椭圆轨迹成形方法与控制技术研究
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摘要
研究了基于运动合成的椭圆内曲面成形方法,重点开展静压主轴椭圆轴心轨迹控制技术研究。构建了基于新型静压轴承和新型伺服节流阀的液压控制系统；研究了新型轴承—转子系统及新型伺服阀节流系统的动力学特性和控制特性；研究了椭圆轴心轨迹的控制技术和方法。为椭圆内曲面加工新方法的实现奠定了理论基础。
开展了椭圆内曲面运动成形基础理论研究,并详细阐述了其实现方案和成形原理。研究了多种轴心公转轨迹与刀尖自转轨迹进行合成时形成椭圆刀尖轨迹的必要与充分条件；研究了刀具初始相位角对形成椭圆刀尖轨迹的影响；给出了多种轴心公转轨迹和不同刀具初始相位角下形成椭圆刀尖轨迹的特征和控制方程。
针对椭圆轴心轨迹的空间要求,开展了椭圆廓形静压轴承的理论研究,给出了其雷诺方程和流量连续性方程等基础性方程及计算方法。提出了动压比的概念来衡量封油面上动压效应的大小,并对主轴轴心在新型静压轴承内运动轨迹为小椭圆时的动压比进行了仿真计算。利用偏导数法研究了半径间隙和椭圆度对新型静压轴承静动态特性参数的影响。
设计了一种基于压电陶瓷的新型伺服节流阀,可以弥补普通电液伺服阀频响较低的缺点。基于新型油腔嵌套式轴承及新型伺服节流阀的结构,构建了轴心运动轨迹的液压控制系统。对新型节流阀的流量公式进行了仿真拟合。利用基于贝叶斯正则算法的BP神经网络对压电陶瓷的位移输出进行了仿真预测。根据动压效应的研究结果对封油面上的油膜力分布进行线性化处理,利用流量平衡方程以及高斯—勒让德积分公式得到了承载油腔以及控制油腔的压力计算公式,这种简化计算方法既简单又可以大大节省计算时间。仿真计算了轴心期望运动轨迹与新型节流阀控制电压的定量关系。
利用最优控制理论对主轴轴心公转轨迹为椭圆的问题进行了最优控制建模。建立了基于新型静压轴承的轴承—转子系统的动力学模型,并以轴心位置坐标为待优化的状态变量,控制外力(这里为油膜合力)为控制变量,以待优化的轴心坐标与期望轴心坐标的偏差作为性能指标,得到系统的最优控制模型。求解勒让德零点以及对状态变量和控制变量近似化,通过高斯伪谱法将最优控制问题又转化成了非线性规划问题,最后通过序列二次规划法仿真得到了轴心运动轨迹的最优控制参数。仿真结果表明轴心的优化位置坐标与期望位置坐标非常接近,高斯伪谱法精度较高且可以应用在轴心运动轨迹的最优控制上。
对主轴轴心的运动轨迹进行了开环控制仿真研究。利用轴心期望轨迹与新型节流阀控制电压的定量关系,通过欧拉方法迭代得到轴心的开环控制仿真轨迹。仿真得到轴心轨迹为不同椭圆度的椭圆时开环控制轨迹图,并对有瞬态干扰力时开环控制的轴心运动轨迹也进行了仿真。仿真结果表明开环控制方法不但可以控制轴心运动轨迹为不同椭圆度的小椭圆,还可以在系统受到干扰时保持较好的鲁棒性。
对新型压电伺服节流阀以及油腔嵌套式轴承系统分别进行了动力学建模,得到系统的传递函数,并进行了前馈解耦。基于轴心期望运动轨迹的周期性特点,采用重复控制算法对系统进行了闭环控制仿真。在MATLAB的simulink环境下对系统进行建模,利用设计的重复控制器对轴心运动轨迹进行了闭环控制的仿真研究。仿真结果表明重复控制算法控制轴心跟踪期望轨迹时具有较高的精度。
Based on the movement forming methods for elliptical inner surface, this paper focuses on carrying out control technology research on elliptical shaft center orbit. The paper builds the hydraulic control system based on new type hydrostatic bearing and servo throttle valve. It also researches the kinetic property and controlling characteristics of new type bearing-rotor system and new type servo throttle valve systems. Control technology and methods of elliptical shaft center orbit are studied. This study lays a theoretical foundation for realization of new machining methods for elliptical inner surface.
