大型矿用齿轮箱运行模态识别与结构动力模型修正研究
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摘要
大型低速重载齿轮传动广泛应用于矿山、冶金工业生产的关键设备中,恶劣工况导致齿轮出现故障概率大,一旦突发事故,将导致整个流水线生产瘫痪或引发重大灾难性事故,目前对大型矿山机械结构动力模型大多是根据设计图建立的确定性模型,其中隐含了过多的假定和简化,使得结构动力特性的模态识别和分析与实际存在较大偏差,因此开展大型矿用齿轮箱运行模态识别方法与结构动力模型修正方法研究具有重要的理论意义和实际应用价值。本文以矿井提升机齿轮箱为对象,研究并提出了多激励下的运行模态识别方法；将随机动力学理论与运行模态识别理论相结合,提出了基于随机结合刚度的大型重载传动设备结构动力模型修正方法,并采用修正后的结构动力模型对齿轮箱动力可靠性应用分析,主要工作内容及成果如下：
(1)首次提出相对频响函数和虚拟频响函数的概念。通过理论推导得到相对频响函数的3个性质,即：在单一力对某一系统结构进行激励时,相对频响函数的零点即是该系统结构的极点；在单一力对某一系统结构进行激励时,在系统极点处,系统结构上任意指定的两点间的相对频响函数收敛于一定值,与这一输入点的力的方向和幅值无关；在多激励对某一系统结构进行激励时,在系统极点处,系统结构上任意指定的两点间的相对频响函数收敛于一定值,与任何输入的力的方向和幅值都无关。
(2)将已导出的相对频响函数3个性质引入到运行模态识别中,提出了多个未知激励下的运行模态识别方法。即当多个未知激励作用于系统结构时,在系统极点处,系统结构上指定的两点间的相对频响函数值与每个激振力无关,这两点间相对频响函数值为常量,而在非系统极点处相对频响函数则是随着激振力变化而不断变化的,其中未知激励可以是白噪声、各种谐波、变频激励以及其它任何方式的激励。
(3)通过将信息熵理论引入到小波模极大值去噪中,得出了一种基于小波熵的模极大值消噪方法。该方法利用小波能量熵理论自适应确定消噪阂值,根据噪声与真实信号在不同尺度上的小波模极大值呈现出的奇异性,去除随小波分解尺度增大而不断减小的小波模极大值,保留随尺度增大而增大的小波模极大值,并重构经有效过滤的剩余小波模极大值,实现强背景噪声下噪声信号与真实信号的有效分离。(4)通过谐波小波包变换及谐波小波包的共振解调,实现对大型矿用齿轮箱实际动力特性的识别。变换后分离出振动信号的调制信息,从而分析齿轮箱工作状态及损伤类型与程度；利用小波变换系数的实部和虚部,得到不同频段上矿用齿轮箱输入轴和输出轴相对相位,把输入轴和输出轴相对相位作为结构动力模型修正的目标参数。
(5)针对大型矿用齿轮箱动力有限元模型的建立,提出了机械结合面的建模方法。该方法在主体部分采用梁壳单元的基础上,各齿轮啮合、各轴承的滚动体与内外环联接的机械结合面处用等效弹簧和等效阻尼来代替。
(6)建立了基于结合刚度的模态频率灵敏度分析力学模型,将随机动力学理论引入到灵敏度分析模型修正方法中,提出了基于随机结合刚度的模态频率动力模型修正方法。对样本响应值进行统计分析得到模态频率的随机结合刚度灵敏度,并对比模态振型,修正相应的结合刚度,从而达到模型修正的目的。修正后对齿轮箱有限元模型进行实验验证,表明了基于随机结合刚度的模态频率动力模型修正方法有效性。
(7)将结构动力模型修正方法应用于齿轮箱动力可靠性分析,提出了基于结构动力模型修正的齿轮箱动力可靠性的研究方法。利用应力强度干涉理论,采用修正后的齿轮箱结构动力模型预测实际不可测点的振动响应,对齿轮箱的危险部位进行基于首次超越破坏机制的动力可靠性灵敏度分析和动力可靠度的分析,根据计算得到对齿轮箱动力可靠性影响最大的三个因素,即：齿轮传动副随机刚度、输入轴承水平方向随机刚度和输出轴上负载。
Large-scale, low-speed, heavy-duty gear transmission system is widely used in key equipment of mining, metallurgical industry production. The Gears have a tendency to fail in the severe working conditions. As the accident or catastrophic accident occurred, the entire assembly line production is probablely knocked out. Most structural dynamic models are deterministic models built according to the design for the mining machinery at present. The modal identification result of the model is very different from real structure, owing to a variety of assumptions and simplifications in the model. Therefore, it has important theoretical significance and practical value to carry out study on large-scale mine gearbox running modal identification methods and structural dynamic model updating method. In this paper, a operational modal identification method is proposed for mine hoister gearbox under multi-excitation; a structural dynamic model updating method is also proposed based on stochastic combining stiffness for large-scale and heavy-duty transmission equipment, by combining stochastic dynamics theory and operational modal identification theory, and the application analysis of gearbox dynamic reliability is based on the updated structural dynamic model. The main works and results are as follows:
(1) First proposed the concept of relative frequency response functions and virtual frequency response function. The three properties of relative frequency response function are proposed by theory deducing, namely:As there is only single exciting force in the structure system, the zero points of relative frequency response function is the system poles; As there is only single exciting force in the structure system, at the system poles, relative frequency response function between any given two points on the system structure converges to a certain value, which has nothing to do with the amplitude and direction of the exciting force; As there are multi-exciting force in the structure system, at the system poles, relative frequency response function between any given two points on the system structure also converges to a certain value, which has nothing to do with the amplitude and direction of the multi-exciting forces.
