轮轨与轮轮接触几何计算研究

对轮轨接触几何计算的迹线法进行了深入研究,给出了两种常用坐标系下'迹线法'的正确计算公式。在此基础上,对轮轮接触几何关系进行了分析,结果表明:轮轮接触点计算并不能像轮轨一样缩减为一维搜索,只能由二维搜索得到,给出了一种简洁的轮轮接触二维搜索算法及公式;同时提供了一种快速搜索轮轨和轮轮接触点的编程方法。

基于空间矢量映射的新型轮轨接触点算法

针对铁道车辆动态轮轨接触问题提出一种新的轮轨几何接触算法——空间矢量映射法。空间矢量映射法根据空间矢量映射原理和轮轨外形的基本特征,将轮轨接触视为空间曲面接触,以轨道截面为基准,以轨面宽度作为轮轨可能接触的最大范围,采用一定的接触点寻找和判定原则,准确地找到车轮在不同横移量和摇头角下的轮轨接触点。并自编一套轮轨关系软件TPLWRSim,以LMA型车轮踏面为例,分别建立轮对与轨道、轮对与滚轮和轮对与槽型轨的三维模型,仿真不同轮对姿态下的轮轨接触状态,并通过与轮轨接触几何外形和磨耗后的车轮踏面接触几何关系的对比验证算法的准确性和有效性。仿真结果表明此算法可很好解决铁道车辆的轮轨几何接触问题,能快速准确地求出轮对任意姿态下与轨道的接触点,并对不同踏面和轨道外形具有很好的适应性。

Mathematic model and tooth contact analysis of a new spiral non-circular bevel gear

A novel spiral non-circular bevel gear that could be applied to variable-speed driving in intersecting axes was proposed by combining the design principles of non-circular bevel gears and the manufacturing principles of face-milling spiral bevel gears.Unlike straight non-circular bevel gears,spiral non-circular bevel gears have numerous advantages,such as a high contact ratio,high intensity,good dynamic performance,and an adjustable contact region.In addition,while manufacturing straight non-circular bevel gears is difficult,spiral non-circular bevel gears can be efficiently and precisely fabricated with a 6-axis bevel gear cutting machine.First,the generating principles of spiral non-circular bevel gears were introduced.Next,a mathematical model,including a generating tooth profile,tooth spiral,pressure angle,and generated tooth profile for this gear type was established.Then the precision of the model was verified by a tooth contact analysis using FEA,and the contact patterns and stress distributions of the spiral non-circular bevel gears were investigated.

Loaded multi-tooth contact analysis and calculation for contact stress of face-gear drive with spur involute pinion

The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur involute pinion were introduced, and their relative errors are below 10%, except edge contact, which turns out that these two methods can compute contact stress of face-gear drive correctly and effectively. An agreement of the localized bearing contact stress is gotten for these two methods, making sure that the calculation results of FEM are reliable. The loaded meshing simulations of multi-tooth FEM model were developed, and the determination of the transmission error and the maximal load distribution factor of face-gear drive under torques were given. A formula for the maximal load distribution factor was proposed. By introducing the maximal load distribution factor in multi-tooth contact zone, a method for calculating the maximal contact stress in multi-tooth contact can be given. Compared to FEM, the results of these formulae are proved to be reliable, and the relative errors are below 10%.

Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade

In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.

Mesh stiffness calculation of cycloid-pin gear pair with tooth profile modification and eccentricity error

Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis （TCA） and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.

Finite element analysis of contact fatigue and bending fatigue of a theoretical assembling straight bevel gear pair

The aim of this work is to propose a 3D FE model of a theoretical assembling straight bevel gear pair to analyze the contact fatigue on the tooth surface and the bending fatigue in the tooth root. Based on the cumulative fatigue criterion and the stress-life equation, the key meshing states of the gear pair were investigated for the contact fatigue and the bending fatigue. Then, the reliability of the proposed model was proved by comparing the calculation result with the simulation result. Further study was performed to analyze the variation of the contact fatigue stress and the bending fatigue stress under different loads. Furthermore, the roles of the driving pinion and the driven gear pair were evaluated in the fatigue life of the straight bevel gear pair and the main fatigue failure mode was determined for the significant gear. The results show that the fatigue failure of the driving pinion is the main fatigue failure for the straight bevel gear pair and the bending fatigue failure is the main fatigue failure for the driving pinion.

Development and validation of a model for predicting wheel wear in high-speed trains

In this paper, we present a comprehensive model for the prediction of the evolution of high-speed train wheel profiles due to wear. The model consists of four modules： a multi-body model implemented with the commercial multi-body software SIMPACK to evaluate the dynamic response of the vehicle and track; a local contact model based on Hertzian theory and a novel method, named FaStrip （Sichani et al., 2016）, to calculate the normal and tangential forces, respectively; a wear model proposed by the University of Sheffield （known as the USFD wear function） to estimate the amount of material removed and its distribution along the wheel profile; and a smoothing and updating strategy. A simulation of the wheel wear of the high-speed train CRH3 in service on the Wuhan-Guangzhou railway line was performed. A virtual railway line based on the statistics of the line was used to represent the entire real track. The model was validated using the wheel wear data of the CRH3 operating on the Wuhan- Guangzhou line, monitored by the authors＇ research group. The results of the predictions and measurements were in good agreement.

Numerical investigation on wheel-turnout rail dynamic interaction excited by wheel diameter difference in high-speed railway

The wheel-rail relationship in turnout is more complicated than that in ordinary track. Profile wear and machining errors of the wheelset cause deviations Of the rolling radius on different wheels. Therefore, wheelsets move to the direction of smaller diameter wheels in search of a new stable state and to change the condition before entering the turnout. Thc main aim of the present work is to examine the wheel-turnout rail dynamic interaction combined with the static contact behaviour. Calculations are performed on a high-speed vehicle CRH2 and the No. 12 turnout of the passenger dedicated line. The wheel-turnout contac! geometric relationship and normal contact behaviour under wheel diameter difference are assessed by the trace principle and finite element method. A high-speed vehicle-turnout coupling dynamic model is established based on SIMPACK software to analyse the wheel-rail dynamic interaction, riding comfort, and wear. Both the wheel diameter amplitudes and distribution patterns are accounted for. The simulation shows that wheel diameter difference can greatly disturb the positions＇ variation of wheel-rail contact points and affect the normal contact behaviour on switch rails by changing the load transition position. The effect of wheel diameter diffierence on wheel-turnout rail dynamic interaction can be divided into three according to its amplitude： when the wheel diameter difference is within 0-1.5 mm, the wheel flange comes into contact with the switch rail in advance, causing a rapidly increased lateral wheel-rail force; when it is within 1.5 2.5 mm, trains are subject to instability under equivalent in-phase wheel diameter difference; when it is larger than 2.5 mm, the continuous flange-switch rail contact helps strengthen the vehicle stability, but increases the wheel-rail wear. It is recommended to control the wheel diameter difference to within 2.5 mm but limit it to 2 mm if it is distributed in-phase.