【摘要】：齒輪傳動(dòng)廣泛應(yīng)用于各類機(jī)械裝置,其動(dòng)力學(xué)性能對(duì)機(jī)械設(shè)備的正常運(yùn)行至關(guān)重要。為滿足低噪聲、長(zhǎng)壽命、高可靠性等要求,必須研究齒輪傳動(dòng)系統(tǒng)設(shè)計(jì)、制造、安裝及運(yùn)行中隨機(jī)性因素的影響。學(xué)術(shù)界在假設(shè)隨機(jī)參數(shù)符合某種特定分布函數(shù)的情況下,研究了參數(shù)隨機(jī)性對(duì)系統(tǒng)動(dòng)態(tài)特性和傳動(dòng)可靠性的影響。然而,鮮有文獻(xiàn)基于區(qū)間數(shù)學(xué)法綜合考慮制造誤差、安裝誤差、載荷波動(dòng)和修形偏差等隨機(jī)性參數(shù)對(duì)齒輪動(dòng)力學(xué)的影響,亦未對(duì)上述隨機(jī)參數(shù)下齒輪傳動(dòng)的可靠性予以評(píng)估。有鑒于此,本文擬以直齒圓柱齒輪為研究對(duì)象,通過建立含隨機(jī)參數(shù)的齒輪系統(tǒng)動(dòng)力學(xué)模型,分析齒輪傳動(dòng)中各隨機(jī)性參數(shù)對(duì)系統(tǒng)動(dòng)力學(xué)行為的影響;在此基礎(chǔ)上,采用應(yīng)力—強(qiáng)度干涉理論分析隨機(jī)參數(shù)工況下齒輪傳動(dòng)的可靠度,并與Monte Carlo法的仿真結(jié)果進(jìn)行對(duì)比。論文主要內(nèi)容包括:1.以直齒圓柱齒輪傳動(dòng)系統(tǒng)為例,在對(duì)齒輪制造誤差、安裝誤差、修形偏差和載荷波動(dòng)等隨機(jī)因素進(jìn)行參數(shù)整定的基礎(chǔ)上,采用集中參數(shù)法建立了計(jì)入隨機(jī)參數(shù)的直齒圓柱齒輪傳動(dòng)系統(tǒng)的動(dòng)力學(xué)模型,推導(dǎo)了該類傳動(dòng)系統(tǒng)的運(yùn)動(dòng)微分方程。這一工作為計(jì)入?yún)^(qū)間參數(shù)的齒輪系統(tǒng)的動(dòng)力學(xué)響應(yīng)求解、隨機(jī)參數(shù)影響分析和傳動(dòng)可靠度計(jì)算提供了模型基礎(chǔ)。2.綜合運(yùn)用切比雪夫擴(kuò)張函數(shù)法和4階變步長(zhǎng)龍格—庫塔法,求解計(jì)入?yún)^(qū)間參數(shù)的直齒圓柱齒輪系統(tǒng)的運(yùn)動(dòng)微分方程以獲得系統(tǒng)的動(dòng)態(tài)響應(yīng)。在此基礎(chǔ)上,進(jìn)一步分析了安裝誤差、齒距偏差、齒形偏差、載荷波動(dòng)和修形偏差等隨機(jī)參數(shù)的變動(dòng)區(qū)間對(duì)直齒圓柱齒輪傳動(dòng)系統(tǒng)動(dòng)態(tài)特性的影響規(guī)律。結(jié)果表明:齒輪安裝誤差的變動(dòng)區(qū)間對(duì)動(dòng)態(tài)特性的影響最大,載荷波動(dòng)的影響次之,齒距偏差再次之,齒形偏差和修形偏差對(duì)動(dòng)態(tài)特性的影響最小。3.以齒輪動(dòng)態(tài)傳遞誤差、齒根彎曲疲勞強(qiáng)度和齒面接觸疲勞強(qiáng)度為可靠性指標(biāo),采用應(yīng)力—強(qiáng)度干涉理論分析了計(jì)入隨機(jī)參數(shù)工況的齒輪傳動(dòng)可靠性,并與Monte Carlo法的仿真結(jié)果進(jìn)行了比對(duì)。結(jié)果表明:隨機(jī)參數(shù)的變動(dòng)對(duì)齒輪傳動(dòng)精度可靠度的影響最大,對(duì)齒根彎曲疲勞強(qiáng)度的可靠度影響次之,對(duì)齒面接觸疲勞強(qiáng)度可靠度的影響最小。
[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.
【學(xué)位授予單位】：安徽工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TH132.41

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