渐开弧面齿轮传动的基本理论及试验研究
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摘要
齿轮传动是依靠轮齿之间的交替推动来传递运动和动力的。在当前，齿轮传动仍然是各类机械与装备中应用最为广泛的一种机械传动形式，在船舶、武器装备、水泥机械、冶金、风电、石化、橡胶、城市交通、起重机械等领域的应用十分广泛，是装备制造业和国防工业极其重要的基础件。机械关键基础件在很大程度上决定着装备的性能，并逐渐成为我国制造业突出的瓶颈之一。在国家中长期科技规划中，关键基础件已被列为优先支持的领域。因此，系统深入地开展高性能传动元件的研究工作，特别是齿轮传动元件的理论和设计方法、制造关键技术和实验研究，奠定其工程应用的基础，具有重要的理论意义和工程实用价值。
渐开弧面齿轮传动是在结合传统的渐开线齿轮传动与圆弧齿轮传动优点的基础上提出来的一种新型齿轮传动形式。它在主动轮和从动轮的渐开线齿廓上，分别选取两条相对应的单值曲线，在这两条单值曲线上的每一点处分别用圆弧齿廓去取代原有的渐开线齿廓，形成新的渐开弧面齿廓，以增大相对曲率半径，提高接触强度。同时，齿面接触迹线具有渐开线的特点，从而使渐开弧面齿轮具有一定的中心距补偿能力。
本文的主要内容如下：
（1）详细论述了渐开弧面齿轮传动啮合的基本原理，讨论了渐开弧面齿轮传动的啮合特性。推导了渐开弧面齿轮传动齿面方程的一般表达式；论证了啮合线方程；讨论了渐开弧面齿轮传动的中心距可分性。
（2）由啮合副滑动率的定义，给出运用啮合副齿廓共轭曲线方程推导啮合副滑动率的通用方法；推导了渐开弧面齿轮传动凸齿轮的齿面接触迹线方程，建立了渐开弧面齿轮传动接触迹线的啮合方程，推导了其共轭的凹齿轮接触迹线方程，并给出了实例计算。
（3）提出了渐开弧面齿轮的设计方法，确定了其基本参数及齿形参数的选择方法，完成了渐开弧面齿轮啮合副齿廓曲面的设计，并给出了计算实例。在此基础上，应用UG等三维实体建模软件，建立了参数化的渐开弧面齿轮三维实体模型。
（4）推导了渐开弧面齿轮传动的接触强度和弯曲强度的理论计算公式。
（5）建立了渐开弧面齿轮传动及传统渐开线齿轮啮合副的接触有限元分析模型，利用ANSYS求解器进行求解，并对结果进行了对比分析，进一步揭示渐开弧面齿轮传动啮合副的接触特性。
（6）根据实验要求，设计了一种以渐开弧面齿轮传动啮合副为主要传动部件的传动装置，并完成了样机试制。
（7）进行关于该渐开弧面齿轮传动装置样机的效率实验测试，以检验是否达到预期的技术要求，实验表明渐开弧面齿轮传动装置的样机具有很高的效率。
The gearing transfers motion and power through the teeth driving alternately. Atpresent, the gearing is still one kind of the most extensively applied mechanicaltransmission in machinery and equipment, which is extensively applied in ships,weapons equipment, cement machinery, metallurgy, wind power, petrochemical, rubber,urban transport, lifting machinery and other fields. It is mechanical key basis parts inmanufacturing and national defence industry, which determine the equipment’sperformance in a great degree, and are gradually becoming an outstanding bottleneck inour national manufacturing. In our national medium-term and long-term scientific andtechnical plans, key basis components are listed as priority supported field. Thereby, ithas important theoretical significance and practical value to systematically carry out thestudy on the meshing theory, design method, manufacturing key technology andexperiment of high performance gear transmission components.
A new tooth profile gear, involute-circular gear, is proposed by integrating involutegear’s advantageous edges with circular tooth gear’s advantages in this research. Theconcept of involute-circular gear is also defined, namely that choosing twosingle-valued curves which are corresponding engaged from the involute profilesbetween driving and driven wheels respectively, and replacing involute profile with theconvex and concave circular arc separately to form new tooth profile at any point ofthese curves to increases the radius of relative curvature and the contact strength.Because the path of contact points has the characteristics of involute, involute-circulargear's center distance is insensitive.
The main content of this thesis was as follows:
(1) Based on differential geometry, basic principles of involute-circular gear wasdemonstrated in detail, and mesh characteristics were discussed. The general equationof tooth surface was established. Equation of meshing line was derived. Insensitivity tocentral distance variation on involute-circular gear was discussed.
(2) Based on the definition of the slip ratio between the meshing pair, a newmethod that the slip ratio could be resolved by the conjugate equation was proposed;Through established meshing equation, the equation of path of contact points of convexgear and conjugated concave gear were derived; Sliding rate calculation method ofinvolute-circular gear was put forward and deduced. And examples were given.
(3) Design method of involute-circular gear was proposed. Method of selection ofthe basic parameters and toothed parameters was determined. Design of theinvolute-circular gear tooth profile surface was completed. After examples were given,the three-dimensional modeling software UG was applied to establish athree-dimensional model of parameterized involute-circular gear.
(4) Theoretic calculation euation of bending strength and contact strength werederived.
(5) Both the tranditial involute gear and the involute-circular gear meshing pair’sfinite elements contact models were built, the analysis result of the contact pair rosolvedin ANSYS was compared for further reveals of contact characteristics ofinvolute-circular gear.
