五自由度并联机床冗余驱动理论与实验研究
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摘要
并联机床是并联机器人学、机械制造和计算机技术等多门学科交叉融合的结晶,与传统数控机床形成很强的互补,具有良好的应用前景和较高的科研价值。基于冗余驱动可以克服奇异位形,增大有效工作空间,改善并联机床驱动平稳性,优化关节驱动力,提高其精度和承载能力的思想,本文对冗余驱动5-UPS/PRPU 5自由度并联机床相关问题进行了深入研究,主要研究内容如下:
分析了冗余驱动5-UPS/PRPU并联机床的运动学关系,推导了位置反解公式和速度公式,建立了冗余驱动下的速度雅可比矩阵。
建立了冗余驱动5-UPS/PRPU并联机床的静力平衡方程。基于力雅可比矩阵,运用影响系数法分析了冗余驱动力对UPS分支受力的影响,为冗余驱动改善UPS分支驱动力提供了理论依据。以静力平衡方程为约束条件,运用力映射矩阵的伪逆对各分支受力和约束力偶矩进行优化,并将优化目标统一量纲。通过数值算例,将冗余驱动与非冗余驱动下机床驱动分支的受力进行了对比分析。
运用拉格朗日法建立了该冗余驱动并联机床的动力学模型,并提出了一种新的冗余驱动力规划方法。运用达朗伯原理求解出机床运动中动平台所需的约束扭矩和可用于实时力控制的冗余驱动力。
应用动力学仿真分析软件ADAMS建立了该冗余驱动并联机床的虚拟样机,根据NC加工代码建立其驱动模型;计算出螺旋副上等效摩擦力,建立了该机床摩擦力模型,并分析了对驱动力矩影响较大的关节摩擦力;根据机床位姿和切削用量等参数建立了切削力模型,实现了切削加工动力学仿真。将动力学仿真结果与理论计算结果进行了对比分析和验证。
在运动学及动力学分析基础上,提出冗余驱动力/位置混合控制策略,开发了该冗余驱动并联机床的控制系统。系统硬件采用开放式结构,由“工控PC机+运动控制卡PMAC”构成,是一种并行双CPU数控系统。以Windows操作系统为平台,采用模块化方法应用Visual Basic 6.0开发了开放式数控系统软件,包括人机交互、安全保障、运动和力/位置混合控制、标定校准、文件管理等各功能模块。通过在冗余驱动分支上安装扭矩传感器实现力矩信号实时反馈,初步实现了该机床冗余驱动的柔顺控制。
对该冗余驱动并联机床进行了一系列实验研究,包括机床定位精度检测、动力学性能测试和切削加工实验。实验结果表明冗余驱动消除了中间约束分支上滑块爬行现象,提高了机床的定位精度和动力学性能。该冗余驱动并联机床运动平稳,可实现复杂曲面的加工。
Parallel Machine Tool (PMT) is the production of many subjects, including parallel robotics, mechanical manufacturing, computer technology and so on. As a useful complement of conventional NC machine tools, PMT has splendid future and high scientific research value. Redundant actuation has become the hot topic because that it can help parallel manipulators eliminate the singular configurations, enlarge effective workspace, and improve its dynamic performance, the precision and bearing capacity. This paper focuses on the research of correlated aspects of the 5-UPS/PRPU PMT with redundant actuation. The main contributions are as follows:
Redundant actuation is introduced into the 5-UPS/PRPU PMT. The inverse kinematic solution and the velocity solution are analyzed. The velocity Jacobian matrix of the PMT with redundant actuation is established.
The static equilibrium equation of the PMT with redundant actuation is established. Based on the force Jacobian matrix, the influence of the redundant actuation to the UPS limbs is studied by means of the influence coefficient method, which provides theoretical basis to improve the mechanical performance of UPS limbs. Take static equilibrium equations as the constraints, the forces and constraint couple is optimized by means of pseudo-inverse method.
The dynamic equation of this PMT with redundant actuation is built by Lagrange Equation. A novel force distribution method is proposed for redundant actuation. The constraint couple of the PRPU limb to the moving platform is deduced with the D’Alembert’s principle. Consequently, the dynamic calculation of the redundant actuation limb is performed, base on which the redundant driving force used in real-time force control can be obtained.
The virtual prototype of PMT is established in ADAMS. Then, the motion controlling model, the friction force model and the cutting force model are created according to numerical control (NC) files and cutting parameters. Importing these models to the prototype of this PMT, the dynamic simulation of the cutting process is carried out by ADAMS software. The joint friction which affects the driving force most is analyzed. At the same time, the simulation results and theoretical results of the dynamics are compared, which showed the correctness of models.
Based on the kinematics and dynamics analysis, the control system is developed for the PMT with redundant actuation. Open architecture composed of PC and PMAC is adopted for the system hardware, which is a parallel double-CPU NC system. The open CNC system software is developed on base of Windows, adopting modularization in Visual Basic 6.0. The system consists of human-machine-interfaces, security assurance, motion force/position hybrid control, calibration, file management and some other function module. Torque sensor is installed on the redundant actuation driving limb to realize real time feedback of torque signal, which realizes the compliance control of PMT primarily.
