Calculation and Analysis of TVMS Considering Profile Shifts and Surface Wear Evolution Process of Spur Gear

Profile shift is a highly effective technique for optimizing the performance of spur gear transmission systems.However,tooth surface wear is inevitable during gear meshing due to inadequate lubrication and long-term operation.Both profile shift and tooth surface wear(TSW)can impact the meshing characteristics by altering the involute tooth profile.In this study,a tooth stiffness model of spur gears that incorporates profile shift,TSW,tooth deformation,tooth contact deformation,fillet-foundation deformation,and gear body structure coupling is established.This model efficiently and accurately determines the time-varying mesh stiffness(TVMS).Additionally,an improved wear depth prediction method for spur gears is developed,which takes into consideration the mutually prime teeth numbers and more accurately reflects actual gear meshing conditions.Results show that consideration of the mutual prime of teeth numbers will have a certain impact on the TSW process.Furthermore,the finite element method(FEM)is employed to accurately verify the values of TVMS and load sharing ratio(LSR)of profile-shifted gears and worn gears.This study quantitatively analyzes the effect of profile shift on the surface wear process,which suggests that gear profile shift can partially alleviate the negative effects of TSW.The contribution of this study provides valuable insights into the design and maintenance of spur gear systems.

Contact surface fatigue life for roller rack pinion system

A roller rack pinion(RRP)system,which consists of a rack-bar and a cam pinion,transforms a rotation motion into linear motion.The rack-bar has a series of roller train and meshes with the cam pinion.First,the exact tooth profile of the cam pinion and the non-undercut condition to satisfy the required performance have been proposed with the introduction of the profile shift coefficient.Then,the load stress factors are investigated under the variation of the shape design parameters to predict the gear surface fatigue limit which is strongly related to the gear noise and vibration at the contact patch.The results show that the pitting life can be extended significantly with the increase of the profile shift coefficient.

Mesh stiffness evaluation of an internal spur gear pair with tooth profile shift

Tooth profile shift will change the thickness of gear teeth and a part of geometrical parameters of a gear pair, thus influencing its mesh stiffness and consequently the dynamic performances. In this paper, an analytical mesh stiffness calculation model for an internal gear pair in mesh considering the tooth profile shift is developed based on the potential energy principle. Geometrical representations of the tooth profile shift are firstly derived, and then fitted into the analytical tooth stiffness model of gears. This model could supply a convenient way for mesh stiffness calculation of profile shifted spur gears. Then, simulation studies are conducted based on the developed model to demonstrate the effects of tooth profile shift coefficient on the tooth compliances and the mesh stiffness of the internal spur gear pair. The results show that tooth profile shift has an obvious influence on the mean value, amplitude variation and phase of the mesh stiffness, from which it can be predicted that the dynamic response of an internal gear transmission system will be affected by the tooth profile shift.

A novel approach for justification of box-triangular germanium profile in SiGe HBTs

This work presents a unique and robust approach for validation of using the box-triangular germanium profile in the base of SiGe heterojunction bipolar transistors, where the methodology considers the simultaneous optimization of the p-type base doping profile in conjunction with the germanium profile in the base. The study analyses the electron motion across the SiGe base in SiGe HBTs, owing to different accelerating electric fields. The analysis first presents a figure of merit, to achieve the minimum electron transit time across the base in conjunction with the increased current gain in n-p-n-SiGe HBTs, which shows a general trend vis-a-vis the advantage of a trapezoid germanium profile, but with additional accuracy as we considered simultaneously optimized p-type base doping. The effect of minority carrier velocity saturation is then included to make the study more detailed. The analysis then investigates the shifted germanium profile in the base to further minimize the base transit time. Finally, it is shown that a shifted germanium profile eventually evolves into a box-triangular Ge-profile in the SiGe base, which could simultaneously minimize the base transit time and reduce emitter delay by virtue of the high current gain. The analysis verifies that for an average Ge-dose of 7.5% Ge across the base, a box-triangular germanium profile in conjunction with an optimum base doping profile has an approximately identical base transit time and a 30% higher current gain, in comparison with an optimum base doping and triangular Ge-profile across the whole base.