Nonuniformity of Isometric Properties of Automotive Driveshafts

Abstract

This paper presents an analysis of the CVJ (constant velocity joint) of automotive driveshafts from a point of view concerning the nonuniformity of isometric properties. In the automotive industry, driveshafts are considered to have constant velocity through its joints: free tripode joints and fixed ball joints, which has been proved by Mtzner’s indirect method and Orain’s direct method for tripod joint. Based on vectorial mechanics, the paper proved the quasi-isometry of velocity for polypod joints such as fixed ball joints. In the meantime, it was computed that the global nonuniformity of constant velocity joints for modern driveshafts based on the Dudita-Diaconescu homokinetic approach for the driveshafts. The nonuniformity of the velocity isometry of driveshafts was computed as a function of the input angular velocity of the driveshaft, angular inclination between the tripod–tulip axis and the midshaft axis and the angular inclination between the bowl axis and midshaft axis. The main aim of this article is how to improve the geometric and kinematic approach to add an important correction when designing the driveshaft dynamics prediction such as: forced torsional vibrations, forced bending–shearing vibrations, and coupled torsional–bending vibrations for the automotive driveshaft in the regions of specific resonances such as principal parametric resonance, internal resonance, combined resonance, and simultaneous resonances. By the way it is added, there are important corrections for the design of driveshafts, for the torsional dynamic behavior prediction, and for bending–shearing dynamic behavior of the driveshafts in the early stages of design. The results presented in the article represent a starting point for future research on dynamic phenomena in the area mentioned previously.

Modeling and Analysis of FBV Movements for Automotive Driveshafts in the PPR Region

“…By analyzing Equations ( 35) and (36), it can be remarked that they represent a system of equations with partial derivatives for the bending-shearing vibrations of a uniform shaft that considers the effects of rotary inertia and shear deformation, with the midshaft being a Timoshenko beam. The boundary conditions are given by Equations ( 39)-( 44) and link the bending-shearing vibrations of the midshaft with the tulip and the bowl through the tulip-tripod and bowl-inner race joints, inducing in the solutions of the system of Equations ( 33)-(38) the next phenomena: the joints of the driveshaft are quasi-isometric [25][26][27] (p. 78), with the effect of geometric nonuniformity of the inertia characteristics of the joints that vary with the rigid angle of rotation for each element of the driveshaft in the directions X 1 , X 2 , X 3 , the effects of the bending deflection and bending-twisting stiffness for the tulip and the bowl, the effects of the bending deflection and bending-twisting damping for each joint of the driveshaft, the rotary inertia effect in bending, and the shearing effect for the midshaft. The novelty of the Hamilton's Principle approach was that it was used for the first time to compute the equations of motion for each AD element and the determination of the boundary conditions, as is noted in Equations ( 26)-(44).…”

“…This considers the nonuniformity of the kinematic isometry of the AD [25,26]. In Equation (61), the terms R TTr , R IrB represent the radii of the tulip-tripod and inner racebowl joints.…”