Hongqi Li Graduate Research Assistant Yung C. Shin Professor School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 Wheel Regenerative Chatter of Surface Grinding In this paper we present a comprehensive dynamic model that simulates surface grinding processes and predict their regenerative chatter characteristics. The model considers special aspects in surface grinding processes, such as interrupted grinding on a series of surfaces and step-like wheel wear along the axial direction due to crossfeed. A new theory for the wheel regenerative chatter mechanism, which describes the regenerative force as a function of not only the instantaneous chip thickness but also the distributed uneven grit wear/dullness, is introduced and applied in the model. Using the model, explanations are provided for those unrevealed wheel regenerative chatter phenomena observed from the experimental results in literature. The model is validated by comparing the simulated chatter frequencies and thresholds with the experimental results. DOI: 10.1115/1.2137752 1 Introduction Chatter is a critical problem for grinding processes because grinding processes are inherently unstable while accuracy and sur- face finish are the two major purposes of grinding processes. Many studies have been conducted on grinding chatter problems, as reviewed by Inasaki et al. 1. Especially there was a blossom of studies in this area during the period of 1969–1970 2. Those studies were mostly for cylindrical grinding processes and rarely for surface grinding processes. Among those studies on surface grinding, Inasaki and Yonetsu 3 experimentally investigated the characteristics of the undulations generated on the wheel due to chatter and the influence of the grinding conditions on the chatter generation process. Later they carried out more experiments to explore the effect of attritious wear on the chatter generation pro- cess 4. Thompson proposed a model to consider the reverse motion 5 and performed some surface grinding tests under chat- ter conditions with different fixture setups for the workpiece 6. There are two types of chatter for cylindrical grinding: work- piece regenerative chatter and wheel regenerative chatter 7–13. Workpiece regenerative chatter occurs at a relative high work- piece speed and grows very fast. This type of chatter can be as- cribed to the force regeneration from the undulations of succes- sively ground surfaces of the workpiece. For surface grinding, however, it is accepted by most researchers that workpiece regen- erative chatter is unlikely to occur because the phase between the successively ground surfaces, which is critical for chatter genera- tion, cannot be maintained due to the interruption caused by the overtravel of the wheel and crossfeed. Thus, the chatter of surface grinding is mainly the other type, wheel regenerative chatter. Ac- cording to the experiments of Inasaki and Yonetsu 3,4 and Thompson 6, the chatter of surface grinding behaves as the wheel regenerative chatter in the following aspects: 1 Chatter occurs even at a very low workpiece speed, and the amplitude of the vibration increases very slowly dur- ing grinding after dressing. 2 At the early stage of chatter, it is difficult to distinguish chatter from forced vibration, or see chatter marks on the workpiece surface. 3 As chatter develops, the waves generated on the wheel surface can be observed or measured, and chatter marks can be seen in some cases. The current theory of wheel regenerative chatter 1 explains that at a low workpiece speed, on one hand, the amplitude of the undulations generated on the workpiece is negligible because of the wave filtering effect; on the other hand, the undulations gen- erated on the wheel surface vary the depth of cut as well as the grinding force. Hence, the corresponding delayed response may magnify the undulations on the wheel and consequently cause instability. Under the wheel regenerative chatter condition, however, undu- lations are generated on the surfaces of both the workpiece and grinding wheel, thus the two-degree-of-freedom geometrical inter- actions caused by both the wheel and workpiece surface undula- tions along the contact length must be modeled accurately for chatter prediction. Since the current theory of wheel regenerative chatter neglects the effects of workpiece undulations and uses only the variation of depth of cut to represent the geometrical interactions in surface grinding, it is too simplistic to describe the real wheel regenerative chatter generation process, and there is no strong proof that it is valid or dominant. In addition, the existing models based on the current wheel regenerative chatter theory cannot explain many experimental observations reported in litera- ture: 1 There is no difference in chatter occurrence whether a single workpiece is continuously or interrupted ground, or a series of workpieces are ground 1. 2 All dominant frequencies under wheel regenerative chatter conditions are approximately the multiplicities of the wheel rotational speed. Figure 1 shows chatter occurrence with three conditions obtained by Thompson 6. 3 Phase delays of chatter vibration and wheel undulations are very small. This observation is actually a support to the previous one. For the test case shown in Fig. 1a with four undulations, a one-revolution delay was re- ported after 4.8 min at 3000 rpm by Thompson 6. Af- ter conversion, the actual phase delay is 0.025°, and the chatter frequency is 0.0017% smaller than four times the wheel speed of 200 Hz. Another experimental result for cylindrical grinding by Snoeys and Brown 7 also shows a small phase delay around 0.15°. 4 As shown in Fig. 2 from Weck and Alldieck 13, more than one dominant frequency can appear under chatter conditions, each of which is approximately a multiplic- ity of the wheel rotational speed. 5 The high-order harmonics of the chatter frequencies can be observed as chatter grows, as shown in Fig. 3 by Hashimoto et al. 11. Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received June 1, 2005; final manuscript received September 8, 2005. Review conducted by A. J. Shih. Journal of Manufacturing Science and Engineering MAY 2006, Vol. 128 / 393 Copyright © 2006 by ASME