非线性振动系统锐共振振动同步与控制同步关键技术研究
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摘要
为保证振动机械的双激振电机能实现稳定的同步运动以及振幅稳定性,传统的振动机械绝大部分都工作在远超共振(z≈3~6)状态,少数工作在近共振(z≈0.8～0.9)状态,随着计算机控制技术的发展,实现双激振电机的同步、同步运动稳定性及振幅稳定问题可以通过综合动力学分析及计算机控制得到很好的解决,因此,基于共振原理用较小的激振力即可获得较大振幅的特点,提出了工作频率比z≈0.95～1.05的双电机同步激振锐共振机械,该类振动机械的显著优点是,在保证振动系统具备所需振幅的前提下,系统的激振力最小,由于其节能、经济、高效的特点,代表了今后振动机械发展过程中一个非常值得探讨的方向。但目前有关振动同步理论的研究大多是对振动机械进行线性或拟线性化处理,在远超共振或近共振状态下展开的。而对于锐共振振动机械,由于系统的多自由度、各部件之间的间隙、摩擦以及材料本身的物理特性等导致非线性因素异常突出,对系统的运动形态有重要的影响,不能再被简单的忽略或线性化处理,使得利用传统的振动同步理论来分析和解释锐共振振动机械的同步现象很困难,甚至不再适用。同时,由于振动机械在锐共振区域内工作,振幅响应对外界诸如：负载波动、环境干扰等影响因素异常敏感,使得在远超共振振动机械应用中已较好解决的振幅稳定性问题,成为锐共振自同步振动机械应用过程中必须研究解决的一个重要内容。由此引发,在研究锐共振振动系统双激振电机振动同步机理的同时,必须综合考虑振动系统的非线性动力学行为,研究基于非线性振动系统动力学分析的振动同步和基于多电机电气控制策略的控制同步问题,解决非线性振动系统锐共振情况下,双激振电机的同步性、同步运动稳定性,以及非线性振动系统锐共振的振幅稳定性,具有重要的理论意义和实际工程应用价值。
为从理论上揭示非线性振动系统锐共振同步运动机理,在本文第二章中利用机械振动学及非线性动力学理论,建立了非线性振动系统的动力学模型,并根据电机学拖动理论,建立了振动系统中激振电机的等效数学模型和非线性电气特性模型。并将两类模型纳入同一分析对象中,组成非线性振动系统的机电耦合动力学模型。
与以往文献大多在远超共振或低临界近共振状态下,进行线性或拟线性化振动系统的双激振电机振动同步理论研究不同,以文中建立的单质体多自由度弱非线性振动系统模型、单质体单自由度强非线性振动系统模型为研究对象,在本文第三章中通过非线性系统平均法、能量法等非线性动力学理论对振动系统进行了理论分析及数值仿真,研究了在非线性振动系统锐共振情况下,双激振电机的振动同步及同步运动稳定性问题,以及由于系统的非线性因素影响,双激振电机可能出现的谐波锐共振谐振同步现象。讨论了振动系统双激振电机间的同步性与系统锐共振频率比之间的关系,以及振动系统的非线性弹性力、阻尼力、惯性力、偏心转子的转动惯量、激振电机的机械电气外特性等诸多因素对双激振电机同步运行的影响。
由于非线性振动系统在锐共振状态下工作,对外界环境扰动的敏感性,易造成各激振电机负载分配不均,使其转速差、相位差发生变动,导致双激振电机不能实现同步,或同步状态极不稳定,并且锐共振情况下系统的振幅响应受外扰极易失稳等特性。使得从非线性振动系统动力学角度研究双激振电机振动同步的同时,还需要研究针对各激振电机的控制同步问题,以及系统锐共振的振幅稳定性控制问题。在本文第四章中,根据目前控制领域中广泛应用的异步电机等效模型,推导了异步电机基于等效模型的传递函数,并依此设计了双激振电机偏差补偿跟踪同步控制策略。在文中4.3节基于交流异步电机的非线性电气特性模型,设计了异步电机转速、转子磁链的模糊自适应估计器,以及基于该估计器的电机矢量控制系统,并由Lyapunov稳定性理论证明了对电机控制的稳定性,随后在此基础上设计了双激振电机输出交叉耦合协调同步控制策略。通过对文中设计的同步控制策略进行讨论及实验仿真分析,得出该控制同步策略能有效实现非线性振动系统锐共振情况下,双激振电机的同步稳定性控制问题。在一定程度上避免了传统文献在大量的假设条件及精确数学模型下,仅实现振动系统远超共振或近共振情况下控制同步的不足。文中4.4节讨论了非线性振动系统锐共振振幅稳定性影响因素,在分析振动系统物料波动对锐共振振幅影响的基础上,设计了非线性振动系统实现振幅稳定的控制策略,并通过仿真实验讨论了文中设计的振幅稳定性控制策略对振动系统锐共振控制的有效性。
为揭示非线性振动系统锐共振情况下,双激振电机的同步运动机理,文中第五章基于非线性振动系统的机电耦合动力学模型,通过定量仿真分析了非线性振动系统的频率俘获锐共振现象,研究了非线性振动系统向锐共振区域逼近时,双激振电机基于振动机体的运动耦合,实现振动同步的过渡过程。讨论了非线性振动系统频率俘获锐共振同步现象与系统刚度、阻尼、双激振电机驱动矩、电机轴摩擦阻矩、偏心转子质心矩等参数之间的关系。给出了非线性振动系统弹簧刚度及阻尼值变化时,机体的振动响应及双电机同步回转可能出现的各种不同运动形式。
本文第六章,在双电机激振锐共振实验台上进行了实验研究,对实际振动机械的锐共振同步运动现象及振幅稳定性控制过程中出现的现象进行了讨论,验证了文中理论推导结果及控制策略的正确性与有效性。
