Use matlab “fminsearch” to design a helical compression spring for a coil-over shock absorber in a small unmanned ground vehicle (ugv) based on the following specifications. you must attach hard copy of your code and matlab output.
minimum weight
must fit over 0.57 inch dia shock body
minimum working force fw = 15 lbf at working length lw = 1.5 inch
minimum factor of safety nfs of 1.0 to prevent static yield at shut length ls (fully compressed)
free length lf = 3.0 inch, total number of coils nt = 14
round steel music wire or round zinc-plated steel music wire
squared (closed) ends or squared-and-ground ends
current design – nt = 14, lf = 3.0 in, od = 0.80 in, d = 0.081 in, w = 0.046 lbf, nfs = 1.30
2) select a spring that most closely matches your optimal design from mcmaster-carr.
optimal design mcmaster-carr
wire diameter d [in]
coil od [in]
total number of coils nt 14
free length lf [in] 3.0
weight [lbf]
coil id [in]
spring rate k [lbf/in]
force at lw [lbf]
shut length ls [in]
factor of safety nfs at ls
mcmaster-carr part number
cost each
3) will your optimal spring buckle at lw? yes no show your work!
extra credit – explore the sensitivity of your design to number of coils and free length.
% t_fminsearch. m - test fminsearch
% hjsiii, 14.10.29
% initial guess
x_start = [ 1 1 ]';
% call
options = optimset( 'display', 'iter' );
[ x_solution, min_val ] = fminsearch( 'biquad', x_start, options )
% bottom of t_fminsearch

function z = biquad( x )
% biquadratic test function for fminsearch
% hjsiii, 14.10.29
% minimum = 3 at x(1)=2 and x(2)=5
z = ( x(1)^2 - 4*x(1) + 4 ) + ( x(2)^2 - 10*x(2) + 25 ) + 3;
% penalty function to provide inequality constraint
% constrained minimum = 3.8 at x(1)=2.4 and x(2)=4.2
%t = 0.5 * x(1) + 3;
%if x(2) > t,
% z = z + 100;
%end
% bottom of biquad

» t_fminsearch
x_solution =
2.
5.
min_val =
3.