轨道结构随机振动和Ⅲ型轨枕可靠性研究
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摘要
基于车辆、轨道耦合系统的思路,建立了满足高速铁路轨道结构动力分析要求的车辆—轨道空间耦合系统振动分析模型。采用该模型,将轨道不平顺视为平稳的各态历经过程,对轨道结构的随机振动规律进行了研究。更进一步,将轨道结构作为随机参数结构,把扣件刚度和道床刚度视为服从正态分布的随机变量,应用Monte Carlo随机有限元方法,对轨道结构的随机振动规律进行了研究。应用可靠度理论,对Ⅲ型混凝土轨枕应用于高速铁路的可靠性进行了研究。本文的主要研究内容和成果如下：
1、基于车辆—轨道耦合系统的思路,建立了满足高速铁路轨道结构随机振动分析要求的车辆—轨道空间耦合系统振动分析模型。该模型为半车空间、耦合、定点模型。模型中轨道结构的钢轨采用连续弹性点支承Euler梁单元。轨枕采用刚体单元,道床在纵向和横向离散为道床块单元。模型边界采用了连续弹性支承半无限长梁单元。采用Hertz非线性轮轨接触关系实现车辆系统与轨道系统的耦合。
2、首次提出了人工轨道短波不平顺的概念,并采用随机波长和随机波深构造了轨道随机不平顺人工短波样本。将人工短波样本与德国高速低干扰随机不平顺样本相结合,给出了高速铁路的轨道随机不平顺样本,为研究高速铁路轨道结构的随机振动规律提供良好的基础。
3、仿真计算了轮轨系统受轨道随机不平顺激励时,轨道结构的随机振动响应,并对计算结果进行了统计分析。
结果表明,车速从160km/h到350km/h时,轨道结构各部件的随机振动响应中,钢轨、轨枕、道床加速度、枕上压力的概率分布均服从正态分布。车辆、轨道结构各部件的随机振动响应随着行车速度的提高,振动加速度、轮轨垂向接触力、枕上压力、路基面应力等均呈现明显增大的趋势,其中以加速度的变化最为明显,轮轨力、枕上压力、路基面应力次之,位移变化相对较小
当行车速度从250km/h增加到350km/h时,车辆、轨道结构的振动响应有一个比较明显的变化,响应出现很大的增加,钢轨加速度由158g增加到581g,轮轨力由280kN增加到350kN,枕上压力由92kN增加到109kN。尤以振动加速度的变化最为明显,其中钢轨和轮对的振动加速度成倍增加,可见速度效应非常突出。
4、对轨道结构各个振动参数进行了详细分析,由于轨道结构的扣件刚度和道床刚度的变化范围较大,而其他参数的变化相对较小,并且轨道结构的振动对刚度的变化比较敏感。因此,将扣件刚度和道床刚度作为服从正态分布的随机变量,并给出了这两个随机参数的模拟样本。
5、将扣件刚度和道床刚度作为服从正态分布的随机变量得到的随机参数样本,与轨道随机不平顺样本一起,作为车辆—轨道耦合振动系统的广义激励,对轮轨系统的随机振动进行了仿真计算,并对计算结果进行了统计分析。
(1)结果表明,轨枕加速度、道床加速度、轮轨力、枕上压力及路基面应力的极大值的分布范围均较大,钢轨加速度极大值分布范围最大,这说明钢轨加速度极大值的变化非常大。
(2)轮轨系统随机振动响应中,钢轨、轨枕、道床加速度、轮轨力、枕上压力的极大值的概率分布在检验水平为0.05时,经χ2检验,均服从极值Ⅰ型分布。
(3)车辆、轨道结构的随机振动响应随着行车速度的提高,呈明显增大趋势,尤其在高速情况下,增幅巨大。这说明高速铁路动力响应非常大,应引起足够重视。
(4)轨道结构的扣件刚度和道床刚度对轮轨系统的随机振动响应影响很大,因此优化高速铁路轨道结构参数,尤其是扣件刚度和道床刚度,并保持其在较小范围内变化显得非常重要。
(5)通过对轮轨力计算结果的研究,提出了我国各速度等级铁路设计轮载的动力系数建议值。160、200、250、300、350km/h的动力系数建议值分别为2.4、2.8、3.0、3.5、3.7。
6、分析并提出了Ⅲ型混凝土轨枕的4种失效模式,分别为轨下截面和枕中截面在疲劳弯矩作用下的开裂失效、混凝土受压区压溃破坏失效。分别对各种失效模式对应的抗力和作用效应的影响因素进行了分析。
7、根据Ⅲ型混凝土轨枕的实际工作状态,提出了符合Ⅲ型混凝土轨枕支承分析的计算图式。该图式设轨枕在受均布反力集度q1的基础上,以轨下截面为对称中心,附加作用一倒梯形反力集度,倒梯形集度高为(q2-q1),上底宽为(2,1+l2),下底宽为l2。基于该图式,计算了Ⅲ型混凝土轨枕的作用效应。
8、提出了由轨枕静载抗裂试验荷载求取轨枕截面抗力,即疲劳承载弯矩和受压区混凝土边缘疲劳压应力的计算方法。
9、给出了作用效应和抗力的分布,其中作用效应的分布服从极值Ⅰ型,抗力的概率分布服从对数正态分布。同时给出了各分布的统计特征参数及其分布函数。
10、应用JC法,对Ⅲ型混凝土轨枕的可靠指标进行了计算。当不考虑抗力折减及作用效应发展系数时,Ⅲ型轨枕的可靠指标为3.583,失效概率为0.00017,即0.017%。当考虑抗力折减及作用效应发展系数时,Ⅲ型轨枕的可靠指标为2.909,失效概率为0.00181,即0.18%。对Ⅲ型轨枕而言,该失效概率是可以接受的。
11、由Ⅲ型混凝土轨枕可靠度初步研究结果表明,Ⅲ型混凝土轨枕可以应用于高速铁路。
Based on the thought of interaction between vehicle and track, the spatial coupled vehicle/track vibration model was built for high speed railway track, and applied in the track irregularity, which was treated as a stationary ergodicity process. The random vibration laws of railway track were investgated. Further more, the random vibration laws were studied by using Monte Carlo random FEM (finite element method) under the condition that the track parameters of fastener stiffness and ballast stiffness are treated as random parameters obeying normal distribution. The reliability of reinforced sleeperⅢwhich will be used in high-speed railway in China was investgated.
