lack of linear relation between the input and output parameters of measurement equipment and also, by the variable transmission rate. Although non-linearity does not affect accuracy, it is considered best when transforming characteristics have a linear nature and thus be able to work in a linear section. For the inductive transducer made by TESA (Switzerland) this is a linear characteristic for a major section of its range and the relative non-linearity [∆nonlin.] remains constant for a wide range [12]. 5.1.2 Technological errors These errors are due to inaccurate manufacturing of certain components and assemblies from the transmission circuit of units or devices or are due to the errors in their mutual position. These errors could have systematic or random nature. Their occurrence often depends on the functions of the measurement equipment and the measuring techniques. Therefore, it is very hard to pre-determine the rate and nature of their effect. In our particular design technological errors could be expected to arise from: inaccurate manufacturing of flat springs; inaccurate positioning of flat springs in relation to each other in the spring parallelogram and spring hinge; inaccurate manufacturing of the transmission bar, etc. The accuracy of the measurement could be influenced by each of the units comprising the measurement equipment. The error of the measurement unit, although prevailing for a number of cases, could not give a full and accurate idea of the accuracy of measurement. This accuracy is determined by the cumulative error for the measurement ∆∑, which includes the following components [13]: 1. 2. 3. The error of the measurement unit (instrument error). The error of the measurement diagram. The error of positioning during measurement. Page 19 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 4. 5. 6. 7. 8. Temperature error. The error caused by the forces applied during the measurement. Adjustment error Subjective error Operational error. Errors 2 and 3 comprise the measurement technique error or the systematic error. When adding separate components it should be kept in mind that each of them could have two parts – systematic and accidental, i.e. ∆I= ±∆mI ± ∆limi Then, ∆∑=±∑∆mI ± √(∆lim12+∆lim22+…+∆limn2) (5.2) The sum of the accidental components of the error is called limit error of the measurement method ∆lim∑ and accepts the sign of the systematic error of the measurement method ∆m∑. The methods used further down to describe errors were adopted from the literature [12]. Several basic types are only being used. (5.1) 5.2 ERRORS OF THE MEASUREMENT UNIT (INSTRUMENT ERROR) The instrument error determining the accuracy of the measurement device is characterized by the largest reading error within the measurement range. Depending on the section of the measurement range being used, the instrument error could be equal or less than the maximum reading error. When the full measurement range is being used, the instrument error is going to be equal to the maximum error. When 2-3 divisions from the measurement device scale are being used the instrument error is going to be equal to the accidental component of its measurement error when the measurement tip is arrested. When operating without arresting or making amplitude measurements (measurement of radial run-out and end play, measurements for shape deviations, etc.) the instrument error is going to be equal to the sum of the accidental component and the backstroke error. In practice, when designing inspection and measurement devices to measure dimensional parameters of components, standard measurement units are usually used from serial production. The accuracy for such units is characterized by the allowable reading error [∆R] or its accidental component – the reading variation V or the average error - σ. Preferably, the average error σ is used. When reading variation is applied it is necessary to point out the number of measurements for which it is determined. In technical measurements, the allowable error [∆R], and hence the instrument error are regarded as accidental values: ∆I =∆limI =[∆R] where ∆I is the instrument error, ∆limI is its accidental component. Page 20 (5.3) MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES When selecting standard measurement equipment the following relation determines the value for the allowable error [13]: [∆R] = 0.7[∆meas] (5.4) For our particular case the allowable measurement error [∆meas] is set to be 10µm. If we substitute in equation (5.4): [∆R] = 7µm. 5.3 ERRORS IN THE MEASUREMENT DIAGRAM The error in the measurement diagram arises as result of the diagram imperfection as a result of which the maximum and minimum values of the inspected dimension are being incomplete. The basic sources for the error of the diagram are dimensional deviations, shape deviations, location deviations and component roughness. 5.3.1 Effect of surface roughness over errors of the measurement diagram When contact measurement is performed it is possible for the measuring tip to fall into the depressions. The reading of the measurement unit will change depending on the positioning of the tip over a depression or projection: ∆dgr = f = -0.125 Sm/r (5.5) where r is the radius of the measuring tip and Sm is the roughness pitch. For our particular case such an error could appear only when measuring the inner diameter and length. When inspecting outer diameter the tips have flat surfaces, i.e. r =∞. As the radius is included in the denominator, ∆dgr = 0. For all other cases we get: ∆dgr = - 3.125µm. 5.4 ERRORS DUE TO POSITIONING IN MEASUREMENT The error in positioning occurs as a result of the inaccurate mutual positioning of the component to be measured and the measurement unit, which leads to misalignment of the measurement line of the measuring device and the reading line for the inspected parameter. This misalignment caused by a mistake in the fixing (securing) section causes the positioning error: ∆pos = xr – x (5.6) where x is the actual value of the parameter being measured and xr is the reading for the value of this parameter or the input signal to the measurement unit. Some basic reasons for the positioning error during measurement are: 1. 2. Failure to observe the principle of unity of bases Errors in the positioning section, measurement contact section and transducer supporting section. Page 21 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 5.4.1 Effect of the violation of the principle of unity of bases According to this principle the measurement and locating bases of the inspected component must be identical for a given measurement. A measurement base is the surface of the inspected component, which forms the dimension being inspected. A locating base is the surface of the inspected component over which it is located in the positioning section of the measuring device. When the principle of unity of bases has been observed no positioning errors occur (5.1), i.e. when measurement of the dimension L is performed (Fig. 5.1a) and this dimension is formed by two measurement bases – the top and bottom face ends of the component, the bottom measurement is identical to the locating base. The diameter dimension D is formed by the cylindrical surface, which is also identical to both the measurement and locating base. Failure to observe the principle of unity of bases results in the occurrence of a positioning error, which is a result of the mutual position of the measurement and locating bases for the component being inspected. The positioning error is determined by the formula: ∆pos = Lmeas - L where L is the actual dimension and Lmeas is the measured dimension. The locating and measurement bases are identical in our particular design, i.e. no positioning error is occurring. 