Abstract Modelling of tooth trajectory and process geometry in peripheral milling of curved

The paper presents modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces. The paper differs from previous work in this area, in two respects. Firstly it deals with milling of variable curvature geometries unlike zero a

Modelling of tooth trajectory and process geometry

in peripheral milling of curved surfaces

V.S. Rao, P.V.M. Rao*

Mechanical Engineering Department, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India

Received 20 July 2004; accepted 13 October 2004

Abstract

The paper presents modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces. The paper differs from previous work in this area, in two respects. Firstly it deals with milling of variable curvature geometries unlike zero and constant curvature geometries dealt in the past. Secondly true tooth trajectories are considered for modelling process geometry in milling of curved surfaces instead of simpler circular tooth trajectories. Mathematical expressions for, feed per tooth along cutter contact path, entry and exits angles of tooth, undeformed chip thickness and surface error are derived and effect of workpiece curvature on these variables is studied. As cutting forces depend on these process variables, physical experiments were also performed to study the effect of workpiece curvature on cutting forces. Process simulation experiments carried out show the need for modelling true tooth trajectories instead of circular tooth trajectories particularly for curved geometries. Results also show that using simpler constant curvature models to variable curvature geometries for the purpose of estimation of process geometry variables could be erroneous.

Keywords: Peripheral milling; Milling process geometry; Curved surfaces; True tooth trajectory

1. Introduction

Assuming the tool and workpiece to be rigid, the shape realized in any milling process depends on three important factors namely, tool geometry, workpiece geometry and relative motion between tool and the workpiece. In a process like peripheral milling, the relative motion between tool and workpiece has two components. One component of motion consists of rotation of tool about its own axis and the second is a feed motion of tool relative to workpiece. A combination of these two motions together with the geometry of tool and its interaction with the workpiece geometry defines the final shape of workpiece. Accurate modelling of tool and workpiece geometries and the relative motion between the two is important for estimation of many machining process related variables such as feed per tooth, entry and exit angles of tooth, undeformed chip thickness, surface error etc.

Surfaces generated in a peripheral milling process can be classified into three major classes: zero curvature or straight surfaces, constant curvature or cylindrical surfaces and variable curvature or free-form surfaces. Estimation of process geometry variables such feed per tooth along cutter contact path, entry and exit angle of tooth and undeformed chip thickness in case of peripheral milling of straight surfaces is trivial, and this has been the subject of research for many years now [1-25]. Some work has also been reported on estimation of these variables in case of peripheral milling of cylindrical surfaces [26]. Estimation of process geometry in case of variable curvature surfaces is not straight forward as these variables are not constant and continuously vary with the workpiece curvature. This variation also leads to change in cutting forces and surface error generated.

Where as many efforts have been made in the past to develop analytical models to estimate process geometry for zero and constant curvature surfaces, the same for variable curvature surfaces has not received any attention. One has an option to extend constant curvature models to variable

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