Estimation of in-process cutting constants in ball-end milling

Abstract

Two methods are presented for the estimation of tangential, radial and axial cutting coefficients for the shearing and ploughing mechanisms from a single set of cutting forces in ball-end milling. These estimation methods are based upon the invertibility of the analytical milling force model, which considers both the shearing and the ploughing mechanisms by incorporating their respective cutting constants in the local force model. The periodic milling forces are established as the convolution integral of the differential local cutting forces and their Fourier coefficients are derived and expressed in a matrix expression as a linear function of the unknown cutting constants in terms of cutting conditions and cutter geometry. This linear expression thus leads to a systematic formulation of the estimation methods allowing the six unknown cutting constants to be determined from the measured milling forces. The first method uses the first harmonic forces as the source signal while the second method extracts the six cutting constants from the average force as well as the first harmonics. Limitations of both estimation methods are discussed. The consistency and accuracy of the estimated cutting constants are confirmed by the experimental results.

On the machining characteristics of H13 tool steel in different hardness states in ball end milling

“…The analytical force model presented by Wang and Zheng [17] has shown that the total milling force is the output of the convolution integration process involving the local cutting force model in Eq. 5 and the geometrical Fig.…”

“…Hence, the complete ball end is submerged and engaged in the cutting process. Six cutting constants for each milling experiment are identified based on the method presented in Wang and Zheng [17]. To illustrate the validity of the identified cutting constants, the simulated milling forces are reconstructed using the six identified cutting constants.…”

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.…”

“…Cutting conditions that render T a1 singular and should be avoided have been discussed in [10] and [11], where it was shown that Eq. 15 is not applicable for a slot milling condition for the cylindrical or ball end cutters with flute numbers larger than 2.…”

“…The various constraints presented above can be alleviated by using two sets of average forces or by using the combination of the average forces and the harmonic forces as presented in [8,9,10,11]. These alternatives will also produce good results as long as the average forces are accurate.…”