2008-07-31 Mass-Spring-Damper-Friction model of vertical axis:

• An optimization routine was added on top of the model to find the best combination of spring-damper-friction to:
  • Minimize the force on the suspension to allow a structure as light as possible
  • Generate no rebound (positive force) that would unloads the spines
  • Minimize the travel needed to absorb the impact
• Optimimum criteria then takes the form of:
  • J = norm(abs(-min(ForcesSpines? ) + (max(ForcesSpines? )>0).*max(ForcesSpines? ) - gain*min(x)))
• By varying the gain, we find different travel-force combinations, as shown here (for 0 to 2 m/s downward velocity):
  
• Optimal Suspension Parameters Table:
  • Optimum damping ratio is about constant at 0.4
  • Friction is almost constant too
  • The spring constant magnitude is inversely proportional to the travel required
    
• Here is one example of the resulting motion-forces:
  

-- AlexisLD - 06 Aug 2008