高性能双压力角非对称齿轮传动啮合机理及承载能力研究
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摘要
随着现代科技的发展,要求齿轮的传动性能不断提高,常用的标准渐开线齿轮越来越难以满足实际生产的要求。由于渐开线齿轮的承载能力与压力角有很大关系,为了提高齿轮传动系统的综合承载能力,降低噪音和振动,设计了一种新型不同压力角的非对称渐开线齿轮。本文对非对称渐开线齿轮的承载能力和啮合特性进行了深入系统的理论分析和试验研究,主要的研究内容如下:
(1)设计了非对称齿条刀具,推导了非对称齿轮齿廓坐标方程和齿根过渡曲线方程以及各齿形参数的几何尺寸计算公式,探讨了齿顶变尖情况,对比了对称齿轮与非对称齿轮的4种齿根过渡曲线,同时建立了非对称齿轮共轭齿形的坐标变换矩阵,研制开发了齿轮自动生成程序,并对轮齿模型进行了仿真分析,为后面的研究奠定了理论基础。
(2)通过迭代计算和优化策略提出非对称齿轮齿根弯曲应力解析法,并推导出非对称齿轮在单、双齿啮合区上、下界点和啮合节点的综合曲率半径和齿面接触应力的解析法计算公式。建立了非对称齿轮齿根弯曲应力有限元分析模型,根据有限元非线性理论建立了非对称齿轮接触应力分析模型,通过两种方法对不同压力角组合的非对称齿轮齿根弯曲应力和齿面接触应力进行了计算与对比,分析了齿根弯曲应力和齿面接触应力在一个啮合周期中的变化规律和相关影响因素,同时给出非对称齿轮传动系统设计方法。
(3)基于非对称齿轮啮合机理和系统时变啮合刚度以及综合传递误差的影响,建立了非对称齿轮非线性动力学模型,利用数值仿真方法对其进行了动力学研究,比较了其各种振动特性,分析了齿轮系统各参数对系统动态特性影响。
(4)基于齿轮啮合原理、轮齿接触分析、摩擦学和传热学,以有限元分析方法和理论分析计算相结合为手段,建立了具有较高计算精度的非对称渐开线齿轮传动温度分析的稳态模型和瞬态模型,系统地分析了非对称齿轮本体温度的分布并对非对称齿轮达到热平衡前温度场变化历程进行了探讨。
(5)对经过修形的双鼓形双压力角非对称齿轮在有误差条件下的轮齿表面与啮合过程作了全面推导,编制了轮齿接触分析(TCA)的计算机数值仿真程序,对双鼓形非对称齿轮与对称齿轮在有安装误差情况下的接触迹和传动误差进行仿真计算和对比。
(6)提出了一套通过线切割加工非对称齿轮的自动加工方案,并用相同毛坯材料加工制造了相同参数的非对称与对称齿轮,在高频疲劳试验机上采用双齿脉动加载方法对其进行疲劳强度对比试验,试验结果验证了理论分析的正确性。
With the development of modern scientific technology, the performance of gear transmission is required to improve correspondingly. The traditional involute gear can hardly meet the practical requirements. Because the pressure angles have an effect on load capacity of involute gear, in order to increase load capacity and decrease noise and vibration of gear transmission system, a new-type unsymmetric involute spur gear was designed with double pressure angles on the driving and coast sides. A theoretical and experimental investigation on the load capacity and meshing characteristics of unsymmetric involute gear was made deeply and systematically in this paper. Detailed researches are as below:
(1) Involute rack-cutter with unsymmetric teeth and different pressure angles was designed. The total tooth profile equations and transition curve equations of tooth root for the unsymmetric involute gear were proposed as well as the geometry formulas for tooth shape. Then the characteristics of the tooth tip were investigated and the four types of transition curve of tooth root for unsymmetric and symmetric gears were established and compared. Furthermore, the coordinates transition matrix for conjugate tooth profile of unsymmetric gear was given. By developing relevant programs, the tooth profile of unsymmetric and symmetric gear were simulated and provided a theoretical basis for the following research.
