Mechanics of boring processes—Part I

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Abstract

Mechanics of boring operations are presented in the paper. The distribution of chip thickness along the cutting edge is modeled as a function of tool inclination angle, nose radius, depth of cut and feed rate. The cutting mechanics of the process is modeled using both mechanistic and orthogonal to oblique cutting transformation approaches. The forces are separated into tangential and friction directions. The friction force is further projected into the radial and feed directions. The cutting forces are correlated to chip area using mechanistic cutting force coefficients which are expressed as a function of chip-tool edge contact length, chip area and cutting speed. For tools which have uniform rake face, the cutting coefficients are predicted using shear stress, shear angle and friction coefficient of the material. Both approaches are experimentally verified and the cutting forces in three Cartesian directions are predicted satisfactorily. The mechanics model presented in this paper is used in predicting the cutting forces generated by inserted boring heads with runouts and presented in Part II of the article [1].

Introduction

The enlargement of holes is achieved via boring operations. The hole diameter is either enlarged with a single insert attached to a long boring bar, or with a boring head which has a diameter equal to the diameter of the hole to be enlarged. Long boring bars statically and dynamically deform under the cutting forces during boring operations. Excessive static deflections may violate the dimensional tolerance of the hole, and vibrations may lead to poor surface, short tool life and chipping of the tool. Predictions of the force, torque and power are required in order to identify suitable machine tool and fixture set up for a boring operation. A comprehensive engineering model, which allows prediction of cutting forces, torque, power, dimensional surface finish and vibration free cutting conditions, is required in order to plan boring operations in the production floor.

Although the other machining processes such as milling, turning and drilling have been studied relatively broader and deeper ([2], [3]), there were only a few attempts to model the cutting forces and stability in boring ([4], [5], [6], [7], [8], [9], [10]). However, the mechanics and dynamics of the boring process have not been sufficiently modeled for an effective prediction of boring process performance. There are fundamental issues which make the boring process somewhat difficult to model for a reliable prediction of process performance.

The boring inserts have nose radius, and may have either uniform or irregular rake face. The distributions of chip thickness, therefore the cutting pressure amplitude and direction, vary as a function of tool nose radius, radial depth of cut and inclination angle. Since the boring bar is long and flexible, it is not possible to remove much larger depths of cuts than the nose radius of the tool, unlike the case of turning and face milling operations. This leads to a non-linear, complex relationship between the cutting force distribution, tool geometry, feedrate and depth of cut. Furthermore, the presence of static and dynamic deflections may influence the engagement conditions, leading to variations in chip load distribution and the cutting pressure.

The cutting forces are usually predicted as a function of uncut chip area that changes in a complex manner in boring due to nose radius and geometry of the tool, and cutting conditions. If the tool rake face has an irregular geometry due to chip breaking grooves and chip-tool contact restriction features, the cutting coefficients are identified using mechanistic models. A series of cutting tests are conducted with the specific tool at different speeds, radial depth of cuts and feedrates. The coefficients are evaluated by curve fitting the force expressions to the measured cutting forces and chip geometry. If the rake face of the tool is smooth and uniform, it is possible to model the cutting edge as an assembly of oblique cutting edges [11]. The cutting pressure at each discrete oblique cutting edge element is modeled by applying the orthogonal to oblique transformation method proposed by Armarego [12], [13]. Both approaches have been considered in this article.

The paper is organized as follows; first the complex geometry of the chip is modeled analytically for various cutting conditions and tool geometry. The cutting forces are modeled as friction and tangential cutting forces. The friction force is resolved in the radial and feed directions, and the direction of the friction force, i.e. the effective lead angle, is experimentally evaluated from the ratio of the two. The effective lead angle is predicted from the geometry of the chip and tool, and the prediction is improved by a mechanistic model based on regression analysis applied to the model and measurements. The cutting coefficients are modeled as empirical functions of cutting speed, cutting edge contact length and uncut chip area. The forces are modeled using orthogonal to oblique cutting transformation when the rake face of the tool is smooth. This method requires only the tool geometry, shear stress, shear angle and average friction coefficient of the orthogonal cutting process for a specific work material. The paper contains experimental verification of proposed models which are used to predict the cutting forces in all three directions.

Section snippets

Chip geometry cut by single insert

The fundamental geometry of a boring insert is characterized by a corner radius (R), side cutting edge angle (γι) and end cutting edge angle (γc) (Fig. 1). The rake face of the tool may have either flat face or irregular chip breaking and chip contact reduction grooves which affect the cutting mechanics. The cutting edge does not usually have chamfer or curvature unless the workpiece material is not hardened steel. The chip area, and therefore the cutting force distribution, vary as a function

Modeling of cutting forces in boring

The cutting forces are represented by the tangential force (Ft) and friction force (Ffr). Later, friction force is resolved into the feed (Ff) and radial directions (Fr) (Figs. 1, and 5). Since the chip thickness distribution at each point along the cutting edge contact point is different and dependent on the insert geometry (R, γι, γc) feedrate (c) and radial depth of cut (a), the distribution of the force along the cutting edge-chip contact zone also varies. At any contact point, the

Conclusions

A comprehensive model of single point boring operations has been presented. The chip geometry removed by curved boring inserts is modeled as a function of tool geometry, feedrate and radial depth of cut. Due to irregular distribution of chip load around the insert’s cutting edge, the amplitudes and directions of distributed cutting forces change as a function of tool geometry and cutting conditions. As a result, the cutting forces in boring have a linear dependency with the chip area, but

Acknowledgements

This research is conducted at The University of British Columbia and sponsored by National Science and Engineering Research Council of Canada (NSERC), Milacron, Pratt & Whitney Canada, Caterpillar and Boeing Corporations.

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