基于压电作动器的齿轮传动系统振动主动控制及算法研究
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摘要
齿轮系统的振动不但会产生噪声和导致传动系统的不稳定，而且会加速传动系统的疲劳损害，使其失效进而产生严重后果。齿轮作为机械传动中的通用基础件，降低其振动噪声对于减少齿轮箱故障、改善工作环境具有重要工程意义。目前齿轮系统的振动噪声控制主要采取被动方式，包括齿轮修形优化、调整转子质量或刚度来改变其动力特性等。为了抑制齿轮啮合误差引起的周期振动噪声，本文结合压电智能材料的应用，将主动控制技术应用在齿轮传动啮合振动主动控制中，基于主动控制轴横向振动的思想，采用主动控制结构，使主动控制力以更直接的方式来控制齿轮啮合点由于传动误差激励而引起的振动，进而达到控制齿轮传动系统振动噪声的目的。论文主要工作如下：
1)为了分析齿轮系统在啮合力的作用下产生的动态响应，首先建立齿轮系统的动力学模型，应用集中质量法建立了由一对渐开线直齿圆柱齿轮组成的传动系统三自由度数学模型，在此模型基础上分析了激励频率和负载对齿轮传动系统动态响应的影响。利用压电堆作动器作为振动主动控制的执行器，提出了用于振动主动控制的齿轮箱主动结构方案。
2)针对影响压电陶瓷作动器输出精度的滞回非线性问题，提出能够精确描述其滞回非线性特性的数学模型，分别采用Preisach模型和PI模型对压电作动器的滞回非线性进行建模，对压电堆的输出特性进行了仿真；在此基础上提出一种开环逆控制方法，应用PI逆模型作为控制器来补偿滞回非线性。仿真结果表明控制器的设计保证了系统的稳定，并有效抑制了压电作动器滞回非线性的影响。
3)为了有效抑制齿轮传动系统由于啮合误差引起的周期振动，采用一种基于自适应滤波算法的振动主动控制方案。分别应用M文件型Level-2S函数和C-MEX S函数编写FxLMS自适应控制算法模块；通过算例验证了控制算法模块的正确性。在保证控制系统的稳定和快速收敛的前提下，深入讨论了用于周期性信号的振动主动控制FxLMS算法收敛条件，并对影响算法性能的内部因素进行了分析，同时分析了在次级通道辨识有误差和延迟的情况下算法的性能，为在实际应用中保证算法收敛并达到最佳控制效果提供重要理论依据。
4)在ADAMS环境下建立了齿轮传动系统虚拟样机，将其作为被控对象子模块，添加到Simulink环境中建立的FxLMS控制系统中，建立起完整的齿轮传动振动主动控制联合仿真系统。联合仿真验证了所建模型以及控制算法的正确性。
5)最后根据所提出的齿轮传动系统振动主动控制方法，构建了齿轮箱与压电堆作动器、传感器和控制器等必要的软、硬件构成的振动主动控制实验系统，进行了快速控制原型半实物实验：通过基于级联自适应陷波器技术提取齿轮啮合振动信号频率进而合成参考信号，利用归一化LMS自适应滤波器对包含压电堆作动器的次级通道进行离线辨识实验，得到次级通道的传递函数；最后将算法代码下载到dSPACE中作为控制器，与内置压电堆作动器的齿轮箱实验台组成快速控制原型进行实验验证。结果表明：由FxLMS算法控制的压电堆作动器对齿轮的啮合振动主动控制效果明显，在不同转速、不同负载情况下啮合振动有15dB-26dB的衰减。实验结果验证了本文提出的齿轮系统主动结构的正确性以及所建控制模块的有效性。
Gearing system is the most important component of rotating machinery and powertransmis-sion device. Due to manufacturing error, meshing impact and some otherinfluence, vibration of the gear pair will be generated in the engaging process. With theexpansion of the tooth surface, the tooth shape error, base pitch error and backlash will bealso increased, which deteriorates the gear transmission. The vibration of the gear systemcan not only produce noise, but also accelerate fatigue of the transmission system.Besides, gear box is the key part of a helicopter of transmission system, which cannotreduce accidents through the redundancy backup, gearbox fault, and it’s a direct threattowards a helicopter flight safety. Typical gearbox vibration contains several tonal signalsmixed with a broadband response. The tonal signals are basically the fundamental gearmesh frequency and their corresponding harmonics generated from the perturbation in thegear meshing process, in which the fundamental gear mesh frequency is the main cause ofthe annoyance problem. In order to suppress this part of the vibration and noise, an activegearbox vibration control structure is developed experimentally to suppress gearboxvibration due to transmission error excitation. At the same time, a filtered-x LMS controlalgorithm is proposed and implemented to generate the appropriate control signals.
