Digital twin modeling and data generation method for ball screws based on rigid flexible hybrid multibody dynamics

The ball screw is widely used for precision linear motion in electric servo mechanisms, and its vibration directly affects control accuracy and reliability. To narrow the gap between simulation and measurement, this study proposes a rigid-flexible-hybrid-multibody-dynamics-based digital twin modeling and data generation method that considers nonlinear rolling-element–raceway contact and friction. The screw, nut, and balls are modeled as rigid bodies, whereas the nut outer sleeve is modeled as a flexible body described by modal coordinates. Within a Lagrangian framework, rigid-flexible coupled equations are established; the equivalent contact stiffness is introduced through the contact potential, while friction is represented as a nonconservative generalized force. Based on modal superposition, a theoretical twin model for sleeve acceleration is constructed. The theoretical twin is validated through frequency-domain least-squares input inversion and time-domain reconstruction, while a RecurDyn rigid-flexible model with nonlinear contact and friction provides a complementary software-simulation validation route. Under identical sampling, sensor layout, and preprocessing conditions, both twin and simulated data agree well with measurements: the time-domain RMS relative errors remain below 10%, and the frequency-domain correlation coefficients are above 0.87. The theoretical twin shows closer agreement on the energy scale, whereas the software simulation better preserves some narrowband spectral details, supporting dynamic analysis, healthy-state data generation, and subsequent fault-oriented DT extensions.