International Journal of Machine Tools & Manufacture 42 (2002) 791–800 Prediction of cutting force distribution and its inﬂuence on dimensional accuracy in peripheral milling X.-W. Liu, K. Cheng * , D. Webb, X.-C. Luo School of Engineering, Leeds Metropolitan University, City Campus, Leeds LS1 3HE, UK Received 23 October 2001; accepted 24 January 2002 Abstract Cutting force has a signiﬁcant inﬂuence on the dimensional accuracy due to tool and workpiece deﬂection in peripheral milling. In this paper, the authors present an improved theoretical dynamic cutting force model for peripheral milling, which includes the size effect of undeformed chip thickness, the inﬂuence of the effective rake angle and the chip ﬂow angle. The cutting force coefﬁcients in the model were calibrated with the cutting forces measured by Yucesan [18] in tests on a titanium alloy, and the model was proved to be more accurate than the previous models. Based on the model, a few case studies are presented to investigate the cutting force distribution in cutting tests of the titanium alloy. The simulation results indicate that the cutting force distribution in the cut-in process has a signiﬁcant inﬂuence on the dimensional accuracy of the ﬁnished part. Suggestions about how to select the cutter and the cutting parameters were given to get an ideal cutting force distribution, so as to reduce the machining error, meanwhile keeping a high productivity.  2002 Elsevier Science Ltd. All rights reserved. Keywords: Cutting force; Distribution; Dimensional accuracy; Peripheral milling 1. Introduction Peripheral milling is widely used in a variety of indus- tries such as automotive, aerospace, textile machinery and other manufacturing industries, where 2D contour parts, i.e., engine components, cams, etc., are milled using helical end mills. In recent years, due to the need for improving the quality of parts, there has been a push toward decreasing the machining errors in peripheral milling. These errors derive from the machine tools, the cutters, the NC programming and the machining process. The errors of the machining process generated in periph- eral milling originate from a number of sources, such as cutting force, tool wear, friction, tool run-out, and chatter vibration. Of these, the machining error due to cutting force is one of the major problems for precision machin- ing. The machining error due to cutting force originates from tool deﬂection and workpiece deﬂection. In order to investigate the inﬂuence of cutting force on machining * Corresponding author. E-mail address: k.cheng@lmu.ac.uk (K. Cheng). 0890-6955/02/$ - see front matter  2002 Elsevier Science Ltd. All rights reserved. PII:S0890-6955(02)00016-0 error, not only accurate cutting force but also the dynamic cutting force distribution should be evaluated. For the cutting force prediction, several models based on theoretical assumptions and experimental obser- vations have been developed and reviewed by Smith and Tlusty [13]. A few enhanced cutting force models have been developed in the last decade [1,4–7,9–11,18]. The inﬂuence of cutter static deﬂection due to cutting force on the machining error is investigated by Kline [8], and Sutherland and DeVor [14]. The machining error was predicted using cantilever beam theory for the cutter deﬂection and ﬁnite element method for the workpiece deﬂection. Cantilever beam theory was also used by Babin [3] in predicting the topography of wall surfaces produced by end mills. In these references, however, the dynamics in the tool/workpiece system was neglected. The inﬂuence of the tool/workpiece system dynamics on surface generation was investigated by Montgomery [10]. The kinematics of the cutter and workpiece vibrations was modelled. Zhang [19,20] introduced the effect of random vibrations on the surface roughness in turning. These vibrations were shown to occur due to the random variation in the micro-hardness of the workpiece material. Elbestawi [6] and Ismail [7] presented a mech-