The Theoretical And Experimental Investigation Of Milling Stability Predictionfor Variable Pitch Or Helix Cutters

Milling is a very commonly advanced manufacturing process, and widely utilized in key industries such as aerospace, shipping, die and mold, and automotive. What is more, manufacturing process in these industries needs a high productivity and precision. Milling chatter is a form of self-excited, unstable vibration, which may result in low machining quality, poor accuracy and surface finish, as well as accelerated tool wear, aside from damaging the cutting spindle and machined part. The use of variable pitch or helix milling tools is a known means to influence and prevent chatter vibration during milling. Due to that its aims are to maximize the material removal rates without chatter through exploring the vibration mechanism and optimizing the machining conditions and tool geometries, the systematic and deep investigation about related problem is very important for increasing the productivity in machining and has great practical value to strengthen the competitiveness of manufacturing industry in China.Since the regeneration effect of the dynamic chip thickness is the most powerful source of self-excitation, the researcher on the stability of milling processes are mainly focused on this problem. For this reason, in this paper, based on the regeneration theory, theoretical analysis and experimental method are used to investigate the milling stability for variable pitch or helix cutters, and aim to develop or perfect the theory in this realm. The main research content are as follows.(1) Considering the different cases of piecewise continuous cutting regions regarding the helix angle, a straightforward analytical integral force model is develop. Based on this model and an up-dated semi-discretization method, a method is proposed to predict the stability lobes for variable pitch cutter. The proposed approach has been verified with the comparisons with prior works, time domain simulations and cutting tests. In addition, considered that there is a few research about the influence of tool geometries on milling stability, the method is also applied to examine the effect of pitch variation types, number of the teeth and helix angle on the stability trends for variable pitch milling.(2) Based on the interpolation to the state items in milling dynamic system, an efficient method for the stability prediction of variable pitch cutter milling is presented. With the help of discretizing the Spindle rotation period and approximating the delay items by Lagrange interpolation and the displacement items by Hermite interpolation, a discrete map form can be obtained, thus the stability can be determined via Floquet theory. The advantage of this algorithm is that:1) compared with the well-known semi-discretization method, this method has much higher computational efficiency (by78%) without loss of any numerical precision.2) The method is also suitable to solve other dynamic systems contained multi-delays.(3) An alternative semi-analytical method for the prediction of the stability lobes of variable helix cutters is proposed. This method contains two key parts, i.e., the technique of transferring the system with distributed delays to that with multiple delays and an updated semi-discretization method which is suitable for the case of system multiple delays changing with time. Meanwhile, based on this method, stability trends as a function of tooth pitch variation and helix angle variation are investigated. Moreover, an efficient method is presented to stability prediction for variable helix cutters after the author apply the time-averaged cutting force coefficients to system equation. Noted that although this method has a better computational efficiency to obtain the stability lobes than that of above method, it may lead to error in some spindle speed domain because of the neglection of the time variation of the cutting force coefficients.(4) Based on the principles of variable pitch model developed by Altintas, an efficient frequency-domain solution to predict the stability for variable helix cutters is developed. The proposed technique has been verified with the comparison with other methods. The results show that the proposed method has high computational efficiency. Thus, it is suited to calculate optimal geometries of milling tools and beneficial for application.