在线动平衡测试的相关信号处理与标定算法研究
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摘要
在高速数控机床的单元技术领域中,加快研究电主轴的在线自动平衡技术,不仅会促进我国高速加工技术的发展,而且具有极其重要的科学意义、工业价值和经济价值。在线主动平衡技术是一个涉及计算机控制、传感器技术、测试技术、数字信号处理技术等多学科交叉的复杂问题,设计合理高效的信号处理算法,提取动不平衡信号并进行不平衡量标定是实现高精度在线动平衡的关键。本课题在国家科技重大专项的资助下,对在线动平衡测试中的不平衡动态响应分析、测试方法、测试信号处理、测试系统标定等核心问题开展研究,主要完成的工作如下：
1、主轴系统不平衡的动态响应分析
根据主轴系统动力学方程,构建主轴系统有限元动力学的实体模型,对主轴系统进行结构模态分析,揭示主轴系统在自由模态下的动力特性。在此基础上通过动力学模型的理论求解和有限元模型的仿真分析,计算了电主轴在不平衡量作用下的传递特性,分析了主轴系统对不平衡引起的动力响应特性以及不同不平衡量的振动响应变化规律。理论求解和数值仿真的结论同时表明：转速不变,阻尼一定时,电主轴不平衡动态响应是与转速同频的简谐振动,且振幅大小与不平衡量成正比。
2、电主轴振动信号的成分分析与趋势项处理
根据在线动平衡测试的原理,对比分析了适合于系统信号采集的几种传感器的原理和特性,并对系统所需的基准信号和振动信号的获取和处理方式分别进行了详细论述。考虑到由于零点漂移等问题,会使加速度信号时域积分后产生趋势项。因此,论文在最小二乘拟合法的基础上,提出了消除趋势项的加速度信号时域积分算法,并通过仿真进行分析验证,为后续的动不平衡信号的特征提取奠定了必要的基础。
3、动不平衡信号及其特征参数的提取算法
针对电主轴振动信号低信噪比、强干扰的特点,设计并验证了两种不平衡信号幅值和相位提取的方法。注意到常规互相关分析提取相位时,会因量化误差和近频干扰而降低相位提取精度,论文提出了一种基于改进的互相关分析的不平衡信号提取方法。在两级FIR滤波器消噪和利用减法运算衰减大幅值信号后,再对互相关运算提取相位和幅值的算法进行了修改简化。实验验证该方法在提取振动信号幅值和相位的精度上比之常规互相关方法有明显改善。
研究表明,自适应冗余第二代小波能有效抑制频率混叠现象,在此基础上,本文提出了一种自适应冗余第二代小波与双变量改进阈值函数相结合的振动信号消噪方法，并通过仿真实验对比分析了不同阈值函数变量参数的取值对信号消噪优劣的影响,验证了双变量改进阈值函数给消噪效果带来的改进。
4、基于改进影响系数法的在线动平衡测试系统标定方法
在分析理想状态下动平衡测试标定模型的基础上,深入剖析了测试系统的主要误差对标定的影响。从三种误差的特性入手,引入一元线性回归理论,提出了具有误差修正功能的影响系数标定模型,并设计了快速收敛的不平衡量标定算法,满足在线动平衡实时性要求。利用同一组标定数据,分别采用常规的影响系数方法和基于一元回归理论的影响系数方法对系统进行标定,对比分析的结果验证了本论文方法的有效性和优越性。
5、在线动平衡测试原型系统
在上述研究的基础上,逐步完善系统软硬件结构,并构建较为成熟的原型系统,经实验验证其满足了电主轴在线动平衡测试的功能和性能要求。
In order to realize the high speed, high efficiency, high precision machining, the most suitable spindle shape of CNC is directly putting stator and rotor into the interior of spindle unit, which forms an integrated structure of that motor rotor is the spindle and the shell of sprindle unit is motor base. The spindle unit is segregates from drive system and integral structure, called motor spindle. In the technology field of motor spindle, it is vital to speed up researching online dynamic balance technology for the development of high-speed and high-precision CNC. The online dynamic balance technology is a complicated problem which includes multidiscipline knowledge, the key of the online dynamic balance technology is designing reasonable and efficient signal processing algorithm, extracting dynamic unbalance signal and calibrating the amount of imbalance. The subject, funded by National Science and Technology Major Project, applying computer control technology and DSP, researches unbalance dynamic response analysis, test method, test signal processing and calibration for test signal of online dynamic balance. The main work is followed.
