MEASUREMENT OF STRESS PATTERN ON ROLL BEARING SUPPORTS BY THERMOELASTICITY

Transcription

1 MEASUREMENT OF STRESS PATTERN ON ROLL BEARING SUPPORTS BY THERMOELASTICITY G. Brustenga, R. Marsili, J. Pirisinu, G.L. Rossi Università degli Studi di Perugia Dipartimento di ingegneria Industriale Via G. Duranti, n 1/A Perugia (Italy) Tel , fa misure@unipg.it ABSTRACT In this work termoelasticity is proposed for the determination of the stress pattern on roll bearing supports. To starting the developent and demonstrate the feasibility of the measurement a special purpose test bench has been developed by multibody and FEM models. A specific code, written in visual basic, was also developed in order to optimize the design and testing parameters of the test bench. The design goal was the possibility to obtain a simple, and therefore useful for reference, stress level and distribution on the roll bearing support. The test bench was therefore realized and used for the definition of the possible reference signal to be used for termoelastic data acquisitions and for perform some first comparison of the measurements with finite element and multibody calculations. 1. INTRODUCTION The problem here addressed starts from some needs epressed by many industries who manufacture structural components of motorcycle engines, car engines and gearbo. On these components typically many roll bearings are mounted and strong dynamic forces are transferred from the rotating to the stationary machine components, therefore generating fatigue stresses and possible failures. The geometry of this kind of components is typically quite comple and its FEM analysis usually is not simple and reliable for many reasons. Also measurements by strain gauge are difficult to perform mainly because of the strong stress gradients concentrated in little areas, where the stress level are at its maimum values, and because of the typical mean effects of the strain gauges inside its area. The idea was therefore to understand how it is possible to use the thermoelasticity measurement technique during the development and test phase of these mechanical components. Termoelasticity, in general, allows to perform non contact measurements on the surface of a mechanical component, of any material or shape, only with the need of an optic access, when it is dynamically stressed. Thermoelasticity is based on the phenomenon of temperature changes on a material when volume changes take places [1]. The phenomenon was first noted by Ghough in 1805 who performed some simple eperiments using strand of rubber. The first observation in metals of what is now known as the thermoelastic effect was made by Weber in 1830 [1]. Recently some measurement systems has been developed, based on termoelastic measurement principle and low-noise and high sensitivity termographic focal plane arrays, able to detect, without contact, the temperature changes on the surface of a mechanical component.

2 The system here used is a Deltatherm 1560, manufactured by Stressphotonics that with proper optics allows to investigate on very wide surfaces of the order of some square meters, or, on the contrary, concentrate the stress analisys on measurement points on an area of 34 mm in order to analyze very small details and locations where high stress gradient takes place, actually with a spatial resolution up to 22 microns. The system is based on a differential termocamera that measure the temperature changes (in time) on the component surface and on a specific control and data processing hardware and software. The system allow to measure the very small temperature changes in time due to the termoelastic effect on the whole mechanical component surface. For data acquisition it is fundamental a sincronization signal, in order to make the acquisitions of the termal images at time instants when steess (and therefore volume changes) are at maimum and minimum values. Averaging of subsequent acquisitions allow to reach a very high termal resolution, thus improving the signal to noise ratio and reduce the effects of disturbing inputs. This is important because temperature changes due to other causes that normally take places and are very high respect those due to the termoelasic effect, but occur at different frequencies and therefore using this averaging and lock-in data processing techniques strongly help to reduce their effects. The data processing software allows, operating in this way, to obtain a map of amplitudes of temperature fluctuations at a specific frequency or, in general, map of correlation coefficients with a particular reference signal. The basic idea of the measurement principle is therefore that stress distribution occur only at this frequency or have the shape of the reference signal on each point of the surface of the mecanical component under analysis. The maimum resolution that can be obtained in terms of averaged temperature difference is of the order of some mk [2-5]. The structure under test must therefore be dynamically loaded, with a frequency sufficiently high, in order to generate on the different point of the component surface temperature cycles or dynamic changes of different amplitudes, reducing as much as possible the effect of conductive heat transfer that could destroy these time temperature fluctuation, if they are not sufficiently faster than conductive heat ecange on the mechanical component surface. The minimum frequency of the applied load depends therefore on the thermal characteristics of the material and on the gradient of the stress fields. Considering a complete adiabatic condition it is possible to have a linear relationship between the mechanical energy and the thermal energy on each point of the structure surface. A linear relationship between the sum of the amplitude of time fluctuations between of the two principal stress σ with the amplitude of the output signal V of each piel of the termographic array (proportional to the temperature fluctuations) can be obtained [1-6]: D R ρ C = P V α T ζ σ (1) where D is a calibration factor, R is a correction factor which compensates for temperaturedependent changes in radiation intensity and wavelength, ρ is the material density, C p is the specific heat at constant pressure, α is the coefficient of thermal epansion, T is the absolute temperature, ζ is the surface emissivity. The resolutions that can be obtained in terms of stress depend on the material characteristics; they are typically 1 Mpa for the steel and 0.4 Mpa for the aluminium [1-6]. 3. DEVELOPMENT OF THE MEASUREMENT TECHNIQUE AND OF THE TEST BENCH When termoelasitic measurement technique is commonly applied, if possible, should be better to paint the surface of the mechanical component in order to increase and make uniform the emissivity ζ. This is tipically acceptable for the application here considered to roll bearing supports both in engines and gearboes. A more difficult problem to solve occur when this measurement techniques is applied on internal combustion engine components, when the engine is operating, because of the presence of very strong temperature fluctuation due to the internal combustion and

