螺旋锥齿轮数字化制造基础应用技术研究
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摘要
螺旋锥齿轮作为相交轴传动的基础元件,由于其重合度高,传动平稳,噪声小,承载能力大,传动比大等优点被广泛应用于汽车、工程机械、矿山机械、航空等领域动力机械关键部件。随着我国制造业的快速发展,上述领域对螺旋锥齿轮的需求量很大,因此提高螺旋锥齿轮加工效率和质量是目前螺旋锥齿轮加工行业追求的目标,而采用螺旋锥齿轮数字化制造是实现这一目标的主要途径。数字化制造基础应用技术软件的核心部分包括齿面接触分析(TCA)技术和齿面误差修正技术,与国外相比还有很大差距,本文从提高TCA计算的稳定性、提高运行速度和分析结果的精确性以及研究齿面误差修正技术的本质出发,以国内外最新的研究成果为基础,采用计算机仿真为方法和手段,对TCA技术和齿面误差修正技术相关的理论及其方法进行了深入的研究。
论文的主要成果及创新点如下:
1、基于啮合理论和加工方法建立了螺旋锥齿轮数学模型,基于该模型建立了螺旋锥齿轮三维实体模型,并提出采用齿面偏差法验证所建立实体模型的精度。该方法对验证采用切齿仿真得到的螺旋锥齿轮实体模型的精度同样适用。
2、为提高齿面接触分析的稳定性将传统的求解齿面接触迹线方程组方程数目减少到了3个,通过论文中推导的初始值自动求解算法,可自动的给出求解该方程的初始值,从而提高了TCA计算的稳定性及运行速度。
3、由于目前采用求解的点接触共轭齿面瞬时接触椭圆基本公式是在微分几何相关理论基础上,在瞬时接触点处二阶近似进行的(进行二阶泰勒展开),计算结果会出现误差;同时采用传统赫兹理论计算接触椭圆时,求解公式和求解过程也比较复杂,对此,本文采用了数值法求解齿面瞬时接触区域,不仅简化了求解过程,而且避免了传统方法求解瞬时接触椭圆法所带来的误差。
4、目前国内外TCA分析得到的接触区的结果都是二维的,本文基于螺旋锥齿轮实体模型,得到了三维的齿面接触区,使得接触区的效果更加直观。
5、建立了基于齿面坐标测量齿面误差修正公式,并验证了该公式的有效性,通过建立各阶误差与机床调整参数调整量关系式,揭示了齿面误差修正的本质。
在本文研究成果的基础上,即可反求推导出弧齿锥齿轮和准双曲面齿轮成套数控制造设备的加工及检测程序软件,从而实现数字化制造。
本论文以国家高技术研究发展计划(863计划)项目“汽车螺旋锥齿轮高效精密加工成套装备”(项目号:2007AA042005)为主要支持。
Spiral bevel gear drives are widely used in the intersecting axis transmission with its high contact ratio, transmitting smoothly, lower noise, higher strengthen and large transmission ratio, such the machinery as transports, construction machinery, mining machinery, aviation and so on. With the development manufacturing, there is a great demand for it. Manufacturing spiral bevel gear efficiently with High Quality is the aim of gear industry, digitized manufacturing for spiral bevel gear is the main way to achieve it. Core of software of digitized manufacturing is Tooth Contact analysis(TCA) and correction of the error of tooth surface, which has great disparity with the western developed country. Based on the latest research results of the meshing theory and by means of computer simulation, stability and running speed in the TCA running process, accuracy of TCA result, essence of correction of the error of tooth surface is research systematically.
In the thesis, the research achievements and creative include:
1. Mathematical model of spiral bevel gear is built based meshing theory and manufacturing method, Method of 3D solid modeling of spiral bevel gear with accurate gear tooth surface based on manufacture method and theory of meshing was developed, Surface deviation method was given to analyze accuracy of the model, the method can be used to analyzed the model get by tooth cutting simulation as well.
2. To improve stability in the process of TCA running, number of equations used for TCA is reduced to three.
3. The classical approach to acquire the instantaneous contact region, based on differential geometry, was expanded with the second-order Taylor-series, which will affect accuracy of result. Both equations and procedure based on the hertz theory for determine the instantaneous contact region is complicated. A new method with numerical solutions to derivate instantaneous contact region is developed in the thesis, which is free of the disadvantages mentioned above
4. Result of contact region by traditionally TCA method is plane, by the method proposed in the thesis Three-dimensional contact region can be obtained, which is more direct.
