双圆弧弧齿锥齿轮传动啮合特性的研究
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摘要
双圆弧弧齿锥齿轮是将双圆弧齿形应用在弧齿锥齿轮上的一种新技术,其特点是在齿长方向和齿高方向,均为凸、凹齿廓相啮合,因此与一般的弧齿锥齿轮相比,它具有承载能力高、使用寿命长的优点,这已被产品试验结果所证实。然而由于双圆弧弧齿锥齿轮齿面几何复杂,研究者较少且不深入等原因,限制了它在我国的使用推广。对双圆弧弧齿锥齿轮传动啮合性能进行仿真分析是深入研究双圆弧弧齿锥齿轮啮合特性的有效手段。因此本文从双圆弧弧齿锥齿轮啮合理论出发,利用线图法、齿面接触分析(Tooth Contact Analysis,TCA)以及虚拟仿真加工等计算机仿真方法和试验手段,对双圆弧弧齿锥齿轮的传动啮合特性进行了研究,为其进一步研究、应用和推广打下必要的基础。
论文的主要研究成果及创新点如下:
1)根据双圆弧弧齿锥齿轮切齿加工原理,进行了双圆弧弧齿锥齿轮的切齿啮合分析,应用运动学法建立了切齿啮合过程中的大、小轮产形轮齿面方程、啮合线方程以及双圆弧弧齿锥齿轮的齿面方程表达式。
2)根据弧齿锥齿轮重合度的定义,给出了双圆弧齿廓弧齿锥齿轮重合度的定义;首次采用线图法分析了其啮合过程,建立了双圆弧齿廓弧齿锥齿轮重合度、多点接触系数和多对齿接触系数计算方法;给出了双圆弧弧齿锥齿轮连续传动的条件。通过线图法可以直观展示轮齿啮合的交替过程,对双圆弧弧齿锥齿轮的传动设计、强度计算、齿轮几何参数的合理选择计算以及深入研究其传动性能,具有重要意义。
3)根据TCA分析原理,首次建立了适合于双圆弧弧齿锥齿轮的齿面接触分析方法;分析了双圆弧弧齿锥齿轮几何特性,并应用混合编程方法编制了仿真分析程序;程序中实现了双圆弧弧齿锥齿轮接触点位置、接触椭圆大小、齿面接触区以及传动误差曲线等有关图形的输出。为双圆弧弧齿锥齿轮的设计提供了有效的手段和方法。
4)根据双圆弧弧齿锥齿轮加工原理,以格里森制铣齿机为对象,首次提出了适用于双圆弧弧齿锥齿轮加工的传统机械式铣齿机调整参数转换为数控铣齿机加工调整参数的方法及转换公式;编写了机床各运动轴参数的求解程序,实现了数控(Numerical Control,NC)程序的生成;应用Pro/Engineer(Pro/E)和数控加工仿真系统VERICUT建立了双圆弧弧齿锥齿轮仿真加工模型,包括机床模型、机床控制器、刀具模型以及齿坯实体模型等;完成了双圆弧弧齿锥齿轮的仿真加工和切齿试验,取得了较好的效果。
5)首次分析了各种单项安装误差对双圆弧弧齿锥齿轮啮合质量的影响。利用TCA技术分析验证了本文提出的重合度计算公式的正确性,仿真结果与试验表明,双圆弧弧齿锥齿轮能得到两条接触线,安装误差对齿高方向的影响较大,对齿长方向的影响较小,双圆弧弧齿锥齿轮加工时,要严格控制齿坯尺寸公差及机床调整参数误差。
本文的研究得到了山西省教育厅科技项目的资助(双圆弧弧齿锥齿轮传动性能研究,编号:200811006)。
As a new type spiral bevel gear transmission,double circular arc spiral bevel gear (DCAPSBG) mesh at convex and concave tooth profile in both longitudinal and latitudinal direction which applied double-circular arc tooth on spiral bevel gear. Therefore, it has higher tooth surface contact strength and tooth root bending strength than Gleason spiral bevel gear, which has been proved by product experiments. For the reason that gear tooth surface geometry of DCAPSBG is complex and lack of researchers and further study, these limit its popularization and application in our country. Research meshing characteristics of DCAPSBG using simulation analysis is an effective way to further study its meshing performance. Thus based on the meshing theory of DCAPSBG, this paper researches on the meshing performance of DCAPSBG applying line graph method, tooth contact analysis (TCA) and virtual simulation manufacturing and experiment, and lays a foundation for further study, application and popularization of DCAPSBG.