(2) Through iteration algorithm and optimization strategy, the analytic calculation formulas of tooth root bending stress for unsymmetric gear were presented. The analytic calculation formulas of general curvature radius and the tooth face contact stress for unsymmetric gear with different pressure angles were developed in the upper and lower points of single and double teeth meshing areas and meshing pitch point. The finite element model for calculating tooth root bending stress of unsymmetric gear is built. Based on nonlinear theory of finite element, the calculation model of tooth face contact stress for unsymmetric gear is established. By two types of method, the bending stress and contact stress for unsymmetric gear with different combinations of pressure angles were calculated and compared. And the change of the tooth root bending stress and tooth face contact stress were investigated in one
engagement period as well as relevant influence factors. Furthermore, systematical design method of unsymmetric gear transmission was proposed.
(3) The nonlinear dynamic model for unsymmetric gear was proposed on the basis of mesh characteristics, the effect of time-variant mesh stiffness and integrated transmission error of unsymmetric gear system. By applying the method of numerical simulation to the research on nonlinear dynamics, vibration characteristics were compared between standard and unsymmetric gear. And the effect of unsymmetric gear system parameters on the dynamic characteristics of transmission system was studied.
(4) Based on the theories of gear engagement, tooth contact analysis, friction and heat transfer, the three-dimensional steady and transient models of finite element for unsymmetric gear were established to investigate temperature distributions and variations along the contact path. The transformation courses of bulk temperature for unsymmetric and symmetric gear were investigated before gear transmission system got steady conditions.
(5) It was proposed that the process of meshing and contact for unsymmetric gear with double pressure angles in case of modified geometry and alignment errors. Computer programs of tooth contact analysis (TCA) of unsymmetric gear and conventional gear have been developed. The computer programs were applied to analyze and compare contact path and transmission errors for double-crowned pinion with unsymmetric tooth profile and standard symmetric gear where alignment errors exist.
(6) A set of manufacture approach for unsymmetric gear was presented based on wire electrical discharge machining (WEDM). The unsymmetric gear and symmetric gear of the same parameters and rough material were manufactured and bending fatigue strength testing was carried on the HF fatigue-testing machine. And the test results demonstrated the validity of theoretical analysis.
(1)设计了非对称齿条刀具,推导了非对称齿轮齿廓坐标方程和齿根过渡曲线方程以及各齿形参数的几何尺寸计算公式,探讨了齿顶变尖情况,对比了对称齿轮与非对称齿轮的4种齿根过渡曲线,同时建立了非对称齿轮共轭齿形的坐标变换矩阵,研制开发了齿轮自动生成程序,并对轮齿模型进行了仿真分析,为后面的研究奠定了理论基础。
(2)通过迭代计算和优化策略提出非对称齿轮齿根弯曲应力解析法,并推导出非对称齿轮在单、双齿啮合区上、下界点和啮合节点的综合曲率半径和齿面接触应力的解析法计算公式。建立了非对称齿轮齿根弯曲应力有限元分析模型,根据有限元非线性理论建立了非对称齿轮接触应力分析模型,通过两种方法对不同压力角组合的非对称齿轮齿根弯曲应力和齿面接触应力进行了计算与对比,分析了齿根弯曲应力和齿面接触应力在一个啮合周期中的变化规律和相关影响因素,同时给出非对称齿轮传动系统设计方法。
(3)基于非对称齿轮啮合机理和系统时变啮合刚度以及综合传递误差的影响,建立了非对称齿轮非线性动力学模型,利用数值仿真方法对其进行了动力学研究,比较了其各种振动特性,分析了齿轮系统各参数对系统动态特性影响。
(4)基于齿轮啮合原理、轮齿接触分析、摩擦学和传热学,以有限元分析方法和理论分析计算相结合为手段,建立了具有较高计算精度的非对称渐开线齿轮传动温度分析的稳态模型和瞬态模型,系统地分析了非对称齿轮本体温度的分布并对非对称齿轮达到热平衡前温度场变化历程进行了探讨。
(5)对经过修形的双鼓形双压力角非对称齿轮在有误差条件下的轮齿表面与啮合过程作了全面推导,编制了轮齿接触分析(TCA)的计算机数值仿真程序,对双鼓形非对称齿轮与对称齿轮在有安装误差情况下的接触迹和传动误差进行仿真计算和对比。
(6)提出了一套通过线切割加工非对称齿轮的自动加工方案,并用相同毛坯材料加工制造了相同参数的非对称与对称齿轮,在高频疲劳试验机上采用双齿脉动加载方法对其进行疲劳强度对比试验,试验结果验证了理论分析的正确性。
