how to represent a piecewise linear stiffness spring in simscape?

I edited a .ssc file for simscape to represent a piecewise linear stiffness spring,but there is always something wrong, when the stiffness changed, the deformation of the spring changed suddenly too(diminishing), and here is the code, can someone help me? Thanks a lot!

component nlspring < foundation.mechanical.translational.branch
  parameters
    spr_rate1 = { 2500, 'N/m' };  % Spring rate
    spr_rate2 = { 4000, 'N/m' };  % Spring rate
    init_def = { 0, 'm' };        % Initial deformation
    change_def = { 2.5e-3, 'm' }; % Stiffness changing deformation
  end

    variables
        x = { 0, 'm '};
    end
    function setup
      if spr_rate1 <= 0
          pm_error('simscape:GreaterThanZero','spr_rate1' )
      end
      if spr_rate2 <= 0
          pm_error('simscape:GreaterThanZero','spr_rate2' )
      end
      if change_def <= 0
          pm_error('simscape:GreaterThanZero','change_def ' )
      end
    end
    equations
        if abs(x) < change_def 
            f == spr_rate1*x;
            v == x.der;
        else
            f == spr_rate2*x;
            v == x.der;
        end
    end
end

Answer 1

[Arnaud Miege]

I think you potentially have a discontinuity around +/-change_def. I would suggest changing the second equation to:

f == spr_rate2*(x-change_def)+spr_rate1*change_def;

to remove the discontinuity. I would also put the v == x.der; equation outside of the if...else statement. Finally, you need to add x = init_def; to the setup function.

HTH,

Arnaud

[fangfines]

Thanks Greatly! it does work.

I only need to convert the "spring rate" that I need to satisfy your equation.

it's an alternative way and quit helpful, but I don't know what's wrong with my equations.

Anyway, thanks very much!