In the thesis, the research achievements and creative contents include:
1)According to cutting principle of DCAPSBG, cutting and meshing analysis is carried on, equation of generating gear tooth surface and the equation of action line in the processing of cutting tooth as well as the tooth surface equations of DCAPSBG are established using kinematics method.
2) According to contact ratio definition of the spiral bevel gear, the contact ration definition of DCAPSBG is proposed; The meshing process is analyzed using line graph method firstly, calculation methods of the contact ration, multi-point contact coefficient and multi-pair contact coefficient are established; The conditions of continuous transmission are proposed. Through the line graph method, the DCAPSBG tooth meshing process can be displayed visually, which has important significance for the design, strength calculation, reasonable selection of gear geometrical parameters and further study of its transmission performance.
3) Based on TCA analysis principle, tooth contact analysis method which is suitable for DCAPSBG is established firstly; Geometric characteristics of DCAPSBG are analyzed, and TCA analysis software are developed using the hybrid programming method; In term of the developed software, contact point location, contact ellipse size, tooth surface contact area as well as the transmission error curve and other relevant graphics can be output. Which provide effective means and methods for the design of DCAPSBG.
4) On the basis of DCAPSBG machining principle, the thesis proposed method and transformation formulas of machine adjustment parameters from traditional milling machine to CNC gear generator with Gleason milling machine as object; The program of solve parameters of axes motion is developed, which can generate NC (Numerical Control, NC) program; Simulation model (including the machine tool model, machine controllers, cutter header model and gear blanks solid model etc.) of DCAPSBG is established by Pro/E and VERICUT; Virtual simulation machining and actual generating tooth are completed with good effect.
5)The influence of several individual installation errors on meshing quality of DCAPSBG is analyzed in the thesis; The correctness of the contact ratio formula is verified by using TCA; The results of simulation and experiments demonstrate that: there are two contact paths on gear tooth surface, the installation error impacts on tooth depth greater and impacts on the tooth length less. We should control dimensional tolerance errors and machine setting parameters errors strictly when generating DCAPSBG tooth.
The thesis is supported by scientific and technological projects of the Education Department of Shanxi Province (No. 200811006).
论文的主要研究成果及创新点如下:
1)根据双圆弧弧齿锥齿轮切齿加工原理,进行了双圆弧弧齿锥齿轮的切齿啮合分析,应用运动学法建立了切齿啮合过程中的大、小轮产形轮齿面方程、啮合线方程以及双圆弧弧齿锥齿轮的齿面方程表达式。
2)根据弧齿锥齿轮重合度的定义,给出了双圆弧齿廓弧齿锥齿轮重合度的定义;首次采用线图法分析了其啮合过程,建立了双圆弧齿廓弧齿锥齿轮重合度、多点接触系数和多对齿接触系数计算方法;给出了双圆弧弧齿锥齿轮连续传动的条件。通过线图法可以直观展示轮齿啮合的交替过程,对双圆弧弧齿锥齿轮的传动设计、强度计算、齿轮几何参数的合理选择计算以及深入研究其传动性能,具有重要意义。
3)根据TCA分析原理,首次建立了适合于双圆弧弧齿锥齿轮的齿面接触分析方法;分析了双圆弧弧齿锥齿轮几何特性,并应用混合编程方法编制了仿真分析程序;程序中实现了双圆弧弧齿锥齿轮接触点位置、接触椭圆大小、齿面接触区以及传动误差曲线等有关图形的输出。为双圆弧弧齿锥齿轮的设计提供了有效的手段和方法。
4)根据双圆弧弧齿锥齿轮加工原理,以格里森制铣齿机为对象,首次提出了适用于双圆弧弧齿锥齿轮加工的传统机械式铣齿机调整参数转换为数控铣齿机加工调整参数的方法及转换公式;编写了机床各运动轴参数的求解程序,实现了数控(Numerical Control,NC)程序的生成;应用Pro/Engineer(Pro/E)和数控加工仿真系统VERICUT建立了双圆弧弧齿锥齿轮仿真加工模型,包括机床模型、机床控制器、刀具模型以及齿坯实体模型等;完成了双圆弧弧齿锥齿轮的仿真加工和切齿试验,取得了较好的效果。
5)首次分析了各种单项安装误差对双圆弧弧齿锥齿轮啮合质量的影响。利用TCA技术分析验证了本文提出的重合度计算公式的正确性,仿真结果与试验表明,双圆弧弧齿锥齿轮能得到两条接触线,安装误差对齿高方向的影响较大,对齿长方向的影响较小,双圆弧弧齿锥齿轮加工时,要严格控制齿坯尺寸公差及机床调整参数误差。
本文的研究得到了山西省教育厅科技项目的资助(双圆弧弧齿锥齿轮传动性能研究,编号:200811006)。