In order to guanrantee the stable synchronization motion and amplitude stability, classical vibrating machine mostly work under the far ultra resonating (z≈3～6) or near resonating (z≈0.8～0.9) conditions. But accompany with the development of computer control technology, the problem of amplitude stabilty can be solved by computer control technology well. So based on the resonance principle that vibrating machine arrived at required amplitude, but the exciting force is the least, the dual-exciting motors synchronization drive sharp resonance vibration machine which work at the frequency radio z≈0.95～1.05has been put out. Because the energy-saving, economical and efficient characteristics of this type vibrating machine, it represents one of the most important development direction of vibrating machine. But at present the related vibration synchronization theory research mostly have been carried out at the far ultra resonating or low critical near resonating conditions for the vibration machine. To the sharp resonance vibrating machine, the dual-exciting sources, multiple-degree-of-freedom and the gap between every components assembly, friction and so on make the nonlinear factors abnormal outstanding, so the nonlinear vibrating system cannot be simply neglected or linearization processed. Which make us comprehensive considerate the nonlinear dynamic behaviors of the vibrating system. And use them to research and settle the synchronization and synchronization motion stability of the dual-exciting motors which used to drive the nonlinear vibrating system under the systemic sharp resonance conditions. The research results have important theoretical significance and practical engineering application value.
In order to disclosure the sharp resonance vibration synchronization motive mechanics of the nonlinear vibrating system from the theoretical perspectives, in the second chapter of this paper, the dynamic model of nonlinear vibrating system had been established based on the machinery dynamics and nonlinear vibration theory. The equivalent numerical simulation model of exciting motor and nonlinear electric characteristics model have been established based on the electric machinery drive theory. Now lead the machine dynamics model and motor model into a uniform research object, which can be used to compose the coupled electromechanical dynamic model for nonlinear vibrating system.
