Study on the Dynamics Behaviour and MBS Modeling Method of a Subway Track Detecting Vehicle

Transcription

1 First International Conference on Rail Transportation Chengdu, China, Jul -1, 17 Stud on the Dnamics Behaviour and MBS Modeling Method of a Subwa Track Detecting Vehicle Zhuang QI 1, Wenlian ZHANG, Pengfei LIU 1 and Qiang LEI 3 1. School of Mechanical Engineering, Shijiazhuang Tiedao Universit, Shijiazhuang 3, China. School of Electrical and Electronics Engineering, Shijiazhuang Tiedao Universit, Shijiazhuang 3, China 3. Sichuan Tongsuan Technolog Co. Ltd., Meishan, Abstract: A subwa track detecting vehicle, whose trail bogie is equipped with a detector frame is studied in this paper. The hinged detector frame brings a super constraint problem which leads the integration difficult of the MBS model. The solution is to substitute a flexible bod for the rigid detector frame. An equivalent model, in which the bushing force is used as the substitution of the hinge joint, is also obtained. A stiffness value of is recommended to model the bushing force. With the dnamics analsis and the results comparison, the influence of the detector frame, which is totall unsprung mass, on the vehicle s dnamics behaviour is studied. Besides, the hinge joint of an iron structure can be generall simplified as a bushing force with stiffness and the accurac of the equivalent model with the bushing force is quite good. Kewords: vehicle dnamics; curving performance; critical velocit; equivalent model 1 Introduction The classical theor of railwa With the subwa development in global cities and the cost increment of the subwa maintenance, the quick methods of track failure detection are becoming more and more important. One of the normal methods which is widel used in China is the application of the track detecting vehicle which is equipped with a frame of detection equipment as shown in Figure 1. The specialit of this track detecting vehicle is the bogie with the detector frame as marked in the figure. The mass of the detector frame, including all the detection equipment, is about 1 tonne and totall unsprung mass which can directl influence the wheel/rail dnamic interaction force. What s more, as the detector frame is supported on the axle boxes via the axle sleeves on the four corners, the relative movement of the front and rear wheelsets is coupled b the structure of the frame. In other words, if the relative aw between the front and rear wheelsets is generated at the vehicle s curve negotiation, the relative movement of the wheelsets will be seriousl affected b the structure of the detector frame. Therefore, the analsis of the detector frame s influence on the vehicle s dnamics behaviour is of importance, which is also the main objective of this research. Fig. 1 Subwa track detecting vehicle

2 As the normal cases, this track detecting vehicle is equipped with two bogies, one is a motor bogie to provide the traction power and the other is a trail bogie to detect the track failure. Each bogie is provided with two levels of suspension. The primar suspension is the guiding arm axle box on which two coil spring are installed. The detector frame is directl hinged on the four axle boxes. The secondar suspension is composed with coil spring, vertical dampers and horizontal dampers. The vehicle structure is shown in details in Figure 1. Based on the vehicle sstem dnamics theor, the whole track detecting vehicle dnamics model is constructed b the MBS (Multi-Bod Sstem) software UM, which is widel applied in the railwa vehicle dnamics field. A rigid-flexible bod coupled modelling method is applied to solve the super constraint problem. The detector frame influence on the vehicle dnamics performance is analsed via the comparison with a none detector frame bogie. Finall, a simple modelling method is introduced and its accurac is discussed. restrained b the track. The axle box onl has 1 DOF which is rotation around the wheelset axle. Besides, each of the four axle boxes provides 3 movement constraints to the detector frame. The connections between the axle box and the bogie frame or between the bogie frame and the car bod, are primar and secondar suspensions respectivel. The coil spring is modeled via the linear force element; the vertical or horizontal damper is modeled via bipolar force element; the guiding arm joint is modeled via the bushing force element; the lateral stop is modeled b the nonlinear force element. Theoretical model The normal MBS modeling of a railwa vehicle usuall regards the component as a rigid bod, which means the flexible deformation of the component in the dnamics model is ignored. Each component is connected b the force elements, such as spring or damper, or b the joints, such as revolution joint or sliding joint. The whole dnamics model is composed with the rigid bodies and connects them via the force elements or joints. However, this normal modeling method has encountered a super constraint problem when the detector frame is modeling. This paper presents a rigid-flexible bod coupled model to solve this problem..1 Super constraint issue Figure illustrates the topological structure of the dnamics model of the trail bogie. The three main rigid bodies, including the car bod, the bogie frame and the detector frame all have DOF (degrees of freedom) relative to the track coordinate. The wheelset has independent DOF and dependent DOF as the vertical movement and rolling rotation DOF are Fig. model Topological structure of dnamics In particular, the detector frame is restrained b the four axle boxes, as there are four spherical hinges at the four corners and each hinge restrains 3 sliding DOF. Then the detector has 3 =1 constrains which is much larger than its DOF. This generates the super constraint problem which leads the difficult of numerical integration and this dnamics model has to be revised.. Rigid-flexible bod coupled model The root of the super constraint problem is the limitation of the number of DOF. One method of increasing the component s DOF is to change the rigid bod to a flexible one. In this case, the detector frame should be modeled as a flexible bod to release its DOF. With the help of ANSYS, the finite element model can be obtained. The element of the

