spring constant lbfin Fw k Lf Lw force at working length lbf Ls Nt d shut

# Spring constant lbfin fw k lf lw force at working

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% spring constant [lbf/in] Fw = k * ( Lf - Lw ); % force at working length [lbf] Ls = Nt * d; % shut length [in] Fs = k * ( Lf - Ls ); % force at shut length [lbf] C = D / d; % spring index Ks = 1 + 0.5/C; % static factor tau = Ks*8*Fs*D / (pi*d*d*d); % shear stress at shut length [psi] Sut = 184649 * ( d ^ -0.1625 ); % ultimate tensile strength, music wire A228 [psi] Sys = 0.45 * Sut; % shear yield strength [psi] Nfs = Sys / tau; % factor of safety for yield % show results disp( ' d OD Nt Lf weight' ) disp( ' [inch] [inch] [inch] [lbf]' ) disp( [ d OD Nt Lf w ] ) disp( ' ID k Fw Ls Nfs' ) disp( ' [in] [lbf/in] [lbf] [inch]' ) disp( [ ID k Fw Ls Nfs ] ) % bottom of pr02_main.m ME 360 Summer 2014 Project 2 Name _________________________ >> pr02_main x_solution = 0.0679 0.7060 min_val = 0.0285 d OD Nt Lf weight [inch] [inch] [inch] [lbf] 0.0679 0.7060 14.0000 3.0000 0.0285 ID k Fw Ls Nfs [in] [lbf/in] [lbf] [inch] 0.5701 10.0034 15.0051 0.9513 1.1506 ME 360 Summer 2014 Project 2 Name _________________________ function w = pr02_spring( x ) % objective function for spring design ME 360 % HJSIII, 12.11.15 % % ARGUMENT INPUTS % x(1) = initial estimate for d = wire DIA [in] % x(2) = initial estimate for OD = outside diameter [in] % % GLOBAL INPUTS % Nt = total number of coils % Lf = free length [in] % % OUTPUT % w = weight of spring [lbf] with penalty weighting % global variables global Nt Lf % extract variables to optimize d = x(1); % wire DIA [in] OD = x(2); % coil OD [in] % given parameters rho = 0.28; % density, music wire A228 [lbm/in/in/in] G = 11.7e6; % torsional modulus for steel music wire [psi] Lw = 1.5; % working length [in] % constraints min_ID = 0.57; % minimum acceptable ID [in] min_Fw = 15.0; % minimum acceptable force at working length [lbf] min_Nfs = 1.0; % minimum factor of safety for yield at shut height % working variables D = OD - d; % coil DIA [in] w = rho * ( pi*d*d/4 ) * (pi*D) * Nt; % weight [lbf] ID = D - d; % inside DIA [in] Na = Nt - 2; % number of active coils for square ends k = d*d*d*d*G / (8*D*D*D*Na); % spring constant [lbf/in] Fw = k * ( Lf - Lw ); % force at working length [lbf] Ls = Nt * d; % shut length [in] Fs = k * ( Lf - Ls ); % force at shut length [lbf] C = D / d; % spring index Ks = 1 + 0.5/C; % static factor tau = Ks*8*Fs*D / (pi*d*d*d); % shear stress at shut length [psi] Sut = 184649 * ( d ^ -0.1625 ); % ultimate tensile strength, music wire A228 [psi] Sys = 0.45 * Sut; % shear yield strength [psi] Nfs = Sys / tau; % factor of safety for yield  • • • 