本文選題：齒輪彎曲強(qiáng)度 + 齒面摩擦因數(shù)　； 參考：《湖南大學(xué)》2013年博士論文

【摘要】：齒輪是重要的基礎(chǔ)件，其設(shè)計(jì)與制造水平影響到機(jī)械裝備的性能和可靠性。開展齒輪強(qiáng)度和齒面摩擦的計(jì)算與試驗(yàn)研究，對(duì)于增大承載能力、提高疲勞壽命、減少摩擦磨損、改善傳動(dòng)性能等具有顯著的意義。關(guān)于齒輪彎曲強(qiáng)度和齒面摩擦的計(jì)算和試驗(yàn)研究較多，以下問(wèn)題值得探索：多種荷載下齒輪彎曲強(qiáng)度計(jì)算的精確建模方法，齒根應(yīng)力和輪齒變形的數(shù)值計(jì)算；能夠表征齒面多樣的摩擦潤(rùn)滑性態(tài)及其變化規(guī)律的過(guò)程模型，齒面關(guān)鍵摩擦參數(shù)的普適計(jì)算方法；基于嚙合理論與摩擦學(xué)、接觸動(dòng)力學(xué)等交叉的齒面沖擊摩擦機(jī)理及定量計(jì)算等。 基于上述問(wèn)題的思考并結(jié)合作者承擔(dān)的相關(guān)課題，提出了本論文的研究論題。重點(diǎn)研究三個(gè)問(wèn)題：多種荷載下齒輪彎曲強(qiáng)度計(jì)算的精確建模方法；齒面摩擦潤(rùn)滑的多態(tài)性模型與計(jì)算方法；齒面摩擦力與摩擦因數(shù)的普適量化計(jì)算方法。主要研究?jī)?nèi)容和創(chuàng)新點(diǎn)如下： 1.對(duì)齒輪有限元精確建模與彎曲強(qiáng)度計(jì)算方法進(jìn)行了研究，通過(guò)比較研究驗(yàn)證了上述方法的正確性。根據(jù)齒輪展成加工原理和坐標(biāo)系矩陣變換法推導(dǎo)出齒形曲線，基于純文本數(shù)據(jù)文件的APDL與MATLAB的混合建模方法，實(shí)現(xiàn)了齒輪幾何模型的精確建模�；诤`差與變形的計(jì)算模型，，推導(dǎo)出彎曲強(qiáng)度計(jì)算力點(diǎn)的位置判別式，可作為彎曲強(qiáng)度計(jì)算力點(diǎn)選取的參考。研究了齒輪彎曲強(qiáng)度有限元計(jì)算的多種有效荷載，通過(guò)對(duì)不同荷載下齒根峰值應(yīng)力和輪齒變形的比較研究發(fā)現(xiàn)：按集中力、線分布力、Hertz接觸面分布力、靜態(tài)接觸力的次序，計(jì)算結(jié)果的精確性不斷提高；移動(dòng)負(fù)荷的動(dòng)載等效分析，較難體現(xiàn)嚙合沖擊效應(yīng)。 2.研究了齒間載荷疊加效應(yīng)、齒高及齒寬方向的載荷分布及輪齒變形和齒根最大拉/壓分布規(guī)律。研究顯示：（1）相鄰齒對(duì)嚙合引起的力疊加效應(yīng)，在齒輪強(qiáng)度精確計(jì)算中不能忽略，嚙合力疊加效應(yīng)對(duì)中心齒受壓側(cè)的影響大于受拉側(cè)，并使輪齒最大變形進(jìn)一步增大。（2）均布荷載、三角分布和三次拋物線分布荷載作用下，齒寬方向的齒根峰值應(yīng)力和接觸區(qū)域輪齒變形的變化規(guī)律，驗(yàn)證了齒端剛度效應(yīng)和輪齒變形及應(yīng)力分布的連續(xù)性；齒向荷載的不均勻性和齒端剛度效應(yīng)，使得齒根最大壓/拉應(yīng)力有所增大，接觸區(qū)域的最大變形略有下降。 3.基于虛擬儀器集成平臺(tái)，提出了通過(guò)無(wú)線應(yīng)變采集卡和路由器傳輸齒根應(yīng)變數(shù)據(jù)的新方法，設(shè)計(jì)了齒根動(dòng)應(yīng)力無(wú)線測(cè)試臺(tái)。通過(guò)多點(diǎn)平均法消除隨機(jī)電噪聲獲取待測(cè)數(shù)據(jù)，將輸入端和輸出端的轉(zhuǎn)速和轉(zhuǎn)矩取平均值，作為計(jì)算模型的加載工況，保證了計(jì)算模型力邊界與試驗(yàn)條件的一致性。測(cè)得的齒根應(yīng)力變化曲線比較準(zhǔn)確地反映了單/雙嚙區(qū)交變、嚙合沖擊及相鄰嚙合齒對(duì)的影響；測(cè)得的最大齒根應(yīng)力與有限元計(jì)算結(jié)果及其他研究者的結(jié)論比較一致，驗(yàn)證了本文提出的無(wú)線測(cè)量方法及上述有限元計(jì)算模型的正確性。獲取了齒面摩擦因數(shù)反求需要用到的試驗(yàn)樣本數(shù)據(jù)，即測(cè)量應(yīng)力。 4.提出了齒面摩擦潤(rùn)滑的多態(tài)性模型。將嚙合傳動(dòng)理論與摩擦學(xué)理論相結(jié)合，對(duì)齒輪傳動(dòng)中的多種摩擦潤(rùn)滑性態(tài)（彈流潤(rùn)滑、邊界潤(rùn)滑、混合潤(rùn)滑、干摩擦、沖擊摩擦等）的形成機(jī)理、特征及存在條件等進(jìn)行了研究。