Research On Gain-Scheduling Control Of Ball Screw Feed Drives Based On Time-Varying Dynamics

As one of the key components of CNC equipments,ball screw feed drives(BSFDs)are normally used to drive and position a spindle or a table,which directly affects the precision retaining ability and maching quality of CNC equipments.The strong rigide-flexible coupling and time-varying dynamics will emerge in the feeding process of BSFDs.The structural vibration can be induced by the nonlinear disturbance.The tracking and positioning performance of BSFDs in the whole feed range can then be deteriorated.On one hand,the PID control strategy could do nothing about the adverse effect caused by the time-varying dynamics.On the other hand,the gain-scheduling(GS)control strategy is good at achiving the desired performance of time-varying systems.Furthermore,the GS control strategy has been studied and applied in flight control systems.Hence,the dynamic modeling and analysis and the identification of the time-varying and rigide-flexible coupling transfer function(TF)for a BSFD are researched.Besides,considering the time-varying dynamics,the application of the GS control strategy to the BSFD is studied to realize the consistent tracking and positioning accuracy of the BSFD in the whole feed range.In order to predict the dynamic behavior of the ball-screw driving carriage,a rigid dynamic modeling method for BSFDs is proposed.Firstly,the BSFD is simplified as a mass-spring system.The contact stiffness of rolling interfaces between the rail and the slider is accurately calculated based on the Hertzian theory.A rigid dynamical model of the BSFD is established using the Lagrange method.The modal testing is conducted to verify the presented model.According to the dynamic model,the parameter-dependent dynamics of the feeding carriage is investigated.The results can contribute to the dynamic optimization design and the TF modeling of BSFDs.In order to possess insight into the rigid-flexible coupling vibration of the BSFD,a comprehensive modeling approach is proposed.The ball screw shaft is represented as a Timoshenko beam with distributed elasticity and inertia.The motor rotor,the spindle and the feeding carriage are deemed as lumped masses.The coupling,the bearing,the screw-nut interface and the linear guide are modeled as concentrated springs and dampers.Taking into account the stiffness coupling between the Timoshenko beam and the mass-spring system,a rigid-flexible coupling dynamic model for the BSFD is established using the Ritz series approach and the Lagrange method.The analytical solution is verified according to the modal testing and the comparative study with other scholars' research.Based on the proposed model,the time-varying dynamic behavior of the BSFD with changing carriage locations is simulated and discussed.The result is helpful to the TF identification of BSFDs.On the basis of the above research,the rigid-flexible coupling TF model of the BSFD is established considering the time-varying and rigid-flexible coupling vibration in the axial and torsional directions.The rigid TF is firstly identified using the least square method.The Stribeck friction model is then identified according to the relationship between the friction torque and the feeding velocity.The flexible TFs of the BSFD for various carriage locations are also identified using the orthogonal polynomial method.Finally,by integrating the identified results,the time-varying and rigid-flexible coupling TF of the BSFD with changing carriage locations is obtained.The synthesized TF provides a fundamental model for the controller design.According to the basic theory of linear parameter varying(LPV)system,the time-varying and rigid-flexible coupling TF of the BSFD is converted to a LPV model.An output-feedback GS controller is designed based on the LPV model.The guideline to tune controller parameters is also provided.For comparative study,a PID controller is synthesized based on the rigid TF of the BSFD.The PID controller is combined with a friction feedforward compensater and a notch filter.The applicability of the notch filter is also discussed.The whole feed range of the BSFD is divided into five sections,in which the tracking experiment is conducted for the two control strategies.The high tracking and positioning performance of the GS controller is verified in the whole feed range of the BSFD.The research not only has a certain scientific value to improve the dynamic modeling and servo control theory for BSFDs,but also contributes to increasing the tracking and positioning accuracy of BSFDs.Besides,it is useful to improve the precision retaining ability and machining quality of CNC equipments.Lastly,it is very important for promoting the development of our CNC equipments and bridging the gap between our and advanced CNC equipments.