交会压力波作用下的高速列车动态响应及机理研究
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摘要
随着我国高速列车的不断发展,很多在以前低速列车运行安全性上被忽略的空气动力学问题,开始受到研究者越来越多的重视。这些空气动力学问题主要有气动阻力问题、横风效应、隧道效应、会车效应等。其中关于会车效应方面的研究主要集中于三个方面：1、交会压力波的基本特性；2、交会压力波对列车运行稳定性的影响；3、交会压力波对列车车体和侧窗安全性的影响。关于第三方面的现有的研究还局限于根据交会压力波对侧窗或包含局部车体的模型研究的结果来评估车体和侧窗的安全性。这些安全性评估方法对于低速列车的钢结构的列车交会安全性评估不会产生较大误差,但随着随着交会速度的提升带来的交会压力波强度的增加以及车身轻量化引起的车体结构的动力学响应的加大,这样的评估方法就可能忽略了车体结构的动力学响应对侧窗和车体安全性的影响。本文的工作主要着眼于高速列车受交会压力波作用下的整体动态响应,及其对侧窗安全性的影响。我们通过有限元方法研究了列车中间车厢模型受交会压力波作用下的动态响应和侧窗安全性评估问题。进而,采用有限元计算和理论分析相结合的方法,通过理论简化模型对列车车体受交会压力波作用下的动态响应的特征和机理进行了研究。论文的具体研究工作总结如下：
(1)高速列车侧窗受交会压力波作用的有限元分析
建立了两种高速列车车型CRH2和CRH3的中间车厢的有限元模型,模型包含三种工况：移动压力波、均布动载和静载荷。对于CRH2模型的研究发现,静载荷工况下的侧窗应力结果低于其他两种。而对于均布动载下的侧窗应力,在较低交会速度时,比移动压力波作用下的侧窗应力高,而随着交会速度的提高,则开始低于后者作用下的侧窗应力。因此,在高速交会的情况下,必须考虑交会压力波的影响。对于CRH3模型的研究,得到的结果与CRH2模型的类似。不过其均布动载工况下的侧窗应力值与移动压力波工况下的侧窗应力值之间的大小关系的转变速度高于CRH2的情况,并且其均布动载工况下的侧窗应力最大值与移动压力波下的侧窗应力最大值的相对误差只有6%,因此,对于CRH3车型来说,可以用均布动载工况下的结果来评估侧窗受交会压力波作用时的安全性。
(2)半无限梁受移动脉冲作用的有限元分析
由于列车车体的结构的复杂性,很难对其内部产生的弯曲波进行研究。本章建立了相应的简化模型,即半无限梁受移动单周期正弦脉冲载荷作用的有限元模型。对于相同的脉宽,移动脉冲存在临界速度,梁中的最大等效应力的平均值在移动脉冲以该速度移动将达到其最大值。临界速度随着移动脉冲脉宽的增加而减小,但在移动脉冲达到临界速度时的最大等效应力的平均值随脉宽的增加而增加。梁中最大弯曲程度出现的位置会随着移动脉冲的作用而逐渐远离移动脉冲作用区域。梁中最大等效应力随位置波动的机理也作了一定的分析。我们采用量纲分析得到了关于临界速度和影响临界速度的因素的经验公式。结果表明临界速度只受弹性波波速、横截面回转半径和脉宽的影响。
(3)半无限(或无限)梁受移动脉冲作用的理论分析
由于数值计算分析的局限性,本章将采用理论分析对简化模型进行研究。基于Bernoulli-Euler梁理论,首先建立了半无限梁受移动脉冲作用的瞬态响应模型,并采用Fourier变换法求得相应的梁的挠度和应力解。通过将梁的挠度结果与有限元结果比较,验证了理论解的有效性。梁中的最大应力值随时间的变化规律是与梁中最大应力值出现处和移动脉冲前段距离随时间的变化规律相一致。同样基于Bernoulli-Euler梁理论,建立了无限梁受移动脉冲作用下的稳态响应模型,采用二维Fourier积分变换方法对梁方程进行求解,最后应用复变函数理论中的留数定理求得梁的挠度和应力的显式解。得到了无限梁受移动脉冲作用下稳态响应的临界速度,将其和瞬态解得到的临界速度以及与脉宽相同周期的简谐波波速三者之间的对比发现,稳态解得到的临界速度临界速度更接近瞬态解的临界速度。稳态解得到的载荷作用区前后方平衡位置的距离表达式可以很好的表征瞬态解载荷后方的挠度,其挠度与移动脉冲的速度无关。进一步求得临界速度的近似解,和瞬态解得到的临界速度几乎完全吻合。根据交会压力波的特点对前面理论解进行修改,得到了梁在受压力波作用下的动态响应。对于同一列车交会产生的压力波,即压力波空间长度一定,也发现了临界速度。在不同压力波长度下,保持压力波幅值和交会速度平方之间的系数不变,梁中最大应力值(当压力波达到相应的临界速度)相同,即表现出不受交会压力波长度变化的影响。
With the development of high-speed train, many aerodynamic problems, which have been neglected when trains ran at low speeds, are being raised with drawing researchers' attentions. The aerodynamic problems mainly are aerodynamic drag problem, cross-wind effects, wind tunnel effects and effects due to trains passing each other, etc. Available researches about the effects due to trains passing each other contain three aspects, basic characteristics of crossing air pressure pulse, the influence of crossing air pressure on the stability of train running and the influence of crossing air pressure on the train body and side windows. The studies on the third aspect are limited to evaluate the safety of train body and side windows subjected to pressure pulse with the model of side windows or part of train body. That method of safety evaluation will not bring large error for the trains running at low speed. But, for the speed-up of train with lighter of train body, it will be lack of consideration of the effect of dynamic response of whole train body on the safety of train body and side windows. The paper focused on studying the dynamic response of whole train body when high-speed train subjected to the crossing air pressure, and the effect of that response on the safety of side windows. The dynamic response of middle carriage subjected to crossing air pressure and the safety evaluation of side windows under that load were investigated by using finite element method. Then, the characteristics and mechanisms of dynamic response of train body subjected to crossing air pressure by analyzing a simplified model with the methods of finite element method and theory model. Main work and findings include:
(1) Finite element analysis of dynamic response of side windows of high-speed trains subjected to crossing air pressure
Two kinds of finite element models of the middle carriages of CRH2and CRH3were built, the loading conditions contained in the models:moving air pressure pulse, uniform dynamic load and static load. Through the study of CRH2model, it was found that the peak stresses side window centers were lower than the other two loading conditions. When the traveling velocity of trains is lower, the peak stresses of side window centers calculated under uniform dynamic load are higher than those of the other two loading situations. As the velocity increases, the peak stresses of side window centers resulted by the moving air pressure pulse exceed those calculated under uniform dynamic load. Hence, the influence of crossing air pressure pulse caused