Main contribution and achievement in this thesis are listed below:
1. The model of spatial coupled vehicle/track system was established for high speed railway. In the model, track irregularity movement was used instead of train movement, rail was modeled as Euler beam element, sleeper and ballast was modeled as gird body element, the boundary was modeled as half-infinite beam element, and Hertz nonlinear contact was applied between wheel and rail.
2. The new concept of artificial short wave of track irregularity was put forward, and a sample of artificial short wave was built. In combined of the sample of short wave and the sample of low disturbance track irregularity of high speed railway in German, a simulated sample of random track irregularity was established to study the vibration laws of track in high speed railway.
3. The vibration of vehicle/track system was calculated under the excitations of random track irregularity, and the results were statistically analyzed. The effect of train speed on vibration was very large.
The results showed that probability distribution of the acceleration of rail, sleeper and ballast, and the force on sleeper obeyed normal distribution. As train speed increases from 160km/h to 350km/h, the vibration responses of vehicle and track (which involve acceleration, contact force between wheel/rail, the force on sleeper, the stress on subgrade, and the displacement of rail, sleeper and ballast) were all increased but in a relatively different manner. The values of acceleration increase were the highest. The values of contact force between wheel/rail, force on sleeper and stress on subgrade were relatively low. The values of displacement increase were the lowest.
When train speed increases from 250km/h to 350km/h, the value of vibration responses had a recognized increase, acceleration of rail increses from 158g to 581g, contact force of wheel/rail increases from 280kN to 350kN, and press force on sleepers increases from 92kN to 109kN,. The increase in value of acceleration was the highest, the value of acceleration of wheelset and rail may be doubled or even more.
4. Samples of fastener and ballast stiffnesses were established, because the variation range of fastener and ballast stiffnesses are wide and fastener and ballast stiffnesses are very sensitive, and the fastener and ballast stiffnesses were treat as random parameters that obey normal distribution through out this work.
5. A sample of random parameter of fastener and ballast stiffnesses and a sample of low disturbance track irregularity of high-speed railway in German were combined as excitation, the random vibration was investigated by simulation calculation, and the results were statistically analyzed.