(2) A operational modal identification method are proposed under unknown multi-exciting forces, by applying three properties of relative frequency response function. That is, as there are multi-exciting forces in the structure system, at system poles, relative frequency response function between any given two points on the system structure also converges to a certain value, which has nothing to do with the amplitude and direction of each of multi-exciting forces, but at the non-system poles, relative frequency response function value between the given two points is changing with the exciting force changes. And unknown multi-exciting forces include white noise, harmonics, variable frequency excitation, and any other way of excitations.
(3) A de-noising method based on wavelet entropy modulus maxima is proposed by combining with the wavelet maximum modulus singularity theory and wavelet energy entropy theory. Using the characteristics that information entropy can be quantitatively described as energy probability distribution in time-frequency domain, the method of adaptively fixing the noise threshold based on wavelet entropy, can effectively remove the continuously decreasing wavelet maximum modulus with the wavelet decomposition scale increasing, can reserve the continuously increasing wavelet maximum modulus with the wavelet decomposition scale increasing, and reconstruct the remaining wavelet maximum modulus after the effectively filtering. The method effectively separated the real signal from the strong background noise.
(4)The actual dynamic characteristics of large-scale mine gearbox is identified by using harmonic wavelet packet transform and harmonic wavelet packet demodulated resonance.The modulated informations are separated from the vibration signal after transformation and the information are applied in analysis of work status, the type of injury and extent of injury for the gearbox. By extracting coefficient of the real and the imaginary in harmonic wavelet packet transform, the relative vibration directions of the input shaft and the output shaft is obtained, which is one of the model updating target parameters.
(5) A mechanical joint modeling method is proposed. The method used beam element and shell element in the gearbox main body, and used equivalent spring and equivalent damper instead of gear engagement, and the inner ring and outer ring connection of the mechanical junction surface.
(6) A mechanical model based on the combining stiffness is applied in modal frequency sensitivity analysis. Stochastic dynamics theory is introduced into the sensitivity analysis model updating method, and a modal frequency dynamic model updating method based on the stochastic combining stiffness is proposed. Obtained modal frequency sensitivity based on the combining stiffness, by analyzing the statistics of the sample response value,and updated corresponding combining stiffness, according to the comparison of mode shapes. It indicates that modal frequency model updating method based on stochastic combining stiffness is effective by experimental verification of the gearbox element model.
