Research On The Adaptive Modeling Theories And Algorithms Of Ball Screw Feed Drive Systems

With the development of modern processing and manufacturing, especially in the high-speed and high-precision machining, CNC machine tools require a higher dynamical performance on feed drive systems. Meanwhile, the emergence of linear drives and virtual-axis hexapod drive takes a challenge to tranditional "Servo motor+Ball screw" feed system. Based on the analysis of the existing feed drive systems, the dissertation indicates that due to the merits of mature processing and designing technology, low cost, and insensitive to the change of force and inertia, the ball screw feed drive system is still an ideal choice if its dynamical performance is improved by choosing control system with appropriate control mode and reasonable parameters, optimizing the mechanical transmission mechanism and obtaining an accurate low-order mathematical model.Expedient mechanical model is the basis condition for designing and analyzing a system, and is the key element to predict the working behaviors of the system. As the ball screw feed drive system is a complicated mechatronics system, the order of theoretical model, which obtained through theoretical modeling, is relatively higher which makes it difficult to analyze and design. Though model reduction can reduce the order of given model, however, its accuracy would be reduced either, which results in difficulties to analyze and design high-precision system. Moreover, modal analysis existes the difficulty of motivation and the reliability of experimental results depends on the technology and experience of the manipulator. It is even more difficult to obtain precise mathematical models of ball screw feed system in different working conditions using theoretical modeling method or modal analysis.In order to obtain a relatively accurate low-order mathematical model of ball screw feed system in different working conditions, a model reference adaptive system based on Lyapunov stability theory is proposed and the modeling methods and theories involved are profoundly reasearched. The main research of the dissertation is as follows:1. Analyzing the latest methods in theoretical modeling and modal analysis of the ball screw feed system, the deficiencies in relevant aspects are founded. The analysis indicates that the order of the mathematical model of ball screw feed drive system, which is obtained by theoretical modeling method, is relatively high, and which makes it difficult to analyze. Moreover, model reduction method is lack of considering practical engineering factors. The experiment modeling method also has some problems, and it exist difficulties in applying incentives, and the reliability of experimental result is not high. So selecting or designing an appropriate modeling method to obtain a lower order mathematical model, which is well-matched the original system in the working conditions, has an important significance for system analysis and controller design.2. Based on the analysis of the components of the mechanical transmission and servo control system of the ball screw feed drive system, the ball screw is modeled by distributing parameters, the transfer functions between ball screw torque and angular velocity, and between ball screw input side stress and velocity are derived, and the force and deformation of ball screw and screw nut is analysed. The mathematical models of the speed detection and controlling unit, position detection and controlling unit as well as AC servo motor are established. All of those provide a theoretical basis to analyze and optimize the mechanical transmission mechanism, configurate servo motor parameters, impove dynamic performance of ball screw feed driving system.3. Expound the theories of model reference adaptive system, established the adaptive controller and adaptive law whose relative order between denominator and numerator is one and two respectively. The design procedures and corresponding control algorithms are also be analyzed.4. The modeling principle as well as the modeling methods of simulation and experiment, which is based on model reference adaptive system, was researched. The main contents are as follows:●Studied the modeling principle based on model reference adaptive theory, taking the controlled object whose relative order is one as an example, and deduced the corresponding mathematical model.●A simulation modeling method based on model reference adaptive system was researched, and a simulation model of the model reference adaptive system was constructed using MATLAB/Simulink. The effectiveness of the simulation modeling method was verified through a case study, in which an equivalent second order model of the high order mathematical model of ball screw feed system was obtained.●The experiment modeling method based on model reference adaptive system was studied, and an experimental platform of the model reference adaptive system based on real-time synchronization motion control platform EtherMAC (Ethernet for Manufacture Automation Control) with standard Ethernet was built. The effectiveness of the modeling method was verified through a case study, in which an equivalent second order model of servo motor system was obtained.5. Based on the experiment platform of model reference adaptive system, the method to obtain the equivalent low-order model of the ball screw feed drive system in the working conditions was studied. The second-order model was conducted when the adjustable system and reference model achieved an exact match through experiment, with the ball screw feed drive system serve as controlled plant, the feedback data of linear encoder as output, and a low-order model, which has excellent dynamic characteristics, as reference model.6. Analyze the response performance indexes and influence factors of ball screw feed system, propose the effective approaches to improve the dynamic performance in both mechanical transmission mechanism and control system. In the mechanical transmission mechanism field, a dynamical model of feed drive system was established with Lagrange equation. The natural frequency of the system was solved with MATLAB software, and the influence of worktable mass, worktable position and stiffness variation of each part on axial first-order natural frequency was analyzed. In the control system field, the influence of the reference model, self-adaptive gain and initial value of adjustable parameters on the performance of feed drive system was studied, and the corresponding solutions were also provided.The dissertation provides a new method to obtain a relatively accurate lower-order mathematical model of ball screw feed system in different working conditions, which gives a theoretical basis for configuring the parameters of control system reasonably and improving the system’s dynamical performance. The achievement has important theoretical and engineering value in predicting the dynamical performance of ball screw feed drive system at the design stage, optimizing the mechanical transmission mechanism, and reducing the production costs.In addition, the model reference adaptive control system as well as the adaptive modeling method and analysis also has important reference value for linear motor drive feed system and other systems.