Dynamic milling stability prediction of thin-walled components based on VPC and VSS combined method
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(2020) 42:336
TECHNICAL PAPER
Dynamic milling stability prediction of thin‑walled components based on VPC and VSS combined method Li Zhang1 · Bo Hao1 · Dongping Xu1 · Mingqiang Dong1 Received: 21 November 2019 / Accepted: 13 May 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract In the milling process, the coupling deflection and the dynamic characteristics of the cutter–workpiece system are time variant as the material removal and the change of cutter position. The milling stability of the system is dynamic because of the time-varying stiffness. In this study, the model of time-varying system has been developed. Variable pitch cutter (VPC) and variable spindle speed (VSS) are, respectively, typical method of passive control and active control to suppress the chatter, and two methods are compatible. The arithmetic of VPC and VSS combined method has been developed and verified effectively. Dynamic milling stability prediction of stiffness time-varying system for thin-walled components based on VPC and VSS combined method has been developed. And then, the dynamic milling stability of stiffness time-varying system for thin-walled components has been predicted. Keywords Thin-walled components · Dynamic milling stability · Stiffness time-varying system · VPC & VSS · SLD List of symbols ae Nominal radial depth of cutting (mm) B0 Initial thickness of workpiece (mm) dt Deflection of cutter (mm) dw Deflection of workpiece (mm) dc Coupling deflection of cutter–workpiece system (mm) N Sum of nodes on contact location of cutter and workpiece Gy Relativity frequency response function of cutter– workpiece system in y-direction (mm/N) Gy(t) Frequency response function of cutter in y-direction (mm/N) Gy(w) Frequency response function of workpiece in y-direction (mm/N) δy(t) Displacement of cutter in y-direction (mm) δy(w) Displacement of workpiece in y-direction (mm) Nc Number of teeth Δψ Pitch increment (°) ψ0 Basic pitch variation (°) Technical Editor: Adriano Fagali de Souza. * Li Zhang [email protected] 1
School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
η Initial phase angle (°) Ω0 Nominal spindle speed value (r/min) T Time period (s) ap Axial depth of cutting (mm) hj(t) Chip thickness (mm) kt Cutting force coefficient in tangential direction (N/ m 2) kr Cutting force coefficient in radial direction (N/m2) q Cutting force exponent ϕst Start angle (°) ϕex Exit angle (°) fz Mean feed per tooth (mm/tooth) m Modal mass (kg) c Damping coefficient (N s/m) k Modal stiffness (N/mm) ξ Damping ratio ωn Natural frequency (Hz)
1 Introduction Vibration in milling process is an important factor inducing the machining quality and milling efficiency of thin-walled components. Vibration control is one of the key technologies to ensure high efficiency and high-precision machining. Some representative studies have been presented such as Bravo et al. [1] and Herranz et al. [2] considered the dynamic
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