动平衡测量的若干关键技术问题研究
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摘要
转子的动平衡性能是电机使用寿命、工作噪声以及能耗的决定性因素之一随着电机转速的日益提高,对电机转子的动平衡性能的要求也越来越严苛,对动平衡机测量系统的精度要求也不断提高。目前,测量系统的精度不高成了国产动平衡产品质量提升的瓶颈问题。由于系统测量误差的可消除性和随机测量误差对测量结果影响的可估计性,采用系统误差的实时修正和随机误差影响的实时评估技术是提高测量系统精度的有效且经济的途径。鉴于动平衡测量过程的系统误差主要体现为影响系数的估计精度,本文研究成果主要体现在以下几个方面：
(1)采用重新标定的方法对测量系统进行校准,针对采用经典统计原理处理标定数据中试重的振动响应测量值的样本数量与停工工时之间的矛盾,提出了基于层次贝叶斯方法的标定数据的处理方法。充分利用试重振动响应和测量方差的先验信息,建立了不同试重水平下振动响应真值和测量方差的联合分布模型,以体现测量方差对振动响应真值估计的影响。并采用马尔科夫链蒙特卡罗(MCMC)方法中的Gibbs抽样法求取其最大后验估计,降低了标定数据估计精度对样本数量的依赖性,实现了小样本条件下标定数据的准确估计,缩短了重新标定所消耗的工时,减少了生产线停工给企业带来的经济损失。
(2)鉴于在生产过程中可以获得高精度的标准测量数据,提出了基于改进卡尔曼滤波的动平衡测量过程的在线校准方法。针对传统的过程状态估计方法在小样本情况下缺乏兼顾追踪状态变化和抑制随机误差干扰的能力,提出了卡尔曼滤波与多元统计过程控制相结合的过程状态调节方法。通过χ2统计量对观测残差进行监控,当测量过程处于可控状态时,采用经典卡尔曼滤波方法以充分利用其抑制随机测量误差的能力；反之,通过χ2统计量对状态预测协方差矩阵进行主动调节,以增强其追踪状态变化的能力；合理地权衡了追踪状态变化和抑制随机误差二者之间的矛盾,提高了测量过程校准的鲁棒性。
(3)鉴于ISO-GUM所提供的测量不确定度评定方法不能解决动平衡测量过程的非线性,也不能体现测量系统寿命周期内的动态性的问题,提出了动平衡测量系统动态不确定度的评定方法。建立了不平衡量与振动响应和影响系数之间的概率传递关系,并以Monte Carlo方法为计算工具确定不平衡量的概率分布。同时,通过对振动响应随机测量方差以及影响系数的动态估计,将测量系统的动态信息融合到测量不确定度的评定中,实现了在测量系统全寿命周期内测量不确定度的精确评价。
(4)针对测量不确定度导致的“误收”和“误废”决策,提出了基于贝叶斯最小决策成本准则的转子动平衡性能评价方法。将决策成本、生产过程波动等信息融合到决策模型中,同时通过贝叶斯统计估计对生产过程的波动进行动态估计,最终提高了质量决策的可靠性。
Dynamic balancing performance is the determinant factor for the service life, working noise and energy consumption of motors. With the increasing of motor rotating speed, the requirements on motor dynamic balancing performance are more and more stringent, which then demands more accurate dynamic balancing machines. Currently, the poor accuracy of the measurement system on domestic dynamic balancing products is the bottleneck to improve their quality of. Due to the fact that system measurement error can be eliminated and the influence of random measurement error on measurement results can be estimated, the most economic and effective way to improve the accuracy of measurement systems is to adopt real time system error elimination technology and to real time evaluate the influence of random error on measurement error. The system error of dynamic balancing measurement process was featured by the estimating accuracy of influence coefficients. Aiming at this situation, the main contributions are listed below:
(1) Under the circumstance that recalibration was adopted to periodically calibrate measurement systems, aiming at the conflict between the number of samples of vibration responses of trial weights and the stoppage time of product assembly line, a hierarchical Bayesian method for dealing with calibration data was proposed. Through this method, the prior information of the vibration responses of trial weights and their estimation variance was sufficiently employed. The joint distribution model of vibration responses and their measurement variance was established to embody the influence of measurement error on the estimator of the true value of vibration responses; furthermore, the Gibbs sampling method of Markov Chain Monte Carlo (MCMC) method was used to obtain their maximum posterior estimation. This method reduced the dependency of estimation accuracy of calibration data on the number of samples and implemented accurate estimation of calibration data under the circumstance of small sample. This could reduce the time of the calibration process and then decrease the loss resulting from the stoppage of the whole assembly line.
