大量程并联式六维力传感器基础理论与实验研究
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摘要
大量程高精度六维力传感器在航空航天、汽车、建筑及造船等许多领域十分急需并具有广泛的应用前景。并联机构具有刚度大、结构稳定、承载能力高、无误差积累、精度高等特点，是设计制造大量程、大测力板六维力传感器的最佳结构方案之一，特别是各向同性并联式六维力传感器更具有应用潜力。本文主要研究大量程并联结构六维力传感器的各向同同性问题，以及预紧式超静定并联式六维力传感器的关键理论和实验问题，丰富和完善并联式六维力传感器的设计理论，为设计制造具有自主知识产权的六维力传感器奠定理论与实验基础。主要研究内容如下：
应用螺旋理论对静定Stewart结构六维力传感器进行静态受力分析，分析经典6/6型和3-3/3-3型双环Stewart结构六维力传感器的结构特点，提出一种等杆长6/3-3型Stewart结构六维力传感器，分别求解得到三种并联结构六维力传感器的静力映射矩阵以及其它关键特性矩阵的解析表达式。
对传感器的各向同性性能指标进行系统分析，结合物理意义逐一分析和比较过去所采用过的各向同性性能评价指标，通过引入解耦性能约束条件，定义满足解耦性能的各向同性指标，引入力和力矩完全各向同性的概念；具体分析传感器满足力和力矩完全各向同性时各个分量的灵敏度和综合灵敏度指标；从整体刚度和灵敏度的角度，总结各向同性的物理意义，并推广到任意分支Stewart结构六维力传感器的性能评估。
采用数学解析推导方法，应用满足解耦性能的各向同性度指标，系统分析经典6/6型Stewart结构六维力传感器的各向同性性能，证明该类结构不可能同时实现力和力矩完全各向同性的性能，进而权衡力和力矩各向同性度指标，得到综合性能指标的最优值；系统分析3-3/3-3型双环结构和6/3-3型结构Stewart力传感器的各向同性性能，推导得到传感器同时满足力和力矩完全各向同性时结构参数之间的解析表达式，确定各向同性解析表达式的有效性及有效区间，给出数值算例和结构实例。
提出一系列整体预紧式六维力传感器结构，对预紧式Stewart结构力传感器的超静定力分配问题进行分析，综合考虑传感器整体刚度和位移协调关系，以简洁的符号表达式描绘出超静定结构各分支杆轴力与六维外力之间的映射关系，进一步从理论上解决了任意分支超静定Stewart结构的超静定受力难题。在此基础上，详细分析和比较采用推导的理论求解公式和基于静力映射矩阵的Moore-Penrose广义逆求解之间的区别和联系，给出了综合考虑分支刚度和静力映射矩阵的广义逆求解超静定受力的表达式。
对预紧式超静定Stewart结构力传感器进行详细分析，完成超静定力传感器的各向同性设计，得到满足力和力矩完全各向同性时结构参数之间的解析表达式；为保证传感器结构稳定性和测量有效性，通过求解约束条件的拉格朗日方程的极值，得到预紧载荷与量程之间的数学关系；基于得到的完全各向同性解析表达式，确定出样机的关键结构参数；对传感器样机进行详细的结构设计，完成预紧支路和传感器的整体方案设计，研制出大量程大测力板六维力传感器样机。
采用线性和非线性两种标定思路，讨论超静定六维力传感器的标定方法，提出一种超静定结构六维力传感器的静定标定方法，将神经网络标定方法用于超静定六维力传感器的标定，进行六维力传感器标定系统设计，研制静态标定加载试验平台，搭建数据采集软硬件系统，对传感器样机进行静态标定实验，给出各种标定方法的实验结果并进行分析比较。
采用机理建模方法、有限元仿真方法和阶跃响应实验方法对传感器样机进行动态特性研究。建立传感器样机的动力学理论模型，推导传感器系统的无阻尼自由振动方程，得到系统的理论固有频率值和振型；借助有限元软件建立传感器样机有限元模型，并进行振动模态分析；对样机进行动态标定实验的初步研究，得到传感器样机的动态性能指标。
The large range and high accuracy six-axis force/torque sensor is urgently neededand has extensive application prospects in aviation, automobile, construction,shipbuilding and some other fields. Parallel mechanism is characterized by excellentrigidity, good structure stability, large load-carrying capacity, not-accumulative error andhigh accuracy. It is one of the best structure patterns in design and manufacture of largerange and dimension six-axis force sensors, especially fully isotropic parallel six-axisforce sensor has great application potentials. This paper focuses on isotropy analysis oflarge range parallel six-axis force sensor, key theory and calibration experiment ofstatically indeterminate pre-stressed six-axis force sensor, aiming to enrich and perfectthe design theory of parallel six-axis force sensor, as well as building the theoretical andexperimental basis for the design and manufacture of six-axis force sensor withindependent intellectual property rights.