5.4.2 Errors of positioning during measurement of internal cylindrical surfaces occurring as a result of the displacement of measurement baseline in respect to the inspected diameter When measuring the diameter of external cylindrical surfaces the measuring device is practically being self-positioned with respect to the diameter of the inspected component thanks to the use of flat measuring shoes. No such self-positioning is observed in double-contact measurements of inner diameters. When measurements on internal cylindrical surfaces are performed a complicated process of compatibility between measuring shoes (the measuring baseline) and the diameter in the inspected section is realized. The measurement error occurs as a result of the displacement of the measurement baseline with respect to the inspected diameter. Displacement could occur either in the plane, which is perpendicular to the axis of the opening, or in the axial plane of the opening. In the first case, a displacement of a chord instead of a diameter is occurring and in the second case, an ellipse diameter is displaced instead of a circle diameter. This error has been kept to a minimum in our particular design thanks to the use of a three-contact measurement layout thus improving accuracy in positioning. (5.7), 5.5 TEMPERATURE ERROR Temperature variations and deviations from the normal range (20˚C) could lead to Page 22 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES the occurrence of errors. The percentage of temperature error in the cumulative error for the measurement technique is considerable and increases with the increase of the inspected dimension. The temperature error occurs as a result of temperature deformations in the section of the dimensional circuit within the measuring diagram when: a. the temperature of the whole system (inspected component, measurement equipment and environment) is changed from the normal when components having different linear expansion coefficients are available either in the inspection device or the component being inspected; b. there is a difference in the temperature of the inspected component and the measuring device (for example, due to component heat-up during processing); c. variations in environmental temperature are observed including operator body heat emission and temperature fluctuations; d. local heat-up of parts of the components being inspected when held by the operator. Determining the cumulative effect of temperature deformations on the error of the measurement technique is very complicated, as this requires information about the physical properties of the material of the parts comprising the measuring device and of the component as well as temperature fields in these components. This information is very limited in real conditions so it is necessary to consider one maximum (marginal) value for the expected temperature error. In this case the concept of “temperature conditions” is used. This refers to a provisional difference in temperature between the inspected component and the measuring device expressed in ˚C, which under ideal conditions would cause the same temperature error, as is the entire complex of really existing causes. These “ideal conditions” refer to the fact that the device and the component have constant temperature content and the linear expansion coefficient of the material they were made of is equal to 11.6 .10¯ l/grad. The temperature conditions should not be understood as the allowable deviation from a 20˚C temperature environment or its fluctuation in the measurement process. Based on the definition given earlier, the temperature error resulting from temperature deformations under certain temperature conditions could be determined by the formula: ∆lt= l. Qt . 11.6. 10-6, where ∆lt is the temperature error; l is the dimension being measured; Qt is the temperature conditions. (5.8) Page 23 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 5.6 ERRORS DUE TO FORCES ACTING DURING MEASUREMENT The errors occurring from forces acting during the measurement (impact errors) occur as a result of the elastic deformations in the sections of the dimensional circuit within the measurement diagram. The basic source for impact errors is the measurement pressure. Measurement pressure and its variations have a critical influence on the accuracy of the measurement technique. Errors caused by measurement pressure depend on the size, shape and material of the inspected component and the stability of all sections within the dimensional circuit of the measurement diagram. 5.6.1 Characteristics of measurement pressure When constant measurement pressure is available in the measuring unit this could lead to certain deformation on some of the parts within the measuring unit and these deformations would still be constant throughout the measurement process. However, measurement pressure changes with the position of the measuring bar (Fig.2.5). The diagram shown on the Figure largely describes the real measurement pressure available at the measuring heads. The following definitions were adopted: ∆P1 - measurement pressure change with penetration of measuring bar down its complete stroke; ∆P2 stroke; ∆P3 - local change in measurement pressure; - measurement pressure change with sensor withdrawal back its complete ∆P’max – maximum hysteresis change in measurement pressure; ∆Pmax - maximum value of measurement pressure. The area of measurement pressure in the diagram characterizes the work necessary to overcome the friction forces in the measurement unit mechanisms when the measurement bar is moved to its end position. The hysteresis change in measurement pressure ∆P’ max is largely due to friction forces between measuring unit moving parts (measuring head) and is practically nonexisting in measuring devices where frictioning pairs have been substituted by elastically deforming elements. The local change ∆P3 is due to the uneven kinematical and force interaction between the moving parts of the measuring device. Errors caused by ∆P1, ∆P2 and ∆Pmax have a systematic character and could be excluded from the result of the measurement. The same refers to errors, caused by ∆P’ max when making amplitude measurements. However, when we keep in mind that ∆P max could show even when a single division of change in movement has occurred, these errors should be regarded as accidental for non-amplitude measurements. Page 24 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES It is hard to pre-determine the values for ∆P3 at the time of measurement so the errors occurring as a result of this change in pressure should also be regarded as accidental values. We used Table 10 [13] to get the data for contact measuring transducers made by TESA and Taylor Holson and these are: P max = 4.2÷20 cN ∆P1 = 0.2÷5 cN ∆P3 max = 0 ∆P’ max = 0.005÷2.2 cN Errors due to measurement pressure could be separated into three groups: 1. Errors due to the elastic deformation in the area of contact between the measuring shoe and the component inspected 2. Errors due to elastic deformations of the component (without the ones in the contact area) 3. Errors due to elastic deformations of the securing unit (carrier) of the measuring device and the parts comprising the unit itself and also, to elastic deformations in some of the other units comprising the measurement device. 5.6.2 CONTACT DEFORMATIONS An elastic deformation – shrinkage occurs at the point of contact between the measuring shoe and the surface of the component. The value of this deformation depends on the material of the shoe and the component and on their shape. When both the shoe and the component are made of steel, contact deformations are determined by the formula: ∆c = 0.43³√P²/r (5.9), where P is the measurement pressure at N, r is the measurement shoe radius in mm and ∆c is the contact deformation (impact error) in µm. Two types of measuring shoe are available for our particular design – spherical (having a radius of 1mm) to measure inner diameter and length, and knife-like shoes to measure outer diameter. We have been considering a flat contact surface for the latter, i.e. the radius equals infinity. This according to the formula means that the impact error is equal to zero. For the other shoes we have: ∆c = 1.26µm 5.7 ERRORS DUE TO ADJUSTMENT OPERATIONS The adjustment operation error of the measurement device for a given dimension depends on the quality of the adjustment unit, the selected adjustment technique and operator’s qualifications. 5.7.1 ADJUSTMENT OPERATION ERRORS DEPENDING ON THE Page 25 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES QUALITY OF THE ADJUSTMENT UNIT The occurrence of such errors is related to the following reasons: a. Friction available in the adjustment unit moving sections, which reduces its marginal sensitivity, i.e. the lowest change in adjustment level that can be achieved with sufficient accuracy via a single movement of the unit’s guide link. b. Misalignment during securing of adjusting element in the proper position – this is determined experimentally by testing a sample or reference part. c. Occurrence of elastic deformations on unit parts as a result of the strong forces necessary to move the adjustment element. d. A reading error on the gauge of the adjustment unit. In this case this is an accidental component of the reading error: ∆adj = ∆limmeas From equation (5.3) we get: ∆adj = 7 µm. 5.7.2 ADJUSTMENT OPERATION ERRORS DEPENDING ON THE SELECTED ADJUSTMENT TECHNIQUE The occurrence of such adjustment errors is related to the following reasons: a. Errors of manufacturing and certification of reference components used for the adjustment b. Violation of the principle of similarity between the adjustment reference (reference component) and the object of measurement. According to this principle, all parameters of the object of measurement and the adjustment reference, both geometrical (size, shape, location, roughness) and mechanical (material, hardness, weight, etc.) should be identical. Measurement and adjustment techniques should also be identical. This principle is often violated and this results in adjustment operation error. For example, when there is a difference in the linear expansion coefficients of the material of the reference and the object of the measurement, the adjustment error will then be determined by the difference in their temperature deformations, i.e. the same way as the temperature error: ∆adj = ∆t When there is a difference in hardness, shape, weight and stability it will be determined by the difference in impact deformations: ∆adj = ∆imp, etc. Therefore, special attention should be paid to the adjustment operation issues so adjustment error is kept within a reasonable range. 