by high-speed trains passing each other must be considered when elevating the safety of side windows. Through the study of CRH3model, it was found that the results were similar with those of CRH2. The differences between two models are that, in the CRH3model, the peak stresses of side window centers calculated under uniform dynamic load are higher than those of the moving air pressure pulse at a higher traveling speed than those in CRH2, and the relative error of peak stress of side window centers between the loading conditions of uniform dynamic load and moving air pressure pulse is6%. The peak stresses of side window centers can be used for the safety evaluation of side windows subjected to crossing air pressure pulse.
(2) Finite element analysis of semi-infinite beam to a moving pulse
Due to the complexity of the structure of train body, it's very difficult to investigate the flexural wave travelling in the structure. A simplified model was built in this chapter, i.e., the finite element model of semi-infinite beam to a moving single sinusoidal pulse was built. For an identical pulse duration, there exists a critical velocity, i.e., the the average value of maximal equivalent stress in the beam reaches its maximum value when the velocity of moving pulse is closed to a critical velocity. The critical velocity decreases as the pulse duration increases. The average value of maximal equivalent stress in the beam increases as the pulse duration increases when the moving pulse moves at critical velocity. The position where the maximum degree of bending appears moves away from the region of moving pulse applied. The mechanism of stress fluctuation was also studied. The material, structural and load parameters influencing the critical velocity were analysed with dimensionless analysis. An empirical formula of the critical velocity with respect to the speed of elastic wave, the gyration radius of the cross-section and the pulse duration was obtained.
(3) Theoretical analysis of semi-infinite or infinite beam to a moving pulse
Due to limitation of the numerical method, in this chapter, the method of theoretical analysis was used to study the simplified model. Based on the Bernoulli-Euler beam theory, the theory model of the semi-infinite beam to a moving pulse was built and solved by Fourier transform. The transient solutions of displacement and stress of semi-infinite beam to a moving pulse were obtained. The effectiveness of the theoretical solution was verified by comparing the displacement of beam with the result of FEA. The variation trend of the maximum stress in the beam changing with time is the same to the distance between the position of maximum stress and the front of moving pulse changing with time. Also based on the Bernoulli-Euler beam theory, the theory model of the infinite beam to a moving pulse was built and solved by Green function, two-dimensional Fourier transform and theorem of residue. The explicit steady-state solutions of displacement and stress of infinite beam to a moving pulse were obtained. For an identical pulse duration, the critical velocity was also found. Comparing it with the critical velocity of transient solution and the speed of harmonic wave whose period is equal to the pulse duration, it was found that the critical velocity of steady-state solution is much closer to the critical velocity of transient solution than the speed of harmonic wave. The expression of the lateral distance of vibration equilibrium positions between the front and behind loading area for the steady-state solution can be a good characterization of the deflection behind the loading area for the transient solution. They are both not affected by the velocity of moving pulse. The approximate solution of critical speed for the steady-state solution was obtained, and it was consistent with the critical speed for the transient solution well. The dynamic response of beam to a crossing air pressure pulse was obtained by modified the above solutions with the characters of crossing air pressure pulse. For the identical trains passing each other, i.e., the length of crossing air pressure pulse is constant, the critical velocity was also found. For constant coefficient of the amplitude of crossing air pressure pulse and the square of velocity trains passing each other, the maximum stresses in the beam are uniform for different lengths of crossing air pressure pulse when the crossing air pressure pulse moves at critical velocity.