Different the previous research which mostly carry out carry out the dual-exciting motors vibration synchronization theory under far more than resonance or low critical near resonance conditions from the view of linear or quasi-linear, in this paper make the single-mass multiple-degree of freedom weakly nonlinear system and single-mass single-degree of freedom strongly nonlinear system as the research object to carry out the vibration synchronization theory research. In the third chapter of this paper, use the nonlinear system average method, energy method and so on to carry out the theoretical analysis. And to analysis the harmonic sharp resonance harmonic vibration synchronization phenomena of the dual exciting motors during the course of the vibrating system motion, because of the systemic nonlinear factors. The relationship between the vibration synchronization of dual-exciting motors and the sharp resonance working frequency of nonlinear system had been discussed in the paper. The influence of the vibrating systemic elastic force, damping force, inertial force and the rotary inertia of eccentric runner, mechanical electric external characteristics of exciting motor and so on to the vibration synchronization of dual-exciting motors have been analyzed also.
When the nonlinear vibrating system works under sharp resonance conditions, the phase difference and rotational speed difference may change because the initial condition difference, technical parameter difference of dual-exciting motors and the synchronization motion is so fragile that can be influenced by outer environment condition. All make from the nonlinear vibrating system dynamics view to research the vibration synchronization for dual-exciting motors, at same time must to research the controlled synchronization problem of dual-exciting motors. In the forth chapter of this paper, the transfer function of equivalent model have been deduced, and the deviation compensation tracking control synchronization strategy have been established in the paper. In the section of4.3, the fuzzy self-adaptive estimator for rotational speed and rotor flux of asynchronous motor have been designed based on the nonlinear electronic characteristic model of ac asynchronous motor, and the vector control system for motor have been established based on the estimator which refer ahead. Based on the front analysis the cross coupling coordination synchronization control scheme for dual exciting motors has been established. From the test discussion and simulation analysis, the conclusion that the controlled synchronization strategy which designed in the paper can make the dual exciting motors realize the controlled synchronization under the nonlinear vibrating system sharp resonance conditions. The controlled synchronization can effective avoid the deficiency of traditional literature only realize the controlled synchronization motion at far more than resonance or low critical near resonance conditions.
In order to discovery the synchronization motion mechanism of dual exciting motors when the nonlinear vibrating system works under sharp resonance conditions. In the fifth chapter, the frequency capture sharp resonance phenomena of nonlinear vibrating system have been quantify simulation analysis, based on the electromechanical coupling dynamics model for nonlinear vibrating system which driven by dual exciting motors. The interrelationship between the non-ideal driving source and body's motion of nonlinear vibrating system had been discussed. And the vibration synchronization transient change law of dual exciting motors had been researched when the nonlinear vibrating system moved to the sharp resonance point. The relationship between the frequency capture sharp resonance synchronization phenomena of nonlinear vibrating system which driven by dual exciting motors and the stiffness, damping of vibrating system, driving torque of dual exciting motors, friction resistance torque, centric torque of eccentric rotor and so on. And the various possible motion forms of vibration response and synchronization rotate for dual exciting motors have been discussed, when the spring stiffness and damping of nonlinear vibrating system changed.
In the sixth chapter, the phenomena of sharp resonance vibration synchronization and amplitude stability controlled have been discussed, based on the practical experiment on sharp resonance experimental table which driven by dual exciting motors. And the correctness of the theoretical study results and controlled strategies which researched in this paper had been proved.