5.7.3 ADJUSTMENT OPERATION ERRORS RELATED TO OPERATOR’S STATE AND QUALIFICATIONS These errors are accidental by nature and are part of the subjective error. During Page 26 (5.10) MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES adjustment they are included in the reading error of the gauge of the adjustment unit used (5.7.1). 5.8 SUBJECTIVE ERROR In the case of our particular design the subjective error in reading is minimized as the output signal is discrete and is shown on the screen. 5.9 OPERATION ERROR The measurement accuracy decreases in the process of operation of the measurement device as a result of the combined action of several physical processes, like: wear, contamination and corrosion on operation surfaces, changes in parts elastic properties as a result of material fatigue, aging of mechanical components and elements of the electrical circuit [13]. All these processes influence various measurement component errors. It is hard to make an advance calculation of their influence because of the strong dependence of output data and particular measurement conditions and whenever this is possible, calculation is only too approximate. Such is the case with the calculation of measuring shoe wear and the rate of adjustment distortion as a result of unreliable securing of the unit on the device, accidental shocks, vibrations, etc. 5.9.1 MEASUREMENT SHOE WEAR (5.11), The value of such wear f could be determined using the equation [11]: ∆oper = f = upLK where u is the relative shoe wear in µm/Pa.m, p is the contact pressure in Pa, L is the friction path of the shoe during measurement in m, K is the total coefficient K = K1.K2.K3, Where K1 is the coefficient determining the rate of contamination in the area, K2 is the coefficient determining the roughness of the inspected surface K2 = 0.5Rz K3 is the coefficient determining the hardness of the inspected surface K3 = 0.02 HRC The contact pressure on friction surfaces is determined using the formula 12]: P=Q /F (5.12) Where Q is the normal force and F is the contact area. This area is determined using the relation: F = 3.14 (2δk .r - δk²) (5.13), Page 27 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Where δk is contact deformations defined by the formula (5.9), and r is the shoe radius. 5.9.2 RATE OF DISTORTION OF THE ADJUSTMENT OF THE MEASURING DEVICE The rate of misalignment depends on the complexity of the measuring device, the accuracy of manufacture and adjustment [13]. It characterizes misalignment τ misal allocated to a single measurement. If the number of measured components n during the time between two successive adjustment operations is defined, i.e. the operational error, ∆oper = n. τmissal (5.14) 6. DEVICE ADJUSTMENT TECHNIQUE The adjustment of the developed multi-dimensional inspection device is performed using reference bushings [13]. The order of adjustment is the following: 1. The carriage supporting the length and outer diameter inspection sections is drawn out. 2. The reference bushing made to meet the minimum requirement of the tolerances for all three dimensions is positioned on the mandrel. 3. The carriage is returned back until it rests securely. 4. The control indication unit is turned on and dimension reading are reset. 5. The stability of the adjustment is checked through multiple draw outs and insertions of the carriage and respective removal and installation of the reference bushing. Page 28 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES REFERENCES 1. M.J. García Tárrago, L. Kari, J. Vinolas, N. Gil-Negrete, Frequency and amplitude dependence of the axial and radial stiffness of carbon-black filled rubber bushings. Polymer Testing, Volume 26, Issue 5, August 2007, Pages 629-638. Jennifer Kadlowec, David Gerrard, Howard Pearlman, Coupled axial–torsional behavior of cylindrical elastomer bushings. Polymer Testing, Volume 28, Issue 2, April 2009, Pages 139-144. Wen-Ming Zhang, Guang Meng, Numerical simulation of sliding wear between the rotor bushing and ground plane in micromotors. Sensors and Actuators A: Physical, Volume 126, Issue 1, 26 January 2006, Pages 15-24. M. Cerit, E. Nart, K. Genel, Investigation into effect of rubber bushing on stress distribution and fatigue behaviour of anti-roll bar. Engineering Failure Analysis, Volume 17, Issue 5, July 2010, Pages 1019-1027. K. K. Choi, W. Duan, Design sensitivity analysis and shape optimization of structural components with hyperelastic material. Computer Methods in Applied Mechanics and Engineering, Volume 187, Issues 1-2, 23 June 2000, Pages 219-243. E. Di Pietro, T. Amemiya, M. Hanada, T. Iga, T. Inoue, Y. Okumura, K. Watanabe, Design and overview of fabrication tests for the 1 MV bushing for ITER NB system. Fusion Engineering and Design, Volumes 66-68, September 2003, Pages 603-608. Heinrich Groh, Inspection, maintenance and repair of explosion protected equipment. Explosion Protection, 2002, Pages 472-484. W.E. Bill Forsthoffer, Reciprocating compressor inspection guidelines. Forsthoffer's Rotating Equipment Handbooks, 2005, Pages 319-361. H.E. Gundtoft, C.C. Agerup, T. Nielsen, A new ultrasonic inspection system for nondestructive examination of precision tubes Part 1. A description of the system. NDT International, Volume 10, Issue 4, August 1977, Pages 171-176. 2. 3. 4. 5. 6. 7. 8. 9. 10. René Peter Schneider, Lucimara R. da Silva, Helder Brandão, Liutas Martinaitis Ferreira, Iron-oxidising microbial biofilms as possible causes of increased friction coefficient in intermediate and lower guide vane bearing bushings at a hydroelectric powerplant in Brazil. International Biodeterioration & Biodegradation, Volume 58, Issue 1, July 2006, Pages 48-58. 11. A. McCrea, D. Chamberlain, R. Navon, Automated inspection and restoration of steel bridges—a critical review of methods and enabling technologies. Automation in Construction, Volume 11, Issue 4, June 2002, Pages 351-373. 12. W.E. Bill Forsthoffer, Reciprocating compressor inspection guidelines. Forsthoffer's Rotating Equipment Handbooks, 2005, Pages 319-361. 13. Jordan T. Maximov, Angel P. Anchev, Modelling of residual stress field in spherical mandrelling process. International Journal of Machine Tools and Manufacture, Volume 43, Issue 12, September 2003, Pages 1241-1251. Page 29 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES B. A TENSION/PRESSURE LOAD TESTING DEVICE PERFORMANCE CHARACTERISTICS OF THE MECHANICAL RIG FOR TENSION/PRESSURE LOAD TESTS The tension/pressure loads testing device is a universal and easy to operate unit. The basic load is applied through a screw-and-nut assembly, which is a standard design, easy and low-cost to manufacture, does not require any special maintenance and is reliable [1]. The test rig is designed and intended to provide tension/pressure loads of 12000 N, which is perfectly sufficient to test all types of plastic materials of a specified tensile strength within 9-130 mPa. The test sample is cylindrical with standard dimensions: Operating length l0 = 50 mm Diameter = 10 mm Results indication is by means of a dynamometric fork and indicator dial, the applied force being transformed into linear deformation. Table 1 shows linear deformation values for tension/pressure fork made of 65 G material and calibrated for 15000 N loads. Table 1 Force 100 N 500 N 1 000 N 2 000 N Deformation 0,21 0,41 0,75 0,92 Force 5 000 8 000 10 000 12 000 15 000 Deformation 1,25 1,89 2,09 2,21 2,42 1. DEVICE OPERATION PRINCIPLE The tension and pressure load testing device has been developed for testing plastic materials and is designed for 12000 N basic tension/pressure force value. The device is a universal type as it can successfully perform either tension or pressure tests only by replacing certain parts and adjusting screw length [2]. For tension tests the sample is positioned in the jaws (item 6) and secured by means of the M8 x 1LH screws (item 4). When the driving nut (item 9) is rotated by means of the arms, the nuts item 10 and item 7 where the moving jaw is positioned move downwards. Thus, the dynamometric fork is actuated (item 14) one jaw of which is secured to the nut item 10 and the other – to the fixed nut (item 16). The downward movement results in pressure being applied to the fork jaw, which is pre-calibrated to indicate forces of up to 15000 N. The jaw thus undergoes deformation and the indicator dial fastened to the fork fixed jaw indicates the Page 30 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES value of this deformation. The same device can also perform pressure tests after certain device adjustments are made and some parts replaced. The position and stroke length of the screw could be adjusted via the nuts (items 9 and 21) before the test sample is positioned in place. The readings of the results are obtained in the same way – using the tension/pressure dynamometric fork [3]. The test sample is positioned in the jaws and secured there the same way as for the tension test using the M8 x 1 screw (item 4). The nut (item 24) moves forward when the arm is rotated thus starting to tension the clamping jaw. The nut (item 10) where one of the jaws of the dynamometric fork is secured also moves forward in turn thus causing the indicator dial to indicate the linear displacement and hence, the force being applied. The machine has been developed based on the screw-and-nut joint principle and is easy and convenient to operate providing sufficient accuracy of readings. This makes it suitable for a wide range of experimental and demonstration applications (in schools, small laboratories, etc.) The screw-and-nut joint need frequent lubrication to provide easier movement and minimum wear [4]. As friction losses in this joint are insignificant we have good reasons to believe the device would provide good accuracy of readings. 