3 structure of the detector frame is modeled b SOLID9. Then MASS1 elements, which are massless, are added on the joints position with the axle boxes and are taken as the interface nodes. The surface nodes on the corners are associated with the massless elements to form a rigid region. The whole model includes 7 nodes and 17 elements. The vibration mode analsis is conducted finall and the modes of vibration, of which natural frequenc ranges from 1.Hz to 1.1Hz, are obtained. The first modes are shown in Figure 3. According to the main range of wheel/rail interaction frequenc, the first modes are applied in the MBS model. 1.Hz.7Hz Generall, if a flexible bod is implemented in a MBS model, one vibration mode can be regarded as one DOF. The first modes are introduced into the MBS model so the super constraints problem can be solved. The implemented flexible detector frame s information is listed in Table 1. Table 1 Information of the implemented flexible detector frame Parameter Mass Value 9.37kg Inertia moment of x axis kg m Inertia moment of axis 139.kg m Inertia moment of z axis 9.33kg m Number of nodes 7 Number of elements 17 Introduced modes Frequenc range 1.~1.3Hz 7.1Hz.19Hz Fig. 3 First vibration modes of the detector frame finite element model For the other rigid components, the motion equation of a DOF bod can be generall expressed as the following equation according to the MBS theor. In which, m is the mass; I is the inertia moment; C is the damping; K is the stiffness; H is the spring height; F(t) is the external excitation. Besides, x, and z represent the longitudinal, lateral and vertical movement respectivel; φ, θ and ψ represent the nodding, rolling and aw rotation respectivel. m x Cxx Cx Cxz x Kxx HK xx / x Fx m... Cx C Cz... K HK / F m z Czx Cz C zz z K zz z Fz Ixx Ix Ixz C HK / K F... I x I I z... C HK xx / K F Izx Iz Iz C K F (1) The whole dnamics model of the track detecting vehicle is composed of 3 subsstems: the trail bogie, the motor bogie and the flexible detector frame. The two bogie subsstems are connected to the car bod via the force element of the secondar suspension; while the flexible subsstem is hinged b the axle boxes. On the UM platform, the whole dnamics model can be built as shown in Figure. In this stud, the wheel and rail profile is the commonl used LM and R respectivel. As the cases are in the neutral speed, FASTSIM method is applied to calculate the wheel/rail dnamic interaction force. The AAR V track spectra is applied as the track excitation. Finall, thanks to the introduction of the flexible subsstem, the numeric analsis of the vehicle dnamics behavior can be conducted favorabl.

