螺旋锥齿轮计算机辅助制造理论与算法研究
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摘要
在螺旋锥齿轮加工制造业广泛采用计算机辅助制造系统,为设计计算,加工理论分析,加工方法检验等方面服务,有助于优化加工过程,检验加工精度,预测加工制造结果。将虚拟制造技术与螺旋锥齿轮的加工制造理论相结合,构建螺旋锥齿轮辅助制造三维平台,研究开发螺旋锥齿轮计算机辅助制造系统的关键技术。
将传统的HFT加工方法转换为数控加工方法,对五轴联动数控螺旋锥齿轮机床的加工运动过程进行仿真,提出一种基于解析计算的切削仿真算法,将刀具切削工件形成齿面的过程离散成一系列刀具圆锥体切削工件层圆的瞬时运动,通过解析计算求解圆锥体和层圆的交点来获得分布均匀的齿面数据点,实现螺旋锥齿轮多次切削可视化仿真。为提高仿真过程中的切削速度采用三角面片缝合齿面来显示切削过程,生成的齿轮采用NURBS曲面显示。
根据齿面数据点、齿坯参数建立齿轮的层圆模型和NURBS体两种模型,在此基础上提出一种可应用于运动NURBS体齿轮的干涉检查算法。该算法将NURBS体齿轮对中齿面干涉、齿面求交问题转化成一个NURBS齿面与另一个齿面上各点的运动轨迹圆的求交问题,进而给出圆与NURBS曲面求交的算法及齿面存在多个干涉区时的曲面求交算法。
在NURBS体模型基础上,建立数控加工齿轮的装配坐标系,进行齿轮的装配,结合干涉检查算法给出啮齿过程的接触点仿真算法,并生成齿面接触轨迹和几何接触区,为齿轮参数优化提供参考。
为了控制齿面的加工质量,基于滚切法加工原理,提出一种采用数值法精确计算齿面残留高度的算法,建立滚切齿面数学模型。该模型确立了刀倾法加工螺旋锥齿轮时齿面残留高度与刀片数量、刀盘转速、摇台转速与摇台转角范围的参数关系,计算齿面不同取样处残留高度的理论值,预估齿面粗糙度。
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设备”(项目号:2007AA042005)为主要支持。
Processing and manufacturing of spiral bevel gears widely adopted computer-aided manufacturing systems for processing design, theoretical analysis, inspection, etc. The virtual manufacturing technology was combined with the manufacturing theory of spiral bevel gear combination to construct three-dimensional spiral bevel gear aided manufacturing platform and provide the support for CNC machine.
A cutting simulation algorithm of spiral bevel gears was put forward to verify the movement in the CNC machine cutting process. The algorithm separated the cutting process into a series of discrete cutting movements. The cutting movement number was quantified by computing the amount of cutting blades. For any discrete movement, the algorithm interpreted the cutter blades and the spiral bevel gear as cones and layer circles respectively. So the data points on the gear tooth surface were generated by calculating the intersection points of the cones and circles. The algorithm adopted analytic calculation and was applied on the multiple cutting movements simulation of the spiral bevel gear. To improve the cutting simulation speed, the triangular patches stitched technology was put forward to display the cutting tooth surface, while the NURBS fitted surface are adopted to show the solid of spiral bevel gear.
To achieve spiral bevel gear pairs’interference points or areas during the meshing movement, an interference check algorithm was put forward. Based on the gear parameters and points on the tooth surface, the algorithm established two kinds of gear models including a series of circles model and NUBRS one to describe the spiral bevel gear. In view of the complexity of NUBRS surface intersection and the characters of meshing movement, this problem was transferred into the intersection between the NUBRS tooth surface of pinion and a series of circles of gear. Meanwhile the intersection algorithm between the circle and NUBRS surface was proposed in the case of single or multi intersection areas.
The simulation method was applied to analyze the meshing process of spiral bevel gear pairs. The gear and pinion were assembled with the assembly constraints. Based on the geometrical bodies’interference check, a contact point simulation algorithm of tooth contact was proposed to estimate the contact condition of tooth surface. The corresponding computer simulation program was developed to generate the instantaneous contact points, compute the transmission errors and describe the contact area.
Based on the tilt generated cutting principle, a numerical algorithm of scallop height was put forward to control the cutting surface quality of spiral bevel gears. The cutting process was described as a series of non-continuous cutting movements of blades. The designed parameters of cutter blades and cutting process parameters were combined to build the mathematical tooth surface model. The mathematical model established the relationship among the scallop height, the blades number, the cutter rotational speed, the roll rate and the roll rotation angle. According to the mathematical model, scallop heights were computed by numerical algorithm and the influence of cutting process parameters was analyzed.
