机电集成超环面传动磁场研究
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摘要
机电集成超环面传动是以超环面行星蜗杆传动为基础,集机械、电磁、控制于一体的新型复合传动。该传动通过磁场间的耦合作用实现运动和动力的传递与输出。因此,对机电集成超环面传动磁性驱动机理及相关问题开展研究具有重要的理论意义与实用价值。本文从磁性啮合原理、磁性驱动机理、构件磁场计算及磁场耦合作用、原理样机的设计与实验等方面对机电集成超环面传动进行了深入系统的研究。
以电磁学理论为基础,分标量磁位和矢量磁位给出了磁场计算的基本公式,给出了三种坐标系下磁场计算表达式。以超环面行星蜗杆传动为基础,结合磁场啮合的特点,分析了机电集成超环面传动的磁性啮合原理,给出了各构件间的啮合运动关系,分单齿啮合和多齿啮合两种情况推导出了机电集成超环面传动的正确啮合条件及正确啮合条件下啮合齿数的计算公式;分析了该传动的受力情况,给出了各构件独立的磁回路及其啮合时的整体磁回路,为磁场的计算奠定了理论基础。
建立了机电集成超环面传动蜗杆单相及三相交流电磁场的计算模型,推导出单相螺旋通电导线在空间产生磁场的计算公式,利用叠加原理得到蜗杆整体磁场的空间分布计算表达式,完成了机电集成超环面传动蜗杆电磁场的分析计算,给出了蜗杆电磁场在不同坐标系下的分解结果,并利用公式对蜗杆线圈的电磁场进行了计算,揭示了蜗杆电磁场空间的分布规律。
以永磁理论为基础,完成了机电集成超环面传动行星轮轮齿磁场及行星轮整体磁场的分析计算,建立了圆柱永磁齿磁场分布的计算模型,推导出圆柱永磁齿磁场在空间分布计算公式,给出永磁齿坐标系和行星轮整体坐标系之间的转换矩阵,利用坐标变换原理得到了行星轮整体磁场的计算公式,对永磁齿轴线和不同轴截面上磁场分布进行了分析计算,得到行星轮磁场空间的分布规律,并通过有限元软件的模拟,验证了推导结果的正确性。
利用有限元方法对机电集成超环面传动定子永磁体螺旋齿的磁场进行了分析计算,建立了定子的有限元模型,从稳定磁场的偏微分方程出发,利用变分原理推导出恒定磁场相应的条件变分问题,对机电集成超环面传动定子永磁体螺旋齿有限元计算中的关键问题进行了详细分析,并利用有限元软件对定子整体磁场和局部磁场进行了计算,得到机电集成超环面传动定子永磁体螺旋齿磁场的分布规律。
建立了机电集成超环面传动定子与行星轮、蜗杆与行星轮磁性耦合的力学模型,给出了行星轮轮齿永磁体的等效电流模型,推导出定子磁场与行星轮磁场、蜗杆电磁场与行星轮磁场相互耦合的磁场力计算公式,得出机电集成超环面传动输出转矩的计算公式,并利用公式对该传动的输出转矩进行了计算,分析了输出转矩的影响因素及影响规律,为该传动的承载能力设计奠定了基础。
完成了机电集成超环面传动原理样机的设计和原理性实验,实验结果验证了理论分析的正确性。
Electromechanical integrated toroidal transmission is a new composite drive based on toroidal drive, which integrated mechanism with electromagnetism and control. By the coupling of magnetic fields, the transition and output of motion and power are completed; therefore, it is important for theoretic analysis and application of the drive system studying drive mechanism and related other problems of electromechanical integrated transmission. This paper investigated thoroughly the principle of magnetic mesh, magnetic drive, calculation of the component magnetic field distribution, the coupling effect of magnetic field and the design of model machine for the electromechanical integrated mechanism.