为从理论上揭示非线性振动系统锐共振同步运动机理,在本文第二章中利用机械振动学及非线性动力学理论,建立了非线性振动系统的动力学模型,并根据电机学拖动理论,建立了振动系统中激振电机的等效数学模型和非线性电气特性模型。并将两类模型纳入同一分析对象中,组成非线性振动系统的机电耦合动力学模型。
与以往文献大多在远超共振或低临界近共振状态下,进行线性或拟线性化振动系统的双激振电机振动同步理论研究不同,以文中建立的单质体多自由度弱非线性振动系统模型、单质体单自由度强非线性振动系统模型为研究对象,在本文第三章中通过非线性系统平均法、能量法等非线性动力学理论对振动系统进行了理论分析及数值仿真,研究了在非线性振动系统锐共振情况下,双激振电机的振动同步及同步运动稳定性问题,以及由于系统的非线性因素影响,双激振电机可能出现的谐波锐共振谐振同步现象。讨论了振动系统双激振电机间的同步性与系统锐共振频率比之间的关系,以及振动系统的非线性弹性力、阻尼力、惯性力、偏心转子的转动惯量、激振电机的机械电气外特性等诸多因素对双激振电机同步运行的影响。
由于非线性振动系统在锐共振状态下工作,对外界环境扰动的敏感性,易造成各激振电机负载分配不均,使其转速差、相位差发生变动,导致双激振电机不能实现同步,或同步状态极不稳定,并且锐共振情况下系统的振幅响应受外扰极易失稳等特性。使得从非线性振动系统动力学角度研究双激振电机振动同步的同时,还需要研究针对各激振电机的控制同步问题,以及系统锐共振的振幅稳定性控制问题。在本文第四章中,根据目前控制领域中广泛应用的异步电机等效模型,推导了异步电机基于等效模型的传递函数,并依此设计了双激振电机偏差补偿跟踪同步控制策略。在文中4.3节基于交流异步电机的非线性电气特性模型,设计了异步电机转速、转子磁链的模糊自适应估计器,以及基于该估计器的电机矢量控制系统,并由Lyapunov稳定性理论证明了对电机控制的稳定性,随后在此基础上设计了双激振电机输出交叉耦合协调同步控制策略。通过对文中设计的同步控制策略进行讨论及实验仿真分析,得出该控制同步策略能有效实现非线性振动系统锐共振情况下,双激振电机的同步稳定性控制问题。在一定程度上避免了传统文献在大量的假设条件及精确数学模型下,仅实现振动系统远超共振或近共振情况下控制同步的不足。文中4.4节讨论了非线性振动系统锐共振振幅稳定性影响因素,在分析振动系统物料波动对锐共振振幅影响的基础上,设计了非线性振动系统实现振幅稳定的控制策略,并通过仿真实验讨论了文中设计的振幅稳定性控制策略对振动系统锐共振控制的有效性。
为揭示非线性振动系统锐共振情况下,双激振电机的同步运动机理,文中第五章基于非线性振动系统的机电耦合动力学模型,通过定量仿真分析了非线性振动系统的频率俘获锐共振现象,研究了非线性振动系统向锐共振区域逼近时,双激振电机基于振动机体的运动耦合,实现振动同步的过渡过程。讨论了非线性振动系统频率俘获锐共振同步现象与系统刚度、阻尼、双激振电机驱动矩、电机轴摩擦阻矩、偏心转子质心矩等参数之间的关系。给出了非线性振动系统弹簧刚度及阻尼值变化时,机体的振动响应及双电机同步回转可能出现的各种不同运动形式。
本文第六章,在双电机激振锐共振实验台上进行了实验研究,对实际振动机械的锐共振同步运动现象及振幅稳定性控制过程中出现的现象进行了讨论,验证了文中理论推导结果及控制策略的正确性与有效性。
In order to guanrantee the stable synchronization motion and amplitude stability, classical vibrating machine mostly work under the far ultra resonating (z≈3～6) or near resonating (z≈0.8～0.9) conditions. But accompany with the development of computer control technology, the problem of amplitude stabilty can be solved by computer control technology well. So based on the resonance principle that vibrating machine arrived at required amplitude, but the exciting force is the least, the dual-exciting motors synchronization drive sharp resonance vibration machine which work at the frequency radio z≈0.95～1.05has been put out. Because the energy-saving, economical and efficient characteristics of this type vibrating machine, it represents one of the most important development direction of vibrating machine. But at present the related vibration synchronization theory research mostly have been carried out at the far ultra resonating or low critical near resonating conditions for the vibration machine. To the sharp resonance vibrating machine, the dual-exciting sources, multiple-degree-of-freedom and the gap between every components assembly, friction and so on make the nonlinear factors abnormal outstanding, so the nonlinear vibrating system cannot be simply neglected or linearization processed. Which make us comprehensive considerate the nonlinear dynamic behaviors of the vibrating system. And use them to research and settle the synchronization and synchronization motion stability of the dual-exciting motors which used to drive the nonlinear vibrating system under the systemic sharp resonance conditions. The research results have important theoretical significance and practical engineering application value.
