高精数控机床永磁直线进给系统机电耦合法向振动研究
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摘要
高精度数控机床的精度已经发展到纳米级阶段,永磁直线伺服进给系统是高精数控机床的核心部件,精密机床直线进给系统振动问题已是不容忽视和不可回避的问题,必须对永磁直线伺服进给系统进行运动学、动力学、机械结构、电气性能等方面综合分析和整体设计,才能全面提高直线伺服进给系统的各项性能指标。本文针对永磁直线伺服进给系统因法向力引起的振动问题,围绕电磁振源、系统动力学、减振优化设计等方面进行了研究。
针对波动的法向力引起直线电动机振动的问题,利用解析法和有限元法计算总结了不同极、槽数配合的永磁直线伺服电机法向力分布的时空变化规律,进一步分析了法向力分布对动子振动的影响规律。分析结果表明,极、槽数的公约数为1或2的近极槽直线电机,在法向力的作用下易引起法向共振。
为分析直线进给系统振动特性,建立了磁—结构耦合系统的数学模型,通过对磁—结构耦合场方程的间接耦合求解,获得机电系统耦合动力学微分方程的解。将直线电机动子与工作台作为一体化结构,分析了工作台系统的动力学特性。在法向力作用下,直线电机动子与工作台作为一体化结构的变形比电机动子单一结构的变形增大,固有频率降低。直线进给系统模态分析表明工作台为系统振动的薄弱环节。
针对高精数控机床振动特性易受机械部件弹性变形的影响,从机电耦合角度出发,将永磁直线进给工作台等效为多自由度的“弹簧—阻尼”系统,用有限元法进行柔性化,应用拉格朗日—麦克斯韦方程建立进给系统多柔性体的机电耦合模型。结合有限元分析软件ANSYS、动力学仿真软件ADAMS建立直线进给系统多柔性体的机电耦合仿真模型。对比分析表明,柔性体、电气控制参数以及谐波扰动对系统振动有显著影响。实验测量的工作台法向加速度与柔性化机电耦合模型的仿真结果相符。
为提高永磁同步直线电动机直线进给系统的抗振能力,采用磁—结构耦合拓扑优化方法对直线进给系统的结构进行优化设计,用伴随矩阵法对磁—结构耦合方程的灵敏度进行分析。以柔度最小和低阶固有频率最大为优化目标,在法向力的作用下分别对直线电机动子、工作台、底座进行结构拓扑优化。分析重构后系统的振动特性表明,在不影响磁场分布的前提下,磁—结构耦合拓扑优化有效地提高了系统动、静态刚度。
对永磁直线伺服电机样机的法向力及振动进行测试。通过设计的测量装置,测量样机在一对极距下的法向力。测量了永磁直线伺服电机进给系统工作台在不同速度、不同载荷条件下的加速度,并分析振动频率。实验验证了建立的直线进给系统多柔体机电耦合模型的正确型。
The accuracy of high-precision CNC machine tools has been developed to the stage of nanometer, and the permanent magnet linear feed system is one of the core components of the direct driven high-precision and high-speed CNC machine tools. The vibration of feed system cannot be ignored and avoided. To comprehensively improve the performance of linear feed system, kinematics, dynamics, mechanics, electric and other aspects must be integratedly designed in permanent magnet linear feed system. In this dissertation, normal vibration of permanent magnet linear feed system due to the normal force acting on the motors was studied. Thereinto, the electromagnetic vibration source, system dynamics and damping optimization design were focused on.
The root cause of vibration of permanent magnet linear servo motor is the normal magnetic forces ripples. The space-time distribution of normal force in PMLSM with different poles/slots number has been calculated with analytical method as well as finite element method (FEM), and the influence regularity of the normal-force distribution on the mover vibration was further analyzed. The results indicate that when the poles and slots have a common divisor equal to one or two, the resonance is liable to produce.
For analyzing the vibration characteristics of linear feed system, the mathematical model for magnetic-structure coupling system was established. Through the indirect coupling calculation on the equation for magnetic-structure coupling field, the coupling-dynamics differential equation for the electromechanical system can be solved. The dynamic characters of worktable system were analyzed supposing the mover of the linear motor and worktable be an integral structure. Under the action of the normal force, the integral structure of worktable system has larger deformation and lower natural frequency than one single motor mover. The modal analysis of linear feed system showed that the workbench is the weak component of the system.
Considering the fact that the vibration characteristics of high-precision CNC machine tools is susceptible to the mechanical components of elastic deformation, linear feed table was taken as equivalence to multi-degree-of-freedom spring-damper system based on global coupling view of the electromechanical system. Then the table was flexible by FEM firstly, and dynamics differential equation for the electromechanical coupling system was further deduced and estabished with the Lagrangian-Maxwell equation. Combined with FEM software of ANSYS and dynamic simulation software of ADAMS, the simulation model for the linear feed system was established. The comparative analysis indicates that the flexibility of structure, electrical control parameters and disturbance frequency all have obvious influence on the vibrations of coupling system. The acceleration from the experimental measurements agrees well with the simulation results.
To improve the stiffness of linear feed system, the structure were designed and reconstructed by magnetic-structure coupling topology optimization method, and the adjoint method was used to calculate the sensitivity of structure response. Aiming to minimize flexibility and maximize the natural frequency, the structural topology optimization on mover, worktable and bed were conducted. Compared with the original structure, the optimized results showed that the static and dynamic stiffness of system were effectively improved under the premise of not influence the magnetic field distribution. Magnetic-structure coupling topology optimization provides an effective method for innovative design of coupled system.