(1) The range of extreme values of rail acceleration, sleeper acceleration, ballast acceleration, wheel/rail force, force on sleeper and stress on subgrade were very wide, but the range of extreme values of rail acceleration were the widest.
(2) Probability distribution of the extreme values of vehicle/track vibration responses obeyed extreme value I distribution checked byχ2 condition in the signifycance level of 0.05.
(3) When the train speed increases, the random vibration responses will increase same as the trend in point 3 above, but the values in comparing with it were much higher. It means that the dynamic responses of high speed railway are very significant, and more attention should be payed to it.
(4) The parameters of high speed railway track structure (especially fastener and ballast stiffnesses) had much more impact to random vibration responses of vehicle/track system, so they should be optimized and remained in a narrow range.
(5) The dynamic coefficients of design wheel load in all speed classes in China by studying the calculation results of wheel/rail forces were put forward. When train speed are 160,200,250,300,350km/h, the adviced coefficients of design wheel load in China are 2.4, 2.8,3.0,3.5,3.7.
6. Four failure modes of concrete sleeperⅢwere established and influence factors of resistance and loading effects of them were analyzed, including concrete cracking and crush failures (because of fatigue bending moment in sleeper section) under rail and in the middle of sleeper section.
7. Based on the real work conditions of concrete sleeperⅢ, a model of sleeper support was build and used to analyze the Concrete sleeperⅢ. In this model, there is a uniform distributed reaction force q1, as well as a pair of revised trapezoidal distributed reaction force which are symmetrical about the sleeper section under the rail, their height are (q2-g1), and their top and bottom edge width are (2l1+l2) and l2 correspondingly. Using the modle, the loading effects of concrete sleeperⅢwere solved.
8. The calculation method to solve sleeper section resistance used static cracking test load, which was established to calculate the fatigue bending moment and the fatigue compressive stress on the edge of compressive concrete.
9. The distributions of loading effects, and resistance were given, also the statistical parameters and distribution functions were given. The distribution of loading effects obeyed extreme value I distribution, but the distribution of resistance obeyed lognormal distribution.
10. Failure probability and reliability index were calculated by JC method. The reliability index and failure probability in case of the resistance reduction and loading effects development factors, were neglected, were 3.583 and 0.017% respectively, but in case they were considered the results were 2.909 and 0.18% respectively. For the concrete sleeperⅢ, both of the failures probability are acceptable.
11. The above research results showed that the concrete sleeperⅢcan be used in high speed railway in China.
