Estimation of mass matrix in machine tool’s weak components research by using symbolic regression

Abstract

Modal mass is the important dynamic parameter in weak component research of machine tool structure and also for its control design and load design. Modal mass matrix is defined as the multiplication of mass matrix of a machine tool and its corresponding modal shape matrix. Currently, the big problem is that the mass matrix is hard to get for the calculation of modal mass matrix. Traditional method such as the finite element method cannot acquire the mass matrix well because the overall mass matrix of complex systems cannot be given by experience and the mass matrix in finite element analysis is so large that the computer hard disk will be blasted. In addition to finite element method, the UMM method is used commonly but the noise contained in the mode of the data processing is mixed into the mass matrix, resulting in the inaccurate result and even failure in severe cases. So, there is an urgent need for a method of directly obtaining the mass matrix based on a general equation of multi-degree-of-freedom vibration system from a data source, and then used to calculate the modal mass. In this paper, Genetic programming algorithm (GP) in symbolic regression as an evolution computation method is used to search out the equation expression structure and its coefficients among a group of variances including displacement, velocity, acceleration and external excitation force. And the mass matrix is contained in the equations’ coefficients. In addition, its performance is compared with LRA method and PSO method.