3 oil flows that occur at same frequency of stress cycles, thus completely masking the termoelastic generated temperature fluctuations. The idea was to develop a different testing technique for internal combustion components, for eample using an eternal electric engine to generate the motion of the engine, obviously analizing only the part of the stresses induced by the motion of the engine components, that anyway are of interest for fast rotating and little i.c. engines, for eample of high power and high performance motorcycles. The work here illustrated was carried on for the analysis and testing of a carter component of a fast rotating motorcycle internal combustion engine. Particularly this work was oriented to perform stress analyses on the supports of some balls bearing of a particular carter, realized in aluminium by fusion, where the presence of some ribs with a not optimal superficial rughness and shapes it produces a stress concentrations and consequent risk of failure of the component. It is difficoult by FEM analysis approach this problem because of the very comple geometry and random shapes, rughness and material properties generated by the production process. The first step was therefore to realize a suitable test bench able to demonstrate the feasibility of measurements by termoelasticity of the typical stress field on a bearing support. Typically, inside an engine or inside a gearbo, the shaft fleural vibrations and mass ecentricity generates a rolling load on the roll bearing support, rotating at the same frequency of the shaft. The goal was therefore to realize a test bench able to produce a similar stress field but easy to analyse with F.E.M models in order to have a reliable comparison with the results eperimentally obtained. For these reason the roll bearing supports was designed as a simple aluminium plate, instead that to directly use the engine carter of comple geometry and average stress level low but with high gradients. The test bench shaft was designed in aluminium in order to have a fleible shaft. The stress on the ball bearing support was obtained by the centrifugal forces produced by an eccentric mass, realized using steel. The rotational speed of this simple rotor was generated trough a chain transmission by a variable speed electric motor. The design of rotating components and of the ball bearing support has been optimized in order to assure a proper stress level, easy to measure by thermoelasticity. In fact the stress on the ball bearing supports depends on the length of the shaft, on its diameter, on the eccentric mass weight and its eccentricity and obviously on the rotational speed. To find the optimal values of this set of parameters a specific code was developed, using visual basic programming language and the well known analytical solutions for fleible rotating shaft. Once fied the shaft length, the mass of the eccentric and its eccentricity, the free variable of the test bench that can be used to change the level (and frequency) of the stress generated on the bearing support is the rotational speed, in fact the increasing of the shaft speed of rotation, increases the applied load (centrifugal forces) and then the bending of the shaft, and this, corresponds to an increase of the eccentricity. This is balanced by the elastic strength of the shaft. Using the multi body simulation software it is possible to analyse the strengths produced by the shaft rotation, and know their amplitude. In the picture number 1 is represented the multi body model and the forces generated on the ball bearing supports are illustrated in picture number 2. Picture 1. Multy body analisys Picture 2. Forces between ball bearing and support

4 The multi body simulation has also been used to obtain the centrifugal strength values produced by the rotation of the eccentric mass, and subsequently used as input for a second FEM model, in order to a better evaluate the stress pattern. In the picture number 3 is shown the mesh of the ball bearing support, the model constraint and the force applied in the middle of the shaft. Picture 3. FEM model realize the test bench Picture 4. FEM result The result shown that the test bench stress levels are well suitable as reference for thermoelastity (picture number 4). The results are relative to a rotation speed of 2000 RPM. In the follows figures are shown the test bench cad design and a picture of it. Picture 5. Test bench relized Picture 6. Test bench cad design 4. MEASURE ON TEST BENCH BY THERMOELASTICITY Once realized and tested the bench some preliminary tests performed, using different sincronization signals taken from the rotating components allow to understand that it was possible to perform the measurement simply by using a strain gauges on the bearing support to syncronize the thermographic acquisitions. The strain gauge has been therefore installed on the eternal surface of the ball bearing support. As previously told the speed of rotation it is an important testing parameter; a first series of tests has been performed at 2000 RPM. In the picture number 7 is shown a typical result obtained: is it possible to see the same stress distribution of the FEM analysis (picture number 8) only in the lower part of the ball bearing support. The differences on the upper part was attribuited to the heat development due to the friction between the ball bearing and its support.