Statics analysis of statically determinate Stewart platform-based force sensor isconducted using screw theory. The structural features of six-axis force sensor based ontraditional 6/6 Stewart platform and two-circle 3-3/3-3 Stewart platform are analyzed andcompared, and a 6/3-3 Stewart platform-based force sensor with equal leg lengths isproposd. The mathematical expressions of force mapping matrices and other featurematrices for these three structures are obtained.
Isotropy indices of six axis force sensor are studied systematically. In combinationwith physical significance, isotropy indices of the past are analyzed and compared one byone. By introducing decoupling performance constraint condition, the force and torqueisotropy indices satisfying decoupling performance are defined, and the concept of fullisotropy is proposed. The sensitivity indices in all directions and comprehensivesensitivity are analyzed concretely when full isotropy are satisfied. The physicalsignificance of isotropy is summarized from the viewpoint of global stiffness andsensitivity. The proposed isotropy indices and the concept of full isotropy are extended toevaluate Stewart platform-based force sensor with arbitrary limbs. By using analytic approach, the isotropy performance of the traditional 6-6 Stewartplatform-based force sensor is studied in detail based on the modified isotropy indicessatisfying decoupling performance, the result indicates that it is impossible to realize fullisotropy in theory, and the best comprehensive isotropy performance is obtained bycompromising the isotropy indices. The isotropy performance of the 3-3/3-3 and 6/3-3Stewart platform-based force sensors are studied systematically. The analytic relations ofkey structural parameters leading to fully isotropic configuration are obtained, classes ofisotropic configurations can be easily obtained from the analytic results. The validsolutions and the valid range of the solutions are determined by using a numericalalgorithm. The numerical examples and fully isotropic structural examples are given.
A series of statically indeterminate pre-stressed six-axis force sensor are proposed.The force analysis of the statically indeterminate pre-stressed structure is carried out byconsidering the stiffness properties and compatibility in deformations, the analyticalrelationship between the axial force and the six-dimensional external force is obtained ina neat form. Furthermore, the statically indeterminate force-distribution difficult problemof Stewart platform with arbitrary limbs is solved thoroughly. On the basis of above, thedifference and relation between the deduced theoretical solution and the solution basedon force mapping matrix’s Moore-Penrose generalized inverse are analyzed andcompared detailedly. The solving formula based on Moore-Penrose generalized inverseincluding the effect of stiffness of all the limbs and force mapping matrix is given.
Systematic analysis of statically indeterminate pre-stressed Stewart platform-basedforce sensor is presented. The fully isotropic design of statically indeterminate Stewartplatform-based force sensor is completed, and the analytic relations of key structuralparameters leading to fully isotropic configuration are obtained. To ensure the structuralstability and measurement validity, the mathematical relation between the pre-tighteningforce and expected range of external loads is obtained by solving the conditionalextremum of the Lagrange function. The key structure parameters of sensor prototype aredetermined based on the deduced analytical expression leading to full isotropy. The detaildesign of the pre-stressing limb and the whole design of sensor prototype are completed,and the prototype of large range six-axis force sensor is manufactured.
The calibration methods of statically indeterminate six-axis force sensor arediscussed using linear and nonlinear scheme. A statically determinate calibration methodof statically indeterminate six-axis force sensor is proposed. The method based on neuralnetwork is introduced to calibrate the statically indeterminate six-axis force sensor. Thestatic calibration system of six axis force sensor is designed. The static calibration deviceis manufactured and the data acquisition hardware and software system is developed. Thestatic calibration experiments of sensor prototype are carried out, the comparison anddiscussion of the calibration results using the various calibration methods are presented.
