Estimation of the Grain Trajectory and Engaging on the Material

*Takenori Ono*

#### **Abstract**

In this chapter, a numerical estimation of the grain trajectory in the grinding process is introduced. The topic describes a fundamental of the numerical theory of the grain trajectory, the estimation of the grain trajectory in the hemispherical grinding stone in the micro grooving process as an application of the numerical estimation.

**Keywords:** grinding process, grain trajectory, numerical model, hemispherical grinding stone, tool posture

#### **1. Introduction**

In this chapter, a theoretical evaluation method of the grain trajectory and its engaging process onto the material in the grinding is introduced. In the first topic, the geometric relationship between the abrasive grain and the material in the cylindrical grinding process, that is, the movement of the abrasive grain and the cutting distance to the material will be described using a mathematical model. In the next topic, we will explain how to theoretically evaluate the resistance generated in the entire working surface of the grindstone, starting from the model of cutting with one abrasive grain for grinding force. In the next topic, to introduce the application of the above topics, a theoretical model of the grain trajectory and engaging depth on the material in the curve generation grinding by the spherical grinding stone will be described. Finally, an evaluation method using a statistical method for basic grinding parameters (Ex. length of successive grains, depth of grain engaging) will be described briefly.