In order to disclosure the sharp resonance vibration synchronization motive mechanics of the nonlinear vibrating system from the theoretical perspectives, in the second chapter of this paper, the dynamic model of nonlinear vibrating system had been established based on the machinery dynamics and nonlinear vibration theory. The equivalent numerical simulation model of exciting motor and nonlinear electric characteristics model have been established based on the electric machinery drive theory. Now lead the machine dynamics model and motor model into a uniform research object, which can be used to compose the coupled electromechanical dynamic model for nonlinear vibrating system.
Different the previous research which mostly carry out carry out the dual-exciting motors vibration synchronization theory under far more than resonance or low critical near resonance conditions from the view of linear or quasi-linear, in this paper make the single-mass multiple-degree of freedom weakly nonlinear system and single-mass single-degree of freedom strongly nonlinear system as the research object to carry out the vibration synchronization theory research. In the third chapter of this paper, use the nonlinear system average method, energy method and so on to carry out the theoretical analysis. And to analysis the harmonic sharp resonance harmonic vibration synchronization phenomena of the dual exciting motors during the course of the vibrating system motion, because of the systemic nonlinear factors. The relationship between the vibration synchronization of dual-exciting motors and the sharp resonance working frequency of nonlinear system had been discussed in the paper. The influence of the vibrating systemic elastic force, damping force, inertial force and the rotary inertia of eccentric runner, mechanical electric external characteristics of exciting motor and so on to the vibration synchronization of dual-exciting motors have been analyzed also.
When the nonlinear vibrating system works under sharp resonance conditions, the phase difference and rotational speed difference may change because the initial condition difference, technical parameter difference of dual-exciting motors and the synchronization motion is so fragile that can be influenced by outer environment condition. All make from the nonlinear vibrating system dynamics view to research the vibration synchronization for dual-exciting motors, at same time must to research the controlled synchronization problem of dual-exciting motors. In the forth chapter of this paper, the transfer function of equivalent model have been deduced, and the deviation compensation tracking control synchronization strategy have been established in the paper. In the section of4.3, the fuzzy self-adaptive estimator for rotational speed and rotor flux of asynchronous motor have been designed based on the nonlinear electronic characteristic model of ac asynchronous motor, and the vector control system for motor have been established based on the estimator which refer ahead. Based on the front analysis the cross coupling coordination synchronization control scheme for dual exciting motors has been established. From the test discussion and simulation analysis, the conclusion that the controlled synchronization strategy which designed in the paper can make the dual exciting motors realize the controlled synchronization under the nonlinear vibrating system sharp resonance conditions. The controlled synchronization can effective avoid the deficiency of traditional literature only realize the controlled synchronization motion at far more than resonance or low critical near resonance conditions.
In order to discovery the synchronization motion mechanism of dual exciting motors when the nonlinear vibrating system works under sharp resonance conditions. In the fifth chapter, the frequency capture sharp resonance phenomena of nonlinear vibrating system have been quantify simulation analysis, based on the electromechanical coupling dynamics model for nonlinear vibrating system which driven by dual exciting motors. The interrelationship between the non-ideal driving source and body's motion of nonlinear vibrating system had been discussed. And the vibration synchronization transient change law of dual exciting motors had been researched when the nonlinear vibrating system moved to the sharp resonance point. The relationship between the frequency capture sharp resonance synchronization phenomena of nonlinear vibrating system which driven by dual exciting motors and the stiffness, damping of vibrating system, driving torque of dual exciting motors, friction resistance torque, centric torque of eccentric rotor and so on. And the various possible motion forms of vibration response and synchronization rotate for dual exciting motors have been discussed, when the spring stiffness and damping of nonlinear vibrating system changed.
In the sixth chapter, the phenomena of sharp resonance vibration synchronization and amplitude stability controlled have been discussed, based on the practical experiment on sharp resonance experimental table which driven by dual exciting motors. And the correctness of the theoretical study results and controlled strategies which researched in this paper had been proved.
引文
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