(1)高速列车侧窗受交会压力波作用的有限元分析
建立了两种高速列车车型CRH2和CRH3的中间车厢的有限元模型,模型包含三种工况：移动压力波、均布动载和静载荷。对于CRH2模型的研究发现,静载荷工况下的侧窗应力结果低于其他两种。而对于均布动载下的侧窗应力,在较低交会速度时,比移动压力波作用下的侧窗应力高,而随着交会速度的提高,则开始低于后者作用下的侧窗应力。因此,在高速交会的情况下,必须考虑交会压力波的影响。对于CRH3模型的研究,得到的结果与CRH2模型的类似。不过其均布动载工况下的侧窗应力值与移动压力波工况下的侧窗应力值之间的大小关系的转变速度高于CRH2的情况,并且其均布动载工况下的侧窗应力最大值与移动压力波下的侧窗应力最大值的相对误差只有6%,因此,对于CRH3车型来说,可以用均布动载工况下的结果来评估侧窗受交会压力波作用时的安全性。
(2)半无限梁受移动脉冲作用的有限元分析
由于列车车体的结构的复杂性,很难对其内部产生的弯曲波进行研究。本章建立了相应的简化模型,即半无限梁受移动单周期正弦脉冲载荷作用的有限元模型。对于相同的脉宽,移动脉冲存在临界速度,梁中的最大等效应力的平均值在移动脉冲以该速度移动将达到其最大值。临界速度随着移动脉冲脉宽的增加而减小,但在移动脉冲达到临界速度时的最大等效应力的平均值随脉宽的增加而增加。梁中最大弯曲程度出现的位置会随着移动脉冲的作用而逐渐远离移动脉冲作用区域。梁中最大等效应力随位置波动的机理也作了一定的分析。我们采用量纲分析得到了关于临界速度和影响临界速度的因素的经验公式。结果表明临界速度只受弹性波波速、横截面回转半径和脉宽的影响。
(3)半无限(或无限)梁受移动脉冲作用的理论分析
由于数值计算分析的局限性,本章将采用理论分析对简化模型进行研究。基于Bernoulli-Euler梁理论,首先建立了半无限梁受移动脉冲作用的瞬态响应模型,并采用Fourier变换法求得相应的梁的挠度和应力解。通过将梁的挠度结果与有限元结果比较,验证了理论解的有效性。梁中的最大应力值随时间的变化规律是与梁中最大应力值出现处和移动脉冲前段距离随时间的变化规律相一致。同样基于Bernoulli-Euler梁理论,建立了无限梁受移动脉冲作用下的稳态响应模型,采用二维Fourier积分变换方法对梁方程进行求解,最后应用复变函数理论中的留数定理求得梁的挠度和应力的显式解。得到了无限梁受移动脉冲作用下稳态响应的临界速度,将其和瞬态解得到的临界速度以及与脉宽相同周期的简谐波波速三者之间的对比发现,稳态解得到的临界速度临界速度更接近瞬态解的临界速度。稳态解得到的载荷作用区前后方平衡位置的距离表达式可以很好的表征瞬态解载荷后方的挠度,其挠度与移动脉冲的速度无关。进一步求得临界速度的近似解,和瞬态解得到的临界速度几乎完全吻合。根据交会压力波的特点对前面理论解进行修改,得到了梁在受压力波作用下的动态响应。对于同一列车交会产生的压力波,即压力波空间长度一定,也发现了临界速度。在不同压力波长度下,保持压力波幅值和交会速度平方之间的系数不变,梁中最大应力值(当压力波达到相应的临界速度)相同,即表现出不受交会压力波长度变化的影响。
With the development of high-speed train, many aerodynamic problems, which have been neglected when trains ran at low speeds, are being raised with drawing researchers' attentions. The aerodynamic problems mainly are aerodynamic drag problem, cross-wind effects, wind tunnel effects and effects due to trains passing each other, etc. Available researches about the effects due to trains passing each other contain three aspects, basic characteristics of crossing air pressure pulse, the influence of crossing air pressure on the stability of train running and the influence of crossing air pressure on the train body and side windows. The studies on the third aspect are limited to evaluate the safety of train body and side windows subjected to pressure pulse with the model of side windows or part of train body. That method of safety evaluation will not bring large error for the trains running at low speed. But, for the speed-up of train with lighter of train body, it will be lack of consideration of the effect of dynamic response of whole train body on the safety of train body and side windows. The paper focused on studying the dynamic response of whole train body when high-speed train subjected to the crossing air pressure, and the effect of that response on the safety of side windows. The dynamic response of middle carriage subjected to crossing air pressure and the safety evaluation of side windows under that load were investigated by using finite element method. Then, the characteristics and mechanisms of dynamic response of train body subjected to crossing air pressure by analyzing a simplified model with the methods of finite element method and theory model. Main work and findings include:
(1) Finite element analysis of dynamic response of side windows of high-speed trains subjected to crossing air pressure
Two kinds of finite element models of the middle carriages of CRH2and CRH3were built, the loading conditions contained in the models:moving air pressure pulse, uniform dynamic load and static load. Through the study of CRH2model, it was found that the peak stresses side window centers were lower than the other two loading conditions. When the traveling velocity of trains is lower, the peak stresses of side window centers calculated under uniform dynamic load are higher than those of the other two loading situations. As the velocity increases, the peak stresses of side window centers resulted by the moving air pressure pulse exceed those calculated under uniform dynamic load. Hence, the influence of crossing air pressure pulse caused by high-speed trains passing each other must be considered when elevating the safety of side windows. Through the study of CRH3model, it was found that the results were similar with those of CRH2. The differences between two models are that, in the CRH3model, the peak stresses of side window centers calculated under uniform dynamic load are higher than those of the moving air pressure pulse at a higher traveling speed than those in CRH2, and the relative error of peak stress of side window centers between the loading conditions of uniform dynamic load and moving air pressure pulse is6%. The peak stresses of side window centers can be used for the safety evaluation of side windows subjected to crossing air pressure pulse.