2. SAFETY REGULATIONS & ENVIRONMENTAL CONSIDERATIONS The tension/pressure testing rig is easy to operate and does not require any specifically acquired knowledge or qualifications as the mechanism is simply driven by means of rotating the arm and the nut of the device. The screw and tested sample should not reached or touched during operation as this might cause injuries. Before the test is carried out one should first check if the test sample is reliably secured in place into the jaws and the M8 screws are securely tightened [4]. It would be useful is the screw is lightly lubricated and the nut run several times along the entire screw before work is begun. The area around the measuring unit should be kept free of contamination. When manufacturing components to higher technical requirements and subjected to thermal treatment it is necessary to perform some mechanical tests to be able to control metal quality and thermal treatment characteristics [4]. Standard samples to be tested in laboratory are made from the specific batch of materials or a specified batch of thermally treated components under equal production conditions. The quantity of tested samples would depend on the nature of the technological process. The materials used in machine building industries are mainly tested for tensile, pressure and torsion characteristics and the mechanical properties of the tested material are determined on the basis of the forces applied and the resulting deformation. Tension tests are usually performed on special machines comprising the following basic mechanisms: loading mechanism, tension force transmitting mechanism and tension force reading mechanism. Machines of breakdown force of 2, 4, 5, 30 and 50t are typically used [4]. Compression tests are usually applied for materials of higher brittleness (cast iron, aluminium alloys, etc.). These are carried out in special machines and also in tension Page 31 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES testing machines where reversing mechanisms are adopted for this purpose to transform tension force into compression force [5]. Samples of either round or square section are usually used for both types of tests described above and for the compression test the height/diameter ratio of the sample should be within 2,5 ÷ 3,0. Cylindrical surfaces of the samples should be concentric and the bearing surfaces are coated with special grease to reduce friction. Figures 1a, b, c and d show a round and a flat sample before and after loading when subjected to fracture as well as the sample deformation curve and Table 2 shows basic dimensions of tested samples [6]. Table 2 Round sample Dia. do 25 20 15 10 8 5 Long lo 250 200 150 100 80 50 Length Short lo 125 100 75 50 40 25 Width bo 30 30 30 30 30 30 Flat sample Thickness ao 25 20 15 10 8 5 Length Long lo 310 280 240 190 170 140 Short lo 155 140 120 95 85 70 Page 32 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES d0 d0 a b0 load P lo b c d a a0 b lo 0.00 elongation δ c breakdocon point d1 lk Figure 1 3. Ps Pmax Page 33 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES TENSION TESTING RIG Tension and compression tests of plastic materials do not involve significant loads due to their lower strength characteristics, as is the case with steel tests [7]. The tensile strength of various plastics varies within σB=(10÷130)MPa. If we chose a ∅10mm sample with a surface area of: Fo = πr2 = 78,54.10-6 m2. The loading force is determined by the formula: σB = Pmax / Fo Pmax = σB.Fo = 130.106.78,54.10-6=10210,2N We assume a maximum loading force of Pmax=12000N. Such load could be applied by means of a screw-nut drive so we chose a screw type loading mechanism comprising a turning screw and a reciprocating nut. To ensure higher load-carrying capacity we select a trapezoid thread screw. Selecting thread and nut material: We choose 45 steel for the screw having a tensile strength of σB=750MPa and bronze CuSn4Zn7Pb5 for the nut with σB=200MPa. The internal screw diameter d1 is: d1 = 5,2. P 5,2.12000 = = 0,0157mm π. σ allw. pr. π.800.10 5 We selected a thread Tp20 x 4 with the following dimensions: - major diameter d = 20 mm - angle diameter d2 = 18 mm - minor diameter d1 = 16 mm - pitch t = 4 mm. Keeping in mind the self-retention requirement for the thread α ≤ ρ, where α is the thread angle tgα = t / πd2 t = thread pitch; r = 5° ÷ 7°. α = arctg 4 t = arctg = 4°2'46" π. d2 π.18 Page 34 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES α = 4°2’46”< 5° ÷ 7°. This shows the self-retention requirement for the thread is met. The strength test for the screw Tp 20x4 is determined by the formula: [1] where [2] σ equ. = σ tens. = σ 2 . + 4. τ 2 . ≤ σ allw. tens. tens tors 4. P 2 π. d1 = 4.12000 π.0,016 F. l 3 0,2. d1 2 = 596,83.105 Pa - is the operational tensile stress. [3] τ tors. = Mtors. 3 0,2. d1 = - is operational torsion stress σallw.tens = 800.105 Pa. F = the force applied at lever end in N; l = lever arm in m. σ tens. = 4.12000 π.0,016 2 = 596,83.10 5 Pa τ tors. = σ equ. = F. l 3 0,2. d1 = 50.0,2 0,2.0,016 3 = 122,07.10 5 Pa σ 2 . + 4. τ 2 . = tens tors (596,83.105 )2 + 4. (122,07.105 )2 = = 644,83.10 5 Pa ≤ σ allw. tens. = 800.10 5 Pa The screw buckling test is performed on the basis of the equation [8]: l = 4.β.l / d1, where β is a coefficient indicating the method of fastening b = 2; l is calculation length of the screw. we assumed: - screw lead path height lH = 100mm; - contact jaw height L = 100mm; - nut height H = t.z, where t is thread pitch and z is number of windings. z= 2 π. d − d1 . ψ. [p] 2 ( 4. F ) Page 35 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Where d is major thread diameter; d1 is minor thread diameter; ψ is coefficient ( ψ = 0,55 ÷ 0,76 ); indicating the uneven load on the windings [p] – allowable contact pressure (for the steel screw/bronze nut version [p] = 70 ÷ 130.105Pa); z = π. 0,02 − 0,016 2 .0,75.130.10 5 2 ( 4.12000 ) = 10,88 < 10 As the requirement for the number of windings < 10 is not met (the nut is not going to bear any load), we choose a 26x5 screw thread of the following dimensions [8]: - major diameter d = 26 mm - angle diameter d2 = 23.5 mm - minor diameter d1 = 20.5 mm - pitch t = 5 mm. - α = 3°52’28” < 5°÷7°. Using equations [1], [2] and [3] we calculated: τtens=363.56 . 105 Pa; τtors = 58.03 . 105 Pa σ equ. = (363,56.105 )2 + 4. (58,03.105 )2 4.12000 = = 38164.10 5 Pa < σ allw. tens. = 400.10 5 ÷ 800.10 5 Pa , z = π. 0,026 2 − 0,0205 2 .0,70.130.10 5 ( ) = 6,56 < 10 Assuming z = 8 windings. The nut height is calculated by the equation: H = t.z = 5.8 = 40mm λ = 4. β. l 4.2.0,25 = = 97,56 d1 0,0205 As 60 ≤ λ ≤ 100 the screw should be checked for buckling by means of the reliability coefficient: Page 36 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 2 π. d1 . (3210 − 116. λ ).10 5 , π.0,0205 2 . (3210 − 116.97,56).10 5 , = = 4. F 4.12000 n = = 5,716 > nallw. = 4,0 The design dimensions for the screw and nut are determined by the formula: - screw head size D = (1,5 ÷ 1,7).d = 40mm - screw head thickness B = (1,3÷1,6).d = 35mm - screw clamp neck size d = (0,6 ÷ 0,7).d = 18mm - nut outer diameter D: D = 4. F π. σ allw. tens. + d2 = 4.12000 π.800.10 5 + 26 2.10 − 6 = 0,029 m Assuming D = 35mm and the designed outer diameter of the bearing shoulder 45mm., the compression stress on the bearing shoulder will be [9] σ comp. = σ comp. = π. ( 4. F −D −6 2 2 D1 ) [ ≤ σ allw. comp. = 600.10 5 Pa ] π. 45 − 35 .10 2 2 ( 4.12000 ) = 190,98.10 5 < σ allw. comp. = 600.10 5 Pa [ ] The height of the bearing shoulder h is determined by the relationship [10]: h ≈ 1 1 . H = .50 = 12,5mm 4 4 τ cut = τ cut = F < τ allw. cut = 150 ÷ 300.10 5 Pa π. D. h F π.35.12,5.10 −6 = 87,3.10 5 < τ allw. cut Lever calculations: Lever length is determined by the formula: l1 = M / P, where P is the force applied on the lever by one operator. P= 50 ÷150N. I assume P = 100N; Page 37 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES M is the momentum induced by the force P. M = M1 + M2; M1 - momentum originating from the friction in the thread; M2 – momentum originating from the friction between screw face surface and the clamping section. d2 . 