ME 360 – P02
Name _________________________
1) 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.
ME 360 – P02
Name _________________________
% 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 =
2.0000
5.0000
min_val =
3.0000