(2) When standard measurement data with higher accuracy was available, an improved Kalman filtering method for the regulation of dynamic balancing measurement process was presented. Aiming at the drawback that conventional state estimation method could not give attention to both the ability of track state change and the ability of suppress the disturbance of random measurement errors, Kalman filtering was combined with multivariate statistical process control. The measurement residual was monitored by theχ2 value. When the measurement process was under control, normal Kalman filtering was adopted to make the best use of its ability in suppressing random measurement errors; when the measurement process was out of control, theχ2 value was used to actively regulate the state prediction covariance to enhance the ability of track state change of Kalman filtering, which made the best tradeoff the conflict between tracking state change and suppressing random errors and improved the robustness of process regulation method.
(3) Aiming at the problem that the method provided by ISO-GUM was incapable in solving the nonlinearity of dynamic balancing measurement process and embodying the dynamics of measurement systems in their lifecycle, a dynamic measurement uncertainty evaluation method for dynamic balancing measurement systems was proposed. By establishing the probability propagation relationship between unbalance and its vibration response, the distribution of unbalance was determined, which took the Monte Carlo method as calculating tools. Meantime, through the dynamic estimation of influence coefficients and the statistical characteristics of random measurement error of vibration responses, the dynamic information of the measurement system was fused into the process of evaluating measurement uncertainty. Ultimately, the accurate evaluation of measurement uncertainty during the lifecycle of measurement systems was achieved.
(4) Regarding to the two wrong decisions of accepting a bad rotor and rejecting a good rotor due to measurement uncertainty, an evaluating method of rotor dynamic balancing performance based on Bayesian minimum decision cost method was proposed. This method adopted the information of the variation of manufacturing processes and decision cost into the decision model, which provided more reference for decision-makers. Meantime, to guarantee the correctness of the above information, the statistical characteristics of the variation of manufacturing process were dynamically estimated by Bayesian statistical estimation method. And finally the reliability of quality decision was improved.
(1)采用重新标定的方法对测量系统进行校准,针对采用经典统计原理处理标定数据中试重的振动响应测量值的样本数量与停工工时之间的矛盾,提出了基于层次贝叶斯方法的标定数据的处理方法。充分利用试重振动响应和测量方差的先验信息,建立了不同试重水平下振动响应真值和测量方差的联合分布模型,以体现测量方差对振动响应真值估计的影响。并采用马尔科夫链蒙特卡罗(MCMC)方法中的Gibbs抽样法求取其最大后验估计,降低了标定数据估计精度对样本数量的依赖性,实现了小样本条件下标定数据的准确估计,缩短了重新标定所消耗的工时,减少了生产线停工给企业带来的经济损失。
(2)鉴于在生产过程中可以获得高精度的标准测量数据,提出了基于改进卡尔曼滤波的动平衡测量过程的在线校准方法。针对传统的过程状态估计方法在小样本情况下缺乏兼顾追踪状态变化和抑制随机误差干扰的能力,提出了卡尔曼滤波与多元统计过程控制相结合的过程状态调节方法。通过χ2统计量对观测残差进行监控,当测量过程处于可控状态时,采用经典卡尔曼滤波方法以充分利用其抑制随机测量误差的能力；反之,通过χ2统计量对状态预测协方差矩阵进行主动调节,以增强其追踪状态变化的能力；合理地权衡了追踪状态变化和抑制随机误差二者之间的矛盾,提高了测量过程校准的鲁棒性。
(3)鉴于ISO-GUM所提供的测量不确定度评定方法不能解决动平衡测量过程的非线性,也不能体现测量系统寿命周期内的动态性的问题,提出了动平衡测量系统动态不确定度的评定方法。建立了不平衡量与振动响应和影响系数之间的概率传递关系,并以Monte Carlo方法为计算工具确定不平衡量的概率分布。同时,通过对振动响应随机测量方差以及影响系数的动态估计,将测量系统的动态信息融合到测量不确定度的评定中,实现了在测量系统全寿命周期内测量不确定度的精确评价。
(4)针对测量不确定度导致的“误收”和“误废”决策,提出了基于贝叶斯最小决策成本准则的转子动平衡性能评价方法。将决策成本、生产过程波动等信息融合到决策模型中,同时通过贝叶斯统计估计对生产过程的波动进行动态估计,最终提高了质量决策的可靠性。
Dynamic balancing performance is the determinant factor for the service life, working noise and energy consumption of motors. With the increasing of motor rotating speed, the requirements on motor dynamic balancing performance are more and more stringent, which then demands more accurate dynamic balancing machines. Currently, the poor accuracy of the measurement system on domestic dynamic balancing products is the bottleneck to improve their quality of. Due to the fact that system measurement error can be eliminated and the influence of random measurement error on measurement results can be estimated, the most economic and effective way to improve the accuracy of measurement systems is to adopt real time system error elimination technology and to real time evaluate the influence of random error on measurement error. The system error of dynamic balancing measurement process was featured by the estimating accuracy of influence coefficients. Aiming at this situation, the main contributions are listed below:
