how to represent a piecewise linear stiffness spring in simscape?

Question

fangfines 2011-3-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/3890-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

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Answer 1

Arnaud Miege 2011-3-24

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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