5. Equations of surface corrections are derived based on coordinate measurement, Essence of correction of the error of tooth surface is revealed by functions between correspond orders of error surface and machine settings.
Based on research results of the thesis, Manufacturing and detecting software for spiral bevel gear and hypiod gear complete set numerical control manufacturing equipment can developed.
The thesis is supported by national“863”project of china: precise and effective complete set manufacturing equipment for auto mobile spiral bevel gear and hypiod gear(No. 2007AA042005).
论文的主要成果及创新点如下:
1、基于啮合理论和加工方法建立了螺旋锥齿轮数学模型,基于该模型建立了螺旋锥齿轮三维实体模型,并提出采用齿面偏差法验证所建立实体模型的精度。该方法对验证采用切齿仿真得到的螺旋锥齿轮实体模型的精度同样适用。
2、为提高齿面接触分析的稳定性将传统的求解齿面接触迹线方程组方程数目减少到了3个,通过论文中推导的初始值自动求解算法,可自动的给出求解该方程的初始值,从而提高了TCA计算的稳定性及运行速度。
3、由于目前采用求解的点接触共轭齿面瞬时接触椭圆基本公式是在微分几何相关理论基础上,在瞬时接触点处二阶近似进行的(进行二阶泰勒展开),计算结果会出现误差;同时采用传统赫兹理论计算接触椭圆时,求解公式和求解过程也比较复杂,对此,本文采用了数值法求解齿面瞬时接触区域,不仅简化了求解过程,而且避免了传统方法求解瞬时接触椭圆法所带来的误差。
4、目前国内外TCA分析得到的接触区的结果都是二维的,本文基于螺旋锥齿轮实体模型,得到了三维的齿面接触区,使得接触区的效果更加直观。
5、建立了基于齿面坐标测量齿面误差修正公式,并验证了该公式的有效性,通过建立各阶误差与机床调整参数调整量关系式,揭示了齿面误差修正的本质。
在本文研究成果的基础上,即可反求推导出弧齿锥齿轮和准双曲面齿轮成套数控制造设备的加工及检测程序软件,从而实现数字化制造。
本论文以国家高技术研究发展计划(863计划)项目“汽车螺旋锥齿轮高效精密加工成套装备”(项目号:2007AA042005)为主要支持。
Spiral bevel gear drives are widely used in the intersecting axis transmission with its high contact ratio, transmitting smoothly, lower noise, higher strengthen and large transmission ratio, such the machinery as transports, construction machinery, mining machinery, aviation and so on. With the development manufacturing, there is a great demand for it. Manufacturing spiral bevel gear efficiently with High Quality is the aim of gear industry, digitized manufacturing for spiral bevel gear is the main way to achieve it. Core of software of digitized manufacturing is Tooth Contact analysis(TCA) and correction of the error of tooth surface, which has great disparity with the western developed country. Based on the latest research results of the meshing theory and by means of computer simulation, stability and running speed in the TCA running process, accuracy of TCA result, essence of correction of the error of tooth surface is research systematically.
In the thesis, the research achievements and creative include:
1. Mathematical model of spiral bevel gear is built based meshing theory and manufacturing method, Method of 3D solid modeling of spiral bevel gear with accurate gear tooth surface based on manufacture method and theory of meshing was developed, Surface deviation method was given to analyze accuracy of the model, the method can be used to analyzed the model get by tooth cutting simulation as well.
2. To improve stability in the process of TCA running, number of equations used for TCA is reduced to three.
3. The classical approach to acquire the instantaneous contact region, based on differential geometry, was expanded with the second-order Taylor-series, which will affect accuracy of result. Both equations and procedure based on the hertz theory for determine the instantaneous contact region is complicated. A new method with numerical solutions to derivate instantaneous contact region is developed in the thesis, which is free of the disadvantages mentioned above
4. Result of contact region by traditionally TCA method is plane, by the method proposed in the thesis Three-dimensional contact region can be obtained, which is more direct.
5. Equations of surface corrections are derived based on coordinate measurement, Essence of correction of the error of tooth surface is revealed by functions between correspond orders of error surface and machine settings.
Based on research results of the thesis, Manufacturing and detecting software for spiral bevel gear and hypiod gear complete set numerical control manufacturing equipment can developed.
The thesis is supported by national“863”project of china: precise and effective complete set manufacturing equipment for auto mobile spiral bevel gear and hypiod gear(No. 2007AA042005).
引文
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