23,510−3 M1 = F. tg( α + ρ). = 12000. tg( 3,8744 + 7). = 27,086Nm 2 2 M2 = 0 l1 = 27,086 = 0,135m 100.2 as we have two handles. The lever diameter d1 is determined by the formula [11]: d1 = P. l1 = 0,1. σ allw. bend 100.0,270 . 0,11000.10 5 = 0,0139 = 14mm 3 3 Assuming d1 = 15 mm. When testing the sample on tension the nut moves forward in one direction and when the compression test is performed its movement is reversed in the opposite direction [12]. This is rather inconvenient when designing dual test equipment for tension and compression tests. Therefore, it is better to have the nut fixed and the screw reciprocating. With this alternative we assumed a screw working length of: L = 2.lH + L, where lH = lead length L = clamping jaw length H is nut height. L = 2.100 + 60 + 40 = 300mm. Then λ = 4. β. l 4.2.0,30 = = 136,58 0,0205 d1 As λ>100, n = 4 π 3 . E. d1 2 64. lk . F = , π 3 .215.1011.0,02054 64.0,62.12000 = 4,25 > 4 Page 38 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 4. CLAMPING THREADS CALCULATIONS FOR FASTENING PLATES The minor thread diameter d1 is calculated by the formula [13]: d1 = 4. F π. σ allw. tens. = 4.12000 π.550.10 5 = 0,016m Assuming 4 screws with 56mm inner diameter and a design diameter of bearing flange of ∅80mm. As a result of this the thread of clamping screws is M6x1. Page 39 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 40 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 41 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 42 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 43 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES REFERENCES 1. Yusof Daud, Margaret Lucas, Zhihong Huang, Modelling the effects of superimposed ultrasonic vibrations on tension and compression tests of aluminium. Journal of Materials Processing Technology, Volume 186, Issues 1-3, 7 May 2007, Pages 179190. Sungchul Yang, Tianxi Tang, Dan G. Zollinger, Ashok Gurjar, Splitting tension tests to determine concrete fracture parameters by peak-load method. Advanced Cement Based Materials, Volume 5, Issue 1, January 1997, Pages 18-28. Carlos García-Garino, Felipe Gabaldón, José M. Goicolea, Finite element simulation of the simple tension test in metals. Finite Elements in Analysis and Design, Volume 42, Issue 13, September 2006, Pages 1187-1197. J. G. M. van Mier, M. R. A. van Vliet, Uniaxial tension test for the determination of fracture parameters of concrete: state of the art. Engineering Fracture Mechanics, Volume 69, Issue 2, January 2002, Pages 235-247. Xiangqian Li, Stephen R. Hallett, Michael R. Wisnom, Navid Zobeiry, Reza Vaziri, Anoush Poursartip, Experimental study of damage propagation in Over-height Compact Tension tests. Composites Part A: Applied Science and Manufacturing, Volume 40, Issue 12, December 2009, Pages 1891-1899. Mohammad Kazem Asgharnia, William A. Brantley, Comparison of bending and tension tests for orthodontic wires. American Journal of Orthodontics, Volume 89, Issue 3, March 1986, Pages 228-236. N. M. Zarroug, R. Padmanabhan, B. J. MacDonald, P. Young, M. S. J. Hashmi, Mild steel (En8) rod tests under combined tension–torsion loading. Journal of Materials Processing Technology, Volumes 143-144, 20 December 2003, Pages 807-813. Bryan E. Barragán, Ravindra Gettu, Miguel A. Martín, Raúl L. Zerbino, Uniaxial tension test for steel fibre reinforced concrete––a parametric study. Cement and Concrete Composites, Volume 25, Issue 7, October 2003, Pages 767-777. Michael R. Wisnom, The effect of fibre rotation in ±45° tension tests on measured shear properties. Composites, Volume 26, Issue 1, 1995, Pages 25-32. 2. 3. 4. 5. 6. 7. 8. 9. 10. K. P. Rao, Emani V. R. Mohan, A vision-integrated tension test for use in sheet-metal formability studies. Journal of Materials Processing Technology, Volume 118, Issues 1-3, 3 December 2001, Pages 238-245. 11. W. Chen, F. Lu, M. Cheng, Tension and compression tests of two polymers under quasi-static and dynamic loading. Polymer Testing, Volume 21, Issue 2, 2002, Pages 113-121. 12. R. Mahmudi, R. Mohammadi, P. Sepehrband, Determination of tearing energy from uniaxial tension tests of aluminum alloy sheet. Journal of Materials Processing Technology, Volume 147, Issue 2, 10 April 2004, Pages 185-190. 13. A. Lindorf, L. Lemnitzer, M. Curbach, Experimental investigations on bond behaviour of reinforced concrete under transverse tension and repeated loading. Engineering Structures, Volume 31, Issue 7, July 2009, Pages 1469-1476. C. Page 44 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES A TORSION TESTING DEVICE 1. INTRODUCTION Every piece of machinery and, under certain situations, components made of another material are subjected under certain conditions to various loads, which they have to bear not only without breaking up but also without showing signs of deformation beyond a specified allowable limit. The design engineer should be aware of the torsion characteristics of both metal and non-metal materials typically involved in his work and these should have their numeric expression. These numeric values are usually obtained through trials by testing the materials using special torsion testing rigs [1]. Various tests could be run depending on the manner the machine components are being loaded during operation. Operational load could either be static when the acting force reaches its maximum value slowly and evenly, or dynamic – when the acting force immediately reaches its maximum value (shocks, for example), or variable – when the loading force periodically and multiply varies its value (and sign, eventually) [1]. With this respect, the types of tests that metal materials used in machine building industries are usually subjected to be static, dynamic and variable load tests [1]. 2. STATIC TESTS The ability of the material to resist against a uniform, slow and evenly changing in value load causing torsion stress is being tested here. The slowly increasing loading force is linked to a slow movement and insignificant acceleration of the test equipment moving parts where inertia forces could be disregarded. In static tests it is possible to determine with sufficient degree of accuracy both the loading force value and the degree of deformation to the tested sample at any moment throughout the test. Torsion tests are usually carried out only rarely and mainly on cylindrical components [2]. Equipment available so far for material torsion testing are of horizontal type, rather bulky with open transmissions, which makes operation harder to handle, maintain and dangerous with respect to safety regulations [3]. During the torsion test it is impossible to accurately determine the loading force and respective deformation value to the tested sample at any time throughout the test due to inertia moments induced in all rotating parts. From a weight point of view such testing equipment is not transportable [3]. We have tried to design a new type of material torsion testing equipment considering the need to avoid all above mentioned disadvantages. Various materials of cylindrical shape could be subjected to torsion tests with it. Here we would like to give a general idea about the machine: Page 45 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 1. The material torsion testing system (machine) is designed to test samples (references) of cylindrical shape having a maximum diameter of φ 23mm for metals. The maximum diameter for non-metal test samples could be larger and is inversely proportionate to 0° 12 120° R Lj L=2Lj +150 Lj Fig. 1 the torsion (yield) breakup stress for the respective material, i.e. a larger diameter of the test sample for smaller breaking stress. The shape of the test sample is shown in Figure 1. The test sample has a test tube shape. The sample sizes are shown in Fig. 1. L j – jaw length of the universal chuck; a - jaw contact surface width. The number of a-wide grooves depends on the number of jaws in the chuck. These are intended to avoid test sample slipping in the chuck as the torsion stress becomes too high. The middle portion of the sample having a diameter d is made to a smaller size, as sample rupture should occur in between the two chucks. The transition between the large and the smaller diameter is by means of a slope (truncated cone) and a chamfer radium of R = 10 ÷15 mm. This is again intended for the same objective – to have the rupture occur between the two supports (chucks). The diameter d should be smooth with no signs of rough machining as rough machining results in the occurrence of strain concentration along the surface of the material [4]. 