趙鑫 金學(xué)松 溫澤峰 王衡禹 吳兵

摘 要：該研究建立了三維瞬態(tài)滾動接觸有限元模型，用于求解速度高至500 km/h的輪軌瞬態(tài)滾動接觸行為。該模型考慮了輪軌的真實幾何形狀，可引入任意接觸面不平順、黏著系數(shù)（或摩擦系數(shù)）沿鋼軌縱向的波動及相對滑移速度對黏著系數(shù)的影響，并可考慮材料的非線性行為。不同的切向接觸載荷，即不同運動狀態(tài)下的車輪所承受的驅(qū)動或制動力，由施加于車軸的隨時間變化的扭矩來控制。模型采用顯式有限元方法，其條件穩(wěn)定特性決定了計算時間步長需取值極小，這使得該模型適合于時域內(nèi)求解輪軌高速滾動過程中的高頻動態(tài)或瞬態(tài)現(xiàn)象，如分析輪軌接觸表面短波長缺陷處（鋼軌焊接接頭、波浪形磨損和車輪扁疤等）的輪軌瞬態(tài)沖擊響應(yīng)。另外，模型中充分考慮了車輛轉(zhuǎn)向架和軌道子系統(tǒng)的主要部件，數(shù)值重現(xiàn)了三維輪對的真實滾動行為，因此車輛—軌道的耦合作用、與高速滾動相關(guān)的自旋、陀螺儀效應(yīng)等因素均包含于模型之中。過去一年多，應(yīng)用上述三維高速瞬態(tài)滾動接觸有限元模型進行了一系列研究。不同速度的模擬結(jié)果發(fā)現(xiàn)，500 km/h以下速度對光滑接觸表面上壓力分布的影響可以忽略，而相應(yīng)的應(yīng)變率隨速度增加而增加。針對很多國家出現(xiàn)的鋼軌表面塌陷現(xiàn)象，即鋼軌接觸帶內(nèi)出現(xiàn)的具有兩瓣特征且第二瓣更大的局部滾動接觸疲勞損傷，也進行模擬研究，結(jié)果顯示其發(fā)生應(yīng)該與軌下膠墊的剛度有很大關(guān)系。車輪滾過鋼軌短波波磨的瞬態(tài)接觸結(jié)果顯示，輪軌接觸力在波磨段呈現(xiàn)出明顯的波動，且當(dāng)波深足夠深時，接觸狀態(tài)會在滾滑—滑動—滾滑間反復(fù)震蕩，從而導(dǎo)致V-M應(yīng)力與摩擦功的波動。跟傳統(tǒng)的基于多體動力學(xué)的車輛—軌道耦合動力學(xué)結(jié)果相比，發(fā)現(xiàn)傳統(tǒng)模型夸大了輪軌間的接觸剛度。另外，隨相對滑動速度變化的摩擦力模型被發(fā)現(xiàn)對輪軌間的切向滾動接觸具有重要的影響。

關(guān)鍵詞：高速列車 滾滑接觸 瞬態(tài)接觸解 驅(qū)動系數(shù) 短波波磨 軌面塌陷 速度相關(guān)的摩擦模型

Abstract：A 3-D transient FE model has been developed to solve the dynamical wheel-rail rolling contact at a speed up to 500 km/h in the time domain. Actual geometries of the wheelset and rail are considered together with the arbitrary irregularity in the contact surfaces， variations of the adhesion coefficient along a rail and the velocity dependence of the friction coefficient. Material nonlinearities can also be included. Different tangential contact loads， either the traction or braking forces， are simulated through specifying a time dependent driving torque applied to the wheel axle.The explicit FE method is employed， so that a tiny time step is required in the simulation due to the conditional stability of the explicit time integration scheme. This makes the model suitable for solving the （high frequency） dynamic or transient wheel-rail rolling contact at high speeds. Moreover， the main components of the vehicle and track systems are included and the actual rolling behavior of the wheelset is reproduced numerically. Therefore， the vehicle-traction interactions， spin of the rolling contact and gyroscopic effect of the rotating wheelset are automatically taken into account.Simulations have shown that the rolling speed has negligible influences on the contact pressure distribution between smooth wheels and rails， while the strain rate does increase with the rolling speed. Studies were also performed to squats， a type of rail rolling contact fatigue observed on many railway networks and with a typical “squatting” shape. It was found that the occurrence of squats， especially its “squatting” shape， was greatly related to the rail pad stiffness. Transient solutions to the wheel-rail rolling contact over corrugation have shown that the contact forces greatly vary at a corrugated site， and the contact state may oscillates between rolling-sliding and sliding； consequently， the V-M stress and frictional work also oscillate at the corrugation. The dynamic contact forces obtained from the FE model were compared with those from a traditional multi-body dynamics model. It was found that the traditional model overestimated the contact stiffness between the wheel and the rail due to the simplifications included. Finally， the velocity dependence of the friction coefficient was included to study its significant influence on tangential contact solutions.In the end， further improvements of the 3-D rolling contact FE model and its future applications are summarized.

Key Words：High-speed train；Rolling-sliding contact；Transient contact solutions；Traction coefficient；Short pitch corrugation；Squats；Velocity dependent friction

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