1. the imbalance dynamic response analysis of the motor spindle
The paper, according to the kinetic equation of motor spindle, constructs finite element solid model and completes the modal analysis, reveals the kinetic characteristics in free modal of motor spindle. Through theoretical solution of kinetic model and simulation analysis of finite element model(FEM), the paper calculates the transfer characteristic of motor spindle in the function of the amount of unbalance, analyses kinetic response characteristics caused by imbalance and the changing rule of vibration response because of different amount of unbalance. The conclusion of theoretical solution and digital simulation simultaneously show that when rotate speed and damp are constant, dynamic response of unbalance is simple harmonic vibration, which is equal to the frequency of rotate speed and the amplitude is proportional to the imbalance amount.
2. the component anaryzing and trend term processing of the vibration signal of motor spindle
The paper, according to the theory of online dynamic balance testing, comparatively analyses the theory and characteristics of several sensors, discusses the gain and process method of reference signal and vibration signal in great detail. Because of zero drift, acceleration signal integral in time-domain will generate trend term. So the paper puts forward a time domain integral algorithm of acceleration signal to eliminate the trend term and proves its effectiveness through simulation, which lays necessary foundation for the subsequent characteristics extraction of dynamic unbalance signal.
3. the extraction and process of the dynamic unbalance signal
The vibration signal of motor spindle is low SNR and with strong interference, the paper designs and verifies two methods for extracting the amplitude and phase of unbalance signal. Pay attention to the low precision of conventional cross-correlation extraction of phase, which is caused by quantization error and nearly frequency interference, the paper puts forward a kind of improved signal extraction method based on cross-correlation. The method modifies and simplifies the algorithm of cross-correlation operation. The experiment verifies that this method obviously improves the extraction precision of amplitude and phase of vibration signal.
The research shows that adaptive redundant second generation wavelet can effectively restrain frequency aliasing. On that basis, the paper comes up with a new algorithm of vibration signal de-noising, which combins adaptive redundant second generation wavelet with double variable improved threshold function. The simulation verifies the improvement of signal de-nosing effect resulted by bringing into double variable improved threshold function.
4. the calibration algorithm of online dynamic balance testing system based on improved influence coefficient method.
On the basis of the analysis of dynamic balance testing calibration model in ideal situation, the paper analyses the influence on calibration because of the main error of measurement. Starting with the three kind of error characteristics, the paper introduces simple linear regression theory and puts forward an influence coefficient calibration model with error correction function, and designs a amount of unbalance calibration algorithm which is rapid convergence and meets real-time requirement of online dynamic balance. Using the same calibration data, the system is separately demarcated by conventional influence coefficient method and the evolutionary influence coefficient method based on simple linear regression theory. The results show the validity and superiority.
5. online dynamic balance testing prototype system
Based on the above research, the paper improves gradually software and hardware of system and builds a prototype system which satisfy the function and characteristics requirements of the online dynamic balance of motor spindle.
1、主轴系统不平衡的动态响应分析
根据主轴系统动力学方程,构建主轴系统有限元动力学的实体模型,对主轴系统进行结构模态分析,揭示主轴系统在自由模态下的动力特性。在此基础上通过动力学模型的理论求解和有限元模型的仿真分析,计算了电主轴在不平衡量作用下的传递特性,分析了主轴系统对不平衡引起的动力响应特性以及不同不平衡量的振动响应变化规律。理论求解和数值仿真的结论同时表明：转速不变,阻尼一定时,电主轴不平衡动态响应是与转速同频的简谐振动,且振幅大小与不平衡量成正比。
2、电主轴振动信号的成分分析与趋势项处理
根据在线动平衡测试的原理,对比分析了适合于系统信号采集的几种传感器的原理和特性,并对系统所需的基准信号和振动信号的获取和处理方式分别进行了详细论述。考虑到由于零点漂移等问题,会使加速度信号时域积分后产生趋势项。因此,论文在最小二乘拟合法的基础上,提出了消除趋势项的加速度信号时域积分算法,并通过仿真进行分析验证,为后续的动不平衡信号的特征提取奠定了必要的基础。
3、动不平衡信号及其特征参数的提取算法
针对电主轴振动信号低信噪比、强干扰的特点,设计并验证了两种不平衡信号幅值和相位提取的方法。注意到常规互相关分析提取相位时,会因量化误差和近频干扰而降低相位提取精度,论文提出了一种基于改进的互相关分析的不平衡信号提取方法。在两级FIR滤波器消噪和利用减法运算衰减大幅值信号后,再对互相关运算提取相位和幅值的算法进行了修改简化。实验验证该方法在提取振动信号幅值和相位的精度上比之常规互相关方法有明显改善。
研究表明,自适应冗余第二代小波能有效抑制频率混叠现象,在此基础上,本文提出了一种自适应冗余第二代小波与双变量改进阈值函数相结合的振动信号消噪方法，并通过仿真实验对比分析了不同阈值函数变量参数的取值对信号消噪优劣的影响,验证了双变量改进阈值函数给消噪效果带来的改进。
4、基于改进影响系数法的在线动平衡测试系统标定方法
在分析理想状态下动平衡测试标定模型的基础上,深入剖析了测试系统的主要误差对标定的影响。从三种误差的特性入手,引入一元线性回归理论,提出了具有误差修正功能的影响系数标定模型,并设计了快速收敛的不平衡量标定算法,满足在线动平衡实时性要求。利用同一组标定数据,分别采用常规的影响系数方法和基于一元回归理论的影响系数方法对系统进行标定,对比分析的结果验证了本论文方法的有效性和优越性。
5、在线动平衡测试原型系统
在上述研究的基础上,逐步完善系统软硬件结构,并构建较为成熟的原型系统,经实验验证其满足了电主轴在线动平衡测试的功能和性能要求。
