SPH分析中的齿轮建模方法研究

对利用光滑粒子动力学(SPH-Smoothed Particle Hydrodynanlics)方法进行轮齿动态力学数值分析中的齿轮建模方法进行了研究.确定了齿轮齿根过渡曲线以及其他部分的参数方程,并根据所确定的参数方程建立了三维齿轮离散粒子模型的数学模型.编制了划分齿轮整体及局部离散粒子的SPH前处理程序.并对划分后齿轮离散粒子与齿轮理论轮廓之间进行了误差分析.分析结果表明,利用此办法可正确划分齿轮的SPH离散化粒子,是一种较好的前处理方法.     

Design of laser interferometric system for measurement of gear tooth flank

A laser interferometric system (LIS) based on oblique incidence and phase shifting technique has been designed for the measurement of gear tooth flank. For a spur involute gear with a module of 2.0, 60 teeth, and a 20-mm facewidth, some critical parameters of the LIS are calculated, the oblique incidence angle is 84.5°, the beam diameter is 20 mm, and the focal length of imaging lens is 100 mm, and the resolution of CCD camera is 1360 × 1024 pixels. To test the capability of the designed LIS, the numerical simulation is done for the LIS. The actual LIS is built on an optical platform and the experiment is carried out. Both interference fringe patterns from the numerical simulation and the actual experiment are good and coincident with each other, which show the designed LIS is feasible.     

二维刚性边值问题的小波-吉尔解法

本文利用微分方程数值解的离散小波表示，讨论了此类方程在满足一定初始条件和边值条件下，在一个方向上利用小波伽辽金法，另一方向上利用吉尔方法进行求解，提出了一种解二维刚性初，边值问题的小波数值算法，计算结果表明，利用该方法所求得的数值解精度高，而且由小波特有的性质，它特别适用于求解带有奇异摄动的刚性问题。     

Gear transmission dynamics: Effects of index and run out errors

This work describes a non-linear dynamic model for the study of the vibration signals generated by gear transmissions. The developed model considers both the parametric excitations due to the variable compliance of bearings and gears, can handle changes in the transmitted torque and allows the integration of the dynamic equations quickly and accurately. This model has been developed previously by the authors to assess the profile deviations on the dynamic behavior of gear transmissions and its influence on the transmitted torque. It also includes the presence of gear defects as cracks and pitting during the calculation of meshing forces. In this paper, the model has been enhanced in order to include two common defects such as index errors and run out or eccentricity errors. Index errors occur as a result of a non-uniform angular distribution of the tooth profiles along the pitch circle. Run out appears due to the displacement of the geometric center of the gear with respect to the center of rotation of the shaft on which it is mounted. Although both errors are caused by different reasons, sometimes they have been confused because of their similitudes. The procedure for including both kinds of errors in the model is described and simulations under several transmitted torques are presented. The results are assessed and compared focusing the attention on certain transmission parameters and magnitudes as transmission error, load forces in the tooth flanks and demodulation techniques on the resulting vibratory signals.     

Gear transmission dynamic: Effects of tooth profile deviations and support flexibility

In this work a non-linear dynamic model of spur gear transmissions previously developed by the authors is extended to include both desired (relief) and undesired (manufacture errors) deviations in the tooth profile. The model uses a hybrid method for the calculation of meshing forces, which combines FE analysis and analytical formulation, so that it enables a very straightforward implementation of the tooth profile deviations. The model approach handles well non-linearity due to the variable meshing stiffness and the clearances involved in gear dynamics, also including the same phenomena linked to bearings. In order to assess the ability of the model to simulate the impact of the deviations on the transmission dynamics, an example is presented including profile deviations under different values of transmitted torque. Several results of this example implementation are presented, showing the model’s effectiveness.     

Numerical solutions to a BBM‐Burgers model with a nonlocal viscous term

In this paper, we numerically investigate the BBM‐Burgers equation with a nonlocal viscous term (1) where is the Riemann‐Liouville half derivative. In particular, we implement different numerical schemes to approximate the solution and its asymptotical behavior. Also, we compare our numerical results with those given in 2013, 2014 for similar models.     

Solving Implicit Equations Arising from Adams-Moulton Methods

A new algorithm is given in this paper, which uses functional iteration to solve the implicit equations generated by the Adams-Moulton method. Compared with traditional function iteration, it has three advantages: (1) the center of the circle of convergence for the iteration moves to the left in h plane; (2) the radius of the circle is much enlarged; (3) for a fixed number of iterations, in practice, we can view it as an explicit method since it has a very large absolute stability region. The method is very suitable for stiff system, especially for very large systems.     

Direct analytical solution of a modified form of the meshing equations in two dimensions for non-conjugate gear contact

The current technological state-of-the-art utilises modified gear profiles, which are in part non-conjugate and therefore cannot be analysed using standard conjugate contact theory. Existing non-conjugate mathematical models require the solution of a system of implicit equations, typically with significant computational effort and need for careful monitoring of solution stability, convergence and selection of initial values. This paper derives a modified form for the fundamental gear meshing equations, which are reduced analytically to a single scalar equation, resulting in improved solution speed and stability. The solution is verified in benchmark tests using real gear geometries.     

Evaluation of thermo-oxidative characteristics of gear oils by different techniques: Effect of antioxidant chemistry

This paper deals with determination of the oxidation stability of gear oils formulated with antioxidants of different chemistries. The oxidation stability has been studied by PDSC, TGA, micro-oxidation, RPVOT and IP 48. The effect of different antioxidants on the thermo-oxidative properties of gear oil is evaluated.