剃齿加工是齿轮精加工的高效工艺，广泛应用于机床、汽车、船舶、航空航天等行业的齿轮生产，具有效率高、成本低及适应性强等优点。然而，剃齿齿形中凹误差问题却是齿轮制造中长期存在的一个技术难题，它不但严重影响工件齿轮齿面精度和啮合传动状态，而且限制了剃齿加工在高精密场合的应用。本文从剃齿重合度、剃齿机床运动和剃齿安装误差三方面研究多源因素对剃齿加工的影响规律，系统地揭示了剃齿齿形中凹误差的形成机理，并提出剃齿加工优化措施(包括剃齿刀优化设计、剃齿机床运动参数优化、剃齿安装误差补偿位移量优化)与非等边剃齿刀设计方法来减小或消除齿形中凹误差，对推动齿轮制造业的发展，实现剃齿高效加工具有重要的理论意义和应用价值。本文的主要研究工作和创新点包括： 考虑剃齿刀齿面容屑槽和切削刃的存在及工件齿轮齿面余量去除的时变状态，建立剃齿分析模型。将剃齿参数的变化等效为重合度的变化，研究剃齿重合度对剃齿加工特性的影响规律，明确重合度与齿形中凹误差的影响关系，并提出剃齿加工特性算法，为剃齿刀优化设计提供理论依据。结果表明增大重合度能一定程度地减小剃齿齿形中凹误差，但过大的重合度会使剃齿传动性能显著下降，而发生较大的振动，影响齿形精度。 构建剃齿切削力模型，提出在切削力理论公式基础上引入剃齿径向力经验指数公式，推导剃齿切削力和切削速度表达式。研究剃齿机床运动对剃齿加工的影响规律，重点分析节圆位置的变化规律。结果表明径向进给运动是影响剃削效果最主要的因素，并分析了其对剃齿加工特性的影响，结合有限元法和剃齿实验验证了模型计算的有效性，阐述剃齿机床运动与剃齿齿形中凹误差的影响关系。 建立含剃齿安装误差的剃齿分析模型，在原有的几何坐标系上引入剃齿安装误差，构造新的坐标转换，推导由剃齿安装误差引起的补偿位移量。研究剃齿安装误差对剃齿加工的影响规律。剃齿实验表明按照补偿位移量来调整机床能合理地控制安装误差，有效地提高齿面精度和加工效率。 综合考虑上述分析，提出剃齿加工优化措施(包括剃齿刀优化设计、剃齿机床运动参数优化、含剃齿安装误差的补偿位移量优化)和非等边剃齿刀的设计方法，结合剃齿实验验证剃齿加工优化的有效性：剃齿加工特性可作为剃齿刀优化设计的有效判据，有效节省反复试剃的生产时间，提高剃齿刀设计效率；剃齿机床运动参数优化可提高工艺效率，改善齿形精度；按照补偿位移量来调整机床能合理地控制安装误差，可有效地提高齿面精度和加工效率；非等边剃齿刀设计能改善剃齿加工过程的平稳性，为消除剃齿齿形中凹误差提供了新的技术思路。 ①本研究得到国家自然科学基金面上项目“多因素耦合剃齿齿形“中凹”误差机理与剃齿刀修形曲线研究”(编号：51475352，2015-2018)的资助。 关键词：齿形中凹误差；剃齿加工特性；重合度；剃齿加工优化；非等边剃齿刀； 论文类型：应用研究

 Shaving processing is an efficient process in the manufacture of gear finishing. It is widely used in the gear production of machine tools, automobiles, ships, aerospace and other industries. It has the advantages of high efficiency, low cost, strong adaptability and convenient adjustment. However, shaving concave error of tooth profile is a long-term problem during the gear manufacturing. It not only affects the tooth flank accuracy as well as the transmission characteristics, but also limits the application of shaving in high-precision occasions. In this paper, the formation mechanism of shaving concave error is studied from the aspects of contact ratio, machine tool motion and alignment error. And the shaving processing optimization methods (including the optimization design of the shaving cutter, the optimization of machine tool parameters and the displacement compensation of the alignment error) are proposed. Also, the non-equal edge shaving cutter is designed to reduce or eliminate the concave error, which has important theoretical and social benefits for promoting the development of the gear industry and achieving efficient processing of shaving tooth. The main contents and innovations work of this paper are as follows: Considering the existence of the chip pocket,the cutting edge of the shaving cutter, and the time-varying state of the gear tooth surface during the allowance removal, a shaving processing analysis model is established, which can accurately reflect the actual shaving process. The algorithm of shaving processing characteristics is proposed, which provides a theoretical basis for the optimal design of the shaving cutter. The change of shaving parameters is attributed to the change of contact ratio. The effect of contact ratio on the shaving processing characteristics is studied, the relationship between the contact ratio and the concave error is defined, and the formation mechanism of the concave error of the shaving tooth shape due to the contact ratio is revealed. The results show that increasing contact ratio can reduce concave error, however, excessive contact ratio will cause the transmission performance to decrease significantly, and the large vibration will occur, which will affect the accuracy of the tooth surface. The shaving cutting force model is constructed, from which the shaving cutting force and cutting speed expression are derived. The influence of the machine tool motion (radial feed motion, axial feed motion and spindle rotation) on shaving process is studied, and the variation law of the pitch circle position is analyzed. The results show that the radial feed motion is the most important factor that affecting the shaving effect, and its influence on the shaving processing characteristics is analyzed. The validity of the model calculation is verified by the shaving experiment. The relationship between the machine tool motion and the concave error is explained as well. The shaving machining model is established, in which the alignment error is introduced in the original geometric coordinate system, driving to a new coordinate transformation, and the compensation displacement caused by the alignment error is deduced. Based on this, the theoretical transmission error, the transmission ratio and the shaving depth error are derived. The effect of shaving alignment error on shaving processing is studied. Adjusting the machine tool according to the compensation displacement can control the installation error reasonably, which can effectively improve tooth flank accuracy and processing efficiency. Considering the above analysis, the shaving processing optimization methods (including the optimization design of the shaving cutter, optimization of the machine tool parameters and the displacement compensation of the alignment error) and the design of non-equal shaving cutter is proposed. Shaving experiments verified the correctness of the shaving process optimization. Under certain specific shaving parameters, when the shaving processing characteristics cannot be further satisfied, the non-equal shaving cutter design is proposed by combining negative displacement shaving and balance shaving principles. The results show that the non-equal shaving cutter makes the shaving process more stable, and the reliability of the non-equal shaving cutter is verified,which provides a new technical solution for eliminating the concave error of the shaving tooth profile. Key words: Concave Error; Shaving Processing Characteristics; Contact Ratio; Shaving Processing Optimization; Non-equal Shaving Cutter; Type of paper: Application Research