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在建立含有安装误差的直齿锥齿轮啮合坐标系的基础上,提出了在一点相切接触的两齿面上利用差曲面的Gauss曲率来表示直齿锥齿轮修形齿面安装误差敏感性的方法。用罚函数法来优化接触椭圆长轴,从而得到对安装误差敏感性低的修形直齿锥齿轮的印痕图。研究表明接触椭圆长轴对齿面敏感性系数的影响最大,优化接触椭圆长轴后可获得较好的接触迹线,接触迹线垂直于根锥时能够降低直齿锥齿轮修形齿面安装误差敏感性。 相似文献
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研究了抛物形齿线圆柱齿轮滚切加工方法和齿面接触分析.在推导滚刀齿面方程的基础上,利用抛物形齿线滚切原理和啮合方程推导了其齿面数学模型;根据两齿面在啮合过程中连续相切条件,建立了考虑安装误差的齿面接触分析(Tooth Contact Analysis,TCA)模型.齿面接触分析仿真结果表明,用抛物形刀具齿廓对齿面修形,可改善齿轮副啮合性能;在安装误差条件下,接触印痕将偏离齿宽中心;通过改变抛物形系数,可降低接触印痕对安装误差敏感性. 相似文献
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为了改善弧线齿圆柱齿轮传动的平稳性和轮齿强度,采用四阶传动误差曲线设计齿轮副。首先确定四阶传动误差曲线的系数,用有具有刀倾的刀盘形成的弧线产形齿条和假想小轮的方法,根据坐标变换和啮合方程,分别推导大轮和小轮的齿面方程。由两齿面在啮合中的连续相切条件,建立了考虑安装误差的轮齿接触分析(TCA)模型。齿轮副啮合仿真的结果表明,该方法可实现四阶传动误差,增大啮合转换点处夹角可使齿轮副平稳过渡,减小齿根的修形量可提高轮齿强度,可降低传动误差曲线对安装误差的敏感性。 相似文献
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利用抛物线代替齿条刀具切削刃上的部分直线,实现人字齿轮齿高修形;通过预控抛物线型传动误差,结合刀具切削刃的方程,推导齿条刀具与轮齿的啮合方程,实现人字齿轮齿向修形。建立人字齿轮弯-扭耦合动力学模型和系统的振动微分方程。根据人字齿轮轮齿接触分析方法(TCA)求出齿高修形和齿向修形齿轮的传动误差,并作为误差激励代入人字齿轮动力学方程中,进行修形人字齿轮的动特性研究。通过计算得出预控抛物线传动误差修形可以降低人字齿轮传动的动载系数,从而更有效地达到减振降噪的目的。 相似文献
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推导了考虑齿向修形与齿廓修形条件下的渐开线变厚齿轮齿面数学方程,采用有限元法建立了相交轴渐开线圆柱与变厚齿轮副有限元啮合模型,研究了单独齿向修形,单独齿廓修形与组合修形等不同的修形方式和修形量对接触印痕、齿根应力与传动误差的影响规律。结果表明:与修形前相比,变厚齿轮和圆柱齿轮单独齿向鼓形修形使得齿面接触区域减小,齿面接触应力与齿根弯曲应力增大,传动误差峰峰值增加;圆柱齿轮齿向边坡修形可以使得接触印痕从小端移动至轮齿中部,解决偏载现象;齿廓鼓形修形使得接触印痕呈现增大趋势,可以消除边缘接触现象;接触印痕对齿廓边坡修形最为敏感;变厚齿轮齿廓鼓形修形和圆柱齿轮齿向边坡修形的组合修形方式明显增加接触印痕面积,降低接触应力和传动误差。 相似文献
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渐开线非圆齿轮的齿廓曲线数学模型 总被引:18,自引:2,他引:18
对于给定的非圆齿轮节曲线,借助于共轭齿条建立齿廓曲线的数学模型。根据渐开线齿轮齿廓成形原理,当共轭齿条分度线在非圆齿轮节曲线上作纯滚动,齿条的齿廓便在齿轮上包络出齿轮的齿廓。因此,首先建立了共轭齿条的数学模型和节曲线纯滚动模型,而后用啮合方程将这两个模型结合起来,经坐标变换后便在齿轮坐标系中获得了非圆齿轮齿廓曲线的数学模型。进一步用计算机图形仿真的方法获得椭圆齿轮的渐开线齿廓曲线图形,验证了该模型的正确性和有效性。该模型为非圆齿轮的加工刀具设计、数控加工程序设计以及轮齿强度分析等提供了基础。 相似文献
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Kinematic errors on helical gear of triple circular-arc teeth 总被引:1,自引:0,他引:1
Two imaginary skew rack cutter curves with stepped triple circular-arc teeth are presented in this paper. A helical gear pair that includes the gear and pinion surfaces was generated by using two matched imaginary skew rack cutter surfaces. The mathematical models of the helical gear pair with stepped triple circular-arc teeth were developed based on theory of gearing. With the use of these models, the analysis of kinematic errors can be illustrated and evaluated by computer programming and tooth contact analysis (TCA). The assembly errors used had several kinds: ideal assembly errors, vertical misalignment angles, horizontal misalignment angles, manufacturing errors of helical angles, and center distance deviation. TCA revealed that the sensitivity of horizontal misalignment angles was lower than that of manufacturing errors of helix angles but higher than that of vertical misalignment angles. 相似文献
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Shyue-Cheng Yang 《The International Journal of Advanced Manufacturing Technology》2006,30(5-6):385-394