The basic theoretical studies are made on movement forming methods for elliptical inner surface, and the implementation scheme and forming principle are clarified in detail. Necessary and sufficient conditions for forming elliptic tool nose orbit, under the condition that multiple shaft center orbits and the tool nose's rotation orbit take synchronous forward synthesis and synchronous backward synthesis, are studied. The influence of initial phase angle of the tool nose on the formation of elliptic tool nose orbit has also been investigated. Characteristics and control equations of elliptic tool nose orbit under the conditions of multiple shaft center orbits and different initial phase angles of the tool nose are given.
In order to meet the space requirement of elliptical shaft center orbit, the hydrostatic bearing whose inner face is an elliptic cylindrical surface is studied. The paper provides the fundamental equations(such as Reynolds equation and flow continuity equation) and their computing methods. The concept of dynamic pressure ratio is put forward to measure the hydrodynamic effect on bearing land, and the dynamic pressure ratio is computed when shaft center orbit is a small elliptical track in the new type hydrostatic bearing. Using partial derivative method, the paper studies the impacts of radius clearance and ovality on new hydrostatic bearing's static and dynamic performance parameters.
The hydraulic control system is built based on special structure of the new nest-pocket bearing and servo throttle valve. A new-type servo throttle is designed based on piezoelectric ceramics, which can make up the disadvantage of low frequency response for ordinary electro-hydraulic servo valve. The flow formula of new servo throttle is obtained using simulation and fitting process. Output displacement of piezoelectric ceramics is predicted utilizing BP neural network(based on bayesian regular algorithms). The pressure value on bearing land is linearly assigned, and recess pressure computational formula of hydrostatic recess and control recess are obtained through combining flow equilibrium equation and Gaussian-Legendre integral formula. The quantitative relationship between expected shaft movement orbit and the control voltage of new type servo throttle is studied.
The model of elliptical shaft center revolution orbit is built based on the optimal control theory. The bearing-rotor system kinetic model is built, and position coordinates of shaft center are taken as optimized state variable, external force(here, it is bearing force) taken as control variable, deviation between optimized shaft center coordinates and expected shaft center coordinates taken as performance index. With the solution of legendre zeros and approximation of state variable and control variable, the optimal control problem is transformed into general nonlinear programming problem using pseudo-spectral method, and at last, optimum control parameters of shaft center orbit are obtained using sequence quadratic programming method. The simulation results indicate that difference between optimized shaft center coordinates and expected shaft center coordinates is very small, and the Gaussian pseudo-spectral method has a advantage of high precision and can be used in optimum controlling of shaft center movement orbit.
The open-loop control simulation is made on the shaft center movement orbit. Using the quantitative relationship between expected shaft movement orbit and control voltage of new type servo throttle valve, the open-loop control simulation orbit is obtain. The shaft center's kinetic parameters are calculated when the shaft center's coordinate is in the expected small ellipse orbit, and active control parameters for throttle valve in hydraulic control system are also solved. Then using the active control parameters, the open-loop control simulation orbits of shaft center are obtained with Euler's method iteration. The open loop control orbits are got when the shaft center orbits are different ovality ellipses, and the open loop control simulation of shaft center is also made when there is the transient disturbance force. The simulation results indicate that open-loop control method can control the shaft center and realize different ovality elliptical shaft center orbits, and keeps good robustness when the system is disturbed.
