Nonlinear dynamic modeling and analysis of spindle-tool assemblies in machining centers

Thesis Type: Postgraduate

Institution Of The Thesis: Middle East Technical University, Faculty of Engineering, Department of Mechanical Engineering, Turkey

Approval Date: 2009

Thesis Language: English

Student: Zekai Murat Kılıç



Chatter is unwanted since it causes deteriorating effects on the milling process. Stability lobe diagrams are developed in order to determine the stable cutting conditions at which chatter-free machining can be made. The need of cutting away more chips to make milling operations quicker has brought the concept of high-speed milling. This increased the importance of estimating stability lobe diagrams of the milling process more accurately. The state-of-art chatter and spindle-toolholder-tool models predict the stability lobe diagram for milling process quite effectively. However, sometimes chatter might occur even at cutting conditions selected using theoretically obtained stability lobe diagrams. One of the reasons for that may be nonlinearities in the system. This being the motivation, in this work, nonlinearities at the bearings of spindle-toolholder-tool system are investigated. In this thesis, cubic nonlinearity is assumed to represent stiffness of a bearing in a spindle-toolholder-tool system. Effects of nonlinearity on stability lobe diagram of a milling process are studied by using the mathematical model developed for such a system. Frequency response function of spindle-toolholder-tool system without bearings is obtained using Timoshenko beam model. Then, bearings are modeled by using describing function theory and coupled to the dynamics of spindle-toolholder-tool modeled. Solution of the equations of motion of the system in frequency domain is obtained via Newton's method with ALC. It is an effective frequency domain method in which turning points on frequency response function are traced. This is important for the system studied, as bearing nonlinearity may introduce turn backs in the response of the system. Case studies are carried out to study the effects of bearing nonlinearity on stability lobe diagram. The effects of the following factors are studied: Magnitude of cutting force, degree of nonlinearity and number of teeth on cutter. Displacement amplitude dependent stiffness of bearings affects the dynamic response due to rigid body modes of the system. It is observed that an increase in cutting force magnitude or in coefficient of bearing nonlinearity results in increase of natural frequencies, thus showing hardening behavior. Shifting of frequencies in the response curve shifts stability lobes related to the affected modes, to the right. For increased number of flutes on cutter, effect of nonlinearity at bearings on stability of the milling process becomes lower. Experimental studies to determine the changes in dynamics of a system during cutting are also carried out in this thesis. Inverse chatter analysis is conducted to obtain modal parameters of a single-degree-of-freedom system using the experiment data. Decrease in natural frequency is observed at high cutting speeds for the particular spindle used. This shift may be due to speed-dependent bearing dynamics and real time adjustment of preload on bearings.