4 v=11km/h v=1km/h Fig. Critical velocit of the model without the detector frame Fig. Whole dnamics model of the subwa track detecting vehicle 3 Dnamics analsis In order to analse the detector frame s influence on the vehicle dnamics behavior, another model, in which the trail bogie has no detector frame is built in the same wa. For the two models, the results of the stabilit, the ride comfort and the curve negotiation abilit are compared. 3.1 Stabilit A peak irregularit is used to calculate the critical speed of the two models. The lateral displacement of the wheelsets in the model with the detector frame is shown in Figure. From the results, we can evaluate the critical velocit of the model with the detector frame is 1km/h v=1km/h v=11km/h Fig. Critical velocit of the model with the detector frame The result of the other model, from which the detector frame is disassembled, is shown in Figure. Its critical velocit can be evaluated to 11km/h. With the comparison of the two models, the detector frame decreases 1.7% of the vehicle s critical velocit. The results indicate that the stabilit of the vehicle is deteriorated b the installation of the detector frame. 3. Ride comfort The maximum acceleration and the Sperling Index are applied to evaluate the ride comfort of the vehicle. The Sperling Index can be obtained as: W 3 a.9 F( f ) () where, a is the car bod s acceleration (cm/s ); f is the vibration frequenc (Hz); F(f) is the correction factor which is related to f. The sensor is positioned on the car bod s floor beond the front bogie s center. The horizontal and vertical a max (maximum acceleration) and SI (Sperling Index) of the two models (without and with the detector frame) are shown in Figure 7 (a)-(d) respectivel. Max Acceleration (m/s ) Sperling Index Fig Velocit (km/h) (a) Horizontal a max Velocit (km/h) (c) Horizontal SI Max Acceleration (m/s ) Sperling Index f Ride comfort results Velocit (km/h) (b) Vertical a max Velocit (km/h) (d) Vertical SI B the comparison of the ride comfort results, we can conclude that the detector frame has little influence either on the vertical or horizontal ride comfort.

5 3.3 Curve negotiation In the curve negotiation case of subwa, the macrogeometr of the track is set as radius 3m, cant 1mm, constant curve length m and transition curve length 1m. The following parameters are taken as the indexes to evaluate the vehicle s curve negotiation abilit: a) maximum wheel/rail lateral force Y (kn), as the track is right curve, the maximum value usuall happens on the left wheel; b) maximum derailment coefficient D, Y D (3) Q where Q is the vertical wheel/rail force (kn); c) maximum wheel load reduction coefficient R, Q Q () l r R Q l Q r d) wear factor M which reflects the power of the friction force, M F da () A where A is the sliding area; τ is the sliding quantit; F t is the tangential force. The results of the above indexes are shown in Figure. With the comparison of the two models, we can see that the curve negotiation abilit is deteriorated b the installation of the detector frame and each index has been increased b about %. However, according to the relative criterion, such as UIC 1, the safet requirements can still be satisfied. 3 3 t Derailment Coefficient Equivalent model Though the flexible method can solve the super constraint problem, the flexible modeling process is ver complicated and needs geometr and material parameters. Besides, the calculation cost of the flexible-rigid coupled model is much higher than the rigid MBS model. In the engineering application, a simple and quick modeling method is in need..1 Equivalent force element The direct idea to substitute the hinge joints is using the bushing force element with the large stiffness. The connection points of this tpe force element are coincident and the stiffness and damper parameters for the DOF can be set. Obviousl, the translation stiffness K j in x,, z axis of the bushing force is related to the flexibilit of the detector frame and its torsion stiffness should be set to to simulate the hinge joint. However, the value of the translation stiffness is difficult to be obtained. To simplif the equivalent model, the translational stiffness in 3 axes is set as the same value and the translational damping C j is set as the linear relationship with K j: C j kk j () where k is a constant and set to. according to experience. After substituting the bushing forces for the hinge joints, the trail bogie model can be built as Figure 9. In this model, the detector frame is a rigid bod which has DOF relative to the track coordinate and is restrained b the bushing forces. 7 7 Velocit (km/h). 7 7 Velocit (km/h) (a) Ymax (b) Dmax Wheel Load Reduction Coefficient Velocit (km/h) Wear Factor (kw) Velocit (km/h) Fig. 9 Equivalent rigid model. Parametric seeking Fig. (c) Rmax Curve negotiation results (d) Mmax The equivalent rigid model should have the same dnamics performance with the flexible model, so we take the indexes of curve negotiation as the evaluation parameters to seek