Dynamics modeling is taken on piezoelectric servo valve and the whole system seperately. The system transferring function is obtained, and feedforward decoupling is taken. Based on periodical characteristic of expected orbit of shaft center, the repetition control algorithm is used as closed-loop control method. Under the simulink environment of MATLAB, the whole system is modeled, and the closed-loop control simulation of the system is made using designed repetition controller. Simulation results show repetitive control algorithm has high validity on controlling shaft center to track expected orbit.
开展了椭圆内曲面运动成形基础理论研究,并详细阐述了其实现方案和成形原理。研究了多种轴心公转轨迹与刀尖自转轨迹进行合成时形成椭圆刀尖轨迹的必要与充分条件；研究了刀具初始相位角对形成椭圆刀尖轨迹的影响；给出了多种轴心公转轨迹和不同刀具初始相位角下形成椭圆刀尖轨迹的特征和控制方程。
针对椭圆轴心轨迹的空间要求,开展了椭圆廓形静压轴承的理论研究,给出了其雷诺方程和流量连续性方程等基础性方程及计算方法。提出了动压比的概念来衡量封油面上动压效应的大小,并对主轴轴心在新型静压轴承内运动轨迹为小椭圆时的动压比进行了仿真计算。利用偏导数法研究了半径间隙和椭圆度对新型静压轴承静动态特性参数的影响。
设计了一种基于压电陶瓷的新型伺服节流阀,可以弥补普通电液伺服阀频响较低的缺点。基于新型油腔嵌套式轴承及新型伺服节流阀的结构,构建了轴心运动轨迹的液压控制系统。对新型节流阀的流量公式进行了仿真拟合。利用基于贝叶斯正则算法的BP神经网络对压电陶瓷的位移输出进行了仿真预测。根据动压效应的研究结果对封油面上的油膜力分布进行线性化处理,利用流量平衡方程以及高斯—勒让德积分公式得到了承载油腔以及控制油腔的压力计算公式,这种简化计算方法既简单又可以大大节省计算时间。仿真计算了轴心期望运动轨迹与新型节流阀控制电压的定量关系。
利用最优控制理论对主轴轴心公转轨迹为椭圆的问题进行了最优控制建模。建立了基于新型静压轴承的轴承—转子系统的动力学模型,并以轴心位置坐标为待优化的状态变量,控制外力(这里为油膜合力)为控制变量,以待优化的轴心坐标与期望轴心坐标的偏差作为性能指标,得到系统的最优控制模型。求解勒让德零点以及对状态变量和控制变量近似化,通过高斯伪谱法将最优控制问题又转化成了非线性规划问题,最后通过序列二次规划法仿真得到了轴心运动轨迹的最优控制参数。仿真结果表明轴心的优化位置坐标与期望位置坐标非常接近,高斯伪谱法精度较高且可以应用在轴心运动轨迹的最优控制上。
对主轴轴心的运动轨迹进行了开环控制仿真研究。利用轴心期望轨迹与新型节流阀控制电压的定量关系,通过欧拉方法迭代得到轴心的开环控制仿真轨迹。仿真得到轴心轨迹为不同椭圆度的椭圆时开环控制轨迹图,并对有瞬态干扰力时开环控制的轴心运动轨迹也进行了仿真。仿真结果表明开环控制方法不但可以控制轴心运动轨迹为不同椭圆度的小椭圆,还可以在系统受到干扰时保持较好的鲁棒性。
对新型压电伺服节流阀以及油腔嵌套式轴承系统分别进行了动力学建模,得到系统的传递函数,并进行了前馈解耦。基于轴心期望运动轨迹的周期性特点,采用重复控制算法对系统进行了闭环控制仿真。在MATLAB的simulink环境下对系统进行建模,利用设计的重复控制器对轴心运动轨迹进行了闭环控制的仿真研究。仿真结果表明重复控制算法控制轴心跟踪期望轨迹时具有较高的精度。
Based on the movement forming methods for elliptical inner surface, this paper focuses on carrying out control technology research on elliptical shaft center orbit. The paper builds the hydraulic control system based on new type hydrostatic bearing and servo throttle valve. It also researches the kinetic property and controlling characteristics of new type bearing-rotor system and new type servo throttle valve systems. Control technology and methods of elliptical shaft center orbit are studied. This study lays a theoretical foundation for realization of new machining methods for elliptical inner surface.