2. The performance parameters of the torsion testing system are: maximum diameter of tested metals dmax = 23 mm; when using an electrical motor and reducer having a gear ratio of up to i = 8 ÷ 10 and power under 1 kW, the test sample has usample= 8 ÷ 10 min-1; when using a flywheel with handle (manual drive without an electrical motor) the flywheel torque is Mtr.max = 46 N.m; flywheel diameter Dmax = 300 mm; indication of torsion momentum is by means of an electrical dynamometer in µA; means are provided to indicate the angle ϕ under which the test sample undergoes rupture (on both scales); Page 46 D=d+10 3÷4 a d MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES - worm reducer having the following parameters: Output shaft power Nw = 5.4 kW; Output shaft speed nw = 80 min-1 Overall dimensions: Width – 360 mm Height – 460 mm Thickness – 220 mm; uses elastic coupling with rubber rings and clicks. - 3. Depending on customers’ requirements the testing system could be used with or without an electrical motor. The cost of the machine would be higher for the first case. The advantage of using the flywheel to induce torsion to the test sample is that the students have a better chance of observing the progress of the test for a longer time. The sample rotates slowly in partial rounds and the size of the section along which rupture is occurring could be measured at any time if desired. The testing system provides visual idea of the process, which leads to material yield (for plastic materials). 4. The torsion testing system involves a self-locking mechanism, i.e. when sample test is interrupted the mechanism is not returned in its starting position as the worm reducer prevents this. This is another moment giving chance to observe the process and make necessary measurements. 5. As mentioned earlier, indication is provided by means of an electrical dynamometer, which provides readings in µA and this necessitates a comparison table or graph to be provided. The following methods are applied to determine torsion force: a. By determining the power consumed throughout the process of torsion; b. By calculations using formulas obtained experimentally; c. By direct measurement using dynamometric equipment. The latter is usually applied in laboratory conditions using hydraulic, electrical or mechanical dynamometers. These devices should meet certain requirements to match indicated results with the actual values of forces: these devices should not cause additional deformations in the set up; they should be small in size and should be independent from the set up; the readings of the dynamometer should match the calibration device readings; in laboratory conditions deviations should be less than 10%; calibration results should be maintained constant throughout the trial after which the dynamometer should again be calibrated; they should exhibit high sensitivity and be safe to use; a recording unit is desirable. Page 47 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES P (N) f P f (µm) Fig. 2 Fig. 3 Torsion load could be measured fairly easy and accurately using an electro-inductive dynamometer. Its principle of operation is based on the deformation its elastic components undergo when subjected to the torsion loads. This is transmitted to electrical inductive transducers, which transform and transmit it to the recording unit where the results of the measurements are being recorded. The transducer comprises an armature and two fixed coils positioned symmetrically from the armature. As the armature is moved under the action of the respective torsion force it induces electromotive voltage, which is being measured and recorded. When measuring torsion forces it is convenient to immediately record their values. This calls for calibration of the dynamometric equipment using an elastic element of specified charactersitics, Figure 2: 6. The elastic element 1 is loaded on a press (eccentric or hydraulic) by the force P to various degrees. The indicator 2 reads the shifts and a curve of P = f(P) is drawn which represents the “fork” type elastic element characteristic, Figure 3. One arrow is positioned under each chuck, which indicates the angle of rotation. The elastic element and the electrical dynamometric equipment are positioned in the upper bearing assembly due to the conditions given above. An example table could be made based on the data read from the device, Table 1 for a random number of locations. Table 1 Νο ϕ1 ° ϕ2 ° ϕ =ϕ1− ϕ 2 ° φδ µµ Π Ν Λ µ Mtors= P.L τtors= Mtors/(0.2d3) Ν/µ2 Νµ  2 3 4 5 The angles of rotation of the top and bottom end of the sample (top and bottom chucks) are measured as rotation is present in both supports – from the worm reducer in the bottom end and in the top end – thanks to the fact, that the “fork” type elastic element is actuated, which is part of the testing arrangement. The difference between these two Page 48 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES angle values is needed to indicate the actual rotation. 7. This material torsion testing system is a rational solution. It is portable, as its body comprises lightweight shaped and sheet metal components. A single operator of no special qualifications quickly and easily operates it. The bracket where one bearing assembly is positioned provides a rather large space for observing experiments and sample tests. The reducer is compact and with small size. The electrical motor rotation (when installed) is transmitted via elastic coupling to the worm reducer uniformly and evenly without shocks. 8. The test system does not use any harmful substances, liquids or oils for its operation. It is not harmful to environment. It is fairly safe to use. A protection cover is installed around the testing area, which is made of transparent material – Plexiglas. The machine would not operate if the protection cover were not mounted in the correct place. If the system locks the supply cable should be disconnected from the mains before you proceed with the repairs. During maintenance routines the supply cable should also be disconnected from the mains. The system should be aligned every time it has been installed or transported. 9. Power supply: The material testing system provides high precision and sufficient accuracy of indicated results thus providing a real idea of the mechanical properties of various types of materials – metal or non-metal when subjected to torsion. Measurement results could be improved if sensor transducers were adopted instead of the electrical dynamometer, which in turn would increase the cost of the equipment. 3. MATERIAL TORSION TEST SYSTEM (ASSEMBLY DIAGRAM) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Bracket Universal chuck Roller bearings Worm gear Worm Electro-inductive dynamometer “Spring fork”-type dynamometer Mechanical arm Flywheel Body Torsion angle indicating arrow Test sample (test bar) Bearing assembly Page 49 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 430 13 1 130 12 11 2 1350 800 10 580 9 350 3 6 4 7 5 8 3.1 Page 50 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES TORSION TESTING EQUIPMENT SPECIFICATION Item 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 MTTS -000-019 MTTS -000-015 MTTS -000-016 MTTS -000-017 MTTS -000-012 MTTS -013-000 MTTS -000-006 MTTS -000-007 MTTS -008-000 MTTS -000-009 MTTS-004-000 Designation Name M24x1.5 Round nut 24 Safety washer 6205 Ball bearing Plate 10x8x35 Key Arm Top shaft Spring fork Sleeve 6206 Ball bearing M10x20 Screw Cap Plate 32211J2 Conical roller bearing Reducer cover Worm Shaft 30207J2 Conical roller bearing Cap Qty. 1 1 1 1 1 1 1 1 1 1 40 1 1 1 1 1 1 1 1 GG-25 GG-25 C45W3 C45W3 GG-25 C45W3 C45W3 50CrV4 C45W3 Material Notes Page 51 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 MTTS -000-035 MTTS -000-036 MTTS -000-037 MTTS -000-038 MTTS -000-039 MTTS -000-040 MTTS -000-031 MTTS -029-000 MTTS -000-027 MTTS -000-021 MTTS -022-000 MTTS -000-023 MTTS -000-024 M10x30 Screw Sleeve Worm gear Reducer base Reducer gasket M10x25 Screw 14x10x45 Key Sleeve 55x67x7 Shaft seal Frame Test tube sample Plate Chuck, universal Elastic coupling 6x5x60 Key Flywheel Handle Top scale Indicating arrow Bottom scale Indicating arrow 8 1 1 1 1 4 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 GG-25 C45W3 C45W3 C45W3 C45W3 C45W3 C45W3 C45W3 GG-25 Rubber C45W3 4. Page 52 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES DESIGN & STRENGTH CALCULATIONS 1. The torsion test technique is required to provide testing of various materials (metal or non-metal materials). 2. The torsion test shall be carried out using cylindrical test samples. 3. The construction of the system shall be a welded type using thin-wall pipes having a square or rectangular section and made of common steel or steel sheet with σ=1; σ= 1.2mm. Thus, the following would be ensured: a) fast and easy assembly of the construction; b) light-weight and low-cost construction; c) easy and technological assembly of components into the construction and similar eventual replacement and repairs 4. The construction shall be made vertical, i.e. the cylindrical sample shall be positioned vertically. This would allow easy access and maintenance. 