A series of experimental investigation for the PMT with redundant actuation are carried out, including the detection for the positioning accuracy of each axis in Cartesian coordinates of the machine, the dynamic performance, and the machining experiments. The experimental result shows that the redundant actuation can eliminate the creeping phenomenon of the slider in the middle constraint limb, improve the positioning accuracy and the dynamic performance. The PMT with redundant actuation achieved smooth moving and the curved surface machining.
分析了冗余驱动5-UPS/PRPU并联机床的运动学关系,推导了位置反解公式和速度公式,建立了冗余驱动下的速度雅可比矩阵。
建立了冗余驱动5-UPS/PRPU并联机床的静力平衡方程。基于力雅可比矩阵,运用影响系数法分析了冗余驱动力对UPS分支受力的影响,为冗余驱动改善UPS分支驱动力提供了理论依据。以静力平衡方程为约束条件,运用力映射矩阵的伪逆对各分支受力和约束力偶矩进行优化,并将优化目标统一量纲。通过数值算例,将冗余驱动与非冗余驱动下机床驱动分支的受力进行了对比分析。
运用拉格朗日法建立了该冗余驱动并联机床的动力学模型,并提出了一种新的冗余驱动力规划方法。运用达朗伯原理求解出机床运动中动平台所需的约束扭矩和可用于实时力控制的冗余驱动力。
应用动力学仿真分析软件ADAMS建立了该冗余驱动并联机床的虚拟样机,根据NC加工代码建立其驱动模型;计算出螺旋副上等效摩擦力,建立了该机床摩擦力模型,并分析了对驱动力矩影响较大的关节摩擦力;根据机床位姿和切削用量等参数建立了切削力模型,实现了切削加工动力学仿真。将动力学仿真结果与理论计算结果进行了对比分析和验证。
在运动学及动力学分析基础上,提出冗余驱动力/位置混合控制策略,开发了该冗余驱动并联机床的控制系统。系统硬件采用开放式结构,由“工控PC机+运动控制卡PMAC”构成,是一种并行双CPU数控系统。以Windows操作系统为平台,采用模块化方法应用Visual Basic 6.0开发了开放式数控系统软件,包括人机交互、安全保障、运动和力/位置混合控制、标定校准、文件管理等各功能模块。通过在冗余驱动分支上安装扭矩传感器实现力矩信号实时反馈,初步实现了该机床冗余驱动的柔顺控制。
对该冗余驱动并联机床进行了一系列实验研究,包括机床定位精度检测、动力学性能测试和切削加工实验。实验结果表明冗余驱动消除了中间约束分支上滑块爬行现象,提高了机床的定位精度和动力学性能。该冗余驱动并联机床运动平稳,可实现复杂曲面的加工。
Parallel Machine Tool (PMT) is the production of many subjects, including parallel robotics, mechanical manufacturing, computer technology and so on. As a useful complement of conventional NC machine tools, PMT has splendid future and high scientific research value. Redundant actuation has become the hot topic because that it can help parallel manipulators eliminate the singular configurations, enlarge effective workspace, and improve its dynamic performance, the precision and bearing capacity. This paper focuses on the research of correlated aspects of the 5-UPS/PRPU PMT with redundant actuation. The main contributions are as follows:
Redundant actuation is introduced into the 5-UPS/PRPU PMT. The inverse kinematic solution and the velocity solution are analyzed. The velocity Jacobian matrix of the PMT with redundant actuation is established.
The static equilibrium equation of the PMT with redundant actuation is established. Based on the force Jacobian matrix, the influence of the redundant actuation to the UPS limbs is studied by means of the influence coefficient method, which provides theoretical basis to improve the mechanical performance of UPS limbs. Take static equilibrium equations as the constraints, the forces and constraint couple is optimized by means of pseudo-inverse method.
The dynamic equation of this PMT with redundant actuation is built by Lagrange Equation. A novel force distribution method is proposed for redundant actuation. The constraint couple of the PRPU limb to the moving platform is deduced with the D’Alembert’s principle. Consequently, the dynamic calculation of the redundant actuation limb is performed, base on which the redundant driving force used in real-time force control can be obtained.
The virtual prototype of PMT is established in ADAMS. Then, the motion controlling model, the friction force model and the cutting force model are created according to numerical control (NC) files and cutting parameters. Importing these models to the prototype of this PMT, the dynamic simulation of the cutting process is carried out by ADAMS software. The joint friction which affects the driving force most is analyzed. At the same time, the simulation results and theoretical results of the dynamics are compared, which showed the correctness of models.
Based on the kinematics and dynamics analysis, the control system is developed for the PMT with redundant actuation. Open architecture composed of PC and PMAC is adopted for the system hardware, which is a parallel double-CPU NC system. The open CNC system software is developed on base of Windows, adopting modularization in Visual Basic 6.0. The system consists of human-machine-interfaces, security assurance, motion force/position hybrid control, calibration, file management and some other function module. Torque sensor is installed on the redundant actuation driving limb to realize real time feedback of torque signal, which realizes the compliance control of PMT primarily.
A series of experimental investigation for the PMT with redundant actuation are carried out, including the detection for the positioning accuracy of each axis in Cartesian coordinates of the machine, the dynamic performance, and the machining experiments. The experimental result shows that the redundant actuation can eliminate the creeping phenomenon of the slider in the middle constraint limb, improve the positioning accuracy and the dynamic performance. The PMT with redundant actuation achieved smooth moving and the curved surface machining.
引文
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