As a new type spiral bevel gear transmission,double circular arc spiral bevel gear (DCAPSBG) mesh at convex and concave tooth profile in both longitudinal and latitudinal direction which applied double-circular arc tooth on spiral bevel gear. Therefore, it has higher tooth surface contact strength and tooth root bending strength than Gleason spiral bevel gear, which has been proved by product experiments. For the reason that gear tooth surface geometry of DCAPSBG is complex and lack of researchers and further study, these limit its popularization and application in our country. Research meshing characteristics of DCAPSBG using simulation analysis is an effective way to further study its meshing performance. Thus based on the meshing theory of DCAPSBG, this paper researches on the meshing performance of DCAPSBG applying line graph method, tooth contact analysis (TCA) and virtual simulation manufacturing and experiment, and lays a foundation for further study, application and popularization of DCAPSBG.
In the thesis, the research achievements and creative contents include:
1)According to cutting principle of DCAPSBG, cutting and meshing analysis is carried on, equation of generating gear tooth surface and the equation of action line in the processing of cutting tooth as well as the tooth surface equations of DCAPSBG are established using kinematics method.
2) According to contact ratio definition of the spiral bevel gear, the contact ration definition of DCAPSBG is proposed; The meshing process is analyzed using line graph method firstly, calculation methods of the contact ration, multi-point contact coefficient and multi-pair contact coefficient are established; The conditions of continuous transmission are proposed. Through the line graph method, the DCAPSBG tooth meshing process can be displayed visually, which has important significance for the design, strength calculation, reasonable selection of gear geometrical parameters and further study of its transmission performance.
3) Based on TCA analysis principle, tooth contact analysis method which is suitable for DCAPSBG is established firstly; Geometric characteristics of DCAPSBG are analyzed, and TCA analysis software are developed using the hybrid programming method; In term of the developed software, contact point location, contact ellipse size, tooth surface contact area as well as the transmission error curve and other relevant graphics can be output. Which provide effective means and methods for the design of DCAPSBG.
4) On the basis of DCAPSBG machining principle, the thesis proposed method and transformation formulas of machine adjustment parameters from traditional milling machine to CNC gear generator with Gleason milling machine as object; The program of solve parameters of axes motion is developed, which can generate NC (Numerical Control, NC) program; Simulation model (including the machine tool model, machine controllers, cutter header model and gear blanks solid model etc.) of DCAPSBG is established by Pro/E and VERICUT; Virtual simulation machining and actual generating tooth are completed with good effect.
5)The influence of several individual installation errors on meshing quality of DCAPSBG is analyzed in the thesis; The correctness of the contact ratio formula is verified by using TCA; The results of simulation and experiments demonstrate that: there are two contact paths on gear tooth surface, the installation error impacts on tooth depth greater and impacts on the tooth length less. We should control dimensional tolerance errors and machine setting parameters errors strictly when generating DCAPSBG tooth.
The thesis is supported by scientific and technological projects of the Education Department of Shanxi Province (No. 200811006).
引文
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