Based on electromagnetic theory, basic equations of the magnetic fields are given about magnetometive scalar and vector under three kinds of coordinates. Based on toroidal drive, magnetic meshing principle of electromechanical integrated toroidal drive is analyzed by combining magnetic mesh characteristic; movement relations of components are presented. The correct meshing conditions and the meshing tooth number formulas of single tooth and multi teeth mesh for the drive are given. The forces for the transmission are analyzed as well. The magnetic circuits of the stator, worm, planet and the total transmission are analyzed, which offer theory basis for magnetic field computation.
The worm magnetic field of the drive is analyzed and calculated. The calculation models of single-phase and tri-phase fields are constructed, the formulas of the 3-D magnetic field for single-phase wires are derived, and the equations of the total magnetic field are obtained by the superposition principle, the decomposing results of the magnetic field under different coordinates are given. The magnetic field of the worm windings is calculated, which shows the distribution of the worm magnetic field.
From the theory of permanent magnet, the planet tooth magnetic field and total planet magnetic field for the electromechanical integrated toroidal drive are studied, the model of magnetic field distribution for cylinder magnet tooth is presented, the formula of spacial field distribution for permanent magnet teeth is derived, the transformation matrix of coordinates between planet tooth and planet is given, the magnetic field formulas of the whole planet is obtained by the principle of coordinate transformation, the distribution of the magnetic field at axis and different axial sections are analyzed. The distribution of the space magnetic field is obtained; the correctness of the result is validated by FEM simulation.
The stator permanent magnetic field of the electromechanical integrated toroidal drive are calculated and analyzed by finite element method. Finite element model of the stator is presented, corresponding conditional variations questions of constant magnetic field are deduced by variation principle from partial differential equations of constant magnetic field, and three steps of variation questions are illustrated. The key problems in finite element method calculation of permanent magnetic field of the drive are analyzed in detail. The whole and partial magnetic fields of the stator are calculated by finite element software, and the distributions of the permanent magnetic field of the stator are obtained.
The mechanical models of electromechanical integrated toroidal drive with magnetic meshing between stator and planet or between worm and planet are established on the base of electromagnetic theory. Equivalent current model of permanent magnetic body of planet tooth is given. The calculating formulas of the magnetic field force between stator and planet or between worm and planet are deduced. The calculating formulas of the output torque of the drive are deduced as well. The output torque of the drive is calculated and analyzed; the influence factors and their influence on output torque are summarized. It offers the design base of the drive.
The principle tests of the drive are done. The results validate correctness of theory analysis.
以电磁学理论为基础,分标量磁位和矢量磁位给出了磁场计算的基本公式,给出了三种坐标系下磁场计算表达式。以超环面行星蜗杆传动为基础,结合磁场啮合的特点,分析了机电集成超环面传动的磁性啮合原理,给出了各构件间的啮合运动关系,分单齿啮合和多齿啮合两种情况推导出了机电集成超环面传动的正确啮合条件及正确啮合条件下啮合齿数的计算公式;分析了该传动的受力情况,给出了各构件独立的磁回路及其啮合时的整体磁回路,为磁场的计算奠定了理论基础。
建立了机电集成超环面传动蜗杆单相及三相交流电磁场的计算模型,推导出单相螺旋通电导线在空间产生磁场的计算公式,利用叠加原理得到蜗杆整体磁场的空间分布计算表达式,完成了机电集成超环面传动蜗杆电磁场的分析计算,给出了蜗杆电磁场在不同坐标系下的分解结果,并利用公式对蜗杆线圈的电磁场进行了计算,揭示了蜗杆电磁场空间的分布规律。
以永磁理论为基础,完成了机电集成超环面传动行星轮轮齿磁场及行星轮整体磁场的分析计算,建立了圆柱永磁齿磁场分布的计算模型,推导出圆柱永磁齿磁场在空间分布计算公式,给出永磁齿坐标系和行星轮整体坐标系之间的转换矩阵,利用坐标变换原理得到了行星轮整体磁场的计算公式,对永磁齿轴线和不同轴截面上磁场分布进行了分析计算,得到行星轮磁场空间的分布规律,并通过有限元软件的模拟,验证了推导结果的正确性。
利用有限元方法对机电集成超环面传动定子永磁体螺旋齿的磁场进行了分析计算,建立了定子的有限元模型,从稳定磁场的偏微分方程出发,利用变分原理推导出恒定磁场相应的条件变分问题,对机电集成超环面传动定子永磁体螺旋齿有限元计算中的关键问题进行了详细分析,并利用有限元软件对定子整体磁场和局部磁场进行了计算,得到机电集成超环面传动定子永磁体螺旋齿磁场的分布规律。
建立了机电集成超环面传动定子与行星轮、蜗杆与行星轮磁性耦合的力学模型,给出了行星轮轮齿永磁体的等效电流模型,推导出定子磁场与行星轮磁场、蜗杆电磁场与行星轮磁场相互耦合的磁场力计算公式,得出机电集成超环面传动输出转矩的计算公式,并利用公式对该传动的输出转矩进行了计算,分析了输出转矩的影响因素及影响规律,为该传动的承载能力设计奠定了基础。
