A new precision hard cutting forces model is developed based on unit cutting model, the transformation between unit and free cutting is promoted. As the characteristics of precision cutting are concerned, the cutting area and the cutting forces generated by the end cutting edge are calculated based on the actual cutting condition in the new cutting force model, the shear angle is predicted by energy approach combined with chip-flow angle and constitutive equation. The predicted results agree well with the experimental data, and the error is low that its high precision could meet the demands of precision hard cutting force prediction. Introduction The cutting force is one of the key physical factors in the cutting process. It plays a critical role to predict the cutting forces under various cutting conditions and work material combination for simulation of surface error and physical properties in cutting process [1-3]. Modeling and prediction of cutting force are a hot research object, and the cutting parameters and manufacturing process of many complex parts are determined proper by the prediction of cutting forces. The precision hard turning technology is a machining approach to take the cutting of quenched-hardening steel as the semi-finishing or finishing process. Hard cutting forces are a key factor to calculate the workpiece deformed value, formation of residual stress, and often used to design the suitable fixture. In this paper, the relationship between unit and free cutting is analyzed based on a unit-cutting model. Combined with chip-flow angle prediction model, a new precision turning force model is developed and proved by experiments. Transfer Unit Cutting Force to Non-free Oblique Cutting force The unit cutting is defined as a cutting tool with a straight-line cutting edge, flat rake and flank face in oblique machining process. Details about the model of unit cutting should be refer to [3-5]. Three factors should be considered in the transfer procedure from unit cutting force to non-free cutting, that is the straight line edge transfer to main cutting edge and side-cutting edge simultaneously, including the effects of chip flow and shear area, the influence of the edge radius, the effect of major cutting edge angle r κ and minor cutting edge angle ' r κ . Only the cutting force on the main cutting edge, i.e. the free cutting of single point tool, is considered, the transformation of unit cutting to non-free cutting can be achieved just rotating the coordinate system ( ) 0 0 0 , , x y z around the cutting velocity V or the direction of P F with angle r κ as expressed in the following: cos sin sin cos c P r Q r R r f Q r R r F F F F F F F F κ κ κ κ = = − = + (1) Key Engineering Materials Online: 2006-07-15 ISSN: 1662-9795, Vols. 315-316, pp 380-384 doi:10.4028/www.scientific.net/KEM.315-316.380 © 2006 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific.net. (Semanticscholar.org-13/03/20,10:39:09) where p F , Q F and R F are the tangential cutting force, radial force and axial force respectively. The resultant cutting force ' R generated by the end cutting edge can be expressed: ( ) ' 0 ' cos γ β φ τ − + = e m sA R (2) where shear stress s τ , frictional angle β , effective shear angle e φ can be derived from traditional theory, ' 0 γ is for the minor rake angle of the end cutting edge: ( ) ( ) + + + = ' ' ' 0 cos cos tan sin tan r r s n r r s arctg κ κ λ γ κ κ λ γ (3) The cutting forces generated by the end cutting edge in the principle section is shown in Fig.1. According to the principle of cutting t force by the end cutting edge, the force components are shown as following: ( ) ( ) ' 0 ' ' 0 ' sin cos γ β γ β − = − = R F R F