同平面轴等直径钩杆空间螺旋线齿轮设计理论研究
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摘要
微机电系统（MEMS）具有结构微型化、功能多样化、智能化、能耗低、灵敏度和工作效率高等优点。微小型/微型机电产品的最主要特征是体积小、重量轻，以小动力的运动传递或者分度运动为主，以动力传递为主的常规传动机构通常不再适用。因此，微小/微传动机构及驱动装置的工作原理、性能特征和设计制造的创新研究已逐渐成为机械学科前沿研究领域的研究热点和重要方向之一。
本文首先针对国内外微小/微传动机构及驱动装置的研究成果进行了系统性的阐述与分析，然后在前期用于正交轴传动的空间曲线啮合轮传动机构的研究基础上，开展了同平面轴等直径钩杆空间螺旋线齿轮设计理论研究。首先，建立了具有普适性的用于同平面内任意角度交叉轴和平行轴传动的空间曲线啮合理论。在此基础上，研究解决等直径钩杆空间螺旋线齿轮传动机构工业化应用的关键问题，从而为构建独立而完整的同平面轴等直径钩杆空间螺旋线齿轮设计理论奠定基础。大量理论分析与实验研究表明，本文研究的同平面轴等直径钩杆空间螺旋线齿轮具有工业化应用的指导性与可行性。
总体来说，本文具体开展了以下几个方面的研究工作：
1.建立了适用于任意角度交叉轴和平行轴传动的空间曲线啮合方程。首先建立了空间曲线啮合坐标系，分析空间曲线啮合的约束条件，推导具备普适性的轴线共面的空间曲线啮合方程。根据主从动钩杆空间矢量关系，得到等直径钩杆空间螺旋线齿轮主从动钩杆的接触线与中心线方程。
2.在轴线共面的空间曲线啮合方程的基础上，推导等直径钩杆空间螺旋线齿轮的重合度设计公式。分析影响等直径钩杆空间螺旋线齿轮重合度的各项参数，研究重合度的几种设计方法。在重合度设计公式及其影响因素基础上，研究主动钩杆的最少齿数，并针对传动连续性和平稳性进行运动学仿真分析和实验研究，验证重合度设计公式的正确性。
3.研究等直径钩杆空间螺旋线齿轮参数标准化设计。分析等直径钩杆空间螺旋线齿轮主从动轮的各项齿形结构参数，包括齿数、螺旋升角、螺距、钩杆直径、齿高等，确定主从动轮坐标系中心距，确定等直径钩杆空间螺旋线齿轮的基本设计参数和基本设计尺寸。为避免主从动轮之间的干涉，修正主从动钩杆中心线和接触线参数取值范围。
4.制定等直径钩杆空间螺旋线齿轮的弯曲疲劳无限寿命设计准则。分别针对等直径钩杆空间螺旋线齿轮啮合传动的主动钩杆和从动钩杆进行受力分析，结合ANSYS有限元数值模拟仿真，推导主动钩杆根部最大名义应力解析式，拟合具有普适性的主动钩杆根部理论应力集中系数的函数表达式。根据疲劳强度理论，结合安全系数法，制定等直径钩杆空间螺旋线齿轮的弯曲疲劳无限寿命设计准则。
5.研究等直径钩杆空间螺旋线齿轮主动钩杆结构优化设计。分析主动钩杆各项螺旋参数与主动钩杆应力和变形之间的变化规律，确定包括螺旋升角在内的各项设计参数的最优取值范围，提高等直径钩杆空间螺旋线齿轮传动副的承载能力和抗变形能力。
Micro-electro mechanical systems (MEMS) have advantages of structure miniaturization,functional diversities, intelligent, low energy consumption, high sensitivity and efficiency.The most important characteristics of MEMS products are small size and light weight, whichare mostly using for low-power motion transmission and dividing movement. Theconventional power transmission is no longer applicable for MEMS. Therefore, theinnovative research of work principle, performance characteristics and the design andmanufacture of small devices or microdevices has become one of the hot and importantresearch fields of mechanical transmission.
The domestic and foreign research results of microdevices are analyzed systematically inthis dissertation. On the basis of space-curve meshing-wheel (SCMW) transmissionmechanism used for orthogonal shaft drive, the coplanar axes spatial helix gear with equaldiameter of tines is researched. The generalized mesh theory is founded firstly, which suits fortransmission between arbitrary angle intersected axes and parallel axes in one plane. The keypoints of industrialized application are researched, which will lay the foundation ofindependent and complete design theory of coplanar axes spatial helix gear with equaldiameter of tines. Lots of analysis and experimental study indicate that the proposed coplanaraxes spatial helix gear with equal diameter of tines has guidance and feasibility forindustrialized application. The detailed work accomplished in this dissertation is as follows.
