螺旋锥齿轮齿面三坐标测量机测量关键技术与测量数据应用研究
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摘要
螺旋锥齿轮是现代传动系统中的重要部件。随着工业的不断发展,对螺旋锥齿轮的高精度制造要求越来越高,在满足有高的承载能力同时还要求传动平稳、低噪音、低振动等工作性能。齿轮测量技术作为加工过程中的重要一环,其地位日益突出。检测手段已由传统的滚检实验发展到基于三坐标测量的真实齿面几何结构检测,进而实现齿面精度控制的数字化制造技术。目前国际上较为广泛地采用专用的齿轮测量中心测量螺旋锥齿轮的几何信息,由于价格昂贵、进口受限且不能用于其他零部件的测量,阻碍了我国螺旋锥齿轮数字化制造的进步,因此应用三坐标测量机这种通用型的零部件几何量测量设备,研究利用三坐标测量机获得螺旋锥齿轮齿面几何信息,进行真实齿面的接触分析和加工调整参数的反调修正,以控制齿面几何精度,对我国齿轮产品质量提高具有重要的理论与工程应用价值。本文的主要研究内容如下：
1.根据螺旋锥齿轮的加工原理,建立了螺旋锥齿轮的齿面数学模型,利用数学软件MATLAB计算出齿面离散点并建立出齿轮的实体模型,为螺旋锥齿轮的齿面测量、真实齿面啮合分析和机床参数的修正奠定了理论基础。
2.研究了基于三坐标测量机的螺旋锥齿轮测量技术。将理论齿面旋转投影后规划测量网格,计算出测量网格点的坐标值和单位法向量坐标值并导入坐标机中。详细分析了坐标机的构成及功能、测量坐标系的变换、测量的旋转定位和测量的具体步骤。进行了测量实验,将理论齿面数据与实测数据比较后得到法向偏差列表,最终得到差曲面图,为螺旋锥齿轮的真实齿面拟合及机床参数的反调提供可靠的依据。
3.探讨了根据实测数据拟合真实齿面并进行有限元分析的方法。建立了真实齿面的数学模型,提出了用有限元软件对真实齿面进行接触分析的方法。
4.利用函数法建立机床加工参数与齿面误差的关系,并运用序列二次规划法求解机床加工参数的修正量,在三坐标测量机上验证该方法的可行性。
Spiral bevel gear is important transmission fundamental component applied in modern gearing. As the marked development of manufacture technology, the acquire for high-precision of the spiral bevel gear is increasing accuracy. With the need of the ability of the high-load bearing, the performance which contains smooth-transmission, low-noise and low-vibration and so forth should be satisfied. So the tooth surface measurement technology playing an increasingly important role in the processing of gears. Nowadays, the measurement have evolved from the traditional contact precision control to the real tooth surface geometrical precision control used on the coordinate measuring machine, to implement digitization technology based on tooth surface geometrical control technology. Presently, the geometric information of the spiral bevel gear is usually measured by the specialized gear measuring center internationally. As the measuring center is high-price and the measurement technique is kept secret, wich prevent the advancement of the digital manufacturing of our national gear industry. Therefore, it is very important to control the geometric precision of tooth for and improving the quality of the gear that research the technology of gear tooth measurement on the coordinate measuring machine which is the universal dimensional measuring equipment. Then, the measurement result will be used to analyze the information of tooth contacting and correct the machine-settings, which would put forth in this paper has theoretical consequences and better applicable value in engineering.
1. According to the manufacturing theory of spiral bevel gear, the mathematic model of tooth surface is established. And the solid model is build after the spots of tooth surface accounted by MATALB. They are the theoretical foundation for the surface measurement, the analyze of the real tooth contact and the correction the machine-settings.
2. Researched the measurement of spiral bevel gear in the coordinate measuring machine. The measuring grid is programmed on the theoretical tooth surface which is projected vortically. The coordinate value of the measuring grid and the unit normal vector coordinates are calculated and imported in the coordinate measuring machine. The contents including the component and the function of the coordinate measuring machine, the conversion between the gear coordinate system and the measurement coordinate system, the tooth rotational position and concrete step of measuring are studied in detail. The measuring experiment is performed. And it is found that the normal errors between the theoretical date and real-test date are calculated in the errors map. Those dates are the reliable basis of fitting the real tooth surface and correcting the machine-settings.
