永磁行星齿轮传动系统动力学研究
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摘要
本文研究了一种新型无接触式传动机构—永磁行星齿轮传动，与传统机械式行星齿轮传动相比，永磁行星齿轮传动系统具有许多优点：不需润滑和冷却；降低维修成本，提高稳定性；启动力矩低且具有过载保护功能；工作效率高；没有磨损和噪声等。在医疗器械、化工设备以及食品加工设备等领域有着广阔的应用前景。
本文介绍了永磁行星齿轮传动系统的工作原理，进行了传动系统的参数分析与设计，从同轴条件、邻接条件、等极距条件、装配条件几方面研究了该传动系统的参数关系。
利用等效电流模型法，推导了磁性齿轮单一轮齿和多轮齿磁感应强度计算公式，在此基础上，推导了太阳轮与行星轮之间、内齿圈与行星轮之间的转矩以及机构输出转矩的计算公式，分析了磁感应强度随场点位置参数的变化规律，以及结构参数对转矩的影响规律；研究结果表明：永磁行星齿轮传动系统的转矩受磁极对数、轮齿径向厚度、轮齿轴向厚度、磁齿轮间气隙以及传动比等参数影响比较大，合理选择参数能够使得该系统结构更加紧凑。
建立了永磁行星齿轮传动系统的平移-扭转振动动力学模型及其动力学微分方程，由径向力和转矩计算表达式推导了磁性齿轮之间的径向和切向磁性耦合刚度，在此基础上，对系统固有频率和振动模态进行了研究，完成了该传动系统各阶模态对系统设计参数的灵敏度公式推导和变化规律分析；研究发现：磁极对数、磁性齿轮轴向厚度、磁齿轮之间气隙以及磁性齿轮径向间隙对系统模态的影响较大，行星轮安装个数大于2时，系统振动模态包括中心构件扭转、中心构件平移和行星轮模态，行星轮安装个数等于2时不存在行星轮模态，而是内齿圈模态和太阳轮模态。
建立了永磁行星齿轮传动系统强迫振动的动力学微分方程，对该系统强迫振动时域和频域响应进行了求解，将外部激励分为输入端激励、输出端激励以及同时综合考虑输入端和输出端激励三种情况，完成了系统强迫振动时域和频域响应分析，分析了结构和性能参数对系统频域响应的影响规律；结果表明：只考虑输出端激励时系统各部件动态位移响应较只考虑输入端激励时大，磁感应强度、磁极对数、磁齿轮间的气隙以及磁齿轮的轴向厚度对各构件的低频振幅影响比较大，进行结构设计时要合理选择系统结构参数，避免系统各部件产生较大的振动。
设计了永磁行星齿轮传动实验样机，搭建了实验平台，对极限转矩以及传动效率进行了测试，将实验测试数据与理论分析结果进行对比分析，证明了理论计算的正确性以及样机参数设计的合理性。
In this paper, a new non-contact drive permanent magnetic planetary gear drive isstudied. Compare with traditional planetary gear drive, the permanent magnetic planetarygear drive has many advantages. The magnetic planetary gear drive does not needlubrication and cooling. It can reduce maintenance and improved reliability. It need lowstarting torque and can offer overload protection. The operating efficiency of the magneticplanetary gear drive is much higher than that of the traditional planetary gear drive. Themagnetic gear drive is without wear and noise.So it can find good application in thetechnical field such as medical apparatus, chemical equipment, food processing equipment,etc.
In this paper, the operating principle of the permanent magnetic planetary gear driveis introduced. Relationship between the parameters of transmission system is researchedfrom the condition of concentricity, the condition of adjacency, the condition of the equalpole distance, and the mounting condition of the drive.
Using the equivalent current method, the equations of the magnetic inductionintensity for one magnetic gear tooth or multiple magnetic gear teeth are deduced. From it,the equations of the torques between the planetary gears and sun gear or crown gear, andthe equation of the output torque for the drive are developed aswell. The magnetic fluxdensity of the magnetic gear teeth and its distribution are investigated. The torquesbetween the gears and their changes along with the main drive parameters are analysed.Results show that the pole pair number, the tooth thickness, the tooth width, and the speedratio of the drive have obvious influence on the magnetic output torques. Reasonableselection of parameters can make the system structure more compact.
The translation-torsion dynamic model for a permanent magnetic planetary geardrive is proposed. Based on the model, the dynamic equations for the permanent magneticplanetary gear drive are given. From the magnetic meshing forces and torques between theelements for the drive system, the tangent and radial magnetic meshing stiffness isobtained. Using these equations, the natural frequencies and the modes of the magnetic planetary gear drive are investigated. The sensitivity of the natural frequencies to thesystem parameters is discussed. Results show that the pole pair number, the tooth width,the air gap and the tooth thickness have obvious effects on the natural frequencies. For theplanetary gear number larger than two, the vibrations of the drive system include thetorsion mode of the center elements, the translation mode of the center elements, and theplanet modes. For the planetary gear number equal to two, the planet mode does not occur,the crown mode and the sun gear mode occur.
The forced vibration equation for the permanent magnetic planetary gear drive iseduced. The time and frequency forced responses are computed and analyzed under threekind of condition，only consider the input excitation, only consider output excitation andconsider input excitation and output excitation comprehensively. The influence ofstructure parameters to frequency forced responses is discussed. Results show that thedynamic displacement when only considering output excitation is larger than that whenonly considering input excitation. Magnetization intensity, pole pair number, air gap andaxial thickness have obvious effects on the low frequency vibration amplitude of elements.Selecting rational system structure parameters is very important, which can avoid systemelements generating larger vibration.