The normal force and the vibration for the prototype of permanent magnet linear servo motor have been tested. And the normal force of the prototype between two polars was measured through designing special testing apparatus. The accelerations of the worktable in the linear feed system with different speeds, loads, and profiles were measured, and then the modal frequencies were analyzed. The experiment results have proved that the coupling model is reasonable and correct.
针对波动的法向力引起直线电动机振动的问题,利用解析法和有限元法计算总结了不同极、槽数配合的永磁直线伺服电机法向力分布的时空变化规律,进一步分析了法向力分布对动子振动的影响规律。分析结果表明,极、槽数的公约数为1或2的近极槽直线电机,在法向力的作用下易引起法向共振。
为分析直线进给系统振动特性,建立了磁—结构耦合系统的数学模型,通过对磁—结构耦合场方程的间接耦合求解,获得机电系统耦合动力学微分方程的解。将直线电机动子与工作台作为一体化结构,分析了工作台系统的动力学特性。在法向力作用下,直线电机动子与工作台作为一体化结构的变形比电机动子单一结构的变形增大,固有频率降低。直线进给系统模态分析表明工作台为系统振动的薄弱环节。
针对高精数控机床振动特性易受机械部件弹性变形的影响,从机电耦合角度出发,将永磁直线进给工作台等效为多自由度的“弹簧—阻尼”系统,用有限元法进行柔性化,应用拉格朗日—麦克斯韦方程建立进给系统多柔性体的机电耦合模型。结合有限元分析软件ANSYS、动力学仿真软件ADAMS建立直线进给系统多柔性体的机电耦合仿真模型。对比分析表明,柔性体、电气控制参数以及谐波扰动对系统振动有显著影响。实验测量的工作台法向加速度与柔性化机电耦合模型的仿真结果相符。
为提高永磁同步直线电动机直线进给系统的抗振能力,采用磁—结构耦合拓扑优化方法对直线进给系统的结构进行优化设计,用伴随矩阵法对磁—结构耦合方程的灵敏度进行分析。以柔度最小和低阶固有频率最大为优化目标,在法向力的作用下分别对直线电机动子、工作台、底座进行结构拓扑优化。分析重构后系统的振动特性表明,在不影响磁场分布的前提下,磁—结构耦合拓扑优化有效地提高了系统动、静态刚度。
对永磁直线伺服电机样机的法向力及振动进行测试。通过设计的测量装置,测量样机在一对极距下的法向力。测量了永磁直线伺服电机进给系统工作台在不同速度、不同载荷条件下的加速度,并分析振动频率。实验验证了建立的直线进给系统多柔体机电耦合模型的正确型。
The accuracy of high-precision CNC machine tools has been developed to the stage of nanometer, and the permanent magnet linear feed system is one of the core components of the direct driven high-precision and high-speed CNC machine tools. The vibration of feed system cannot be ignored and avoided. To comprehensively improve the performance of linear feed system, kinematics, dynamics, mechanics, electric and other aspects must be integratedly designed in permanent magnet linear feed system. In this dissertation, normal vibration of permanent magnet linear feed system due to the normal force acting on the motors was studied. Thereinto, the electromagnetic vibration source, system dynamics and damping optimization design were focused on.
The root cause of vibration of permanent magnet linear servo motor is the normal magnetic forces ripples. The space-time distribution of normal force in PMLSM with different poles/slots number has been calculated with analytical method as well as finite element method (FEM), and the influence regularity of the normal-force distribution on the mover vibration was further analyzed. The results indicate that when the poles and slots have a common divisor equal to one or two, the resonance is liable to produce.
For analyzing the vibration characteristics of linear feed system, the mathematical model for magnetic-structure coupling system was established. Through the indirect coupling calculation on the equation for magnetic-structure coupling field, the coupling-dynamics differential equation for the electromechanical system can be solved. The dynamic characters of worktable system were analyzed supposing the mover of the linear motor and worktable be an integral structure. Under the action of the normal force, the integral structure of worktable system has larger deformation and lower natural frequency than one single motor mover. The modal analysis of linear feed system showed that the workbench is the weak component of the system.
Considering the fact that the vibration characteristics of high-precision CNC machine tools is susceptible to the mechanical components of elastic deformation, linear feed table was taken as equivalence to multi-degree-of-freedom spring-damper system based on global coupling view of the electromechanical system. Then the table was flexible by FEM firstly, and dynamics differential equation for the electromechanical coupling system was further deduced and estabished with the Lagrangian-Maxwell equation. Combined with FEM software of ANSYS and dynamic simulation software of ADAMS, the simulation model for the linear feed system was established. The comparative analysis indicates that the flexibility of structure, electrical control parameters and disturbance frequency all have obvious influence on the vibrations of coupling system. The acceleration from the experimental measurements agrees well with the simulation results.
To improve the stiffness of linear feed system, the structure were designed and reconstructed by magnetic-structure coupling topology optimization method, and the adjoint method was used to calculate the sensitivity of structure response. Aiming to minimize flexibility and maximize the natural frequency, the structural topology optimization on mover, worktable and bed were conducted. Compared with the original structure, the optimized results showed that the static and dynamic stiffness of system were effectively improved under the premise of not influence the magnetic field distribution. Magnetic-structure coupling topology optimization provides an effective method for innovative design of coupled system.
The normal force and the vibration for the prototype of permanent magnet linear servo motor have been tested. And the normal force of the prototype between two polars was measured through designing special testing apparatus. The accelerations of the worktable in the linear feed system with different speeds, loads, and profiles were measured, and then the modal frequencies were analyzed. The experiment results have proved that the coupling model is reasonable and correct.
引文
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