目的 针对齿轮传动系统在高速与复杂载荷工况下,由齿侧间隙非线性变化引发的振动增强与啮合不稳定等问题,研究其对齿轮传动系统非线性动态特性的影响机制。方法 本文引入分形理论,基于W-M（Weierstrass-Mandelbrot）函数建立齿侧间隙模型,并结合Hertz接触理论与集中质量法构建多自由度斜齿轮系统非线性动力学模型。利用SolidWorks与Adams搭建虚拟样机,对比分析不同工况（空载/150 N额定载荷、12 000 r/h与18 000 r/h转速）下不同分形间隙时的系统响应。由于分形维数是决定分形间隙的关键参数,本研究将其作为控制变量,探讨其对系统响应的影响。结果 研究表明,高速空载时,低分形维数会引发非线性振动增强;而在负载情况下,高分形维数有助于提高系统稳定性,但在高速运行时会加剧高频扰动。进一步分析发现,当分形维数D=1.5时,可在动态稳定性与加工成本之间取得较优平衡。结论 本研究为斜齿轮传动系统动态特性分析提供了理论基础,并对齿侧间隙优化设计具有一定的指导意义。
Abstract
The work aims to study the vibration enhancement and engagement instability caused by the nonlinear change of tooth flank clearance in gear transmission systems under high-speed and complex load conditions and to study its influence mechanism on the nonlinear dynamic characteristics of gear transmission systems. The fractal theory was applied to establish a tooth flank clearance model based on the W-M (Weierstrass-Mandelbrot) function. Combined with the Hertz contact theory and the lumped mass method, a nonlinear dynamic model of a multi-degree-of-freedom helical gear system was constructed. A virtual prototype was built using SolidWorks and Adams, and the system responses under different conditions (no-load/150 N rated load, 12 000 r/h and 18 000 r/h) and different fractal clearances were compared and analyzed. Since the fractal dimension was a key parameter determining the fractal clearance, this study took it as a control variable to explore its impact on the system response. The research showed that at high speed and no-load, a low fractal dimension could cause an increase in nonlinear vibration, while under load, a high fractal dimension helped improve system stability but intensified high-frequency disturbances at high speeds. Further analysis revealed that at fractal dimension D=1.5, a better balance could be achieved between dynamic stability and processing cost. This study provides a theoretical basis for the dynamic characteristic analysis of helical gear transmission systems and has certain guiding significance for the optimization design of tooth flank clearance.
关键词
动力学建模 /
齿侧间隙 /
分形维数 /
Adams
Key words
dynamic modeling /
tooth flank clearance /
fractal dimension /
Adams
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基金
北京印刷学院校级项目（KYCPT202513）;北京市教育委员会-市自然科学基金（KZ202210015019）;北京市属高等学校高水平科研创新团队建设支持计划（BPHR20220107）
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