5. When preparing the assembly diagram some standard parts and components could be used such as: a. Universal chucks for lathes of the smallest available size as the torsion force and eventual break-up of the metal cylindrical test sample would be rather high. Chucks provide a rather high clamping force for the test sample. b. Worm reducer – the gear ratio should be high and this could be ensured by this type of reducer. The torsion force is high. This could be achieved by a reducer having a high gear ratio (i = 40÷50) driven by means of an electrical motor having a typical power of max 1kW-1.5kW, for example [5]. This reducer might also be manufactured following respective design and strength calculations if a suitable ready-made one is not readily available. c. 1 – 1.5 kW DC electrical motor Above materials selected for the construction and respective standard parts and components are intended to provide a cheaper construction. A construction built-up of standard profiles and thin-wall sheet metal by means of welding is far more preferable than a die-cast construction made with thick plates. The design tendencies are directed at using materials such as the ones adopted for our case thus guaranteeing lowest product cost to the required quality. 6. Design and strength calculations d. Under simple torsion the test sample would have to be rotated (twisted) not more than a single round before break-up [6]. For this reason the mechanism intended to provide this torsion should have a high torque of its output shaft. It would also be necessary that it provide self-locking in a specified position during the test of the sample. The test sample should be rotated slowly at only a few degrees. A high gear ratio reducer of a small size and namely, a worm reducer could provide this. The reducer could be driven by either an electrical motor or manually, by means of a flywheel. e. The next step is measuring the loading force (torque) on the sample under test. Page 53 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES The following techniques are applies to determine this: i. by determining the power consumed in the torsion process; ii. by calculations using formulas obtained from experiments; iii. by direct measurement using dynamometric equipment [7]. The latter is typically used in laboratory conditions and hydraulic, electrical or mechanical dynamometers could be used. In order for the indicated results to consistent with the actual forces involved the equipment should meet several requirements [8]: - they should not cause additional deformation to the construction; - they should be small in size; - the readings from the dynamometer should coincide (within a specified limit) with the calibration unit readings; in laboratory conditions deviations should be no greater than 10%; - calibration check results should be maintained constant throughout the experiment and the dynamometer should again be calibrated afterwards; - they should exhibit high sensitivity and be safe to use; - it is desirable that they have a recording device. Force measurements could be performed relatively fast and accurate using an electro-inductive dynamometer. The principle of operation of this equipment is based on the deformation that it elastic elements undergo when subjected to the torsion force. This is transmitted to electrical-inductive transducers, which in turn transform and transmit it to the recording device where the results of the measurement are being recorded [9]. The Fig. 1 transducer comprises an armature and two fixed coils positioned symmetrically from the armature. As the armature is moved under the action of the respective torsion force it induces electromotive voltage, which is being measured and recorded. When measuring torsion forces it is convenient to immediately record their values. This calls for calibration of the dynamometric equipment using an elastic element of specified charactersitics [10]. Figure 1 shows a “fork”-type dynamometer used for calibration checks of the electro-inductive dynamometer. First, the curve p=p(f) is made, which represents the fork characteristics. The dynamometer is loaded sequentially with specified forces and the deformations are red from the indicating dial in µm. The results thus obtained are being plotted in a co-ordinate system to a specified scale, the straight line thus obtained is the fork characteristic (Fig. 2). Page 54 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES P (N) Then calibration check is carried out on the dynamometric equipment. The dynamometer is positioned on the table of a universal milling machine – Figure 3. The originating force is measured and the torque M = P.l is hence calculated. Calibration is carried out under sequential loading and unloading conditions. Sensor transducers could also be used to read the torque instead of electrical inductive dynamometer [11]. f (µm) Fig. 2 7. Calculations and design of the worm reducer In order to make this we shall need to figure out what would be approximate the moment of torsion Mtors and the test sample diameter, respectively needed to attain material yield and eventual break up. We assume the test sample is made of 45 steel (a heavier testing alternative) [12]. From the table of allowable material stress used in machine building practice we select for 45 steel: τs = 22.5. 107 N/m2 – yield strength. Then from: τ tors = d =3 M tors M tors = Wtors 0.2 xd 3 M tor 0 . 2 xτ s where: Fig. 3 M (N.m) N2 , [Nm] n2 is the test sample torque. M bi = 9554 We choose an electrical motor of Nmot = 6÷7 kW, u = 1450 rpm as the force needed to break up the sample is too high. i = 18 is the gear ratio of the worm reducer. We assumed: I (mA) N2 = Nmot. η = 6.75. 0.80 = 5.4 kW = 0.80 - worm drive efficiency coefficient n mot 1450 = ≈ 80[rpm] i 18 5 .4 M b 2 = 9554 = 645[N / m 2 ] 80 M tors = M b2 = 645[N / m 2 ] Page 55 n2 = d =3 645 = 0.024[m] 0.2 x 22.5 x107 Fig. 4 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Mb2- worm wheel shaft torque This means that to be able to break up the test sample it should have a diameter smaller than 24mm. We assumed a diameter of the test sample d = 15÷20. 7a. Determining the number of worm strokes zw and the number of teeth zg of the worm gear wheel. a) Number of worm strokes zw The allowable minimum number of teeth is between 26 and 28 teeth. If we assume a single stroke worm we will get a number of teeth that is lower than the minimum so we assume zw = z [12]. b) Number of gear teeth zg zg = i . zw = 18. 2 = 36 7b. Module determination The front module is determined by the equation: ms = 3 1.7M b2 .ν .k zk .y .q.ο allw .bend M b2 = 645[Nm] k = 1.5 as the load varies, = 1 – indicates teeth wear, zg = 36 – number of worm gear teeth, y - tooth shape coefficient. It is defined by: λ = 14°2′14″ - angle of spiral, from the table ze = zk 36 = = 39.6 3 3 cos λ cos 14°2'14" zworm= z and q = 8, i.e. y = 0.6 from the table ze = 40 σallow.bnd.= 460. 105 N/m2 – bending stress for bronze. According to the standard we assumed ms = 7 and q = 9. 1.7 x 645 x1.5 36 x 0.6 x 460 x10 5 3 m = 0.0059[m] =⎞5.9[mm] ⎛ zk + 1⎟ ⎜ 180 x10 3 ⎜ q ⎟ .M .k .k ≤ σ σc = b2 c g all .c . ⎜ A ⎟ zk ⎟ ⎜ q ⎠ ⎝ m=3 where A= k hp ms (q + zc ) 7 x (9 + 36 ) = = 157.5[mm] 2 2 3 3 7c. ⎛z ⎞ ⎛ 36 ⎞ = 1 + ⎜ k ⎟ .(1 − ℵ) = 1 + ⎜ ⎟ .(1 − 0.6 ) ≈ 1.05 ⎝ 71 ⎠ ⎝ϑ ⎠ Teeth contact strength check [13] Page 56 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES For insignificant load variations I assumed χ = 0.6. I select from the table for zw=2 and q = 9 a worm deformation coefficient θ = 71. kid – dynamic coefficient; when Vsl <3m/s, kd = 1. Vsl – sliding speed, σall.c = 2100 . 105 N/m2 ⎞ ⎛ 36 +1 ⎟ ⎜ 180 x10 3 ⎜ 9 ⎟ .645 x1x1.05 ≤ 2090 x10 5 [N / m 2 ] σc = 36 ⎜ 157.5 x10 −3 ⎟ ⎟ ⎜ 9 ⎠ ⎝ The operational voltage σc= 2090 . 105 N/m2 < σall.c = 2100 . 105 N/m2 – so the contact strength requirement is met. Further calculations are made on the basis of the adopted module ms = 7mm. 7d. Determining the basic dimensions of the worm and worm gear wheel: 3 a. worm Diameters of dividing, external and internal cylinders: dd.w = ms.q = 7. 9 = 63mm De.w = ms(q+2) = 7(9 + 2) = 77mm Di.w = ms(q-2.4) = 7(9-2.4) = 46.2mm The length of the cut section of the worm is L = (11+0.6.zg) ms = (11+0.6 . 36). 7 = 92mm b. worm gear wheel Diameters of the base, external and internal circles: db.g = ms.zg= 7.36 = 252mm De.g = ms (zg+2) = 7. (36+2) = 266mm Di.g = ms (zg - 2.4) = 7.(36 - 2.4) = 235.2mm The largest external diameter would be obtained when zw = z; B = 0.75. Dew = 0.75. 77 = 58mm 8. Approximate calculation of shafts Page 57 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 8a Determining the diameter of worm shaft output end: This is determined using the formula: d1 = 3 M tor 46 =3 = 0.0226[m] = 23[mm] 0.2 τ all .tors 0.2 x 200 x10 5 τall.tors = 200. 105 N/m2 is the reduced allowable torsion. Where Mtors. = Mshft = 46N is the shaft torque; The diameter of the output end of the worm shaft shall not be much different than the diameter of the motor shaft and should match the selected coupling hub opening. The diameter of the electrical motor shaft is dmot = 38mm. We assumed the coupling has a hub opening diameter not larger than 38mm [14]. We assumed the diameter of the shaft output end is d1 = 35mm. We assumed a design value for the roller bearings neck diameter of dA=dB = 40mm. Other dimensions to be determined after the suitable roller bearings have been selected. 