1、基于车辆—轨道耦合系统的思路,建立了满足高速铁路轨道结构随机振动分析要求的车辆—轨道空间耦合系统振动分析模型。该模型为半车空间、耦合、定点模型。模型中轨道结构的钢轨采用连续弹性点支承Euler梁单元。轨枕采用刚体单元,道床在纵向和横向离散为道床块单元。模型边界采用了连续弹性支承半无限长梁单元。采用Hertz非线性轮轨接触关系实现车辆系统与轨道系统的耦合。
2、首次提出了人工轨道短波不平顺的概念,并采用随机波长和随机波深构造了轨道随机不平顺人工短波样本。将人工短波样本与德国高速低干扰随机不平顺样本相结合,给出了高速铁路的轨道随机不平顺样本,为研究高速铁路轨道结构的随机振动规律提供良好的基础。
3、仿真计算了轮轨系统受轨道随机不平顺激励时,轨道结构的随机振动响应,并对计算结果进行了统计分析。
结果表明,车速从160km/h到350km/h时,轨道结构各部件的随机振动响应中,钢轨、轨枕、道床加速度、枕上压力的概率分布均服从正态分布。车辆、轨道结构各部件的随机振动响应随着行车速度的提高,振动加速度、轮轨垂向接触力、枕上压力、路基面应力等均呈现明显增大的趋势,其中以加速度的变化最为明显,轮轨力、枕上压力、路基面应力次之,位移变化相对较小
当行车速度从250km/h增加到350km/h时,车辆、轨道结构的振动响应有一个比较明显的变化,响应出现很大的增加,钢轨加速度由158g增加到581g,轮轨力由280kN增加到350kN,枕上压力由92kN增加到109kN。尤以振动加速度的变化最为明显,其中钢轨和轮对的振动加速度成倍增加,可见速度效应非常突出。
4、对轨道结构各个振动参数进行了详细分析,由于轨道结构的扣件刚度和道床刚度的变化范围较大,而其他参数的变化相对较小,并且轨道结构的振动对刚度的变化比较敏感。因此,将扣件刚度和道床刚度作为服从正态分布的随机变量,并给出了这两个随机参数的模拟样本。
5、将扣件刚度和道床刚度作为服从正态分布的随机变量得到的随机参数样本,与轨道随机不平顺样本一起,作为车辆—轨道耦合振动系统的广义激励,对轮轨系统的随机振动进行了仿真计算,并对计算结果进行了统计分析。
(1)结果表明,轨枕加速度、道床加速度、轮轨力、枕上压力及路基面应力的极大值的分布范围均较大,钢轨加速度极大值分布范围最大,这说明钢轨加速度极大值的变化非常大。
(2)轮轨系统随机振动响应中,钢轨、轨枕、道床加速度、轮轨力、枕上压力的极大值的概率分布在检验水平为0.05时,经χ2检验,均服从极值Ⅰ型分布。
(3)车辆、轨道结构的随机振动响应随着行车速度的提高,呈明显增大趋势,尤其在高速情况下,增幅巨大。这说明高速铁路动力响应非常大,应引起足够重视。
(4)轨道结构的扣件刚度和道床刚度对轮轨系统的随机振动响应影响很大,因此优化高速铁路轨道结构参数,尤其是扣件刚度和道床刚度,并保持其在较小范围内变化显得非常重要。
(5)通过对轮轨力计算结果的研究,提出了我国各速度等级铁路设计轮载的动力系数建议值。160、200、250、300、350km/h的动力系数建议值分别为2.4、2.8、3.0、3.5、3.7。
6、分析并提出了Ⅲ型混凝土轨枕的4种失效模式,分别为轨下截面和枕中截面在疲劳弯矩作用下的开裂失效、混凝土受压区压溃破坏失效。分别对各种失效模式对应的抗力和作用效应的影响因素进行了分析。
7、根据Ⅲ型混凝土轨枕的实际工作状态,提出了符合Ⅲ型混凝土轨枕支承分析的计算图式。该图式设轨枕在受均布反力集度q1的基础上,以轨下截面为对称中心,附加作用一倒梯形反力集度,倒梯形集度高为(q2-q1),上底宽为(2,1+l2),下底宽为l2。基于该图式,计算了Ⅲ型混凝土轨枕的作用效应。
8、提出了由轨枕静载抗裂试验荷载求取轨枕截面抗力,即疲劳承载弯矩和受压区混凝土边缘疲劳压应力的计算方法。
9、给出了作用效应和抗力的分布,其中作用效应的分布服从极值Ⅰ型,抗力的概率分布服从对数正态分布。同时给出了各分布的统计特征参数及其分布函数。
10、应用JC法,对Ⅲ型混凝土轨枕的可靠指标进行了计算。当不考虑抗力折减及作用效应发展系数时,Ⅲ型轨枕的可靠指标为3.583,失效概率为0.00017,即0.017%。当考虑抗力折减及作用效应发展系数时,Ⅲ型轨枕的可靠指标为2.909,失效概率为0.00181,即0.18%。对Ⅲ型轨枕而言,该失效概率是可以接受的。
11、由Ⅲ型混凝土轨枕可靠度初步研究结果表明,Ⅲ型混凝土轨枕可以应用于高速铁路。
Based on the thought of interaction between vehicle and track, the spatial coupled vehicle/track vibration model was built for high speed railway track, and applied in the track irregularity, which was treated as a stationary ergodicity process. The random vibration laws of railway track were investgated. Further more, the random vibration laws were studied by using Monte Carlo random FEM (finite element method) under the condition that the track parameters of fastener stiffness and ballast stiffness are treated as random parameters obeying normal distribution. The reliability of reinforced sleeperⅢwhich will be used in high-speed railway in China was investgated.
Main contribution and achievement in this thesis are listed below:
1. The model of spatial coupled vehicle/track system was established for high speed railway. In the model, track irregularity movement was used instead of train movement, rail was modeled as Euler beam element, sleeper and ballast was modeled as gird body element, the boundary was modeled as half-infinite beam element, and Hertz nonlinear contact was applied between wheel and rail.