The experimental prototype of the permanent magnetic planetary gear drive isdesigned, and measure the maximum torque and transmission efficiency. The validity oftheoretical calculation and rationality of parameter design are proved by comparing theexperimental data and theoretical analysis results.
本文介绍了永磁行星齿轮传动系统的工作原理，进行了传动系统的参数分析与设计，从同轴条件、邻接条件、等极距条件、装配条件几方面研究了该传动系统的参数关系。
利用等效电流模型法，推导了磁性齿轮单一轮齿和多轮齿磁感应强度计算公式，在此基础上，推导了太阳轮与行星轮之间、内齿圈与行星轮之间的转矩以及机构输出转矩的计算公式，分析了磁感应强度随场点位置参数的变化规律，以及结构参数对转矩的影响规律；研究结果表明：永磁行星齿轮传动系统的转矩受磁极对数、轮齿径向厚度、轮齿轴向厚度、磁齿轮间气隙以及传动比等参数影响比较大，合理选择参数能够使得该系统结构更加紧凑。
建立了永磁行星齿轮传动系统的平移-扭转振动动力学模型及其动力学微分方程，由径向力和转矩计算表达式推导了磁性齿轮之间的径向和切向磁性耦合刚度，在此基础上，对系统固有频率和振动模态进行了研究，完成了该传动系统各阶模态对系统设计参数的灵敏度公式推导和变化规律分析；研究发现：磁极对数、磁性齿轮轴向厚度、磁齿轮之间气隙以及磁性齿轮径向间隙对系统模态的影响较大，行星轮安装个数大于2时，系统振动模态包括中心构件扭转、中心构件平移和行星轮模态，行星轮安装个数等于2时不存在行星轮模态，而是内齿圈模态和太阳轮模态。
建立了永磁行星齿轮传动系统强迫振动的动力学微分方程，对该系统强迫振动时域和频域响应进行了求解，将外部激励分为输入端激励、输出端激励以及同时综合考虑输入端和输出端激励三种情况，完成了系统强迫振动时域和频域响应分析，分析了结构和性能参数对系统频域响应的影响规律；结果表明：只考虑输出端激励时系统各部件动态位移响应较只考虑输入端激励时大，磁感应强度、磁极对数、磁齿轮间的气隙以及磁齿轮的轴向厚度对各构件的低频振幅影响比较大，进行结构设计时要合理选择系统结构参数，避免系统各部件产生较大的振动。
设计了永磁行星齿轮传动实验样机，搭建了实验平台，对极限转矩以及传动效率进行了测试，将实验测试数据与理论分析结果进行对比分析，证明了理论计算的正确性以及样机参数设计的合理性。
In this paper, a new non-contact drive permanent magnetic planetary gear drive isstudied. Compare with traditional planetary gear drive, the permanent magnetic planetarygear drive has many advantages. The magnetic planetary gear drive does not needlubrication and cooling. It can reduce maintenance and improved reliability. It need lowstarting torque and can offer overload protection. The operating efficiency of the magneticplanetary gear drive is much higher than that of the traditional planetary gear drive. Themagnetic gear drive is without wear and noise.So it can find good application in thetechnical field such as medical apparatus, chemical equipment, food processing equipment,etc.
In this paper, the operating principle of the permanent magnetic planetary gear driveis introduced. Relationship between the parameters of transmission system is researchedfrom the condition of concentricity, the condition of adjacency, the condition of the equalpole distance, and the mounting condition of the drive.
Using the equivalent current method, the equations of the magnetic inductionintensity for one magnetic gear tooth or multiple magnetic gear teeth are deduced. From it,the equations of the torques between the planetary gears and sun gear or crown gear, andthe equation of the output torque for the drive are developed aswell. The magnetic fluxdensity of the magnetic gear teeth and its distribution are investigated. The torquesbetween the gears and their changes along with the main drive parameters are analysed.Results show that the pole pair number, the tooth thickness, the tooth width, and the speedratio of the drive have obvious influence on the magnetic output torques. Reasonableselection of parameters can make the system structure more compact.
The translation-torsion dynamic model for a permanent magnetic planetary geardrive is proposed. Based on the model, the dynamic equations for the permanent magneticplanetary gear drive are given. From the magnetic meshing forces and torques between theelements for the drive system, the tangent and radial magnetic meshing stiffness isobtained. Using these equations, the natural frequencies and the modes of the magnetic planetary gear drive are investigated. The sensitivity of the natural frequencies to thesystem parameters is discussed. Results show that the pole pair number, the tooth width,the air gap and the tooth thickness have obvious effects on the natural frequencies. For theplanetary gear number larger than two, the vibrations of the drive system include thetorsion mode of the center elements, the translation mode of the center elements, and theplanet modes. For the planetary gear number equal to two, the planet mode does not occur,the crown mode and the sun gear mode occur.
The forced vibration equation for the permanent magnetic planetary gear drive iseduced. The time and frequency forced responses are computed and analyzed under threekind of condition，only consider the input excitation, only consider output excitation andconsider input excitation and output excitation comprehensively. The influence ofstructure parameters to frequency forced responses is discussed. Results show that thedynamic displacement when only considering output excitation is larger than that whenonly considering input excitation. Magnetization intensity, pole pair number, air gap andaxial thickness have obvious effects on the low frequency vibration amplitude of elements.Selecting rational system structure parameters is very important, which can avoid systemelements generating larger vibration.
The experimental prototype of the permanent magnetic planetary gear drive isdesigned, and measure the maximum torque and transmission efficiency. The validity oftheoretical calculation and rationality of parameter design are proved by comparing theexperimental data and theoretical analysis results.
引文
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