Physics-based mathematical modeling of wear in ball screw drives

Abstract

Ball screw drives are widely used to provide linear motion in Computer Numerical Control (CNC) machine tools. During prolonged operation, exposure to excessive cutting forces, or accidental collisions, the contact interfaces between the screw, balls, and nut experience accelerated wear and surface damage. The resulting degradation reduces the positioning accuracy of the feed drive, leading to dimensional errors and increased rejection of machined parts. This thesis presents a physics-based mathematical model of wear evolution at the screw–ball–nut contact interfaces and investigates its influence on vibration characteristics for condition monitoring and fault diagnosis. The proposed simulation model correlates vibration signatures with the severity and location of wear and generates synthetic data for training artificial neural networks (ANNs). The screw is modeled using Timoshenko beam elements, while the nut and table assembly are represented as rigid masses. The contact stiffness at the screw–ball–nut interfaces is formulated using the Hertzian contact model incorporating the coupled axial and torsional deformations of the flexible screw. The position-dependent dynamics of the feed drive are captured by accounting for the motion of the nut–table assembly along the screw. Wear-induced degradation at the contact interfaces is incorporated into the Hertzian stiffness formulation. As the screw rotates, recirculating balls generate periodic excitation forces whose frequencies depend on the location and extent of wear. The entry and exit of balls from the loaded contact zone produce transient excitations, while ball-passing frequencies excite the modes of the ball screw drive. The system dynamics are formulated in the frequency domain and the state-space time domain to simulate wear scenarios involving the screw, balls, and nut. The proposed model is validated through experiments. The developed simulation framework generates representative vibration data for training ANN-based condition monitoring systems for ball screw drives. Rather than relying on large experimental datasets, the proposed approach enables ANN models to be trained primarily using physics-based simulated data and calibrated with a limited number of experiments to account for the characteristics of machine, sensor, and sensor location. This reduces the experimental effort while improving the practicality and adaptability of machine health monitoring systems.