(1) Under the circumstance that recalibration was adopted to periodically calibrate measurement systems, aiming at the conflict between the number of samples of vibration responses of trial weights and the stoppage time of product assembly line, a hierarchical Bayesian method for dealing with calibration data was proposed. Through this method, the prior information of the vibration responses of trial weights and their estimation variance was sufficiently employed. The joint distribution model of vibration responses and their measurement variance was established to embody the influence of measurement error on the estimator of the true value of vibration responses; furthermore, the Gibbs sampling method of Markov Chain Monte Carlo (MCMC) method was used to obtain their maximum posterior estimation. This method reduced the dependency of estimation accuracy of calibration data on the number of samples and implemented accurate estimation of calibration data under the circumstance of small sample. This could reduce the time of the calibration process and then decrease the loss resulting from the stoppage of the whole assembly line.
(2) When standard measurement data with higher accuracy was available, an improved Kalman filtering method for the regulation of dynamic balancing measurement process was presented. Aiming at the drawback that conventional state estimation method could not give attention to both the ability of track state change and the ability of suppress the disturbance of random measurement errors, Kalman filtering was combined with multivariate statistical process control. The measurement residual was monitored by theχ2 value. When the measurement process was under control, normal Kalman filtering was adopted to make the best use of its ability in suppressing random measurement errors; when the measurement process was out of control, theχ2 value was used to actively regulate the state prediction covariance to enhance the ability of track state change of Kalman filtering, which made the best tradeoff the conflict between tracking state change and suppressing random errors and improved the robustness of process regulation method.
(3) Aiming at the problem that the method provided by ISO-GUM was incapable in solving the nonlinearity of dynamic balancing measurement process and embodying the dynamics of measurement systems in their lifecycle, a dynamic measurement uncertainty evaluation method for dynamic balancing measurement systems was proposed. By establishing the probability propagation relationship between unbalance and its vibration response, the distribution of unbalance was determined, which took the Monte Carlo method as calculating tools. Meantime, through the dynamic estimation of influence coefficients and the statistical characteristics of random measurement error of vibration responses, the dynamic information of the measurement system was fused into the process of evaluating measurement uncertainty. Ultimately, the accurate evaluation of measurement uncertainty during the lifecycle of measurement systems was achieved.
(4) Regarding to the two wrong decisions of accepting a bad rotor and rejecting a good rotor due to measurement uncertainty, an evaluating method of rotor dynamic balancing performance based on Bayesian minimum decision cost method was proposed. This method adopted the information of the variation of manufacturing processes and decision cost into the decision model, which provided more reference for decision-makers. Meantime, to guarantee the correctness of the above information, the statistical characteristics of the variation of manufacturing process were dynamically estimated by Bayesian statistical estimation method. And finally the reliability of quality decision was improved.
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