6 the stiffness value of the bushing force. In the first stage, the seeking range is set cursoril as 1,, 3 and kn/m. The results, including the flexible model, are shown in Figure. The results indicate that, for seeking the most same condition with the flexible model, 3 ~ kn/m is the favorable stiffness zone. Wheel Load Reduction Coefficient Fig. 1 kn/m kn/m 3 kn/m kn/m 7 7 Velocit (km/h) (a) Ymax 1 kn/m kn/m 3 kn/m kn/m 7 7 Velocit (km/h) (c) R max Derailment Coefficient Wear Factor (kw) 1 st seeking stage results kn/m kn/m 3 kn/m kn/m 7 7 Velocit (km/h) (b) Dmax 1 kn/m kn/m 3 kn/m kn/m 7 7 Velocit (km/h) (d) M max In the second seeking stage, we seek in the zone of 1~MN/m and set the seeking steps as, 3,,,, 7, MN/m. The results, including the flexible model, are shown in Figure 11. The results indicate that, on one hand, for Y max and Mmax, the influence of stiffness value is little; for D max and R max, the best choice should be. So the bushing force can be set as K j= and C j=kn s/m. Wheel Load Reduction Coefficient MN/m MN/m MN/m MN/m 7 7 Velocit (km/h) (a) Y max MN/m MN/m MN/m MN/m 7 7 Velocit (km/h) Derailment Coefficient MN/m MN/m MN/m MN/m 7 7 Velocit (km/h) (b) D max MN/m MN/m MN/m MN/m 7 7 Velocit (km/h) Results comparison In order to verif the accurac of the rigid model, the curve negotiation and stabilit analsis are redone and the results of the rigid model and the flexible model are compared..1 Curve negotiation The relative error of curve negotiation results between the rigid model and flexible model are shown in Figure 1. Fig. 1.9% 7 7 Velocit (km/h) (a) Ymax.79% 7 7 Velocit (km/h) (c) R max Relative error 3.% 7 7 Velocit (km/h) (b) Dmax.% 7 7 Velocit (km/h) (d) M max From the results, we can see that, the maximum relative error of all the indexes are less than 7% which means that the rigid model has a good accurac and can satisf the engineering calculation requirement.. Stabilit The critical velocit test is done for the rigid model and the results are shown in Figure 13. The critical velocit of the rigid model is km/h which slightl larger than the flexible model 1km/h and the relative error is 1.% which is larger and the curve negotiation analsis Fig. 11 (c) Rmax nd seeking stage results (d) Mmax v=km/h v=3km/h Fig. 13 Critical velocit of the rigid model

7 From the above comparison, we can generall simplif the hinge joint of an iron structure as a bushing force with stiffness. In this wa, the dnamics model can avoid the super constraint problem and eas to be built. Besides, the accurac of the equivalent model with the bushing force is quite good. Conclusions AMESim [J]. China Railwa Science, 13, 3(3) :79-. QI Zhuang, LI Fu, DING Junjun, et al. Lateral nonlinear dnamics model of air spring for high speed EMU [J]. China Railwa Science, 1, 3(): UIC 1: 9. Testing and approval of railwa vehicles from the point of view of their dnamic behaviour - Safet - Track fatigue - Running behaviour [S]. International Union of Railwas, 9. The stud object of this paper is a track detecting subwa vehicle whose distinguishing feature is the trail bogie with a detector frame. The super constraint problem is solved b the implement of the flexible bod. With the dnamics analsis, the detector frame deteriorates the stabilit and the curve negotiation abilit of the vehicle, but the safet indexes are still satisfing. To simplif the flexible model, the bushing force element is applied to substitute the hinges joints and the stiffness is set to. In the results comparison between the equivalent model and the flexible model, the maximum relative error of the curve negotiation and the critical velocit is less than 7% and 1.% respectivel, which means that is equivalent model can also satisf the engineering calculation accurac. Acknowledgement This work was supported National Natural Science Foundation of China (No. 13). References Bruni S, Vinolas J, Berg M, et al. Modelling of suspension components in a rail vehicle dnamics context [J]. Vehicle Sstem Dnamics, 11, 9(7): 1-7. Docquier N, Fisette P, Jeanmart H. Multiphsic modeling of railwa vehicles equipped with pneumatic suspensions [J]. Vehicle Sstem Dnamics, 7, (): -. Zhai, W. M., Cai, C. B., and Guo, S. Z. (199). Coupling model of vertical and lateral vehicle/track interactions. Vehicle Sstem Dnamics, (1), QI Zhuang, LI Fu, HUANG Yunhua, et al. Stud on the pneumatic simulation model of railwa vehicle air spring sstem based on