(7) Structural dynamic model updating method is applied to the gearbox dynamic reliability analysis, and based on the model updated a gearbox dynamic reliability research methods is proposed. By using of gearbox structural dynamic model updated, to predict the vibration response of the real unmeasured point, based on stress strength interference theory; and by analyzing dangerous position of the gearbox, the reliability sensitivity and dynamic reliability analysis is carried out based on the theory of First Passage Failure mechanism. According to solved results, obtained the most important three factors for gearbox dynamic reliability, namely:the stochastic stiffness of gear pairs, the stochastic stiffness of input bearing in horizontal direction and the load of output shaft.
(1)首次提出相对频响函数和虚拟频响函数的概念。通过理论推导得到相对频响函数的3个性质,即：在单一力对某一系统结构进行激励时,相对频响函数的零点即是该系统结构的极点；在单一力对某一系统结构进行激励时,在系统极点处,系统结构上任意指定的两点间的相对频响函数收敛于一定值,与这一输入点的力的方向和幅值无关；在多激励对某一系统结构进行激励时,在系统极点处,系统结构上任意指定的两点间的相对频响函数收敛于一定值,与任何输入的力的方向和幅值都无关。
(2)将已导出的相对频响函数3个性质引入到运行模态识别中,提出了多个未知激励下的运行模态识别方法。即当多个未知激励作用于系统结构时,在系统极点处,系统结构上指定的两点间的相对频响函数值与每个激振力无关,这两点间相对频响函数值为常量,而在非系统极点处相对频响函数则是随着激振力变化而不断变化的,其中未知激励可以是白噪声、各种谐波、变频激励以及其它任何方式的激励。
(3)通过将信息熵理论引入到小波模极大值去噪中,得出了一种基于小波熵的模极大值消噪方法。该方法利用小波能量熵理论自适应确定消噪阂值,根据噪声与真实信号在不同尺度上的小波模极大值呈现出的奇异性,去除随小波分解尺度增大而不断减小的小波模极大值,保留随尺度增大而增大的小波模极大值,并重构经有效过滤的剩余小波模极大值,实现强背景噪声下噪声信号与真实信号的有效分离。(4)通过谐波小波包变换及谐波小波包的共振解调,实现对大型矿用齿轮箱实际动力特性的识别。变换后分离出振动信号的调制信息,从而分析齿轮箱工作状态及损伤类型与程度；利用小波变换系数的实部和虚部,得到不同频段上矿用齿轮箱输入轴和输出轴相对相位,把输入轴和输出轴相对相位作为结构动力模型修正的目标参数。
(5)针对大型矿用齿轮箱动力有限元模型的建立,提出了机械结合面的建模方法。该方法在主体部分采用梁壳单元的基础上,各齿轮啮合、各轴承的滚动体与内外环联接的机械结合面处用等效弹簧和等效阻尼来代替。
(6)建立了基于结合刚度的模态频率灵敏度分析力学模型,将随机动力学理论引入到灵敏度分析模型修正方法中,提出了基于随机结合刚度的模态频率动力模型修正方法。对样本响应值进行统计分析得到模态频率的随机结合刚度灵敏度,并对比模态振型,修正相应的结合刚度,从而达到模型修正的目的。修正后对齿轮箱有限元模型进行实验验证,表明了基于随机结合刚度的模态频率动力模型修正方法有效性。
(7)将结构动力模型修正方法应用于齿轮箱动力可靠性分析,提出了基于结构动力模型修正的齿轮箱动力可靠性的研究方法。利用应力强度干涉理论,采用修正后的齿轮箱结构动力模型预测实际不可测点的振动响应,对齿轮箱的危险部位进行基于首次超越破坏机制的动力可靠性灵敏度分析和动力可靠度的分析,根据计算得到对齿轮箱动力可靠性影响最大的三个因素,即：齿轮传动副随机刚度、输入轴承水平方向随机刚度和输出轴上负载。
Large-scale, low-speed, heavy-duty gear transmission system is widely used in key equipment of mining, metallurgical industry production. The Gears have a tendency to fail in the severe working conditions. As the accident or catastrophic accident occurred, the entire assembly line production is probablely knocked out. Most structural dynamic models are deterministic models built according to the design for the mining machinery at present. The modal identification result of the model is very different from real structure, owing to a variety of assumptions and simplifications in the model. Therefore, it has important theoretical significance and practical value to carry out study on large-scale mine gearbox running modal identification methods and structural dynamic model updating method. In this paper, a operational modal identification method is proposed for mine hoister gearbox under multi-excitation; a structural dynamic model updating method is also proposed based on stochastic combining stiffness for large-scale and heavy-duty transmission equipment, by combining stochastic dynamics theory and operational modal identification theory, and the application analysis of gearbox dynamic reliability is based on the updated structural dynamic model. The main works and results are as follows:
(1) First proposed the concept of relative frequency response functions and virtual frequency response function. The three properties of relative frequency response function are proposed by theory deducing, namely:As there is only single exciting force in the structure system, the zero points of relative frequency response function is the system poles; As there is only single exciting force in the structure system, at the system poles, relative frequency response function between any given two points on the system structure converges to a certain value, which has nothing to do with the amplitude and direction of the exciting force; As there are multi-exciting force in the structure system, at the system poles, relative frequency response function between any given two points on the system structure also converges to a certain value, which has nothing to do with the amplitude and direction of the multi-exciting forces.
