A Frequency Domain Force Model With Shearing and Ploughing Mechanisms for a Generalized Helical End Mill

Abstract

For a generalized helical end mill, this paper presents a frequency domain force model considering the ploughing as well as the shearing mechanisms. The differential chip load and the corresponding cutting forces are first formulated through differential geometry for a general helical cutting edge. The differential cutting force is assumed to be a linear function of the chip load with a proportional shearing force and a constant ploughing force. The total milling force in the angle domain is subsequently composed through convolution integration and analyzed by Fourier analysis. The frequency domain model has the parameters of a general milling process all integrated in a single framework with their roles clearly defined so that Fourier coefficients of the milling force can be obtained for any analytically definable helical cutter. Applications are illustrated for three common helical cutters: the cylindrical, taper, and ball end mills. Furthermore, as an inverse application, a linear algebraic equation is formulated for the identification of six cutting constants from the average forces of two slot milling tests. Demonstration and verification of the milling force model as well as the identification of cutting constants are carried out through experiments with three types of milling cutters.

Extracting cutting constants via harmonic force components for a general helical end mill

“…Earlier works on the establishment of the dualmechanism cutting constants have been based on the orthogonal cutting test data [7]; this test data is then transformed to the cutting constants for a ball end cutter according to its cutting edge geometry. Based on the analytical milling force model, recent works have shown that these cutting constants can be conveniently identified from the average forces of two cutting tests in [8,9] and estimated online from the forces of a single cutting test for a cylindrical end mill in [10] and for a ball end mill in [11]. This online identification of cutting constants make possible the real-time monitoring of the milling process by making available to the user the detailed information about both the shearing and the ploughing processes.…”

“…Under this coordinate arrangement, the total milling forces for an N-flute general helical end mill in the angle domain have been presented by Wang and Zheng [9] as a Fourier series expression with Fig. 1 The cutting geometry and parameters in a general cutting configuration for a general helical end mill…”

“…2 are the directional matrices for the shearing and ploughing mechanisms respectively and reflect the effects of the radial and axial cutting constants as well as the elevation angle on the shearing and ploughing force vectors, P s (Nk,b) and P p (Nk,b). These elemental force vectors and the directional matrices for the shearing and ploughing mechanisms of a general helical end mill were shown in [9] to be…”

“…1. The abovementioned geometric functions, h¢(b) and w(b), and the integration boundary functions, h 1 (b), h 2 (b), b 1 , and b 2 , for a general helical end mill including the cylindrical, ball end and taper end mill have been addressed in [9]. For a cylindrical end mill with a constant radial depth of cut, h 1 (b) and h 2 (b) in Eqs.…”

“…Although k can be calculated from the three complex Fourier coefficients of any kth harmonic component of the milling force, the magnitudes of the Fourier coefficients have been shown to decrease in proportion to k -2 in [9] and it is more appropriate to use the first harmonic coefficients for the highest signal to noise ratio. In that case, Eq.…”