Abstract
A nonlinear dynamic model of spindle-cutter coupling system under cutting force, which takes into account the cutter stiffness and the nonlinearity of bearing clearance, is established. Analysis of the cross-section of a two-flute end mill is conducted to determine cutter stiffness. Then, the calculated cutter stiffness is introduced into the nonlinear dynamic model of coupling system. In the modeling of cutting force, the cutting width takes into account the cutter tip displacement. Moreover, nonlinear dynamic characteristics of spindle-cutter coupling system are studied and the effects of bearing clearance on the response of cutter tip are discussed as well, considering unbalanced force. The numerical results show that the bearing clearance strongly affects the equilibrium position. With different values of bearing clearance and rotation speed, the responses of cutter tip exhibit periodic, quasi-periodic and chaotic characteristics. Dynamic characteristics of spindle-cutter system depends on the bearing clearance and rotation speed. The proper bearing clearance and rotation speed should be chosen to ensure a stable cutting and high cutting rate according to the bifurcation diagram. The response of the cutter tip is a quasi-periodic motion when the cutting force is considered. The time-domain response of cutter tip predicted by nonlinear dynamic analysis can provide the basis for machining error prediction.
Highlights
With the development of manufacturing industry, the machining speed has increased considerably over the past years and the spindle tool system is one of the key components in ensuring machining precision and accuracy
The proper bearing clearance and rotation speed should be chosen to ensure a stable cutting and high cutting rate according to the bifurcation diagram
A nonlinear dynamic model of spindle-cutter coupling system under cutting force, which takes into account the stiffness of cutter and the nonlinearity of bearing clearance, is established in this research
Summary
With the development of manufacturing industry, the machining speed has increased considerably over the past years and the spindle tool system is one of the key components in ensuring machining precision and accuracy. Based on Hertz contact force formulation, Zhang et al [2] established a six-degree-of-freedom model for investigating a machine-tool spindle system supported with ball bearings. The effects of negative bearing clearance on the dynamic response and stability of the machine tool spindle system with unbalanced force were investigated. Gao et al [11] established a dynamic model of spindle-cutter coupling system including the gyroscopic effects and shear deformation. Based on Riccati transformation, the dynamic characteristic of the system was analyzed by using the whole transfer matrix method; the research focused on the vibration mode of the system and did not involve transient response of cutter tip. A nonlinear dynamic model of spindle-tool coupling system based on the second Newton's law is established considering milling cutter stiffness, cutting force, and clearance of bearing. Transient response of cutter tip is predicted and analyzed under cutting force as well
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