A mathematical representation for surface grinding is developed. The main feature of the model is that it takes into account the reversing motion of the workpiece, typical to surface grinding. The most general steady state solution is applied to the governing equations to give insight into the dynamic behavior of surface grinding. The theory predicts that steady state surface grinding vibrations can exist. They occur at a frequency which is always higher than the system’s uncoupled resonant frequency and slightly dependent on the workpiece’s direction of motion. Further, the model predicts the existence of wheel lobes. The lobes precess around the wheel according to their size, the wheel wear coefficient, and the chatter amplitude. The model suggests that the lobes can produce a rough ground surface even in the absence of dynamic grinding forces. As Part 2 of the presentation, some test results are offered in support of the mathematical theory of Part 1.

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