(2) A operational modal identification method are proposed under unknown multi-exciting forces, by applying three properties of relative frequency response function. That is, as there are multi-exciting forces in the structure system, at system poles, relative frequency response function between any given two points on the system structure also converges to a certain value, which has nothing to do with the amplitude and direction of each of multi-exciting forces, but at the non-system poles, relative frequency response function value between the given two points is changing with the exciting force changes. And unknown multi-exciting forces include white noise, harmonics, variable frequency excitation, and any other way of excitations.
(3) A de-noising method based on wavelet entropy modulus maxima is proposed by combining with the wavelet maximum modulus singularity theory and wavelet energy entropy theory. Using the characteristics that information entropy can be quantitatively described as energy probability distribution in time-frequency domain, the method of adaptively fixing the noise threshold based on wavelet entropy, can effectively remove the continuously decreasing wavelet maximum modulus with the wavelet decomposition scale increasing, can reserve the continuously increasing wavelet maximum modulus with the wavelet decomposition scale increasing, and reconstruct the remaining wavelet maximum modulus after the effectively filtering. The method effectively separated the real signal from the strong background noise.
(4)The actual dynamic characteristics of large-scale mine gearbox is identified by using harmonic wavelet packet transform and harmonic wavelet packet demodulated resonance.The modulated informations are separated from the vibration signal after transformation and the information are applied in analysis of work status, the type of injury and extent of injury for the gearbox. By extracting coefficient of the real and the imaginary in harmonic wavelet packet transform, the relative vibration directions of the input shaft and the output shaft is obtained, which is one of the model updating target parameters.
(5) A mechanical joint modeling method is proposed. The method used beam element and shell element in the gearbox main body, and used equivalent spring and equivalent damper instead of gear engagement, and the inner ring and outer ring connection of the mechanical junction surface.
(6) A mechanical model based on the combining stiffness is applied in modal frequency sensitivity analysis. Stochastic dynamics theory is introduced into the sensitivity analysis model updating method, and a modal frequency dynamic model updating method based on the stochastic combining stiffness is proposed. Obtained modal frequency sensitivity based on the combining stiffness, by analyzing the statistics of the sample response value,and updated corresponding combining stiffness, according to the comparison of mode shapes. It indicates that modal frequency model updating method based on stochastic combining stiffness is effective by experimental verification of the gearbox element model.
(7) Structural dynamic model updating method is applied to the gearbox dynamic reliability analysis, and based on the model updated a gearbox dynamic reliability research methods is proposed. By using of gearbox structural dynamic model updated, to predict the vibration response of the real unmeasured point, based on stress strength interference theory; and by analyzing dangerous position of the gearbox, the reliability sensitivity and dynamic reliability analysis is carried out based on the theory of First Passage Failure mechanism. According to solved results, obtained the most important three factors for gearbox dynamic reliability, namely:the stochastic stiffness of gear pairs, the stochastic stiffness of input bearing in horizontal direction and the load of output shaft.
引文
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