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The prediction on surface roughness and surface geometry in peripheral milling operation is a crucial but tedious task. The current researches concerned are almost based on circular tooth trajectory assumption to simplify analysis and modeling, and some models derived from true tooth trajectory are not concise enough or have certain limitation when put into practice. A novel idea on account of the principle of curvature circle approximation to true tooth path curve in cutting contact point nearby is presented, and the relevant mathematical theory is established. Then by means of specific curvature circles, mathematical models and analysis methods of surface roughness are discussed systematically, which cover two situations-cutting with and without runout effect. The validity and superiority of the models are demonstrated by experimental studies and numerical simulations. Finally, based on the suggested models and analytical methods, the effects of runout, feed rate, and cutter geometry on surface roughness and geometry are studied in depth, and several significant mathematical formulas and quantitative conclusions are reached, which would contribute to the theory of milled surface studies.

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