By means of mechanism modeling method, finite element method and step responseexperiment method, the dynamic characteristic of sensor prototype is studied. Thedynamics theory model of sensor prototype is built. The non damping free vibrationequation of the sensor system is derived out, and the theoretical natural frequency andvibration mode of the prototype are given. The finite element model of sensor prototypeis built and the modal analysis is presented. The preliminary study of dynamic calibrationexperiment is carried out and the dynamic performance indices of the sensor prototypeare obtained.
应用螺旋理论对静定Stewart结构六维力传感器进行静态受力分析，分析经典6/6型和3-3/3-3型双环Stewart结构六维力传感器的结构特点，提出一种等杆长6/3-3型Stewart结构六维力传感器，分别求解得到三种并联结构六维力传感器的静力映射矩阵以及其它关键特性矩阵的解析表达式。
对传感器的各向同性性能指标进行系统分析，结合物理意义逐一分析和比较过去所采用过的各向同性性能评价指标，通过引入解耦性能约束条件，定义满足解耦性能的各向同性指标，引入力和力矩完全各向同性的概念；具体分析传感器满足力和力矩完全各向同性时各个分量的灵敏度和综合灵敏度指标；从整体刚度和灵敏度的角度，总结各向同性的物理意义，并推广到任意分支Stewart结构六维力传感器的性能评估。
采用数学解析推导方法，应用满足解耦性能的各向同性度指标，系统分析经典6/6型Stewart结构六维力传感器的各向同性性能，证明该类结构不可能同时实现力和力矩完全各向同性的性能，进而权衡力和力矩各向同性度指标，得到综合性能指标的最优值；系统分析3-3/3-3型双环结构和6/3-3型结构Stewart力传感器的各向同性性能，推导得到传感器同时满足力和力矩完全各向同性时结构参数之间的解析表达式，确定各向同性解析表达式的有效性及有效区间，给出数值算例和结构实例。
提出一系列整体预紧式六维力传感器结构，对预紧式Stewart结构力传感器的超静定力分配问题进行分析，综合考虑传感器整体刚度和位移协调关系，以简洁的符号表达式描绘出超静定结构各分支杆轴力与六维外力之间的映射关系，进一步从理论上解决了任意分支超静定Stewart结构的超静定受力难题。在此基础上，详细分析和比较采用推导的理论求解公式和基于静力映射矩阵的Moore-Penrose广义逆求解之间的区别和联系，给出了综合考虑分支刚度和静力映射矩阵的广义逆求解超静定受力的表达式。
对预紧式超静定Stewart结构力传感器进行详细分析，完成超静定力传感器的各向同性设计，得到满足力和力矩完全各向同性时结构参数之间的解析表达式；为保证传感器结构稳定性和测量有效性，通过求解约束条件的拉格朗日方程的极值，得到预紧载荷与量程之间的数学关系；基于得到的完全各向同性解析表达式，确定出样机的关键结构参数；对传感器样机进行详细的结构设计，完成预紧支路和传感器的整体方案设计，研制出大量程大测力板六维力传感器样机。
采用线性和非线性两种标定思路，讨论超静定六维力传感器的标定方法，提出一种超静定结构六维力传感器的静定标定方法，将神经网络标定方法用于超静定六维力传感器的标定，进行六维力传感器标定系统设计，研制静态标定加载试验平台，搭建数据采集软硬件系统，对传感器样机进行静态标定实验，给出各种标定方法的实验结果并进行分析比较。
采用机理建模方法、有限元仿真方法和阶跃响应实验方法对传感器样机进行动态特性研究。建立传感器样机的动力学理论模型，推导传感器系统的无阻尼自由振动方程，得到系统的理论固有频率值和振型；借助有限元软件建立传感器样机有限元模型，并进行振动模态分析；对样机进行动态标定实验的初步研究，得到传感器样机的动态性能指标。
The large range and high accuracy six-axis force/torque sensor is urgently neededand has extensive application prospects in aviation, automobile, construction,shipbuilding and some other fields. Parallel mechanism is characterized by excellentrigidity, good structure stability, large load-carrying capacity, not-accumulative error andhigh accuracy. It is one of the best structure patterns in design and manufacture of largerange and dimension six-axis force sensors, especially fully isotropic parallel six-axisforce sensor has great application potentials. This paper focuses on isotropy analysis oflarge range parallel six-axis force sensor, key theory and calibration experiment ofstatically indeterminate pre-stressed six-axis force sensor, aiming to enrich and perfectthe design theory of parallel six-axis force sensor, as well as building the theoretical andexperimental basis for the design and manufacture of six-axis force sensor withindependent intellectual property rights.