結(jié)合齒輪系統(tǒng)的復(fù)雜性和傳動(dòng)中出現(xiàn)的摩擦過(guò)渡特性，提出了齒輪傳動(dòng)摩擦潤(rùn)滑的多態(tài)性概念和過(guò)程模型。根據(jù)齒面是否出現(xiàn)局部干摩擦，提出將混合潤(rùn)滑分為Ⅰ型（不含局部干摩擦）和Ⅱ型（含局部干摩擦）。最后，研究了混合潤(rùn)滑Ⅰ型的構(gòu)成模型及其齒面摩擦力/摩擦因數(shù)的計(jì)算方法。 5.提出了基于齒根計(jì)算應(yīng)力和測(cè)量應(yīng)力的齒面摩擦因數(shù)反求方法。研究發(fā)現(xiàn)，輪齒在單嚙上界點(diǎn)嚙合時(shí)，齒根非接觸區(qū)的最大拉/壓應(yīng)力對(duì)齒面摩擦具有較高的靈敏性，其中最大拉應(yīng)力的靈敏度比壓應(yīng)力高出近1倍。在此基礎(chǔ)上，提出了以計(jì)算應(yīng)力和測(cè)試應(yīng)力為變量構(gòu)建優(yōu)化目標(biāo)函數(shù)，利用隔代映射小種群遺傳算法與有限單元程序，反求干摩擦狀態(tài)下的齒面摩擦因數(shù)。根據(jù)反求的齒面摩擦因數(shù)，研究了齒面摩擦對(duì)齒根應(yīng)力和輪齒變形的影響。 6.提出了將線外嚙入沖擊階段分為沖擊、刮行和正常嚙合三個(gè)階段，基于齒輪嚙合原理與數(shù)值反推技術(shù)，計(jì)算含系統(tǒng)誤差和輪齒變形的線外嚙入沖擊幾何位置、沖擊速度及沖擊摩擦因數(shù)。主要研究結(jié)論：（1）考慮到影響嚙入沖擊的主要誤差項(xiàng)、輪齒變形和齒面載荷均沿嚙合作用線方向，提出了在該方向上構(gòu)建“系統(tǒng)等效誤差－輪齒綜合變形”計(jì)算模型。（2）按統(tǒng)計(jì)分布規(guī)律將基節(jié)偏差、法向側(cè)隙和齒廓修形量沿嚙合線合成為系統(tǒng)等效誤差；將彎曲、壓縮、剪切、接觸等變形沿作用線合成為輪齒綜合變形；再將系統(tǒng)等效誤差與輪齒綜合變形進(jìn)行二次合成，用以判斷線外嚙入沖擊點(diǎn)的初始幾何位置。（3）根據(jù)輪齒變形－載荷歷程曲線按搜索法反推出線外嚙入沖擊點(diǎn)的輪齒綜合變形，據(jù)此推算出線外嚙入初始點(diǎn)的位置和沖擊力；建立線外嚙入沖擊摩擦模型和計(jì)算沖擊摩擦因數(shù)。
[Abstract]:The gear is an important foundation. Its design and manufacturing level affects the performance and reliability of the mechanical equipment. The calculation and test of the gear strength and the friction of the tooth surface have significant significance for increasing the bearing capacity, improving the fatigue life, reducing the friction and wear, and improving the transmission performance. There are many problems in calculation and experiment. The following problems are worth exploring: the exact modeling method for calculating the bending strength of gears under various loads, the numerical calculation of the tooth root stress and the deformation of the gear teeth; the process model which can characterize the variety of friction lubrication state and the changing law of the tooth surface, and the universal calculation method of the key friction parameters of the tooth surface; Friction mechanism and quantitative calculation of tooth surfaces such as meshing theory, tribology, contact dynamics and so on.
