本文選題：半解析法 + 共軛梯度法��； 參考：《重慶大學(xué)》2013年碩士論文

【摘要】：本論文研究了高分子聚合物粘彈性材料的接觸力學(xué)行為。通過對粘彈性材料蠕變和應(yīng)力松弛相關(guān)特性研究，建立相應(yīng)的數(shù)學(xué)、力學(xué)模型，分析和計算了粘彈性接觸界面的力學(xué)行為。新開發(fā)的算法能有效避免全解析法和全數(shù)值解的弊端，做到快速求解復(fù)雜表面的粘彈性接觸問題。 本論文提出了一種基于半解析法（SAM）的粘彈性接觸快速算法。由于蠕變效應(yīng)具有路徑相關(guān)性，需計算時考慮前步求解結(jié)果。首先用解析的方法得到基本解，然后使用疊加原理得到任意基本解的組合解，并使用共軛梯度法（CGM）和快速傅里葉變換（FFT）求解接觸壓力。該方法能有效克服解析法只能求解簡單邊界條件，以及全數(shù)值法的計算效率低下的弊端。特別是在粗糙表面接觸研究上體現(xiàn)出良好的優(yōu)越性。通過對比鋼球壓入三參數(shù)固體模型和Maxwell材料的解析解，驗證該算法的正確性。進(jìn)一步，本文采用半解析法（SAM）對單峰體表面、V型脊表面和正弦粗糙表面的粘彈性接觸進(jìn)行了研究。通過分析紋理表面對壓力和應(yīng)力的影響，揭示粘彈性材料破壞機(jī)理并實(shí)現(xiàn)接觸零件的性能優(yōu)化。并得到結(jié)論：表面紋理顯著影響接觸壓力和接觸面積；給定一個時刻，光滑表面的接觸面積最大；隨著時間的增加，，接觸壓力降低而接觸面積增加。然后，本文研究了典型加工表面的粘彈性接觸行為，分析了磨削加工實(shí)測表面的接觸特性，微凸體峰頂部分壓力最大，壓力隨微凸體的分布而呈起伏狀。粗糙表面微凸體間的接觸會引起接觸壓力的劇烈震蕩，接觸區(qū)分布在許多不連通區(qū)域，隨著時間的增加，接觸區(qū)逐漸聯(lián)通。 最后，本方法用來分析水潤滑橡膠合金軸承橡膠中粘彈性材料的接觸問題，采用將橡膠合金軸承接觸等效為線接觸的方法。論文分別對水潤滑橡膠合金軸承的工作面形狀、硫化橡膠和加載壓力等影響因數(shù)做了研究，得到不同工況下接觸壓力分布的特點(diǎn)和變化規(guī)律。結(jié)果表明：水潤滑橡膠合金軸承橡膠硫化之后，彈性模量顯著提高，可以有效地提高軸承的負(fù)載能力與耐磨性能，確保了極端工況條件下的正常運(yùn)行。此外，平面型水潤滑橡膠合金軸承抗摩擦效果優(yōu)于凹面型軸承，可以承擔(dān)更大的壓力。
[Abstract]:In this paper, the contact mechanics behavior of viscoelastic materials is studied. Through the study of the creep and stress relaxation properties of viscoelastic materials, the corresponding mathematical and mechanical models are established and the mechanical behavior of the viscoelastic contact interface is analyzed and calculated. The new algorithm can effectively avoid the disadvantages of the full analytical method and the full numerical solution. We can quickly solve the viscoelastic contact problem of complex surfaces.
In this paper, a fast algorithm for viscoelastic contact based on semi analytic method (SAM) is proposed. Due to the path dependence of the creep effect, the result of the forward step is considered when the calculation is needed. First, the basic solution is obtained by the analytic method. Then the combination of the basic solutions is obtained by the superposition principle, and the conjugate gradient method (CGM) and fast Fu Li are used. Ye Bianhuan (FFT) is used to solve the contact pressure. This method can effectively overcome the problem that the analytical method can only solve the simple boundary conditions and the low efficiency of the total numerical method. In particular, it shows good superiority in the rough surface contact study. By comparing the analytical solution of the three parameter solid model and the Maxwell material of the steel ball pressure, the calculation is verified. Further, the viscoelastic contact of the surface of the single peak body, the V type ridge surface and the sine rough surface is studied by semi analytic method (SAM). By analyzing the effect of the texture surface on the pressure and stress, the failure mechanism of the viscoelastic material is revealed and the performance of the contact zero is optimized. The conclusion is that the surface texture is obvious. The contact area of the contact pressure and the contact area is affected. The contact area of the smooth surface is the largest at a given time, and the contact area increases with the increase of time. Then, the viscoelastic contact behavior of the typical surface is studied. The contact characteristics of the surface of the grinding machining, the partial pressure of the top of the micro convex body peak are analyzed. The maximum pressure is fluctuating with the distribution of the micro convex body. The contact between the rough surface of the micro convex body will cause the violent shock of contact pressure. The contact area is distributed in many disconnected regions. With the increase of time, the contact area is gradually connected.
Finally, this method is used to analyze the contact problem of the viscoelastic material in the rubber bearing rubber of water lubricated rubber alloy, and the contact of the rubber alloy bearing is equivalent to the line contact. The influence factors of the working face, vulcanized rubber and loading pressure of the water lubricated rubber bearing are studied in this paper, and the contact is obtained under different working conditions. The characteristics and change rules of pressure distribution show that the elastic modulus of the rubber bearing rubber is improved remarkably after the vulcanization of the rubber bearing rubber, which can effectively improve the bearing capacity and wear resistance, and ensure the normal operation under the extreme working conditions. In addition, the friction effect of the plane type water lubricated rubber alloy bearings is superior to the concave surface. Type bearing, which can bear greater pressure.
【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：O343.3;TH133.3

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本文編號：2009278