渐开线圆柱齿轮齿廓修形设计及动态接触分析

发布时间：2018-04-09 15:32

本文选题：渐开线　切入点：圆弧蜕变曲线　出处：《太原理工大学》2012年硕士论文

【摘要】：由于渐开线圆柱齿轮有着良好的传递性能、加工刀具简单、工艺成熟等优点,所以被广泛应用于机械传动中。然而由于齿轮轮齿存在的弹性变形、热变形和不可避免的制造、安装误差,会使渐开线齿轮在啮合过程中产生啮入啮出冲击、振动和噪声,若仅仅凭借提高加工和安装精度来改善传动性能,必会增加制造成本。大量的实践和理论研究证明,对渐开线齿廓进行适当的修形能够有效地改善齿轮运行性能,提高其承载能力。传统上采用的“修顶挖根”法,在结合如修形量、修形曲线、修形高度、起点以及终点等诸多参数对齿轮进行修形之后,虽然也取得了一定的效果,但是修形的同时齿轮齿廓曲线的连续性也遭到了破坏,影响传动的平稳性。圆弧蜕变曲线与渐开线在几何形态上有着相似性,且具有易加工的特点。为了保证修形后齿廓曲线的连续性,减少啮合振动的发生,本文结合圆弧蜕变曲线方程建立了一个简单的逼近数学模型,来逼近理论修形后的渐开线,利用逼近后得出的曲线参数加工出圆弧蜕变曲线轮廓砂轮,用以磨削渐开线齿轮,以此希望得出更符合齿轮传动要求的齿轮。首先,讲述了齿廓修形的相关理论原理,然后介绍了Pro/E软件的功能和特点,并详述了如何运用Pro/E建立精确标准的直齿圆柱齿轮,为以后的修形计算和有限元动态接触分析做基础。其次,讲述了传统的齿轮齿廓修形方法,结合相应的理论采用抛物线对渐开线齿廓进行了简单地修形,为后面介绍的新的修形方法提供计算依据。然后详细介绍了圆弧蜕变曲线的成形原理,通过图形变换原理将圆弧蜕变曲线坐标变换到渐开线所在坐标系中,建立曲线逼近数学模型,拟合逼近理论修形后的渐开线,同时利用得出的优化参数建立圆弧蜕变曲线齿廓齿轮。最后,在ANSYS/LS-DYNA中分别对标准渐开线和修形后的圆弧蜕变曲线两种齿廓齿轮啮合模型进行了齿轮啮合动态接触分析,并通过结果对比分析得出,圆弧蜕变曲线齿轮性能相比渐开线齿轮有所改善。文中也指出,用于加工磨削的圆弧蜕变曲线廓形砂轮易于获得,因此本课题的研究有一定的实际意义。
[Abstract]:Involute cylindrical gear has been widely used in mechanical transmission because of its good transmission performance, simple machining tool, mature technology and so on.However, due to the elastic deformation, thermal deformation and inevitable manufacturing and installation error of gear teeth, involute gears will be engulfed in and out of shock, vibration and noise in the course of meshing.If only by improving the processing and installation accuracy to improve transmission performance, it will increase manufacturing costs.A large number of practical and theoretical studies have proved that the proper modification of involute tooth profile can effectively improve the gear performance and its bearing capacity.The traditional "topping and root digging" method has been used to modify gears, although some results have been achieved after combining with such parameters as shape modification, shape modification curve, shape modification height, starting point and end point, etc.However, the continuity of gear profile curve is also destroyed, which affects the smoothness of transmission.Arc degenerate curve and involute are similar in geometry and easy to process.In order to ensure the continuity of tooth profile curve after modification and reduce the occurrence of meshing vibration, a simple approximate mathematical model is established in this paper, combining with the equation of arc degenerate curve, to approximate the involute after theoretical modification.The grinding wheel of circular arc degenerated curve profile is machined by using the curve parameters obtained after approaching, which can be used to grinding involute gear, so as to obtain the gear which meets the requirements of gear transmission more.Firstly, the related theory of tooth profile modification is introduced, then the functions and characteristics of Pro/E software are introduced, and how to use Pro/E to establish accurate and standard straight cylindrical gear is described in detail.It provides the foundation for the later shape modification calculation and the finite element dynamic contact analysis.Secondly, the traditional gear profile modification method is described, and the parabola is used to modify the involute profile, which provides the basis for the calculation of the new modification method.Then the forming principle of arc degenerate curve is introduced in detail. The coordinate of arc degenerate curve is transformed into the coordinate system of involute by graphic transformation principle, and the mathematical model of curve approximation is established, and the involute after the modification of approximation theory is fitted.At the same time, the optimized parameters are used to establish the gear profile of arc degenerate curve.Finally, two kinds of gear meshing models of standard involute and modified arc profile are analyzed in ANSYS/LS-DYNA, and the results are compared and analyzed.Compared with involute gear, the performance of arc degenerate curve gear is improved.It is also pointed out that the arc degenerate curve profile grinding wheel is easy to be obtained, so the research of this subject has certain practical significance.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH132.41

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