Mechanistic force model coefficients: A comparison of linear regression and nonlinear optimization

• This paper examines the dependence of specific force coefficients milling process parameters.
• The average force, linear regression and instantaneous force, nonlinear optimization methods are applied.
• Cutting tests were performed and the specific force coefficients were calculated using the two methods.
• A technique for extending the force measurement bandwidth is presented.
• Milling stability experiments were conducted to validate the calculated specific force coefficients.

This paper describes a comparative study devised to examine the dependence of specific force coefficients, which are used in mechanistic cutting force models, on various milling process parameters such as feed per tooth, spindle speed, milling configuration, and radial immersion. Two methods are described for determining the specific force coefficients: (1) the average force, linear regression method; and (2) the instantaneous force, nonlinear optimization method. A series of test cuts were performed and the specific force coefficients calculated using the two methods were compared. Additionally, a technique for extending the bandwidth over which the cutting forces were measured using a commercially available cutting force dynamometer is presented. Finally, a series of milling stability experiments were conducted to validate the calculated specific force coefficients. It was found that milling process parameters such as feed per tooth, spindle speed, and radial immersion exhibit a nonlinear relationship with the specific force coefficients.