3. Discussed the technology of fitting real tooth surface based on the real-test dates and the finite element analysis. The mathematic model of the real surface is built, and the contact analyze of real gears is complete by the finite element software.
4. The Sequential Quadratic Programming method is advanced to solve the over determined set of the machine tool regulation parameter and the normal error of the tooth. Some instances of real tooth surface measurement and machine-settings correction calculation are experimented on the coordinate measuring machine
1.根据螺旋锥齿轮的加工原理,建立了螺旋锥齿轮的齿面数学模型,利用数学软件MATLAB计算出齿面离散点并建立出齿轮的实体模型,为螺旋锥齿轮的齿面测量、真实齿面啮合分析和机床参数的修正奠定了理论基础。
2.研究了基于三坐标测量机的螺旋锥齿轮测量技术。将理论齿面旋转投影后规划测量网格,计算出测量网格点的坐标值和单位法向量坐标值并导入坐标机中。详细分析了坐标机的构成及功能、测量坐标系的变换、测量的旋转定位和测量的具体步骤。进行了测量实验,将理论齿面数据与实测数据比较后得到法向偏差列表,最终得到差曲面图,为螺旋锥齿轮的真实齿面拟合及机床参数的反调提供可靠的依据。
3.探讨了根据实测数据拟合真实齿面并进行有限元分析的方法。建立了真实齿面的数学模型,提出了用有限元软件对真实齿面进行接触分析的方法。
4.利用函数法建立机床加工参数与齿面误差的关系,并运用序列二次规划法求解机床加工参数的修正量,在三坐标测量机上验证该方法的可行性。
Spiral bevel gear is important transmission fundamental component applied in modern gearing. As the marked development of manufacture technology, the acquire for high-precision of the spiral bevel gear is increasing accuracy. With the need of the ability of the high-load bearing, the performance which contains smooth-transmission, low-noise and low-vibration and so forth should be satisfied. So the tooth surface measurement technology playing an increasingly important role in the processing of gears. Nowadays, the measurement have evolved from the traditional contact precision control to the real tooth surface geometrical precision control used on the coordinate measuring machine, to implement digitization technology based on tooth surface geometrical control technology. Presently, the geometric information of the spiral bevel gear is usually measured by the specialized gear measuring center internationally. As the measuring center is high-price and the measurement technique is kept secret, wich prevent the advancement of the digital manufacturing of our national gear industry. Therefore, it is very important to control the geometric precision of tooth for and improving the quality of the gear that research the technology of gear tooth measurement on the coordinate measuring machine which is the universal dimensional measuring equipment. Then, the measurement result will be used to analyze the information of tooth contacting and correct the machine-settings, which would put forth in this paper has theoretical consequences and better applicable value in engineering.
1. According to the manufacturing theory of spiral bevel gear, the mathematic model of tooth surface is established. And the solid model is build after the spots of tooth surface accounted by MATALB. They are the theoretical foundation for the surface measurement, the analyze of the real tooth contact and the correction the machine-settings.
2. Researched the measurement of spiral bevel gear in the coordinate measuring machine. The measuring grid is programmed on the theoretical tooth surface which is projected vortically. The coordinate value of the measuring grid and the unit normal vector coordinates are calculated and imported in the coordinate measuring machine. The contents including the component and the function of the coordinate measuring machine, the conversion between the gear coordinate system and the measurement coordinate system, the tooth rotational position and concrete step of measuring are studied in detail. The measuring experiment is performed. And it is found that the normal errors between the theoretical date and real-test date are calculated in the errors map. Those dates are the reliable basis of fitting the real tooth surface and correcting the machine-settings.
3. Discussed the technology of fitting real tooth surface based on the real-test dates and the finite element analysis. The mathematic model of the real surface is built, and the contact analyze of real gears is complete by the finite element software.
4. The Sequential Quadratic Programming method is advanced to solve the over determined set of the machine tool regulation parameter and the normal error of the tooth. Some instances of real tooth surface measurement and machine-settings correction calculation are experimented on the coordinate measuring machine
引文
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