面向使用性能的人字齿轮对称度误差评定方法研究

Research on evaluation method of symmetry error of herringbone gear oriented to performance

齿轮副接触线的性质反映了齿轮传动的啮合性能,为了研究人字齿轮对称度误差对啮合传动的影响,从人字齿轮使用性能角度考虑,提出一种通过测量人字齿轮两侧轮齿中同侧齿面啮合瞬时接触线来评定对称度误差的方法。首先,根据渐开线人字齿轮齿廓的几何特征,并结合斜齿轮接触线的定义,给出人字齿轮接触线和基于接触线的对称度误差的定义。其次,建立人字齿轮接触线的数学模型,模拟构造理论接触线和叠加误差的实际接触线离散数据,利用最小二乘法对模拟数据进行拟合,获得实际接触线。最后,通过计算两侧轮齿中同侧齿面啮合瞬时接触线交点到人字齿轮对称中心平面的距离,得到人字齿轮的齿面接触线对称度误差。算例表明,人字齿轮周向成120°夹角的2个轮齿接触线的对称度误差分别为0.019007和0.019772 mm,与通过测量螺旋线获得的对称度误差0.019089和0.019816 mm基本一致,该方法为面向使用性能的人字齿轮对称度误差的测量、评定奠定了基础。

The nature of the contact line of the gear pair reflects the meshing performance of the gear transmission.In order to study the influence of the herringbone gear′s symmetry error on the meshing transmission,considered from the perspective of performance of the herringbone gear,a kind of method was proposed to evaluate the symmetry error by measuring the instantaneous contact line of the teeth surface on the same side of the gear teeth on both sides of the herringbone gear.Firstly,according to the geometric characteristics of the tooth profile of the involute herringbone gear and the definition of the contact line of the helical gear,the definition of the contact line of the herringbone gear and the symmetry error based on the contact line was given.Secondly,the contact line mathematical model of the herringbone gear was established,the theoretical contact line and the actual contact line discrete data with the superposition error were simulated and constructed,and the least square method was used to fit the simulated data to obtain the actual contact line.Finally,by calculating the distance from the intersection of the contact line of the teeth surface on the same side to the symmetrical center plane of the herringbone gear when the gear teeth on both sides are meshed instantaneously,the symmetry error of the tooth surface contact line of the herringbone gear was obtained.The calculation example shows that the symmetry errors of the contact lines of the two gear teeth with an angle of 120° in the circumferential direction of the herringbone gear are 0.019 007 and 0.019 772 mm respectively,which are basically consistent with the symmetry errors of 0.019 089 and 0.019 816 mm obtained by measuring the spiral line.The method proposed has laid the foundation for the measurement and evaluation of the symmetry error of herringbone gears oriented to performance.