At first, a gear pair system model is built to assist in the design of the experimentalactive structure, to gain a better understanding of the nature of gear response due totransmission error excitation. Based on an active shaft transverse vibration controlconcept, an active internal gearbox structure, combined with the piezoelectric actuator, isdeveloped to suppress gear pair vibration due to transmission error excitation in a directway.
Complex nonlinear hysteresis is present in virtually all piezoelectric actuators. Thesenonlinearities can excite unwanted dynamics which reduced system performance andeven lead to unstable system operation, especially in active vibration control applicationsowing to phase lag. The paper describes a compensator design method for invertiblecomplex hysteretic nonlinearities based on Prandtl-Ishlinskii hysteresis operator. Linearinequality constraints for the parameters guarantee the unique solvability of theidentification problem and the invertability of the identified model. The correspondingcompensator can be directly calculated and thus efficiently implemented from the modelby analytical transformation laws. This allows an efficient implementation of the compensator for real-time control. Finally，the compensator design method is used togenerate an inverse feed forward controller, results of simulation proved the method'savailability.
Active vibration control use an active anti-force from secondary path to suppress orattenuate vibration and noises，one of the control algorithms is filtered-x least meansquare (FxLMS) adaptive algorithm. Based on structure of FxLMS algorithm, Level-2S-function is used to build a new FxLMS blocks in MATLAB/Simulink and apply it inoffline vibration active control system simulation. On the condition of convergence,performance analysis is given by adjusting the interior parameters to test the controlalgorithm block. Finally, the custom FxLMS block is downloaded to DSpace as controller,and used in hardware-in-the-loop simulation of active vibration control on a geartransmission system. Results verify the custom FxLMS block’s feasibility built byLevel-2S-function and control algorithm’s efficiency.
A gearbox test-bed is also developed with a piezoelectric actuator inside for applyingcontrol forces to the shaft. Lastly, the custom FxLMS block is downloaded to DSpace ascontroller. Experiment results showe that the proposed FxLMS controller performs aneffective performance. Up to35dB of gearbox vibration has been attenuated at somefundamental gear mesh frequency.
1)为了分析齿轮系统在啮合力的作用下产生的动态响应，首先建立齿轮系统的动力学模型，应用集中质量法建立了由一对渐开线直齿圆柱齿轮组成的传动系统三自由度数学模型，在此模型基础上分析了激励频率和负载对齿轮传动系统动态响应的影响。利用压电堆作动器作为振动主动控制的执行器，提出了用于振动主动控制的齿轮箱主动结构方案。
2)针对影响压电陶瓷作动器输出精度的滞回非线性问题，提出能够精确描述其滞回非线性特性的数学模型，分别采用Preisach模型和PI模型对压电作动器的滞回非线性进行建模，对压电堆的输出特性进行了仿真；在此基础上提出一种开环逆控制方法，应用PI逆模型作为控制器来补偿滞回非线性。仿真结果表明控制器的设计保证了系统的稳定，并有效抑制了压电作动器滞回非线性的影响。
3)为了有效抑制齿轮传动系统由于啮合误差引起的周期振动，采用一种基于自适应滤波算法的振动主动控制方案。分别应用M文件型Level-2S函数和C-MEX S函数编写FxLMS自适应控制算法模块；通过算例验证了控制算法模块的正确性。在保证控制系统的稳定和快速收敛的前提下，深入讨论了用于周期性信号的振动主动控制FxLMS算法收敛条件，并对影响算法性能的内部因素进行了分析，同时分析了在次级通道辨识有误差和延迟的情况下算法的性能，为在实际应用中保证算法收敛并达到最佳控制效果提供重要理论依据。
4)在ADAMS环境下建立了齿轮传动系统虚拟样机，将其作为被控对象子模块，添加到Simulink环境中建立的FxLMS控制系统中，建立起完整的齿轮传动振动主动控制联合仿真系统。联合仿真验证了所建模型以及控制算法的正确性。
5)最后根据所提出的齿轮传动系统振动主动控制方法，构建了齿轮箱与压电堆作动器、传感器和控制器等必要的软、硬件构成的振动主动控制实验系统，进行了快速控制原型半实物实验：通过基于级联自适应陷波器技术提取齿轮啮合振动信号频率进而合成参考信号，利用归一化LMS自适应滤波器对包含压电堆作动器的次级通道进行离线辨识实验，得到次级通道的传递函数；最后将算法代码下载到dSPACE中作为控制器，与内置压电堆作动器的齿轮箱实验台组成快速控制原型进行实验验证。结果表明：由FxLMS算法控制的压电堆作动器对齿轮的啮合振动主动控制效果明显，在不同转速、不同负载情况下啮合振动有15dB-26dB的衰减。实验结果验证了本文提出的齿轮系统主动结构的正确性以及所建控制模块的有效性。
