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MRA Moment Method


MMM calculates over 100 engineering vehicle parameter outputs at up to 2500 combinations of steering wheel angle and vehicle sideslip angle. These outputs are normally viewed with the MMM post-processing programs, but for detailed study and debugging they are also written to an ASCII output file. For a listing of outputs recorded by MMM, click here.

Force-Moment Diagram.  Click to enlarge. The fundamental graph constructed from MMM output is the Force-Moment Diagram. One such diagram, in this case a CN-AY diagram, is shown at right. This diagram reflects the entire maneuvering envelope for linearly and angularly accelerating the vehicle. MRA has a vast amount of experience interpreting these diagrams.

Some of this interpretation, analogous to results obtained from skidpad tests, has been included in the post-processing. These include plots of understeer gradient, steering sensitivity, stability index, trimmed steering wheel angle, trimmed vehicle sideslip angle and control gain, among others. Representative plots are shown below.

Trimmed Lateral Acceleration.  Click to enlarge. Stability Index.  Click to enlarge.

Steering Sensitivity.  Click to enlarge. Understeer Gradient.  Click to enlarge.

A very useful feature of the MMM post-processing is the "Friction Circle" program. This program allows the user to navigate a cursor around the Force-Moment Diagram and examine the corresponding vehicle state. One such "snapshot" is shown below.

Friction Circle Program.  Click to enlarge.

This graphical and numeric representation of the vehicle presents the following information at any point of interest on the Force-Moment Diagram:

  • Vehicle speeds, linear and angular
  • Vehicle accelerations
  • Vehicle steer and sideslip angles
  • Path radius
  • Individual tire parameters:
    • Wheel loads
    • Steer angle, slip angle, inclination angle
    • Ride position (jounce/rebound)
    • Wheel torque
    • Tire usage (percent of maximum force capability in use)
    • Deflections due to compliances

MRA has developed other post-processing techniques to obtain an additional information from the MMM output. One such capability is "trim change analysis". This focuses on how the stability and control of the vehicle changes when the longitudinal trim of the vehicle is changed (as in dropped-throttle, braking, etc.). Another technique uses MMM data to approximate transient vehicle responses.

MMM is a powerful tool to study, analyze and troubleshoot the "big picture" of vehicle stability, control and handling. Its unique solution technique quickly and efficiently provides a wealth of information not easily obtainable from any other type of simulation.


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