(6) According to the experimental requirements, a transmission equipment whosemain transmission parts is involute-circular gear was designed. And a prototype ofinvolute-circular gearing was manufactured and assembled.
(7) Efficiency test on the prototype of involute-gear was carried out to test whetherthe sample meet the expected technical requirements. And experiments show that theprototype involute cambered gear transmission is with high efficiency.
渐开弧面齿轮传动是在结合传统的渐开线齿轮传动与圆弧齿轮传动优点的基础上提出来的一种新型齿轮传动形式。它在主动轮和从动轮的渐开线齿廓上，分别选取两条相对应的单值曲线，在这两条单值曲线上的每一点处分别用圆弧齿廓去取代原有的渐开线齿廓，形成新的渐开弧面齿廓，以增大相对曲率半径，提高接触强度。同时，齿面接触迹线具有渐开线的特点，从而使渐开弧面齿轮具有一定的中心距补偿能力。
本文的主要内容如下：
（1）详细论述了渐开弧面齿轮传动啮合的基本原理，讨论了渐开弧面齿轮传动的啮合特性。推导了渐开弧面齿轮传动齿面方程的一般表达式；论证了啮合线方程；讨论了渐开弧面齿轮传动的中心距可分性。
（2）由啮合副滑动率的定义，给出运用啮合副齿廓共轭曲线方程推导啮合副滑动率的通用方法；推导了渐开弧面齿轮传动凸齿轮的齿面接触迹线方程，建立了渐开弧面齿轮传动接触迹线的啮合方程，推导了其共轭的凹齿轮接触迹线方程，并给出了实例计算。
（3）提出了渐开弧面齿轮的设计方法，确定了其基本参数及齿形参数的选择方法，完成了渐开弧面齿轮啮合副齿廓曲面的设计，并给出了计算实例。在此基础上，应用UG等三维实体建模软件，建立了参数化的渐开弧面齿轮三维实体模型。
（4）推导了渐开弧面齿轮传动的接触强度和弯曲强度的理论计算公式。
（5）建立了渐开弧面齿轮传动及传统渐开线齿轮啮合副的接触有限元分析模型，利用ANSYS求解器进行求解，并对结果进行了对比分析，进一步揭示渐开弧面齿轮传动啮合副的接触特性。
（6）根据实验要求，设计了一种以渐开弧面齿轮传动啮合副为主要传动部件的传动装置，并完成了样机试制。
（7）进行关于该渐开弧面齿轮传动装置样机的效率实验测试，以检验是否达到预期的技术要求，实验表明渐开弧面齿轮传动装置的样机具有很高的效率。
The gearing transfers motion and power through the teeth driving alternately. Atpresent, the gearing is still one kind of the most extensively applied mechanicaltransmission in machinery and equipment, which is extensively applied in ships,weapons equipment, cement machinery, metallurgy, wind power, petrochemical, rubber,urban transport, lifting machinery and other fields. It is mechanical key basis parts inmanufacturing and national defence industry, which determine the equipment’sperformance in a great degree, and are gradually becoming an outstanding bottleneck inour national manufacturing. In our national medium-term and long-term scientific andtechnical plans, key basis components are listed as priority supported field. Thereby, ithas important theoretical significance and practical value to systematically carry out thestudy on the meshing theory, design method, manufacturing key technology andexperiment of high performance gear transmission components.
A new tooth profile gear, involute-circular gear, is proposed by integrating involutegear’s advantageous edges with circular tooth gear’s advantages in this research. Theconcept of involute-circular gear is also defined, namely that choosing twosingle-valued curves which are corresponding engaged from the involute profilesbetween driving and driven wheels respectively, and replacing involute profile with theconvex and concave circular arc separately to form new tooth profile at any point ofthese curves to increases the radius of relative curvature and the contact strength.Because the path of contact points has the characteristics of involute, involute-circulargear's center distance is insensitive.
The main content of this thesis was as follows:
(1) Based on differential geometry, basic principles of involute-circular gear wasdemonstrated in detail, and mesh characteristics were discussed. The general equationof tooth surface was established. Equation of meshing line was derived. Insensitivity tocentral distance variation on involute-circular gear was discussed.
(2) Based on the definition of the slip ratio between the meshing pair, a newmethod that the slip ratio could be resolved by the conjugate equation was proposed;Through established meshing equation, the equation of path of contact points of convexgear and conjugated concave gear were derived; Sliding rate calculation method ofinvolute-circular gear was put forward and deduced. And examples were given.
(3) Design method of involute-circular gear was proposed. Method of selection ofthe basic parameters and toothed parameters was determined. Design of theinvolute-circular gear tooth profile surface was completed. After examples were given,the three-dimensional modeling software UG was applied to establish athree-dimensional model of parameterized involute-circular gear.
(4) Theoretic calculation euation of bending strength and contact strength werederived.
(5) Both the tranditial involute gear and the involute-circular gear meshing pair’sfinite elements contact models were built, the analysis result of the contact pair rosolvedin ANSYS was compared for further reveals of contact characteristics ofinvolute-circular gear.
(6) According to the experimental requirements, a transmission equipment whosemain transmission parts is involute-circular gear was designed. And a prototype ofinvolute-circular gearing was manufactured and assembled.
(7) Efficiency test on the prototype of involute-gear was carried out to test whetherthe sample meet the expected technical requirements. And experiments show that theprototype involute cambered gear transmission is with high efficiency.
引文
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