完成了机电集成超环面传动原理样机的设计和原理性实验,实验结果验证了理论分析的正确性。
Electromechanical integrated toroidal transmission is a new composite drive based on toroidal drive, which integrated mechanism with electromagnetism and control. By the coupling of magnetic fields, the transition and output of motion and power are completed; therefore, it is important for theoretic analysis and application of the drive system studying drive mechanism and related other problems of electromechanical integrated transmission. This paper investigated thoroughly the principle of magnetic mesh, magnetic drive, calculation of the component magnetic field distribution, the coupling effect of magnetic field and the design of model machine for the electromechanical integrated mechanism.
Based on electromagnetic theory, basic equations of the magnetic fields are given about magnetometive scalar and vector under three kinds of coordinates. Based on toroidal drive, magnetic meshing principle of electromechanical integrated toroidal drive is analyzed by combining magnetic mesh characteristic; movement relations of components are presented. The correct meshing conditions and the meshing tooth number formulas of single tooth and multi teeth mesh for the drive are given. The forces for the transmission are analyzed as well. The magnetic circuits of the stator, worm, planet and the total transmission are analyzed, which offer theory basis for magnetic field computation.
The worm magnetic field of the drive is analyzed and calculated. The calculation models of single-phase and tri-phase fields are constructed, the formulas of the 3-D magnetic field for single-phase wires are derived, and the equations of the total magnetic field are obtained by the superposition principle, the decomposing results of the magnetic field under different coordinates are given. The magnetic field of the worm windings is calculated, which shows the distribution of the worm magnetic field.
From the theory of permanent magnet, the planet tooth magnetic field and total planet magnetic field for the electromechanical integrated toroidal drive are studied, the model of magnetic field distribution for cylinder magnet tooth is presented, the formula of spacial field distribution for permanent magnet teeth is derived, the transformation matrix of coordinates between planet tooth and planet is given, the magnetic field formulas of the whole planet is obtained by the principle of coordinate transformation, the distribution of the magnetic field at axis and different axial sections are analyzed. The distribution of the space magnetic field is obtained; the correctness of the result is validated by FEM simulation.
The stator permanent magnetic field of the electromechanical integrated toroidal drive are calculated and analyzed by finite element method. Finite element model of the stator is presented, corresponding conditional variations questions of constant magnetic field are deduced by variation principle from partial differential equations of constant magnetic field, and three steps of variation questions are illustrated. The key problems in finite element method calculation of permanent magnetic field of the drive are analyzed in detail. The whole and partial magnetic fields of the stator are calculated by finite element software, and the distributions of the permanent magnetic field of the stator are obtained.
The mechanical models of electromechanical integrated toroidal drive with magnetic meshing between stator and planet or between worm and planet are established on the base of electromagnetic theory. Equivalent current model of permanent magnetic body of planet tooth is given. The calculating formulas of the magnetic field force between stator and planet or between worm and planet are deduced. The calculating formulas of the output torque of the drive are deduced as well. The output torque of the drive is calculated and analyzed; the influence factors and their influence on output torque are summarized. It offers the design base of the drive.
The principle tests of the drive are done. The results validate correctness of theory analysis.
引文
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