Design And Analysis Of An Open Differential

An automobile differential gear system is used to establish a differential motion between left and right driving axle which provides a smooth turning of the vehicle. When a vehicle takes a turn then the wheels at outermost position requires to cover a large distance than that of the innermost wheels. This speed variation can be achieved by using a differential gear system. It also transmits the power from the propeller shaft to each axle. A rear wheel drive vehicle requires a differential at the rear axle while all-wheel drive vehicle requires differential gear system for each and every axle. In this paper, an open differential is designed for a leading automobile and analysed the ability to work without failure. The analysis was done using the modified Lewis equation, Hertzian contact stress equation and AGMA equations. The analytical results were compared with results obtained by FEA. It is observed that results obtained from Lewis criterion are more conservative as compared to AGMA. The results obtained from modified Lewis, Hertzian contact stress and AGMA are in good agreement with the results obtained from FEA.

DEVICE FOR IN VITRO WEAR ANALYSIS OF BIOMATERIALS IN THE HINGED PROSTHESIS CONFIGURATION

We have developed a device that, coupled to the tribometer, allows movement simulation of the hinged type knee prosthesis. Two tests were performed using the samples designed and one test without the device using a pin-on-flat configuration. For the first and the third tests, the metallic samples were used as machined while for the second one they were electrolytically polished. The test parameters were running length of 0.663 rad and compression load of 22.35 N. The Hertzian contact stress of 15.93 MPa obtained between the samples designed is close to that for the real prosthesis. The measured volumetric wear revealed the influence of roughness of the counterpart surface on the wear behavior. The device has allowed its coupling to the tribometer without any interference on its functioning thus making a contribution to the scientific investigations related to wear behavior of a couple of different biomaterials.

A Vibration Model of Ball Bearings with a Localized Defect Based on the Hertzian Contact Stress Distribution

To study the vibration mechanism of ball bearings with localized defects, a vibration model of a ball bearing based on the Hertzian contact stress distribution is proposed to predict the contact force and vibration response caused by a localized defect. The calculation of the ball-raceway contact force when the ball passes over the defect is key to establishing a defect vibration model. Hertzian contact theory indicates that the contact area between the ball and the raceway is an elliptical contact surface; therefore, a new approach is used to calculate the ball-raceway contact force in the defect area based on the stress distribution and the contact area. The relative motion between the inner ring, the outer ring, and the balls is considered in the proposed model, and the Runge-Kutta algorithm is used to solve the vibration equations. In addition, vibration experiments of a bearing with an outer ring defect under different loads are performed. The numerical signals and experimental signals are compared in the time and frequency domains, and good correspondence between the numerical and experimental results is observed. Comparisons between the traditional model and the proposed model reveal that the proposed model provides more reasonable results.

Planar Tooth Profile Synthesis for Relative Curvature

This paper is the first that uses the new conjugation curvature theory [1] to directly synthesize conjugate tooth profiles with the given relative curvature that determines the Hertzian contact stress. Conjugation curvature theory offers a systematic methodology to synthesize the relative curvature for a tooth pair. For any given relative curvature between the contact tooth profiles, a generating point can be located on an auxiliary body. Under the rolling motion among the pinion pitch, the gear pitch and the pitch on the auxiliary body, the generating point will trace fully conjugate profiles on the pinion and gear bodies with the given relative curvature at the instant of the contact. Full conjugation throughout the contact of the profiles is guaranteed with the three instant centers remaining coincident [1]. The methodology is demonstrated with a planar tooth profile synthesis with given relative curvature. One may find that the Wildhaber-Novikov tooth profile, which is known to have low relative curvature and Hertzian contact stress, and its variations become special cases under such methodology.

Curvature Analysis and Hertzian Contact Stress of a Modified Curvilinear Gear Set With Localized Bearing Contact

This paper investigates the contact ellipse and contact stress of a modified curvilinear gear set with localized bearing contact. The proposed modified curvilinear gear set with profile modifications was generated by male fly cutters with a circular-arc normal section. This gear drive exhibits point contact and parabolic transmission error under an ideal meshing condition according to the results of tooth contact analysis. The principal directions and curvatures of the mating pinion and gear surfaces were derived from those of the generating surfaces on the basis of differential geometry and theory of gearing. The Hertzian contact stress and contact ellipses of the mating tooth surfaces were determined with our developed computer program based on formulae of curvature analysis and Hertzian contact theory. Numerical examples were also provided to demonstrate the computational results.

Determination of All Stress Components of Axisymmetric Stress State in Photoelastic Tomography

In this paper we describe the application of photoelastic tomography for determining stresses in glass. The basic equations of linear approximation in photoelastic tomography are presented. Since these equations permit direct determination only of the axial and shear stress, a method for calculating the other stress components is described. In the case of the residual stresses, it uses the equilibrium equation and the generalized sum rule. In the case of stresses due to external loads, it uses the equilibrium and compatibility equations. It is shown, both graphically and analytically, that integration of these equations must start at the axis and proceed along the positive direction of the radial axis. As an example, residual stresses in the stem of a wine glass are determined. Results are verified by comparing the birefringence, calculated from the determined stress state, with measured birefringence. The numerical algorithm for the case of stresses due to external loads is verified by using the theoretical solution for a Hertzian contact stress problem.

Effect of Lubricant on Surface Rolling Contact Fatigue Cracks

This study performed the finite element analysis of the cycle of stress intensity factors at the surface initiated rolling contact fatigue crack tip under Hertzian contact stress including an accurate model of friction between the faces of the crack and the effect of fluid inside the crack. A two-dimensional model of a rolling contact fatigue crack has been developed with FRANC-2D software. The model includes the effect of Coulomb friction between the faces of the crack. The fluid in the crack was assumed not only to lubricate the crack faces and reduce the crack face friction coefficient but also to generate a pressure.