MODELLING AND SIMULATION OF COMPLEX AND COMPLIANT CONTACTS OF GEAR TRANSMISSIONS, IN CONSIDERATION OF NOMINAL AND REAL GEOMETRIES AND KINEMATICS.

Abstract

An important aspect of gear design is the computer-aided modeling of gear tooth contact. It enables to evaluate the design of gears and the process of tooth contact, transmission errors (TE), tooth wear, alignment errors, vibration and noise. Contemporary gear tooth contact analysis models are multiple equation systems which rely on numerical solution techniques. Tooth contact analysis (TCA) is a crucial tool for designing and evaluating the efficiency of the gears in transmission systems. It stands for a significant approach to analyze contact locations, contact ratios, and kinematic errors in gear teeth. Gear manufacturers in various fields can greatly enhance the technology and quality of gears by simulating meshing and bearing contact on a computer. Additionally, TCA is a helpful method for forecasting a transmission's key characteristics, including the path of contact on the tooth surfaces and the motion graph. The necessity to analyze non-conjugate meshing and surface contact led to the development of numerous tooth contact analysis approaches, such as parametric mathematical model or finite element simulation. These methods handle the contact problem by applying the surface tangency condition, which leads to a set of nonlinear equations that must typically be solved numerically. The original suggestion of the most well-known solution was presented by Litvin F. L. and his team, where they suggested the set of generalized five nonlinear contact equations with five unknown parameters, which forms the foundation of conventional TCA algorithm. Since these equations are nonlinear, an iterative process is used to calculate certain values. However, the main problem with this method is that each simulation requires careful selection of the initial or "guess" values for the convergence of parameters in an iterative process. Later, Litvin F. L. and his colleagues proposed the “local synthesis method” to eventually determine appropriate "guess values" and obtain convergence to lessen the systemic lack of stability in this solution. Although, this resulted in a computationally expensive and impractical implementation. In this dissertation, by analytically transforming the same contact conditions as in the conventional model, a novel TCA method was presented to resolve convergense issue. As a result, a mathematical model of five conventional nonlinear tooth contact equations with five free parameters was reduced to a system of two nonlinear equations with only two unknown parameters in order to achieve more stable, accurate and fast converging algorithm. The proposed model was compared with the well-established conventional Tooth Contact Analysis (TCA) method in terms of accuracy, computational efficiency, and convergence probability, thereby showing its superiority in terms of computationally efficient of the numerical solution. By using new TCA model the impact of tooth surface to various misalignments and modifications on different types of gears is examined, in order to determine the most suitable design approach and establish acceptable values for tooth modifications. Additionally, the present study investigated the effects of three types of longitudinal crowning and tip/root profile relief on gear meshing.