The basic theoretical studies are made on movement forming methods for elliptical inner surface, and the implementation scheme and forming principle are clarified in detail. Necessary and sufficient conditions for forming elliptic tool nose orbit, under the condition that multiple shaft center orbits and the tool nose's rotation orbit take synchronous forward synthesis and synchronous backward synthesis, are studied. The influence of initial phase angle of the tool nose on the formation of elliptic tool nose orbit has also been investigated. Characteristics and control equations of elliptic tool nose orbit under the conditions of multiple shaft center orbits and different initial phase angles of the tool nose are given.
In order to meet the space requirement of elliptical shaft center orbit, the hydrostatic bearing whose inner face is an elliptic cylindrical surface is studied. The paper provides the fundamental equations(such as Reynolds equation and flow continuity equation) and their computing methods. The concept of dynamic pressure ratio is put forward to measure the hydrodynamic effect on bearing land, and the dynamic pressure ratio is computed when shaft center orbit is a small elliptical track in the new type hydrostatic bearing. Using partial derivative method, the paper studies the impacts of radius clearance and ovality on new hydrostatic bearing's static and dynamic performance parameters.
The hydraulic control system is built based on special structure of the new nest-pocket bearing and servo throttle valve. A new-type servo throttle is designed based on piezoelectric ceramics, which can make up the disadvantage of low frequency response for ordinary electro-hydraulic servo valve. The flow formula of new servo throttle is obtained using simulation and fitting process. Output displacement of piezoelectric ceramics is predicted utilizing BP neural network(based on bayesian regular algorithms). The pressure value on bearing land is linearly assigned, and recess pressure computational formula of hydrostatic recess and control recess are obtained through combining flow equilibrium equation and Gaussian-Legendre integral formula. The quantitative relationship between expected shaft movement orbit and the control voltage of new type servo throttle is studied.
The model of elliptical shaft center revolution orbit is built based on the optimal control theory. The bearing-rotor system kinetic model is built, and position coordinates of shaft center are taken as optimized state variable, external force(here, it is bearing force) taken as control variable, deviation between optimized shaft center coordinates and expected shaft center coordinates taken as performance index. With the solution of legendre zeros and approximation of state variable and control variable, the optimal control problem is transformed into general nonlinear programming problem using pseudo-spectral method, and at last, optimum control parameters of shaft center orbit are obtained using sequence quadratic programming method. The simulation results indicate that difference between optimized shaft center coordinates and expected shaft center coordinates is very small, and the Gaussian pseudo-spectral method has a advantage of high precision and can be used in optimum controlling of shaft center movement orbit.
The open-loop control simulation is made on the shaft center movement orbit. Using the quantitative relationship between expected shaft movement orbit and control voltage of new type servo throttle valve, the open-loop control simulation orbit is obtain. The shaft center's kinetic parameters are calculated when the shaft center's coordinate is in the expected small ellipse orbit, and active control parameters for throttle valve in hydraulic control system are also solved. Then using the active control parameters, the open-loop control simulation orbits of shaft center are obtained with Euler's method iteration. The open loop control orbits are got when the shaft center orbits are different ovality ellipses, and the open loop control simulation of shaft center is also made when there is the transient disturbance force. The simulation results indicate that open-loop control method can control the shaft center and realize different ovality elliptical shaft center orbits, and keeps good robustness when the system is disturbed.
Dynamics modeling is taken on piezoelectric servo valve and the whole system seperately. The system transferring function is obtained, and feedforward decoupling is taken. Based on periodical characteristic of expected orbit of shaft center, the repetition control algorithm is used as closed-loop control method. Under the simulink environment of MATLAB, the whole system is modeled, and the closed-loop control simulation of the system is made using designed repetition controller. Simulation results show repetitive control algorithm has high validity on controlling shaft center to track expected orbit.
引文
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