2. The new concept of artificial short wave of track irregularity was put forward, and a sample of artificial short wave was built. In combined of the sample of short wave and the sample of low disturbance track irregularity of high speed railway in German, a simulated sample of random track irregularity was established to study the vibration laws of track in high speed railway.
3. The vibration of vehicle/track system was calculated under the excitations of random track irregularity, and the results were statistically analyzed. The effect of train speed on vibration was very large.
The results showed that probability distribution of the acceleration of rail, sleeper and ballast, and the force on sleeper obeyed normal distribution. As train speed increases from 160km/h to 350km/h, the vibration responses of vehicle and track (which involve acceleration, contact force between wheel/rail, the force on sleeper, the stress on subgrade, and the displacement of rail, sleeper and ballast) were all increased but in a relatively different manner. The values of acceleration increase were the highest. The values of contact force between wheel/rail, force on sleeper and stress on subgrade were relatively low. The values of displacement increase were the lowest.
When train speed increases from 250km/h to 350km/h, the value of vibration responses had a recognized increase, acceleration of rail increses from 158g to 581g, contact force of wheel/rail increases from 280kN to 350kN, and press force on sleepers increases from 92kN to 109kN,. The increase in value of acceleration was the highest, the value of acceleration of wheelset and rail may be doubled or even more.
4. Samples of fastener and ballast stiffnesses were established, because the variation range of fastener and ballast stiffnesses are wide and fastener and ballast stiffnesses are very sensitive, and the fastener and ballast stiffnesses were treat as random parameters that obey normal distribution through out this work.
5. A sample of random parameter of fastener and ballast stiffnesses and a sample of low disturbance track irregularity of high-speed railway in German were combined as excitation, the random vibration was investigated by simulation calculation, and the results were statistically analyzed.
(1) The range of extreme values of rail acceleration, sleeper acceleration, ballast acceleration, wheel/rail force, force on sleeper and stress on subgrade were very wide, but the range of extreme values of rail acceleration were the widest.
(2) Probability distribution of the extreme values of vehicle/track vibration responses obeyed extreme value I distribution checked byχ2 condition in the signifycance level of 0.05.
(3) When the train speed increases, the random vibration responses will increase same as the trend in point 3 above, but the values in comparing with it were much higher. It means that the dynamic responses of high speed railway are very significant, and more attention should be payed to it.
(4) The parameters of high speed railway track structure (especially fastener and ballast stiffnesses) had much more impact to random vibration responses of vehicle/track system, so they should be optimized and remained in a narrow range.
(5) The dynamic coefficients of design wheel load in all speed classes in China by studying the calculation results of wheel/rail forces were put forward. When train speed are 160,200,250,300,350km/h, the adviced coefficients of design wheel load in China are 2.4, 2.8,3.0,3.5,3.7.
6. Four failure modes of concrete sleeperⅢwere established and influence factors of resistance and loading effects of them were analyzed, including concrete cracking and crush failures (because of fatigue bending moment in sleeper section) under rail and in the middle of sleeper section.
7. Based on the real work conditions of concrete sleeperⅢ, a model of sleeper support was build and used to analyze the Concrete sleeperⅢ. In this model, there is a uniform distributed reaction force q1, as well as a pair of revised trapezoidal distributed reaction force which are symmetrical about the sleeper section under the rail, their height are (q2-g1), and their top and bottom edge width are (2l1+l2) and l2 correspondingly. Using the modle, the loading effects of concrete sleeperⅢwere solved.
8. The calculation method to solve sleeper section resistance used static cracking test load, which was established to calculate the fatigue bending moment and the fatigue compressive stress on the edge of compressive concrete.
9. The distributions of loading effects, and resistance were given, also the statistical parameters and distribution functions were given. The distribution of loading effects obeyed extreme value I distribution, but the distribution of resistance obeyed lognormal distribution.
10. Failure probability and reliability index were calculated by JC method. The reliability index and failure probability in case of the resistance reduction and loading effects development factors, were neglected, were 3.583 and 0.017% respectively, but in case they were considered the results were 2.909 and 0.18% respectively. For the concrete sleeperⅢ, both of the failures probability are acceptable.
11. The above research results showed that the concrete sleeperⅢcan be used in high speed railway in China.
引文
[1]何华武.快速发展的中国高速铁路.西南交通大学110周年学术报告,2006
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