Design considerations and simulation of a rolling-contact gearless automotive differential

Abstract

This paper presents the design considerations, the kinematical simulation and the FE analysis of a differential mechanism which involves the rolling contact of two cam-track disks with four equally-spaced spherical rollers sliding in a cage much resembling a rolling bearing. The obvious benefit of this concept in the field of power transmissions is the potential replacement of gears in planetary reducers and differentials by cams. The side gears of a conventional open differential are replaced by two identical cam-track disks, while the spider gears are replaced by rolling elements that is, balls, cylinders or tapered cylinders. Practically, the well-known rolling bearing concept is generalized, where the circular tracks are replaced by wavy curves. In order to assess the performance of the mechanism, the shape of the tracks is considered for two distinct cases and a rigorous mathematical modeling follows regarding the kinematics of the mechanism. The results were validated through kinematical simulations and FE analysis was carried out coupled with fatigue life computation for a typical passenger vehicle differential, indicating that service life in the order of 200,000 km is feasible.

Power Transmission Using Circular Elements Bounded by Given Central Angle in Rolling Contact

“…Based on the above data, in conjunction with a typical input torque M t,crown = 260 Nm applied to the crown attached on the cage, for the above inclination angle we apply Equations ( 26) and (27) to derive the normal forces on the outer (F out n ) and the inner track (F in n ), respectively. Furthermore, regarding the derivation of a large value for R e , after many trials, which all resulted in high stress values, acceptable stresses were obtained for at least the following design details (these reference values are close to those of the prototype, for which a finite element analysis has been documented in [23]):…”

“…One of the possible applications of the proposed curves is the gearless differential, of which a full study, including sinusoidal curves as well as stress (finite element) and fatigue analyses, may be found in [23].…”

“…The advantage of the proposed circular cams is the supposed self-regulation of the differential device to variable road conditions without additional means (i.e., those used in locking and limited slip ones). Note that if the central angle α c is relatively small with respect to the coefficient of friction between the outer support of the cam-track disks in the housing (for design details, see [21]), i.e., when tan(α c /2) < µ, the wedge shown in Figure 6 obeys the rule of the inclined plane, a self-blocking performance has been noticed [23]. In other words, the entire mechanism operates as an equivalent one-dimensional inclined plane in the circumferential direction.…”

“…In order to make further analysis easy, we assume that the angles are small and that similarity conditions between the outer and inner track are assumed; thus, according to [23], the sum of the two contact angles is constant:…”

“…A recent study has shown that sinusoidal-and circular-shaped cam-track disks can achieve rolling contact, while a finite element analysis has indicated that service life in the order of 200,000 km is feasible [23]. Despite this fact, since the commercial software that was used, RecurDyn ® V9R3, is based on spline representation, there are doubts as to whether the circular track was accurately represented.…”