In this paper a method for the modified profile of a rack cutter is presented. The deviation function method is used to reshape a rack cutter. The author proposes a modified geometry of a rack cutter to generate the driving gear of internal gear pairs. Based on the double envelope concept, the driven gear of a set of internal gear pairs can be determined. In this study, the Von-Mises stress analysis of the reshaped internal gear pairs was carried out and the specific phenomena was also investigated. The results show that it is possible to compensate elastic deformation and reduce contact stress between conjugate gear pairs. In addition, according to the tooth contact analysis on the gear pairs, reshaped gears and conventional gears have also been investigated. Computerized design of internal gears using the proposed method and simulation of their meshing and contact stress analysis of asymmetric internal gears has been developed. The developed method is illustrated with numerical examples. 相似文献
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Mathematical model and undercutting of cylindrical gears with curvilinear shaped teeth 总被引:1,自引:0,他引:1
A rack cutter with a curved-tooth is considered the generating tool for the generation of the proposed gear, and a mathematical model of cylindrical gears with curvilinear shaped teeth is developed according to the gearing theory. The developed computer program can develop profiles of the curvilinear-tooth gear with point contacts. The developed gear tooth mathematical model is used to investigate the tooth undercutting of curvilinear-tooth gears via differential geometry and the numerical method. 相似文献
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He Zeyin Lin Tengjiao Luo Tianhong Deng Tao Hu Qiguo 《Journal of Mechanical Science and Technology》2016,30(11):4859-4867
An approach for a mathematical model and contact analysis of helical gears including tip relief, root relief, end relief and longitudinal crowning modification was developed. First, tooth profile equations of non-modified involutes, tip reliefs, root reliefs and fillets were derived after applying gear principles and coordinate transformation to transverse cross section profiles of a rack cutter. Then the intersecting lines between different profiles were solved through by Gauss-Newton numerical method. Parametric modeling program of modified helical gears was obtained to automatically generate exact gear surfaces of tip reliefs, root reliefs, end reliefs and longitudinal crowning modifications via Matlab code. Subsequently, an example of helical gear pair in practical engineering was presented, and the solid model and finite element model with modification were established. Finally, the dynamic contact characteristic of helical gear pair was calculated by three-dimensional dynamic contact finite element method. It is expected that the proposed approach can be applied in analyzing the effect of modification on radiation noise prediction of gear system in further study. 相似文献
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环面渐开线齿轮是一种对安装误差不敏感,无须修形就具有良好啮合性能,并且加工便捷的新型齿轮。根据环面渐开线齿轮的加工原理,从产形齿条的齿面方程出发,推导了凸环面渐开线齿轮和凹环面渐开线齿轮的完整齿面方程;利用MATLAB编程计算出环面渐开线齿轮齿面上点的三维坐标值,生成了精确齿面,并在Pro/E中建立了齿轮的实体模型;基于齿面数学模型,通过计算仿真对环面渐开线齿轮的根切与尖化现象进行了分析,获得了环面渐开线齿轮的根切界限曲线、尖化初始点以及不发生根切与尖化现象的最大齿宽;根据已生成的齿面进行有安装误差条件下的齿轮接触分析,证明了环面渐开线齿轮对安装误差不敏感。
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针对圆柱型螺旋渐开线齿轮不易滚削加工的问题,构造出一种碟形螺旋渐开线齿轮,使其滚削加工成为可能。根据齿轮啮合原理及特殊的加工方法,由产形齿条的齿面方程,推导了碟形螺旋渐开线齿轮的渐开螺旋面、过渡曲面及齿根面的方程。采用MATLAB编程得到碟形螺旋渐开线齿轮齿面的点三维坐标值。由生成的齿面上点的三维坐标值,在Pro/E中构建了碟形螺旋渐开线齿轮精确实体模型,为该齿轮的接触分析与有限元分析奠定了基础。 相似文献