8b. Worm wheel shaft d2 = 3 where 0.2 τ allow .tors M tors .=3 645 = 0.048[m] = 48[mm] 0.2 x 300 x10 5 Mtors.w = 645 N.m is the moment of torsion of the wheel shaft; τall.tors = 300 . 105 N/m2 – allowable torsion stress for 45 steel. assuming dw = 50mm. We assumed design values for the other shaft diameters. Bearings neck diameters dc = dD = 55mm. The diameter of the shaft underneath the gear dw.g = 60mm. As the shaft has been re-dimensioned we do not need to make any strength checks. 9. Forces of interaction between the worm and the worm wheel a. Worm peripheral force P1 and worm wheel axial force Pa: P1 = Pa2 = 2M b1 d g1 = 2 x 46 = 1460[N ] 0.063 Where Mshft.1 = 46 N.m dd.1 = 63 mm – worm pitch diameter. b. Worm axial force Pa and worm wheel peripheral force: P2 = Pa1 = 2M b 2 2 x 645 = = 5100[N ] d g2 0.252 Page 58 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Where Mshft.2 = 645 N.m dd.2 = 252 mm – worm gear pitch diameter c. Radial forces Pw.1 and Pw.2 of the worm and worm gear: Pr1 = Pr2 = P2 .tgα = 5100.tg 20° = 1850[N ] 10. Support reactions, bending and equivalent momentums of the worm shaft a. Reactions in the A and B supports of the worm shaft Radial reactions in the XY plane: From the force P1 acting symmetrically: RAY = RBY = P1/2 = 1460/2 = 730 N. Radial reactions in the XZ plane: From the force Pw.1: R’AZ = R’BZ = Pw.1/2 = 1850/2 = 925 N. From the force Pa1: ∑MB = 0; d g1 2 = =0 − R " Az .l + Pa1 R " Az = R " Bz Pa 1d g1 5100.0.063 = 640[N ] 2l 2 x 0.025 = R " Az = 640[N ] Where l≈dd 2 = 250mm is the distance between supports. Reactions resultant from the forces Pw.1 and Pa.1: RAZ = R’AZ – R’’AZ = 925 – 640 = 285 N RBZ = R’BZ + R’’BZ = 925 + 640 = 1565 N Resultant reactions from the forces P1, Pw.1 and Pa.1 2 2 R A = R Ay + R Az = 790 2 + 285 2 = 795[N ] 2 2 R B = R By + R Bz = 730 2 + 1565 2 = 1730[N ] Axial reactions in the support B: AB = Pa.1 Bending and torsion momentums diagrams for the worm shaft [15] Bending and torsion momentums diagrams of the worm gear shaft [15] Page 59 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES l MB1 RA RAz A RAy RAy P1 Mz=-93 N.m Pr1 in the plane õó RBy P1 Pa1 RB RBz B RCz C RC RCy dg2 l1 l1/2 RDy P2 Pa2 in the plane õó RBy RCy P2 RDy D RDz RD L/2 Mz=191 N.m in the plane õz R'Az Pr1 R'Bz R'Cy in the plane õz Pr2 M'y=-70N.m R'Dy R"Az dg1/2 Pa1 R"Bz dg2/2 M'y=115N.m R"Cz R"Dz Pa2 M"y=80 N.m M"y M"y=92N.m My of Pr2 and Pa2 M"y My of Pr1 and Pa1 M"y=-162N.m M"y=195N.m Mres of P2 , Pr2 and Pa2 Mres of P1 , Pr1 and Pa1 M"res =216N.m M"rez=250N.m Mtors=46.8N.m Mtors=615N.m Page 60 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES b. Bending momentums in the endangered section of the worm shaft Bending momentum in the XY plane: From the force P1 MZ = -RAY . l/2 = - 730 . 0.250/2 = -93 N.m Bending momentums in the XZ plane: From the force Pw.1 M’Y = R’A . l/2 = 925 . 0.250/2 = 115 N.m From the force Pa 1 on the left and right of the section: M’’ Y = P’’ A . l/2 = -640 . 0.250/2 = - 80 N.m M’’ Y = R B . l/2 = 640 . 0.250/2 = 80 N.m Bending momentums resultant from the forces Pw 1 and Pa 1: MIY = M’Y - M’’Y = 115 – 80 = 35 N.m MIIY = M’Y + M’’Y = 115 + 80 = 195 N.m Bending momentums resultant from the forces P1, P w 1 and Pa 1: I 2 ' M res = M z + M y 2 II M res = M z ( ) + (M ) 2 = = (− 93 )2 + 35 2 = 99.5[Nm] = 216[Nm] " 2 y (− 93 )2 + 195 2 c. Equivalent momentums in the endangered section I M equ = II M equ = (M ) + (M ) = 99.5 + 46 = 99.5[Nm] (M ) + (M ) = 216 + 46 = 220[Nm] 2 I res ' tors 2 2 2 2 II res " 2 y 2 2 11. Support reactions bending and equivalent momentums of the worm gear shaft [15] a. Reactions in the supports C and D of the worm gear shaft Radial reactions in the XY: From the force P2 RCY = RDY = P2/2 = 5100/2 = 2550 N; From the force Pw 2 RCY = R’DZ = Pw2/2 = 1850/2 = 925N; From the force Pa 2 ∑MD = 0; II R cz = -R’’Cz . l + Pa 2 . dd 2/2 = 0 Pa 2 .d d 2 1460 x 0.252 = = 1230[N ] 2.l 2 x 0.150 Page 61 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES where l1 = 150 mm is the distance between supports. R’’Dz = R’’C = 1230 N Reactions resultant from the forces P’w 2 and Pa: RCz = R’Cz - R’’Cz = 925 – 1230 = - 305 N RDz = R’Dz + R’’Dz = 925 + 1230 = 2155 N The resultant reactions from the forces P2, Pw 2 and Pa: 2 2 R c = R cy + R cz = 2550 2 + (− 305 ) = 2560[N ] 2 2 2 R D = R Dy + R Dz = 2550 2 + 2155 2 = 3340[N ] The axial reaction in the support D: AD = Pa 2 = 1460 N. b. Bending momentums in the endangered section of the worm gear shaft [15] Bending momentum in the XZ plane : From the force P2 MZ = RCY . l1 /2 = 2550 . 0.150/2 = 191 N.m Bending momentums in the XZ plane: From the force Pw 2 M’Y = -RCZ . l 1 /2 = -925 . 0.150/2 = -70 N.m; From the force Pa 2 left and right from the section: M’’Y = R”CZ . l 1 /2 = 1230 . 0.150/2 = 92 N.m; M’’Y = -R’’DZ . l 1 /2 = -1230 . 0.150/2 = -92 N.m; The resultant bending momentums from the forces Pw 2 and Pa 2 MIY = M’Y + M’’Y = -70 + 90 = 20 N.m MIIY = M’Y + M’’Y = - 70 - 92 = - 162 N.m The resultant bending momentum from the forces P2, Pw 2 and Pa 2: 2 I I M res = M z + M y 2 II M pes = M z ( ) + (M ) 2 = 1912 + (− 20 ) = 192[Nm ] 2 II 2 y = 1712 + (− 162 ) = 250[Nm] 2 c. Equivalent momentums in the endangered section: I 2 I M equ = M tors + M res II 2 M equ = M tors ( ) + (M ) 2 = 645 2 + 192 2 = 642[Nm] = 645 2 + 250 2 = 683[Nm] Page 62 2 II res MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES 12. Bearings selection a. for the worm shaft The following forces act on the supports: Radial RA = 795 N.; RB = 1130 N and axial Pa 1= 5100 N. The shaft rotates at u = 1440 rpm. Bearing necks diameters are : d A = dB = 44 mm. Duration h = 6000 hours; temperature – under 100°C. Bearing load under normal operation is even, without shocks. The construction of bearing assemblies can be made using the following arrangement: we select two conical roller bearings for the support B, which are capable of bearing both radial and axial thrusts. A single row radial ball bearing is selected for the support A. - Selecting support B bearing The axial component SB = 1.3 RB . tgα = 1.3 . 1730 . tg 12° = 4475 N For dual conical roller bearings the equivalent load is determined by the formula: QB = (0.5 RB . kk + 0.385 A . cotg β) kd . kt = = (0.5 . 1750 . 1 + 0.385 . 5100 . cotg 12°) 1.1 = 9365 N, where kk = 1 – kinematical coefficient; kd = 1 – dynamic coefficient; kt = 1 – temperature coefficient. The load-bearing capacity is determined by the formula: C = QB (u.h)0.3 = 9365 . 113.8 = 1070000 N = 1070 kN, where (u.h)0.3 = (1450 . 5000)0.3 = 110 + 190.7/330 = 113.8 is determined by interpolation. From the roller bearing catalogue we selected bearing No.7608 having Ctabl. = 1400kN > c = 1070 kN and the following dimensions: d= 40 mm D = 90 mm T = 35 ÷35.5 mm Selecting the support A bearing: QA = RA. kk kd . kt = 795 N Page 63 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES C = QA . (n.h)0.3 = 795 . 113.8 = 90500 N = 90.5 kN We selected bearing No.208 with Ctabl. = 390 kN and dimensions: d = 40 mm D = 80 mm B = 18 mm b. Selecting worm gear shaft bearings Acting forces are radial RC = 2560 N and RD = 3340 N and axial force Pa 2 = 1460 N. The shaft rotates at u2 = 80 rpm. Neck diameters are dC = dD = 55. We selected conical roller bearings SC = 1.3 RC . tg β = 1.3 . 2560 . tg 12o = 705 N SD = 1.3 RD . tgβ = 1.3 . 3340 . tg 12o = 920 N Aexp = Pa 2 + SC – SD = 1460 + 705 – 920 = 1245 N - This force is born by support D. QD = (RD . kk + m . Aexp) . kδ .kt = (3340 + 1.5 . 1245) = 5210 N, Where m = 1.5 is the equalization factor for conical roller bearings. C = QD (u.h)0.3 = 5210 . 48 = 250000 N. From the bearings [14] we selected bearing No 7211 having Ctabl = 990 kN > C = 250 kN and the following dimensions: d = 55mm; D = 100 mm; T = 23÷22.5 mm Page 64 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 65 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 66 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 67 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 68 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 69 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 70 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 71 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 72 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 73 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 74 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES Page 75 MULTIDIMENSIONAL COMPONENT INSPECTION DEVICES REFERENCES 1. K. Bruyère Garnier, R. Dumas, C. Rumelhart, M. E. Arlot, Mechanical characterization in shear of human femoral cancellous bone: torsion and shear tests. 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Mayer, Ultrasonic torsion and tension–compression fatigue testing: Measuring principles and investigations on 2024-T351 aluminium alloy. International Journal of Fatigue, Volume 28, Issue 11, November 2006, Pages 1446-1455. Page 77