5 Picture 7 Thermoelastic result Picture 8 Thermoelstic result In fact the bending of the shaft generates a relative rotation between the internal and eternal ball bearing housing and accordingly a greater friction in the part in compression and then a greater development of heat, that clearly results to be in phase with the measured stresses. This effect was not observed at lower angular speed, below 2000 rpm. In these conditions the observed effect it is mainly the bending of the of the ball bearing support, and in this case, the same distribution can be obtained from the thermographic image (figure 9) and from the multi body analysis (figure 10). Picture 9 F.E.M result Picture 10 Thermoelstic result The differences observed can also be due to the fact that in the model FEM the shaft is perfectly constrained with the ball bearing, without considering the eisting real gap and alos are not considered some strengths due to skew, due to the not perfect connection, that can generate stress on the support. The net step of this work will be the testing, using the measurement and testing technique developed of typical engine components. These tests has been started simply using an alternative sollecitation on a not rotating shaft, connected to a ball bearing of a motorcycle engine carter. The first results obtained are illustrated in picture number 12.

6 Picture 11 engine ball bearing support Picture 12 Thermoelstic result The first studies here illustrated, the test bench realized and the tests carried out have shown some possibilities to perform measurements by termoelasticity for the determination of the stress field distribution on ball bearing supports. Of relevance is the fact that it seems possible sincronize the termoelastic acquisitions with the signal of a strain gauges glued on the eternal part of the bearing support without the need of comple sincronization with the rotating components inside. 5. EXPERIMENTAL CALIBRATION AND UNCERTAINTY ANALYSIS Normally, when sincronized temperature difference maps are measured, in order to obtain the proportional stress distribution is not used eq. 1 but an eperimental scale factor directly between the sum of principal stress σ and the amplitude of infrared piel output signal V is calculated from a deformation measurement in a point of the structure under test by using at least two strain gauges [1]. The scale factor between the sum of the principal stress and the amplitude of the output signal of each piel of the termographic array can be calculated by the following equation: E( ε + ε y ) K = (2) V (1 ν ) where E is the Young modulus of the material, ν is the Poisson modulus, (ε +ε y) is the sum of the principal strains and V is the RMS of the signal measured by each infrared sensor of the termographic array [5]. The calibration can be done using specimens of analogous material and emissivity characteristics. These specimens can be beams which are fied at one end and loaded at other one applying a sinusoidal load to have the same stress level measured on the roll bearing support. The calibration can be otherwise performed directly on parts of the same structure under analysis if a sufficient uniform stress field can be found in the area where the strain gauge are applied. Repeated measurements of the principal strains on the same area of a beam and the relative measure of the infrared intensity radiation, allow to estimate the calibration factor K. Repeated measurements varying the applied load, the observation area and the ecitation frequency (between 15 and 50 Hz) make possible to have the best available estimate of the thermoelastic constant k. Was calculated an epected value: k = 0,14 MPa/mV. The eperimental standard deviation was s ( k) = MPa/mV. The composed uncertainty on the value of the thermolastic constant K can be determined basing on relationship (2) as follow: K( E) K ( ε ) K( ε y) K ( V ) K ( ν ) (3) K = E + ε + ε y + V + ν E ε ε V ν y

7 Assuming an relative uncertainty of 2% on the Poisson and Young modulus of the materials, of 2% on the determination of the principal strain ε and 2% on the RMS of the signal measured by the infrared sensor V, the combined standard uncertainty is K = , and so relative uncertainty is K = 9% (4) K Even if this value is quite hight it is acceptable for the application here proposed because more uncertainty causes are actually present in FEM and/or strain gauges approach to the eperimental design of the component here considered for the reasons previously illustrated. 6. CONCLUSIONS AND DEVELOPMENTS The problem of measure rotating stress field on roll bearing supports by termoelasticity has been approached. A test bench for measurement technique development has been designed, realized and used for founding a proper reference signal for thermal acquisitions and demonstrate the feasibility of the measurement of the stress field distribution by some first comparisons with FEM and BEM calculations. The uncertainty of the measurement technique has been evaluated and it is acceptable for the application of industrial interest. Futher developments will allow to perform tests, using the test bench developed, on typical engine and gearbo components in order to have a new measurement and testing technique useful to validate BEM and FEM models of these components. REFERENCES 1. Harwood N., Cummings W.M., Thermoelastic Stress Analysis Adam Hilger Shiratori, M., Miyoshi, T., Nakanishi, T., Noda, T., Hanada, Detection of crack and measurement of stress intensity factors by infrared video system, JSME International Journal, series I, 33, 3, (1990), pp Belgen, M. H., "Structural Stress Measurements with an Infrared Radiometer", ISA, Trans., vol. 6, Huang, Y.M., Abdel Mohsen, H.H., Rowlands, R.E., Determination of Individual Stresses Thermoelastically, Eperimental Mechanics, Vol. 30 (1), 1990, Lesniak, J.R., Thermoelastic data improvements, Proceedings of 1993 SEM Spring Conference on Eperimental Mechanics, Dearborn, Michigan, pp Offermann, S., Beaudoin, J.L., Bissieu, C., Frick, H., Thermoelastic Stress Analysis Under Nonadiabatic Conditions, Eperimental Mechanics, Vol. 37 (4), 1997, pp