Railway Bogies with Radial Elastic Wheelsets

Transcription

1 EUROMECH Colloquium 409, University of Hannover, March 6 9, 2000 Railway Bogies with Radial Elastic Wheelsets H. Claus and W. Schiehlen Contents: Introduction MBS Model and Excitation Model Improvements and Simulation Results Outlook Conclusion

2 Introduction DFG project: Radial Elastic wheelsets. Motivation: Influence of radial elasticity on vertical dynamics of the carbody. conventional wheelset Required: Valid vertical model in medium frequency range. Criterion: Transmission of vibration leading to the brumming noise experienced in ICE coaches. Model improvements: Consideration of inertia of springs and elasticity of bogie frame. Comparison: Dynamics using conventional or radial elastic wheelsets. radial elastic wheelset

3 Implemented Excitation Geometrical track irregularities left G G right Stochastic process Polygonalized Wheels Polygonalized wheels changes their radius periodically according to the number n of polygons. The resulting vertical excitation frequency f depends on the vehicle velocity v and the number of polygons. In this study the excitation amplitude is chosen as 0.4 mm and polygon number as n=4. Excitation due to polygonalized wheels V [m 3 /rad] vertical excitation by track V Track V White noise spatial frequency F [1/m] Excitation frequeny f [Hz] n= Velocity v [km/h]

4 MBS Model 1 Vertical model: 1/4 passenger coach carbody bogie frame wheelset ground secondary suspension primary suspension excitation, rheonomic joint Rigid bodies: carbody bogie frame wheelset Resonance phenomena are due to vertical dynamics of entire system, carbody undergoes forced vibrations. Carbody considered as rigid.

5 Simulation Results, Model 1 Vertical acceleration of carbody, PSD [m 2 /s 3 ] White Noise Track irreg. and sinusoidial excitation structural analysis Track irregularities no medium frequent resonance round wheels 100 Hz polygonalized wheels 10 Frequency [Hz] 100 Vertical acceleration of carbody can indicate forces which lead to the brumming noise. Medium frequency excitations do not affect vehicle model 1.

6 MBS Model 2 Improvements (Jaschinski 1992) carbody Model equiped either with static or dynamic secondary suspension. Static secondary suspension Dynamic secondary suspension bogie frame wheelset Suspended track and sleeper track body ground Detailed investigation of secondary suspension and approximation of its frequency response.

7 Simulation Results, Model 2 Static secondary suspension Dynamic secondary suspension Vertical acceleration of carbody, PSD [m 2 /s 3 ] White Noise Track irregularities Track irreg. and sinusoidial excitation 100 Hz 10 Frequency [Hz] 100 Vertical acceleration of carbody, PSD [m 2 /s 3 ] White Noise Track irregularities narrow peaks Track irreg. and sinusoidial excitation 100 Hz 10 Frequency [Hz] 100 Medium frequency excitations rarely affect the vehicle model 2.

8 MBS Model 3 Flexible Multibody System Model carbody Used set of eigen modes: (half model) eigen mode 83 Hz flexible bogie frame wheelset eigen mode 90 Hz track body eigen mode 94 Hz ground

9 Flexible Multibody System body reference system undeformed shape deformed shape relative displacement of a material point: with u(c, t) (c) y e (t) and relative orientation: A(c, t) I ~ (c, t) (c, t) (c) ye (t) absolute position and orientation: inertial system and r(c, t) r 1 (t) c u(c, t) S(c, t) S 1 (t) A(c, t) Literature: A. A. Shabana (1989) F. Melzer (1994) Equations of motion with principle of D Alembert: M(y)ẏ. (t) k c (y, ẏ) k i (y) q(y, ẏ, t) with y(t) [y s y e ] T

10 Simulation Results, Model 3 Model comprises flexible bogie frame and conventional wheels. Static secondary suspension Dynamic secondary suspension Vertical acceleration of carbody, PSD [m 2 /s 3 ] White Noise Track irregularities elasticity of bogie frame Track irreg. and sinusoidial excitation 83.3 Hz 10 Frequency [Hz] Hz Vertical acceleration of carbody, PSD [m 2 /s 3 ] White Noise Track irregularities wide range Track irreg. and sinusoidial excitation 83.3 Hz 100 Hz 10 Frequency [Hz] 100 Medium frequency excitation affect vehicle model 3 sincerely.

11 MBS Model 4 (radial elastic wheels) carbody flexible bogie frame wheelset wheel rim track body ground dynamic secondary suspension primary suspension radial elasticity excitation, rheonomic joint Model 4 comprises Rigid bodies: carbody wheelset wheel rim track body Flexible body: bogie frame Model 4 is similar to model 3 but equiped with radial elastic wheels.

12 Simulation Results Vertical acceleration of carbody, PSD [m 2 /s 3 ] White Noise Track irregularities smaller amplitudes Track irreg. and sinusoidial excitation elastic wheels rigid wheels 10 Frequency [Hz] 100 Model 3 (with conventional wheels) Model 4 (with radial elastic wheels) Radial elastic wheels may reduce the vehicle vibrations and noise.

13 Outlook Design Variations rubber wheel suspension pneumatic wheel suspension basis of optimization of vehicle structural dynamics rubber high stiffness of wheel rim radial elasticity: small set of parameter variables larger set of parameter variables spatial stiffness due to prestressed rubber membran

14 Conclusion Geometrical track irregularities as well as with polygonized wheels are used as excitation. Implementation of inertia of springs and flexible bogie frame leads to considerably higher acceleration amplitudes of the carbody especially in freqency range Hz ( ICE brumming ). Radial elastic wheels may reduce these medium frequency vibrations in comparison to conventional ones.