Contents
CASE STUDY 7B
clear, clc, home
fprintf('The date and time: %s \n \n', datestr(now))
fprintf('CorrectedStrengthEnglishSh function: \n \n')
help CorrectedStrengthEnglishSh
fprintf('\n')
The date and time: 29-Dec-2008 12:46:24
CorrectedStrengthEnglishSh function:
Calculates correction factors and uses these vaues to find the corrected
strength (yeild or endurance). Shows C values.
Synopsis: [S] = CorrectedStrengthSh(load, size, surf, temp, reliab,
S_prime)
input: load = (required) 'bending' or 'axial'. Must be a string. Use
bending case for all cases that are non-axial.
size = (required) Must be a structured array. size must contain
size.shape: 'rectangle' or 'circle'
size.rotation: 'nonrotating' or 'rotating'
size.dim: 1x1 (radius of circle) or 1x2 (height - the
cubed length, and width); must be in inches.
surf = (required) 'ground' or 'machined' or 'hot-rolled' or
'as-forged' or 1.
temp = (required) 0 to 1020 degrees F
reliab = (required) 50, 90, 99, 99.9, 99.99, or
99.999 percent
mat = (required) 'steel', 'iron', or 'aluminum'. Must be a
sting.
S_ut = (required) The ultamate tensile strength. Must be in
kpsi.
output: S = corrected strength value in kpsi.
Note: For the following variables 1 can be assigned to them:
load, surf, temp, and reliab. When this occurs the C value for
theses variables is simply made equal to one.
All values must be constants, no matricies allowed. Use the following to
get around this rule though:
use matix for the size, mat, or other variable, for example:
Reliability = [50, 90, 99];
len = length(Reliability);
S = ones(1,len);
for coun = 1:len
reliab = Reliability(coun);
S(1,coun) = CorrectedStrengthEnglish(load, size, surf, temp, reliab, mat, S_ut);
end
Given and Assumes
fprintf('----------------------- \n \n')
fprintf('----- Given Data: ----- \n \n')
fprintf('----------------------- \n \n')
fprintf('d_p, diameter of pinion (in)')
d_p = 4
fprintf('r_g, radius of the gear (in). ')
r_g = 5.000
fprintf('T_max, maximum Torque (lb*in)')
T_max = 800
fprintf('T_min, minimum Torque (lb*in)')
T_min = -250
fprintf('Sut, ultamate tensile strength (psi)')
Sut = 64*1000
S_ut = 64;
fprintf('Sut, yield strength (kpsi)')
Sy = 54
fprintf('Nsf, safety factor')
Nsf = 3
fprintf('PA, pressure angle (degrees)')
PA = 20
AGMA = 'Full-Depth';
Loading = 'HPSTC';
Phi = PA*(pi/180);
fprintf('load, type of load applied')
load = 'bending'
fprintf('o.shape, shape of cross section for output shaft \n')
size_o.shape = 'circle';
fprintf('o.rotation, rotate value for output shaft \n')
size_o.rotation = 'rotating';
fprintf('o.dim, radius dimension for output shaft (in)')
size_o.dim = 1.1423
fprintf('i.shape, shape of cross section for input shaft \n')
size_i.shape = 'circle';
fprintf('i.rotation, rotation value for input shaft \n')
size_i.rotation = 'rotating';
fprintf('i.dim, radius dimension for input shaft (in)')
size_i.dim = 0.8686
fprintf('surf, surface condition')
surf = 'machined'
fprintf('temp, temperature (degrees F)')
temp = 70
fprintf('reliab, reliability (percent)')
reliab = 50
fprintf('mat, material used')
mat = 'steel'
fprintf('Kt, goemetric stress consentration facter - assumed. ')
Kt = 3
-----------------------
----- Given Data: -----
-----------------------
d_p, diameter of pinion (in)
d_p =
4
r_g, radius of the gear (in).
