Part 1: Introduction to the simplified model of wheel-rail contact mechanics for non-Hertzian problems
Wheel-rail contact is an important issue in many areas of transport, especially in rail transport. Understanding the mechanical behavior of this contact can not only improve the efficiency of wheel-rail systems, but also increase their service life. Traditionally, Hertzian contact theory is the main method for analyzing wheel-rail contact problems. However, Hertzian contact theory has some limitations, especially for non-Hertzian problems. This prompted the emergence of simplified models of wheel-rail contact mechanics for non-Hertzian problems.
In this article, we will introduce in detail the simplified model of wheel-rail contact mechanics for non-Hertzian problems and provide a complete code implementation using Python language.
1.1 Hertzian contact mechanics and its limitations
Hertzian contact theory describes mechanical behavior based on the contact between elastic bodies. It is very effective in describing wheel-rail contact phenomena in many practical applications. However, Hertzian contact theory falls short when it comes to nonlinear, inelastic, or other complex behaviors.
1.2 The importance of non-Hertzian contact mechanics
Considering these limitations of Hertzian contact theory, researchers began to seek other methods to describe the nonlinear behavior of wheel-rail contact. This is where the non-Hertzian contact mechanics model comes in. This model can better describe the real behavior of wheel-rail contact under certain conditions, such as high speed, high load or other non-linear conditions.
1.3 Simulation using Python
Python is a powerful programming language suitable for a variety of applications, including mechanics simulations. Through Python, we can easily implement a simplified model of wheel-rail contact mechanics for non-Hertzian problems and visualize it.
1.3.1 Python code implementation
First, we need to import some necessary libraries:
import numpy