2K-H型摆线针轮行星传动性能理论的研究
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摘要
旋转手柄式座椅调角器为一齿差2K-H针摆行星传动机构,它将调角功能和自锁功能集于一体,结构紧凑、操作方便、调节力矩小、调节精度高,且较利于改为电机驱动,广泛用于各型轿车、面包车座椅椅背角度的无级调节。
由于该机构使用要求为低的调节力矩和高的自锁力矩,而调节力矩和自锁力矩是相互制约的,因而必须在传动性和自锁性之间建立一个平衡。本论文的工作就是要建立符合实际工况的正、逆传动输出力矩与运动学参数间关系的精确的数学模型,以期在理论指导下进行产品的优化设计,使其在满足自锁性能的基础上最大限度地增强调节功能。
提出以实际齿廓公法线方向的距离为齿侧间隙的新定义,据此提出移距修形摆轮和数控加工摆轮在传动中的齿侧间隙和几何转角的精确计算方法,计算调角器实际啮合参数,啮合状态仿真有效说明方法的正确性。进一步研究修形量、修形方式、加工步长对啮合特性的影响,得出有价值的结论。
对2K-H针摆行星传动机构进行力学分析,建立考虑齿廓间摩擦、轴承摩擦、齿廓弹性变形及部件重量的有隙啮合状态的力学模型,修改齿廓间作用力和变形的线性关系,建立输出力矩与输入力矩和运动学参数间的关系。通过调角器静力学实验,验证计算模型的正确性。
对2K-H针摆行星轮系的转化机构建立效率计算的数学模型,计算调角器机构正逆传动效率,在效率测试仪上进行调角器转化机构的效率测试,试验结果证明效率模型的正确性。
利用所建立的力学模型和效率模型,分析影响传动性能的相关因素,提出提高自锁力矩降低驱动力矩的有效方法。提出根据拟定的啮合位置进行齿廓修形的新方法。并用该方法对汽车座椅调角器自锁性能进行改进。
上述研究成果集中于用Matlab编制的2K-H针摆行星传动设计软件,可供用户在设计中,根据结构参数进行齿侧间隙、空回转角及驱动力矩和自锁力矩的计算,为进一步参数优化与齿形优化提供计算基础。
The one-tooth-difference 2K-H cycloid-needle planetary transmission mechanism is used extensively for continuous adjustment of the seat back angle on various automobiles. The mechanism provides both the angle-adjusting function and the self-locking function. It also features a compact structure, ease of operation, a small adjusting moment, a high precision of adjustment, and the adaptability to being motor-driven.
For the purpose of seat back angle adjustment, the transmission mechanism must have both properties of a small adjusting moment and a large self-locking moment. The two requirements, however, in general conflict with each other and a balance between the driving or adjusting performance and the self-locking performance has to be carefully achieved. The dissertation is devoted to build an accurate mathematical model that describes the dependence of the positive and the negative output moments on the kinematic parameters of the transmission mechanism. Such a model provides a theoretical basis to design optimization in order to maximize the adjusting performance while maintaining self-locking performance.
A new definition of the backlash between gear teeth is proposed for the first time. The backlash is defined as the minimum distance between the teeth of a pair of gears in the direction of their common normal. Based on this definition, a method is presented for calculating the backlashes and the geometrical angles for theoretically modified tooth profiles and for tooth profiles fabricated by CNC machines. It is used for calculating actual the number of teeth at meshing. The method is tested with simulations of meshing states and is used to investigate the effects of tooth profile modifications and machining steps on the performance meshing.
Based on the mechanical analysis of the 2K-H cycloid-needle planetary transmission mechanism, a model for the meshing state with backlash is proposed. The model, which takes into account of the friction between tooth profiles and the friction at bearings and elastic deformation of meshing teeth profile and the weights of accessories, corrects the linear relationship of force and deformation between meshing teeth profile, relates the output moment with input moment and kinematic parameters. The model is verified by comparing with static measurements on the angle-adjusting mechanism.
A mathematical model of the instantaneous and average efficiencies of the conversion mechanism of the original 2K-H epicycle gear train is proposed, and is used for calculating the mechanical efficiency of both the positive and the negative transmissions. The calculated efficiencies of the conversion mechanism of the angle adjustor are in good agreement with experimental measurements. The output moments inferred from the efficiency model are consistent with the direct calculations using the method proposed in 2.
The effects of various factors on the performances of the transmission mechanism are analyzed using the models proposed in 2 and 3. Effective measures to increase the self-locking moment and/or to reduce the adjusting moment are presented. A new method of tooth profile modification, i.e., modifying teeth according to the meshing position, is proposed and is used to improve the self-locking performance of a rotary-handle angle-adjusting mechanism for automobile seat backs.