r_g =
5
T_max, maximum Torque (lb*in)
T_max =
800
T_min, minimum Torque (lb*in)
T_min =
-250
Sut, ultamate tensile strength (psi)
Sut =
64000
Sut, yield strength (kpsi)
Sy =
54
Nsf, safety factor
Nsf =
3
PA, pressure angle (degrees)
PA =
20
load, type of load applied
load =
bending
o.shape, shape of cross section for output shaft
o.rotation, rotate value for output shaft
o.dim, radius dimension for output shaft (in)
size_o =
shape: 'circle'
rotation: 'rotating'
dim: 1.1423
i.shape, shape of cross section for input shaft
i.rotation, rotation value for input shaft
i.dim, radius dimension for input shaft (in)
size_i =
shape: 'circle'
rotation: 'rotating'
dim: 0.8686
surf, surface condition
surf =
machined
temp, temperature (degrees F)
temp =
70
reliab, reliability (percent)
reliab =
50
mat, material used
mat =
steel
Kt, goemetric stress consentration facter - assumed.
Kt =
3
Solution
fprintf('---------------------------------------------- \n \n')
fprintf('----- Calculation of Tangential Forces: ------ \n \n')
fprintf('---------------------------------------------- \n \n')
fprintf('Ft_max = T_max / r_g')
Ft_max = T_max / r_g
fprintf('Ft_min = T_min / r_g')
Ft_min = T_min / r_g
fprintf('----------------------------------------- \n \n')
fprintf('----- Calculation of Total Forces: ------ \n \n')
fprintf('----------------------------------------- \n \n')
fprintf('F_max = Ft_max / cos(Phi)')
F_max = Ft_max / cos(Phi)
fprintf('F_min = Ft_min / cos(Phi)')
F_min = Ft_min / cos(Phi)
fprintf('------------------------------------ \n \n')
fprintf('----- Calculation of Moments: ------ \n \n')
fprintf('------------------------------------ \n \n')
fprintf('M_max = F_max * (d_p/4)')
M_max = F_max * (d_p/4)
fprintf('M_min = F_min * (d_p/4)')
M_min = F_min * (d_p/4)
fprintf('-------------------------------------------------- \n \n')
fprintf('----- Calculation of Mean/Aplitude Moments: ------ \n \n')
fprintf('-------------------------------------------------- \n \n')
fprintf('Mm = (1/2) * (M_max + M_min)')
Mm = (1/2) * (M_max + M_min)
fprintf('Ma = (1/2) * (M_max - M_min)')
Ma = (1/2) * (M_max - M_min)
fprintf('-------------------------------------------------- \n \n')
fprintf('----- Calculation of Mean/Aplitude Torques: ------ \n \n')
fprintf('-------------------------------------------------- \n \n')
fprintf('Tm = (1/2) * (T_max + T_min)')
Tm = (1/2) * (T_max + T_min)
fprintf('Ta = (1/2) * (T_max - T_min)')
Ta = (1/2) * (T_max - T_min)
fprintf('--------------------------------------------------- \n \n')
fprintf('----- C factores and strength of output shaft ----- \n \n')
fprintf('--------------------------------------------------- \n \n')
Se_o = CorrectedStrengthEnglishSh(load, size_o, surf, temp, reliab, mat, S_ut);
fprintf('-------------------------------------------------- \n \n')
fprintf('----- C factores and strength of input shaft ----- \n \n')
fprintf('-------------------------------------------------- \n \n')
Se_i = CorrectedStrengthEnglishSh(load, size_i, surf, temp, reliab, mat, S_ut);
fprintf('------------------------------- \n \n')
fprintf('----- Corrected strengths ----- \n \n')
fprintf('------------------------------- \n \n')
fprintf('Se_i, Corrected strength for input shaft (psi)')
Se_i = Se_i.*1000
fprintf('Se_o, Corrected strength for output shaft (psi)')
Se_o = Se_o.*1000
fprintf('------------------------------- \n \n')
fprintf('----- Notch Sensitivities ----- \n \n')
fprintf('------------------------------- \n \n')
fprintf('r, notch radius - assumed.')
r = 0.01
fprintf('a_b, Neubers constant for bending stress (in).')