Gearing system is the most important component of rotating machinery and powertransmis-sion device. Due to manufacturing error, meshing impact and some otherinfluence, vibration of the gear pair will be generated in the engaging process. With theexpansion of the tooth surface, the tooth shape error, base pitch error and backlash will bealso increased, which deteriorates the gear transmission. The vibration of the gear systemcan not only produce noise, but also accelerate fatigue of the transmission system.Besides, gear box is the key part of a helicopter of transmission system, which cannotreduce accidents through the redundancy backup, gearbox fault, and it’s a direct threattowards a helicopter flight safety. Typical gearbox vibration contains several tonal signalsmixed with a broadband response. The tonal signals are basically the fundamental gearmesh frequency and their corresponding harmonics generated from the perturbation in thegear meshing process, in which the fundamental gear mesh frequency is the main cause ofthe annoyance problem. In order to suppress this part of the vibration and noise, an activegearbox vibration control structure is developed experimentally to suppress gearboxvibration due to transmission error excitation. At the same time, a filtered-x LMS controlalgorithm is proposed and implemented to generate the appropriate control signals.
At first, a gear pair system model is built to assist in the design of the experimentalactive structure, to gain a better understanding of the nature of gear response due totransmission error excitation. Based on an active shaft transverse vibration controlconcept, an active internal gearbox structure, combined with the piezoelectric actuator, isdeveloped to suppress gear pair vibration due to transmission error excitation in a directway.
Complex nonlinear hysteresis is present in virtually all piezoelectric actuators. Thesenonlinearities can excite unwanted dynamics which reduced system performance andeven lead to unstable system operation, especially in active vibration control applicationsowing to phase lag. The paper describes a compensator design method for invertiblecomplex hysteretic nonlinearities based on Prandtl-Ishlinskii hysteresis operator. Linearinequality constraints for the parameters guarantee the unique solvability of theidentification problem and the invertability of the identified model. The correspondingcompensator can be directly calculated and thus efficiently implemented from the modelby analytical transformation laws. This allows an efficient implementation of the compensator for real-time control. Finally，the compensator design method is used togenerate an inverse feed forward controller, results of simulation proved the method'savailability.
Active vibration control use an active anti-force from secondary path to suppress orattenuate vibration and noises，one of the control algorithms is filtered-x least meansquare (FxLMS) adaptive algorithm. Based on structure of FxLMS algorithm, Level-2S-function is used to build a new FxLMS blocks in MATLAB/Simulink and apply it inoffline vibration active control system simulation. On the condition of convergence,performance analysis is given by adjusting the interior parameters to test the controlalgorithm block. Finally, the custom FxLMS block is downloaded to DSpace as controller,and used in hardware-in-the-loop simulation of active vibration control on a geartransmission system. Results verify the custom FxLMS block’s feasibility built byLevel-2S-function and control algorithm’s efficiency.
A gearbox test-bed is also developed with a piezoelectric actuator inside for applyingcontrol forces to the shaft. Lastly, the custom FxLMS block is downloaded to DSpace ascontroller. Experiment results showe that the proposed FxLMS controller performs aneffective performance. Up to35dB of gearbox vibration has been attenuated at somefundamental gear mesh frequency.
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