First of all, the generalized space curve mesh theory is established for transmissionmotion between arbitrary intersected axes and parallel axes in one plane. Based on the spacemesh coordinate systems, constraint conditions of space mesh are indicated and the vectorrelationships between the driving and driven tines are analyzed. Then the equations of thecontact curves and the central curves of the driving and driven tines of coplanar axes spatialhelix gear are deduced.
Secondly, the design formula of contact ratio is deduced based on the generalized meshequation of coplanar axes spatial helix gear. Impacting factors of the contact ratio areanalyzed, and different design methods for contact ratio are discussed. The least tooth numberof the driving wheel is studied, according to the impacting factors. Then material samples aremanufactured for kinematics simulation and experiments. Numerical examples illustrate thedesign formula of contact ratio and the kinematics performance of the coplanar axes spatialhelix gear mechanism.
Thirdly, the standardized parameters design for spatial helix gear with equal diameter oftines is worked out. The tooth profile structure parameters for the spatial helix gear with equaldiameter of tines are studied, including tooth number, helical angle, helical pitch, diameter oftines, height of teeth etc., and the central distance of the coordinate systems is determined.Then the basic design parameter and basic design size of spatial helix gear with equaldiameter of tines are determined. The parameters value scope of central curve of the drivingand driven tines are corrected to avoid interference between the bodies of the wheels.
Fourthly, a design criterion of bending fatigue infinite lifetime for spatial helix gear withequal diameter of tines is presented. Applied forces and the maximum localized stressesbetween the meshing tines of spatial helix gear with equal diameter of tines are analyzed.Analytic formula for the maximum nominal stress at the end of the tine is deduced, combinedwith ANSYS simulation. The equation of theoretical stress concentration factor is fittednumerically, which suits for the general application situation. According to fatigue theory, thedesign criterion of bending fatigue infinite lifetime for spatial helix gear with equal diameterof tines is presented, combined with safety factor method. Then a numerical exampleillustrates the design criterion.
Fifthly, optimization design for driving tine’s structure of spatial helix gear with equaldiameter of tines is presented. The variation between the skew parameters and the stress anddeformation of the driving tine is analyzed, and the optimum value scope of the skewparameters including helix angle with equal diameter of tines are determined, which willhighly improve the carrying capacity and anti-distortion capacity of the spatial helix gearmechanism.
本文首先针对国内外微小/微传动机构及驱动装置的研究成果进行了系统性的阐述与分析，然后在前期用于正交轴传动的空间曲线啮合轮传动机构的研究基础上，开展了同平面轴等直径钩杆空间螺旋线齿轮设计理论研究。首先，建立了具有普适性的用于同平面内任意角度交叉轴和平行轴传动的空间曲线啮合理论。在此基础上，研究解决等直径钩杆空间螺旋线齿轮传动机构工业化应用的关键问题，从而为构建独立而完整的同平面轴等直径钩杆空间螺旋线齿轮设计理论奠定基础。大量理论分析与实验研究表明，本文研究的同平面轴等直径钩杆空间螺旋线齿轮具有工业化应用的指导性与可行性。
总体来说，本文具体开展了以下几个方面的研究工作：
1.建立了适用于任意角度交叉轴和平行轴传动的空间曲线啮合方程。首先建立了空间曲线啮合坐标系，分析空间曲线啮合的约束条件，推导具备普适性的轴线共面的空间曲线啮合方程。根据主从动钩杆空间矢量关系，得到等直径钩杆空间螺旋线齿轮主从动钩杆的接触线与中心线方程。
2.在轴线共面的空间曲线啮合方程的基础上，推导等直径钩杆空间螺旋线齿轮的重合度设计公式。分析影响等直径钩杆空间螺旋线齿轮重合度的各项参数，研究重合度的几种设计方法。在重合度设计公式及其影响因素基础上，研究主动钩杆的最少齿数，并针对传动连续性和平稳性进行运动学仿真分析和实验研究，验证重合度设计公式的正确性。
3.研究等直径钩杆空间螺旋线齿轮参数标准化设计。分析等直径钩杆空间螺旋线齿轮主从动轮的各项齿形结构参数，包括齿数、螺旋升角、螺距、钩杆直径、齿高等，确定主从动轮坐标系中心距，确定等直径钩杆空间螺旋线齿轮的基本设计参数和基本设计尺寸。为避免主从动轮之间的干涉，修正主从动钩杆中心线和接触线参数取值范围。
4.制定等直径钩杆空间螺旋线齿轮的弯曲疲劳无限寿命设计准则。分别针对等直径钩杆空间螺旋线齿轮啮合传动的主动钩杆和从动钩杆进行受力分析，结合ANSYS有限元数值模拟仿真，推导主动钩杆根部最大名义应力解析式，拟合具有普适性的主动钩杆根部理论应力集中系数的函数表达式。根据疲劳强度理论，结合安全系数法，制定等直径钩杆空间螺旋线齿轮的弯曲疲劳无限寿命设计准则。
5.研究等直径钩杆空间螺旋线齿轮主动钩杆结构优化设计。分析主动钩杆各项螺旋参数与主动钩杆应力和变形之间的变化规律，确定包括螺旋升角在内的各项设计参数的最优取值范围，提高等直径钩杆空间螺旋线齿轮传动副的承载能力和抗变形能力。