Based on the thinking of the above problems and combining the related topics of the author, this paper puts forward the research topic of this thesis. It focuses on three problems: the accurate modeling method of the calculation of the bending strength of gear under various loads; the polymorphism model and calculation method of the friction lubrication of the tooth surface; the universal quantitative calculation method of the friction force and the friction factor of the tooth surface The main research contents and innovation points are as follows:
1. the precise modeling of the gear finite element and the calculation method of the bending strength are studied. The correctness of the method is verified by comparison and research. The tooth profile is derived from the principle of gear forming and the coordinate system matrix transformation. The geometric model of the gear is realized by the mixed modeling method of APDL and MATLAB based on the pure text data file. Based on the calculation model with error and deformation, the position discriminant of the calculation force point of bending strength is derived, which can be used as a reference for the calculation of the force point of the bending strength. The various effective loads of the finite element calculation of the bending strength of the gear are studied, and the comparison of the peak stress and the tooth deformation of the tooth root under different loads is found. According to the concentration force, the line distribution force, the distribution force of the Hertz contact surface, the order of the static contact force and the accuracy of the calculation result, the dynamic load equivalent analysis of the moving load is difficult to reflect the impact effect of the meshing.
2. the load distribution between the teeth, the load distribution in the direction of tooth height and tooth width, and the distribution of the tooth deformation and the maximum tension / pressure distribution of the tooth root are studied. The study shows: (1) the force superposition effect caused by the engagement of the adjacent teeth can not be ignored in the accurate calculation of the gear strength, and the effect of the superposition effect of the meshing force on the compression side of the central tooth is greater than that of the tension side, and the effect of the superposition of the meshing force is greater than that of the tension side. The maximum deformation of the gear tooth is further increased. (2) the variation of tooth root peak stress and tooth deformation in the contact area under the action of uniform load, triangular distribution and three parabolic load. The stiffness effect of the tooth and the continuity of the tooth deformation and stress distribution, the inhomogeneity of the tooth load and the effect of the tooth end stiffness are verified. The maximum pressure / tensile stress of the tooth root is increased, and the maximum deformation of the contact area decreases slightly.
3. based on the virtual instrument integration platform, a new method of transmitting the tooth root strain data through the wireless strain acquisition card and router is proposed. The tooth root dynamic stress wireless test table is designed. The multipoint averaging method is used to eliminate the random electrical noise to obtain the data to be measured, and the speed and torque of the input and output ends are taken as the calculation model. The force boundary of the calculated model is consistent with the test conditions. The measured tooth root stress change curve accurately reflects the influence of the alternating of single / double meshing, the impact of meshing and the adjacent meshing tooth pairs, and the maximum root stress measured by the finite element method is in agreement with the results of the finite element calculation and the other researchers. The wireless measurement method and the correctness of the above finite element calculation model are obtained. The test data, that is, the measurement stress, is obtained from the reverse calculation of the friction coefficient of the tooth surface.
4. a polymorphic model of friction lubrication of tooth surface is proposed. The mechanism, characteristics and conditions of various frictional states (elastohydrodynamic lubrication, boundary lubrication, mixed lubrication, dry friction and impact friction) in gear transmission are studied by combining the meshing transmission theory with the tribological theory, and the complexity of the gear system and the complexity of the gear system are also studied. The concept and process model of the polymorphism of friction lubrication in gear transmission are proposed in the transmission. According to the local dry friction of the tooth surface, it is proposed to divide the mixed lubrication into type I (without local dry friction) and type II (including local dry friction). Finally, the composition model of the mixed lubrication type I and its tooth surface friction are studied. The calculation method of force / friction factor.
5. the inverse method of the tooth surface friction factor based on the tooth root calculation stress and the measurement stress is proposed. It is found that the maximum tensile / pressure stress of the tooth root non contact area has high sensitivity to the tooth surface friction, and the maximum tensile stress sensitivity is nearly 1 times higher than the compressive stress when the tooth is meshing at the upper boundary point of the single Rog. The optimization objective function is constructed by calculating the stress and the test stress, and the friction factor of the tooth surface in the dry friction condition is calculated by using the small population genetic algorithm and the finite element program, and the effect of the tooth surface friction on the tooth root stress and the tooth deformation is studied.
6. it is proposed that the stage of out of line meshing impact is divided into three stages: impact, scraping and normal meshing. Based on the gear meshing principle and numerical backstepping technology, the geometric position, impact velocity and impact friction factor of the external meshing, the impact velocity and the impact friction factor are calculated. The main conclusions are as follows: (1) the main errors that affect the meshing impact are taken into account. The difference term, the tooth deformation and the load of the tooth surface are all along the direction of the rodent cooperating line, and the calculation model of the "system equivalent error - the comprehensive deformation of the gear tooth" is proposed in this direction. (2) according to the statistical distribution law, the base section deviation, the normal side gap and the tooth profile modification amount are synthesized into the system equivalent error along the meshing line, and the bending, compression, shear, contact and so on are changed. The composite deformation of the gear tooth is formed along the line of action, and then the equivalent error of the system and the comprehensive deformation of the tooth are synthesized two times to judge the initial geometric position of the impact point. (3) according to the tooth deformation load course curve, the comprehensive deformation of the gear tooth is deduced from the search method, and the outer rodent is calculated. The location and impact force of the initial point are established, and the impact friction model is calculated and the impact friction factor is calculated.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2013
【分類號(hào)】：TH132.41

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