Statics analysis of statically determinate Stewart platform-based force sensor isconducted using screw theory. The structural features of six-axis force sensor based ontraditional 6/6 Stewart platform and two-circle 3-3/3-3 Stewart platform are analyzed andcompared, and a 6/3-3 Stewart platform-based force sensor with equal leg lengths isproposd. The mathematical expressions of force mapping matrices and other featurematrices for these three structures are obtained.
Isotropy indices of six axis force sensor are studied systematically. In combinationwith physical significance, isotropy indices of the past are analyzed and compared one byone. By introducing decoupling performance constraint condition, the force and torqueisotropy indices satisfying decoupling performance are defined, and the concept of fullisotropy is proposed. The sensitivity indices in all directions and comprehensivesensitivity are analyzed concretely when full isotropy are satisfied. The physicalsignificance of isotropy is summarized from the viewpoint of global stiffness andsensitivity. The proposed isotropy indices and the concept of full isotropy are extended toevaluate Stewart platform-based force sensor with arbitrary limbs. By using analytic approach, the isotropy performance of the traditional 6-6 Stewartplatform-based force sensor is studied in detail based on the modified isotropy indicessatisfying decoupling performance, the result indicates that it is impossible to realize fullisotropy in theory, and the best comprehensive isotropy performance is obtained bycompromising the isotropy indices. The isotropy performance of the 3-3/3-3 and 6/3-3Stewart platform-based force sensors are studied systematically. The analytic relations ofkey structural parameters leading to fully isotropic configuration are obtained, classes ofisotropic configurations can be easily obtained from the analytic results. The validsolutions and the valid range of the solutions are determined by using a numericalalgorithm. The numerical examples and fully isotropic structural examples are given.
A series of statically indeterminate pre-stressed six-axis force sensor are proposed.The force analysis of the statically indeterminate pre-stressed structure is carried out byconsidering the stiffness properties and compatibility in deformations, the analyticalrelationship between the axial force and the six-dimensional external force is obtained ina neat form. Furthermore, the statically indeterminate force-distribution difficult problemof Stewart platform with arbitrary limbs is solved thoroughly. On the basis of above, thedifference and relation between the deduced theoretical solution and the solution basedon force mapping matrix’s Moore-Penrose generalized inverse are analyzed andcompared detailedly. The solving formula based on Moore-Penrose generalized inverseincluding the effect of stiffness of all the limbs and force mapping matrix is given.
Systematic analysis of statically indeterminate pre-stressed Stewart platform-basedforce sensor is presented. The fully isotropic design of statically indeterminate Stewartplatform-based force sensor is completed, and the analytic relations of key structuralparameters leading to fully isotropic configuration are obtained. To ensure the structuralstability and measurement validity, the mathematical relation between the pre-tighteningforce and expected range of external loads is obtained by solving the conditionalextremum of the Lagrange function. The key structure parameters of sensor prototype aredetermined based on the deduced analytical expression leading to full isotropy. The detaildesign of the pre-stressing limb and the whole design of sensor prototype are completed,and the prototype of large range six-axis force sensor is manufactured.
The calibration methods of statically indeterminate six-axis force sensor arediscussed using linear and nonlinear scheme. A statically determinate calibration methodof statically indeterminate six-axis force sensor is proposed. The method based on neuralnetwork is introduced to calibrate the statically indeterminate six-axis force sensor. Thestatic calibration system of six axis force sensor is designed. The static calibration deviceis manufactured and the data acquisition hardware and software system is developed. Thestatic calibration experiments of sensor prototype are carried out, the comparison anddiscussion of the calibration results using the various calibration methods are presented.
By means of mechanism modeling method, finite element method and step responseexperiment method, the dynamic characteristic of sensor prototype is studied. Thedynamics theory model of sensor prototype is built. The non damping free vibrationequation of the sensor system is derived out, and the theoretical natural frequency andvibration mode of the prototype are given. The finite element model of sensor prototypeis built and the modal analysis is presented. The preliminary study of dynamic calibrationexperiment is carried out and the dynamic performance indices of the sensor prototypeare obtained.
引文
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