【摘要】：齒輪傳動廣泛應(yīng)用于各類機械裝置,其動力學(xué)性能對機械設(shè)備的正常運行至關(guān)重要。為滿足低噪聲、長壽命、高可靠性等要求,必須研究齒輪傳動系統(tǒng)設(shè)計、制造、安裝及運行中隨機性因素的影響。學(xué)術(shù)界在假設(shè)隨機參數(shù)符合某種特定分布函數(shù)的情況下,研究了參數(shù)隨機性對系統(tǒng)動態(tài)特性和傳動可靠性的影響。然而,鮮有文獻基于區(qū)間數(shù)學(xué)法綜合考慮制造誤差、安裝誤差、載荷波動和修形偏差等隨機性參數(shù)對齒輪動力學(xué)的影響,亦未對上述隨機參數(shù)下齒輪傳動的可靠性予以評估。有鑒于此,本文擬以直齒圓柱齒輪為研究對象,通過建立含隨機參數(shù)的齒輪系統(tǒng)動力學(xué)模型,分析齒輪傳動中各隨機性參數(shù)對系統(tǒng)動力學(xué)行為的影響;在此基礎(chǔ)上,采用應(yīng)力—強度干涉理論分析隨機參數(shù)工況下齒輪傳動的可靠度,并與Monte Carlo法的仿真結(jié)果進行對比。論文主要內(nèi)容包括:1.以直齒圓柱齒輪傳動系統(tǒng)為例,在對齒輪制造誤差、安裝誤差、修形偏差和載荷波動等隨機因素進行參數(shù)整定的基礎(chǔ)上,采用集中參數(shù)法建立了計入隨機參數(shù)的直齒圓柱齒輪傳動系統(tǒng)的動力學(xué)模型,推導(dǎo)了該類傳動系統(tǒng)的運動微分方程。這一工作為計入?yún)^(qū)間參數(shù)的齒輪系統(tǒng)的動力學(xué)響應(yīng)求解、隨機參數(shù)影響分析和傳動可靠度計算提供了模型基礎(chǔ)。2.綜合運用切比雪夫擴張函數(shù)法和4階變步長龍格—庫塔法,求解計入?yún)^(qū)間參數(shù)的直齒圓柱齒輪系統(tǒng)的運動微分方程以獲得系統(tǒng)的動態(tài)響應(yīng)。在此基礎(chǔ)上,進一步分析了安裝誤差、齒距偏差、齒形偏差、載荷波動和修形偏差等隨機參數(shù)的變動區(qū)間對直齒圓柱齒輪傳動系統(tǒng)動態(tài)特性的影響規(guī)律。結(jié)果表明:齒輪安裝誤差的變動區(qū)間對動態(tài)特性的影響最大,載荷波動的影響次之,齒距偏差再次之,齒形偏差和修形偏差對動態(tài)特性的影響最小。3.以齒輪動態(tài)傳遞誤差、齒根彎曲疲勞強度和齒面接觸疲勞強度為可靠性指標(biāo),采用應(yīng)力—強度干涉理論分析了計入隨機參數(shù)工況的齒輪傳動可靠性,并與Monte Carlo法的仿真結(jié)果進行了比對。結(jié)果表明:隨機參數(shù)的變動對齒輪傳動精度可靠度的影響最大,對齒根彎曲疲勞強度的可靠度影響次之,對齒面接觸疲勞強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)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TH132.41

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