Micro-electro mechanical systems (MEMS) have advantages of structure miniaturization,functional diversities, intelligent, low energy consumption, high sensitivity and efficiency.The most important characteristics of MEMS products are small size and light weight, whichare mostly using for low-power motion transmission and dividing movement. Theconventional power transmission is no longer applicable for MEMS. Therefore, theinnovative research of work principle, performance characteristics and the design andmanufacture of small devices or microdevices has become one of the hot and importantresearch fields of mechanical transmission.
The domestic and foreign research results of microdevices are analyzed systematically inthis dissertation. On the basis of space-curve meshing-wheel (SCMW) transmissionmechanism used for orthogonal shaft drive, the coplanar axes spatial helix gear with equaldiameter of tines is researched. The generalized mesh theory is founded firstly, which suits fortransmission between arbitrary angle intersected axes and parallel axes in one plane. The keypoints of industrialized application are researched, which will lay the foundation ofindependent and complete design theory of coplanar axes spatial helix gear with equaldiameter of tines. Lots of analysis and experimental study indicate that the proposed coplanaraxes spatial helix gear with equal diameter of tines has guidance and feasibility forindustrialized application. The detailed work accomplished in this dissertation is as follows.
First of all, the generalized space curve mesh theory is established for transmissionmotion between arbitrary intersected axes and parallel axes in one plane. Based on the spacemesh coordinate systems, constraint conditions of space mesh are indicated and the vectorrelationships between the driving and driven tines are analyzed. Then the equations of thecontact curves and the central curves of the driving and driven tines of coplanar axes spatialhelix gear are deduced.
Secondly, the design formula of contact ratio is deduced based on the generalized meshequation of coplanar axes spatial helix gear. Impacting factors of the contact ratio areanalyzed, and different design methods for contact ratio are discussed. The least tooth numberof the driving wheel is studied, according to the impacting factors. Then material samples aremanufactured for kinematics simulation and experiments. Numerical examples illustrate thedesign formula of contact ratio and the kinematics performance of the coplanar axes spatialhelix gear mechanism.
Thirdly, the standardized parameters design for spatial helix gear with equal diameter oftines is worked out. The tooth profile structure parameters for the spatial helix gear with equaldiameter of tines are studied, including tooth number, helical angle, helical pitch, diameter oftines, height of teeth etc., and the central distance of the coordinate systems is determined.Then the basic design parameter and basic design size of spatial helix gear with equaldiameter of tines are determined. The parameters value scope of central curve of the drivingand driven tines are corrected to avoid interference between the bodies of the wheels.
Fourthly, a design criterion of bending fatigue infinite lifetime for spatial helix gear withequal diameter of tines is presented. Applied forces and the maximum localized stressesbetween the meshing tines of spatial helix gear with equal diameter of tines are analyzed.Analytic formula for the maximum nominal stress at the end of the tine is deduced, combinedwith ANSYS simulation. The equation of theoretical stress concentration factor is fittednumerically, which suits for the general application situation. According to fatigue theory, thedesign criterion of bending fatigue infinite lifetime for spatial helix gear with equal diameterof tines is presented, combined with safety factor method. Then a numerical exampleillustrates the design criterion.
Fifthly, optimization design for driving tine’s structure of spatial helix gear with equaldiameter of tines is presented. The variation between the skew parameters and the stress anddeformation of the driving tine is analyzed, and the optimum value scope of the skewparameters including helix angle with equal diameter of tines are determined, which willhighly improve the carrying capacity and anti-distortion capacity of the spatial helix gearmechanism.
引文
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