In order to realize the high speed, high efficiency, high precision machining, the most suitable spindle shape of CNC is directly putting stator and rotor into the interior of spindle unit, which forms an integrated structure of that motor rotor is the spindle and the shell of sprindle unit is motor base. The spindle unit is segregates from drive system and integral structure, called motor spindle. In the technology field of motor spindle, it is vital to speed up researching online dynamic balance technology for the development of high-speed and high-precision CNC. The online dynamic balance technology is a complicated problem which includes multidiscipline knowledge, the key of the online dynamic balance technology is designing reasonable and efficient signal processing algorithm, extracting dynamic unbalance signal and calibrating the amount of imbalance. The subject, funded by National Science and Technology Major Project, applying computer control technology and DSP, researches unbalance dynamic response analysis, test method, test signal processing and calibration for test signal of online dynamic balance. The main work is followed.
1. the imbalance dynamic response analysis of the motor spindle
The paper, according to the kinetic equation of motor spindle, constructs finite element solid model and completes the modal analysis, reveals the kinetic characteristics in free modal of motor spindle. Through theoretical solution of kinetic model and simulation analysis of finite element model(FEM), the paper calculates the transfer characteristic of motor spindle in the function of the amount of unbalance, analyses kinetic response characteristics caused by imbalance and the changing rule of vibration response because of different amount of unbalance. The conclusion of theoretical solution and digital simulation simultaneously show that when rotate speed and damp are constant, dynamic response of unbalance is simple harmonic vibration, which is equal to the frequency of rotate speed and the amplitude is proportional to the imbalance amount.
2. the component anaryzing and trend term processing of the vibration signal of motor spindle
The paper, according to the theory of online dynamic balance testing, comparatively analyses the theory and characteristics of several sensors, discusses the gain and process method of reference signal and vibration signal in great detail. Because of zero drift, acceleration signal integral in time-domain will generate trend term. So the paper puts forward a time domain integral algorithm of acceleration signal to eliminate the trend term and proves its effectiveness through simulation, which lays necessary foundation for the subsequent characteristics extraction of dynamic unbalance signal.
3. the extraction and process of the dynamic unbalance signal
The vibration signal of motor spindle is low SNR and with strong interference, the paper designs and verifies two methods for extracting the amplitude and phase of unbalance signal. Pay attention to the low precision of conventional cross-correlation extraction of phase, which is caused by quantization error and nearly frequency interference, the paper puts forward a kind of improved signal extraction method based on cross-correlation. The method modifies and simplifies the algorithm of cross-correlation operation. The experiment verifies that this method obviously improves the extraction precision of amplitude and phase of vibration signal.
The research shows that adaptive redundant second generation wavelet can effectively restrain frequency aliasing. On that basis, the paper comes up with a new algorithm of vibration signal de-noising, which combins adaptive redundant second generation wavelet with double variable improved threshold function. The simulation verifies the improvement of signal de-nosing effect resulted by bringing into double variable improved threshold function.
4. the calibration algorithm of online dynamic balance testing system based on improved influence coefficient method.
On the basis of the analysis of dynamic balance testing calibration model in ideal situation, the paper analyses the influence on calibration because of the main error of measurement. Starting with the three kind of error characteristics, the paper introduces simple linear regression theory and puts forward an influence coefficient calibration model with error correction function, and designs a amount of unbalance calibration algorithm which is rapid convergence and meets real-time requirement of online dynamic balance. Using the same calibration data, the system is separately demarcated by conventional influence coefficient method and the evolutionary influence coefficient method based on simple linear regression theory. The results show the validity and superiority.
5. online dynamic balance testing prototype system
Based on the above research, the paper improves gradually software and hardware of system and builds a prototype system which satisfy the function and characteristics requirements of the online dynamic balance of motor spindle.
引文
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