With the development of modern scientific technology, the performance of gear transmission is required to improve correspondingly. The traditional involute gear can hardly meet the practical requirements. Because the pressure angles have an effect on load capacity of involute gear, in order to increase load capacity and decrease noise and vibration of gear transmission system, a new-type unsymmetric involute spur gear was designed with double pressure angles on the driving and coast sides. A theoretical and experimental investigation on the load capacity and meshing characteristics of unsymmetric involute gear was made deeply and systematically in this paper. Detailed researches are as below:
(1) Involute rack-cutter with unsymmetric teeth and different pressure angles was designed. The total tooth profile equations and transition curve equations of tooth root for the unsymmetric involute gear were proposed as well as the geometry formulas for tooth shape. Then the characteristics of the tooth tip were investigated and the four types of transition curve of tooth root for unsymmetric and symmetric gears were established and compared. Furthermore, the coordinates transition matrix for conjugate tooth profile of unsymmetric gear was given. By developing relevant programs, the tooth profile of unsymmetric and symmetric gear were simulated and provided a theoretical basis for the following research.
(2) Through iteration algorithm and optimization strategy, the analytic calculation formulas of tooth root bending stress for unsymmetric gear were presented. The analytic calculation formulas of general curvature radius and the tooth face contact stress for unsymmetric gear with different pressure angles were developed in the upper and lower points of single and double teeth meshing areas and meshing pitch point. The finite element model for calculating tooth root bending stress of unsymmetric gear is built. Based on nonlinear theory of finite element, the calculation model of tooth face contact stress for unsymmetric gear is established. By two types of method, the bending stress and contact stress for unsymmetric gear with different combinations of pressure angles were calculated and compared. And the change of the tooth root bending stress and tooth face contact stress were investigated in one
engagement period as well as relevant influence factors. Furthermore, systematical design method of unsymmetric gear transmission was proposed.
(3) The nonlinear dynamic model for unsymmetric gear was proposed on the basis of mesh characteristics, the effect of time-variant mesh stiffness and integrated transmission error of unsymmetric gear system. By applying the method of numerical simulation to the research on nonlinear dynamics, vibration characteristics were compared between standard and unsymmetric gear. And the effect of unsymmetric gear system parameters on the dynamic characteristics of transmission system was studied.
(4) Based on the theories of gear engagement, tooth contact analysis, friction and heat transfer, the three-dimensional steady and transient models of finite element for unsymmetric gear were established to investigate temperature distributions and variations along the contact path. The transformation courses of bulk temperature for unsymmetric and symmetric gear were investigated before gear transmission system got steady conditions.
(5) It was proposed that the process of meshing and contact for unsymmetric gear with double pressure angles in case of modified geometry and alignment errors. Computer programs of tooth contact analysis (TCA) of unsymmetric gear and conventional gear have been developed. The computer programs were applied to analyze and compare contact path and transmission errors for double-crowned pinion with unsymmetric tooth profile and standard symmetric gear where alignment errors exist.
(6) A set of manufacture approach for unsymmetric gear was presented based on wire electrical discharge machining (WEDM). The unsymmetric gear and symmetric gear of the same parameters and rough material were manufactured and bending fatigue strength testing was carried on the HF fatigue-testing machine. And the test results demonstrated the validity of theoretical analysis.
引文
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