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基于应力—强度干涉理论的齿轮传动可靠性研究

发布时间:2018-11-17 18:12
【摘要】:齿轮传动广泛应用于各类机械装置,其动力学性能对机械设备的正常运行至关重要。为满足低噪声、长寿命、高可靠性等要求,必须研究齿轮传动系统设计、制造、安装及运行中随机性因素的影响。学术界在假设随机参数符合某种特定分布函数的情况下,研究了参数随机性对系统动态特性和传动可靠性的影响。然而,鲜有文献基于区间数学法综合考虑制造误差、安装误差、载荷波动和修形偏差等随机性参数对齿轮动力学的影响,亦未对上述随机参数下齿轮传动的可靠性予以评估。有鉴于此,本文拟以直齿圆柱齿轮为研究对象,通过建立含随机参数的齿轮系统动力学模型,分析齿轮传动中各随机性参数对系统动力学行为的影响;在此基础上,采用应力—强度干涉理论分析随机参数工况下齿轮传动的可靠度,并与Monte Carlo法的仿真结果进行对比。论文主要内容包括:1.以直齿圆柱齿轮传动系统为例,在对齿轮制造误差、安装误差、修形偏差和载荷波动等随机因素进行参数整定的基础上,采用集中参数法建立了计入随机参数的直齿圆柱齿轮传动系统的动力学模型,推导了该类传动系统的运动微分方程。这一工作为计入区间参数的齿轮系统的动力学响应求解、随机参数影响分析和传动可靠度计算提供了模型基础。2.综合运用切比雪夫扩张函数法和4阶变步长龙格—库塔法,求解计入区间参数的直齿圆柱齿轮系统的运动微分方程以获得系统的动态响应。在此基础上,进一步分析了安装误差、齿距偏差、齿形偏差、载荷波动和修形偏差等随机参数的变动区间对直齿圆柱齿轮传动系统动态特性的影响规律。结果表明:齿轮安装误差的变动区间对动态特性的影响最大,载荷波动的影响次之,齿距偏差再次之,齿形偏差和修形偏差对动态特性的影响最小。3.以齿轮动态传递误差、齿根弯曲疲劳强度和齿面接触疲劳强度为可靠性指标,采用应力—强度干涉理论分析了计入随机参数工况的齿轮传动可靠性,并与Monte Carlo法的仿真结果进行了比对。结果表明:随机参数的变动对齿轮传动精度可靠度的影响最大,对齿根弯曲疲劳强度的可靠度影响次之,对齿面接触疲劳强度可靠度的影响最小。
[Abstract]:Gear transmission is widely used in all kinds of mechanical devices, and its dynamic performance is very important to the normal operation of mechanical equipment. In order to meet the requirements of low noise, long life and high reliability, it is necessary to study the influence of random factors in the design, manufacture, installation and operation of gear transmission system. Under the assumption that the random parameters conform to a certain distribution function, the influence of the randomness of the parameters on the dynamic characteristics and transmission reliability of the system is studied. However, few literatures based on interval number method have considered the influence of random parameters such as manufacturing error, installation error, load fluctuation and shape modification deviation on gear dynamics, and the reliability of gear transmission under the above random parameters has not been evaluated. In view of this, this paper takes spur cylindrical gear as the research object, through establishing the dynamic model of gear system with random parameters, analyzes the influence of random parameters in gear transmission on the dynamic behavior of the system. On this basis, the reliability of gear transmission under random parameter condition is analyzed by using the stress-strength interference theory, and compared with the simulation results of Monte Carlo method. The main contents of this paper are as follows: 1. Taking the spur gear transmission system as an example, on the basis of parameter tuning of random factors such as gear manufacturing error, installation error, shape modification deviation and load fluctuation, etc. The dynamic model of spur gear transmission system with random parameters is established by means of lumped parameter method, and the differential equation of motion of this kind of transmission system is derived. This work provides a model basis for solving the dynamic response of gear system with interval parameters, the influence analysis of random parameters and the calculation of transmission reliability. The Chebyshev expansion function method and the fourth order variable step Runge-Kutta method are used to solve the differential equations of motion of the spur gear system with interval parameters to obtain the dynamic response of the system. On this basis, the influence of random parameters such as installation error, pitch deviation, tooth shape deviation, load fluctuation and modification deviation on the dynamic characteristics of spur gear transmission system is analyzed. The results show that the influence of gear mounting error range on the dynamic characteristics is the biggest, the load fluctuation is the second, the gear pitch deviation is the second, and the tooth profile deviation and modification deviation have the least effect on the dynamic characteristics. 3. Taking the dynamic transmission error of gear, the bending fatigue strength of tooth root and the contact fatigue strength of tooth surface as reliability indexes, the reliability of gear transmission is analyzed by using the theory of stress-strength interference. The results are compared with the simulation results of Monte Carlo method. The results show that the variation of random parameters has the greatest influence on the accuracy reliability of gear transmission, the second on the bending fatigue strength of tooth root, and the least on the reliability of tooth surface contact fatigue strength.
【学位授予单位】:安徽工业大学
【学位级别】:硕士
【学位授予年份】:2017
【分类号】:TH132.41

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