The thesis is supported by national“863”project of china: precise and effective complete set manufacturing equipment for auto mobile spiral bevel gear and hypoid gear (No.2007AA042005).
将传统的HFT加工方法转换为数控加工方法,对五轴联动数控螺旋锥齿轮机床的加工运动过程进行仿真,提出一种基于解析计算的切削仿真算法,将刀具切削工件形成齿面的过程离散成一系列刀具圆锥体切削工件层圆的瞬时运动,通过解析计算求解圆锥体和层圆的交点来获得分布均匀的齿面数据点,实现螺旋锥齿轮多次切削可视化仿真。为提高仿真过程中的切削速度采用三角面片缝合齿面来显示切削过程,生成的齿轮采用NURBS曲面显示。
根据齿面数据点、齿坯参数建立齿轮的层圆模型和NURBS体两种模型,在此基础上提出一种可应用于运动NURBS体齿轮的干涉检查算法。该算法将NURBS体齿轮对中齿面干涉、齿面求交问题转化成一个NURBS齿面与另一个齿面上各点的运动轨迹圆的求交问题,进而给出圆与NURBS曲面求交的算法及齿面存在多个干涉区时的曲面求交算法。
在NURBS体模型基础上,建立数控加工齿轮的装配坐标系,进行齿轮的装配,结合干涉检查算法给出啮齿过程的接触点仿真算法,并生成齿面接触轨迹和几何接触区,为齿轮参数优化提供参考。
为了控制齿面的加工质量,基于滚切法加工原理,提出一种采用数值法精确计算齿面残留高度的算法,建立滚切齿面数学模型。该模型确立了刀倾法加工螺旋锥齿轮时齿面残留高度与刀片数量、刀盘转速、摇台转速与摇台转角范围的参数关系,计算齿面不同取样处残留高度的理论值,预估齿面粗糙度。
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设备”(项目号:2007AA042005)为主要支持。
Processing and manufacturing of spiral bevel gears widely adopted computer-aided manufacturing systems for processing design, theoretical analysis, inspection, etc. The virtual manufacturing technology was combined with the manufacturing theory of spiral bevel gear combination to construct three-dimensional spiral bevel gear aided manufacturing platform and provide the support for CNC machine.
A cutting simulation algorithm of spiral bevel gears was put forward to verify the movement in the CNC machine cutting process. The algorithm separated the cutting process into a series of discrete cutting movements. The cutting movement number was quantified by computing the amount of cutting blades. For any discrete movement, the algorithm interpreted the cutter blades and the spiral bevel gear as cones and layer circles respectively. So the data points on the gear tooth surface were generated by calculating the intersection points of the cones and circles. The algorithm adopted analytic calculation and was applied on the multiple cutting movements simulation of the spiral bevel gear. To improve the cutting simulation speed, the triangular patches stitched technology was put forward to display the cutting tooth surface, while the NURBS fitted surface are adopted to show the solid of spiral bevel gear.
To achieve spiral bevel gear pairs’interference points or areas during the meshing movement, an interference check algorithm was put forward. Based on the gear parameters and points on the tooth surface, the algorithm established two kinds of gear models including a series of circles model and NUBRS one to describe the spiral bevel gear. In view of the complexity of NUBRS surface intersection and the characters of meshing movement, this problem was transferred into the intersection between the NUBRS tooth surface of pinion and a series of circles of gear. Meanwhile the intersection algorithm between the circle and NUBRS surface was proposed in the case of single or multi intersection areas.
The simulation method was applied to analyze the meshing process of spiral bevel gear pairs. The gear and pinion were assembled with the assembly constraints. Based on the geometrical bodies’interference check, a contact point simulation algorithm of tooth contact was proposed to estimate the contact condition of tooth surface. The corresponding computer simulation program was developed to generate the instantaneous contact points, compute the transmission errors and describe the contact area.
Based on the tilt generated cutting principle, a numerical algorithm of scallop height was put forward to control the cutting surface quality of spiral bevel gears. The cutting process was described as a series of non-continuous cutting movements of blades. The designed parameters of cutter blades and cutting process parameters were combined to build the mathematical tooth surface model. The mathematical model established the relationship among the scallop height, the blades number, the cutter rotational speed, the roll rate and the roll rotation angle. According to the mathematical model, scallop heights were computed by numerical algorithm and the influence of cutting process parameters was analyzed.
The thesis is supported by national“863”project of china: precise and effective complete set manufacturing equipment for auto mobile spiral bevel gear and hypoid gear (No.2007AA042005).
引文
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