(2) Finite element analysis of semi-infinite beam to a moving pulse
Due to the complexity of the structure of train body, it's very difficult to investigate the flexural wave travelling in the structure. A simplified model was built in this chapter, i.e., the finite element model of semi-infinite beam to a moving single sinusoidal pulse was built. For an identical pulse duration, there exists a critical velocity, i.e., the the average value of maximal equivalent stress in the beam reaches its maximum value when the velocity of moving pulse is closed to a critical velocity. The critical velocity decreases as the pulse duration increases. The average value of maximal equivalent stress in the beam increases as the pulse duration increases when the moving pulse moves at critical velocity. The position where the maximum degree of bending appears moves away from the region of moving pulse applied. The mechanism of stress fluctuation was also studied. The material, structural and load parameters influencing the critical velocity were analysed with dimensionless analysis. An empirical formula of the critical velocity with respect to the speed of elastic wave, the gyration radius of the cross-section and the pulse duration was obtained.
(3) Theoretical analysis of semi-infinite or infinite beam to a moving pulse
Due to limitation of the numerical method, in this chapter, the method of theoretical analysis was used to study the simplified model. Based on the Bernoulli-Euler beam theory, the theory model of the semi-infinite beam to a moving pulse was built and solved by Fourier transform. The transient solutions of displacement and stress of semi-infinite beam to a moving pulse were obtained. The effectiveness of the theoretical solution was verified by comparing the displacement of beam with the result of FEA. The variation trend of the maximum stress in the beam changing with time is the same to the distance between the position of maximum stress and the front of moving pulse changing with time. Also based on the Bernoulli-Euler beam theory, the theory model of the infinite beam to a moving pulse was built and solved by Green function, two-dimensional Fourier transform and theorem of residue. The explicit steady-state solutions of displacement and stress of infinite beam to a moving pulse were obtained. For an identical pulse duration, the critical velocity was also found. Comparing it with the critical velocity of transient solution and the speed of harmonic wave whose period is equal to the pulse duration, it was found that the critical velocity of steady-state solution is much closer to the critical velocity of transient solution than the speed of harmonic wave. The expression of the lateral distance of vibration equilibrium positions between the front and behind loading area for the steady-state solution can be a good characterization of the deflection behind the loading area for the transient solution. They are both not affected by the velocity of moving pulse. The approximate solution of critical speed for the steady-state solution was obtained, and it was consistent with the critical speed for the transient solution well. The dynamic response of beam to a crossing air pressure pulse was obtained by modified the above solutions with the characters of crossing air pressure pulse. For the identical trains passing each other, i.e., the length of crossing air pressure pulse is constant, the critical velocity was also found. For constant coefficient of the amplitude of crossing air pressure pulse and the square of velocity trains passing each other, the maximum stresses in the beam are uniform for different lengths of crossing air pressure pulse when the crossing air pressure pulse moves at critical velocity.
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