A MATLAB software package that integrates all work mentioned above is developed. The package is used for the design of the 2K-H cycloid-needle planetary transmission mechanism. It calculates the adjusting moment, the self-locking moment, tooth backlashes, and void angles from known kinematic parameters. The package provides a basis for further design optimization such as the optimization of kinematic parameters and the optimization of the tooth profile modification.
由于该机构使用要求为低的调节力矩和高的自锁力矩,而调节力矩和自锁力矩是相互制约的,因而必须在传动性和自锁性之间建立一个平衡。本论文的工作就是要建立符合实际工况的正、逆传动输出力矩与运动学参数间关系的精确的数学模型,以期在理论指导下进行产品的优化设计,使其在满足自锁性能的基础上最大限度地增强调节功能。
提出以实际齿廓公法线方向的距离为齿侧间隙的新定义,据此提出移距修形摆轮和数控加工摆轮在传动中的齿侧间隙和几何转角的精确计算方法,计算调角器实际啮合参数,啮合状态仿真有效说明方法的正确性。进一步研究修形量、修形方式、加工步长对啮合特性的影响,得出有价值的结论。
对2K-H针摆行星传动机构进行力学分析,建立考虑齿廓间摩擦、轴承摩擦、齿廓弹性变形及部件重量的有隙啮合状态的力学模型,修改齿廓间作用力和变形的线性关系,建立输出力矩与输入力矩和运动学参数间的关系。通过调角器静力学实验,验证计算模型的正确性。
对2K-H针摆行星轮系的转化机构建立效率计算的数学模型,计算调角器机构正逆传动效率,在效率测试仪上进行调角器转化机构的效率测试,试验结果证明效率模型的正确性。
利用所建立的力学模型和效率模型,分析影响传动性能的相关因素,提出提高自锁力矩降低驱动力矩的有效方法。提出根据拟定的啮合位置进行齿廓修形的新方法。并用该方法对汽车座椅调角器自锁性能进行改进。
上述研究成果集中于用Matlab编制的2K-H针摆行星传动设计软件,可供用户在设计中,根据结构参数进行齿侧间隙、空回转角及驱动力矩和自锁力矩的计算,为进一步参数优化与齿形优化提供计算基础。
The one-tooth-difference 2K-H cycloid-needle planetary transmission mechanism is used extensively for continuous adjustment of the seat back angle on various automobiles. The mechanism provides both the angle-adjusting function and the self-locking function. It also features a compact structure, ease of operation, a small adjusting moment, a high precision of adjustment, and the adaptability to being motor-driven.
For the purpose of seat back angle adjustment, the transmission mechanism must have both properties of a small adjusting moment and a large self-locking moment. The two requirements, however, in general conflict with each other and a balance between the driving or adjusting performance and the self-locking performance has to be carefully achieved. The dissertation is devoted to build an accurate mathematical model that describes the dependence of the positive and the negative output moments on the kinematic parameters of the transmission mechanism. Such a model provides a theoretical basis to design optimization in order to maximize the adjusting performance while maintaining self-locking performance.
A new definition of the backlash between gear teeth is proposed for the first time. The backlash is defined as the minimum distance between the teeth of a pair of gears in the direction of their common normal. Based on this definition, a method is presented for calculating the backlashes and the geometrical angles for theoretically modified tooth profiles and for tooth profiles fabricated by CNC machines. It is used for calculating actual the number of teeth at meshing. The method is tested with simulations of meshing states and is used to investigate the effects of tooth profile modifications and machining steps on the performance meshing.
Based on the mechanical analysis of the 2K-H cycloid-needle planetary transmission mechanism, a model for the meshing state with backlash is proposed. The model, which takes into account of the friction between tooth profiles and the friction at bearings and elastic deformation of meshing teeth profile and the weights of accessories, corrects the linear relationship of force and deformation between meshing teeth profile, relates the output moment with input moment and kinematic parameters. The model is verified by comparing with static measurements on the angle-adjusting mechanism.
A mathematical model of the instantaneous and average efficiencies of the conversion mechanism of the original 2K-H epicycle gear train is proposed, and is used for calculating the mechanical efficiency of both the positive and the negative transmissions. The calculated efficiencies of the conversion mechanism of the angle adjustor are in good agreement with experimental measurements. The output moments inferred from the efficiency model are consistent with the direct calculations using the method proposed in 2.
The effects of various factors on the performances of the transmission mechanism are analyzed using the models proposed in 2 and 3. Effective measures to increase the self-locking moment and/or to reduce the adjusting moment are presented. A new method of tooth profile modification, i.e., modifying teeth according to the meshing position, is proposed and is used to improve the self-locking performance of a rotary-handle angle-adjusting mechanism for automobile seat backs.
A MATLAB software package that integrates all work mentioned above is developed. The package is used for the design of the 2K-H cycloid-needle planetary transmission mechanism. It calculates the adjusting moment, the self-locking moment, tooth backlashes, and void angles from known kinematic parameters. The package provides a basis for further design optimization such as the optimization of kinematic parameters and the optimization of the tooth profile modification.
引文
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