Rapid identification method for nonlinear feed drive model parameters using integral driven friction decoupling and dimensionality reduction of cost function

Abstract

The increasing use of digital twins in machine tool design and control requires feed drive models for simulating the system dynamics. Achieving higher accuracy in digital twin applications involves incorporating nonlinear friction models, such as the Stribeck curve or LuGre friction model, into the feed drive models. However, the process of identifying model parameters, such as the equivalent mass and friction parameters, is time-consuming and challenging due to the complexity of multivariable cost functions. In addition, the quantitative evaluation of identification accuracy is challenging. This paper proposes a rapid and accurate method for identifying feed drive model parameters via integral-driven elimination-based friction decoupling and cost function dimensionality reduction. In the equivalent mass identification, friction is decoupled to eliminate the nonlinearity in the identification process. In the feed drive model, the equivalent mass is the coefficient of acceleration, and the friction is modeled as a function of velocity. The friction terms can be modified into conservative terms with respect to velocity by multiplying those with acceleration. By setting the integral interval using driving direction, the friction terms are eliminated, and the resulting feed drive model becomes a linear equation that is composed of only applied force and equivalent mass-related terms. This friction-decoupled equation allows equivalent mass identification through linear regression. In addition, linear equations are derived for friction parameter identification, with slopes corresponding to the Stribeck and LuGre friction parameters, excluding the Stribeck velocity and micro stiffness coefficients. These friction parameters are then expressed as functions of the Stribeck velocity and micro stiffness coefficient. The resulting equations are incorporated into the cost functions for iterative computations, leading to reduced dimensionality. Simulation and experimental results confirm the capability of the proposed method for rapid and accurate identification.