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            Equations of Motion for Train Derailment Dynamics
      

      
  Document Series
              Other Reports


      
  Author
          VOLPE


      
Report Number
              RTDF2007-46009

  Office
              RRD


      Subject
                    Hazardous Materials


      

      

      
      
              
                  
      
              
  Document
              ASME_RTDF2007_46009.pdf (94.02 KB)

      
              This paper describes a planar or two-dimensional model to examine the gross motions of rail cars in a generalized train derailment. Three coupled, second-order differential equations are derived from Newton’s Laws to calculate rigid-body car motions with time. Car motions are defined with respect to a right-handed and fixed (i.e., non-rotating) reference frame. The rail cars are translating and rotating but not deforming. Moreover, the differential equations are considered as stiff, requiring relatively small time steps in the numerical solution, which is carried out using a FORTRAN computer code. Sensitivity studies are conducted using the purpose-built model to examine the relative effect of different factors on the derailment outcome. These factors include the number of cars in the train makeup, car mass, initial translational and rotational velocities, and coefficients of friction. Derailment outcomes include the number of derailed cars, maximum closing velocities (i.e., relative velocities between impacting cars), and peak coupler forces. Results from the purpose-built model are also compared to those from a model for derailment dynamics developed using commercial software for rigid-body dynamics called Automatic Dynamic Analysis of Mechanical Systems (ADAMS). Moreover, the purpose-built and the ADAMS models produce nearly identical results, which suggest that the dynamics are being calculated correctly in both models.
      
            
      
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              Last updated: Tuesday, September 25, 2012 U.S. DEPARTMENT OF TRANSPORTATION

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