a_b = 0.10^2
fprintf('q_b, Notch Sensitivity for bending stress in keyway. \n')
fprintf('q_b = 1 / (1 + sqrt(a_b/r))')
q_b = 1 / (1 + sqrt(a_b/r))
fprintf('a_t, Neubers constant for torsion stress (in).')
a_t = 0.075^2
fprintf('q_t, Notch Sensitivity for torsion stress in keyway. \n')
fprintf('q_t = 1 / (1 + sqrt(a_t/r))')
q_t = 1 / (1 + sqrt(a_t/r))
fprintf('------------------------------------------------ \n \n')
fprintf('----- Fatigue Stress Consentration Factors ----- \n \n')
fprintf('------------------------------------------------ \n \n')
fprintf('Kf, Fatigue Stress Consentration Factors for bending stress in keyway. \n')
fprintf('Kf = 1 + q_b*(Kt - 1)')
Kf = 1 + q_b*(Kt - 1)
fprintf('Kfs, Fatigue Stress Consentration Factors for tortion stress in keyway. \n')
fprintf('Kfs = 1 + q_t*(Kt - 1)')
Kfs = 1 + q_t*(Kt - 1)
fprintf('Kfm = Kf \n')
Kfm = Kf;
fprintf('Kfsm = Kfs \n \n')
Kfsm = Kfs;
fprintf('--------------------------------- \n \n')
fprintf('----- Diameter Calculations ----- \n \n')
fprintf('--------------------------------- \n \n')
fprintf('d_output, output diameter (in)')
d_output = (((32.*Nsf)./pi).* ...
((sqrt((Kf.*Ma).^2 + (3/4).*(Kfs.*Ta).^2)./Se_o) + ...
(sqrt((Kfm.*Mm).^2 + (3/4).*(Kfsm.*Tm).^2)./Sut))).^(1/3)
fprintf('Tm_in, mean tourque for inner shaft (lbf*in) \n')
fprintf('Tm_in = 0.4*Tm')
Tm_in = 0.4*Tm
fprintf('Ta_in, alternating tourque for inner shaft (lbf*in) \n')
fprintf('Ta_in = 0.4*Ta')
Ta_in = 0.4*Ta
fprintf('d_input, input diameter (in)')
d_input = (((32.*Nsf)./pi).* ...
((sqrt((Kf.*Ma).^2 + (3/4).*(Kfs.*Ta_in).^2)./Se_i) + ...
(sqrt((Kfm.*Mm).^2 + (3/4).*(Kfsm.*Tm_in).^2)./Sut))).^(1/3)
----------------------------------------------
----- Calculation of Tangential Forces: ------
----------------------------------------------
Ft_max = T_max / r_g
Ft_max =
160
Ft_min = T_min / r_g
Ft_min =
-50
-----------------------------------------
----- Calculation of Total Forces: ------
-----------------------------------------
F_max = Ft_max / cos(Phi)
F_max =
170.2684
F_min = Ft_min / cos(Phi)
F_min =
-53.2089
------------------------------------
----- Calculation of Moments: ------
------------------------------------
M_max = F_max * (d_p/4)
M_max =
170.2684
M_min = F_min * (d_p/4)
M_min =
-53.2089
--------------------------------------------------
----- Calculation of Mean/Aplitude Moments: ------
--------------------------------------------------
Mm = (1/2) * (M_max + M_min)
Mm =
58.5298
Ma = (1/2) * (M_max - M_min)
Ma =
111.7387
--------------------------------------------------
----- Calculation of Mean/Aplitude Torques: ------
--------------------------------------------------
Tm = (1/2) * (T_max + T_min)
Tm =
275
Ta = (1/2) * (T_max - T_min)
Ta =
525
---------------------------------------------------
----- C factores and strength of output shaft -----
---------------------------------------------------
C_load =
1
C_size =
0.8579
C_surf =
0.8969
C_temp =
1
C_reliab =
1
S_prime =
32
--------------------------------------------------
----- C factores and strength of input shaft -----
--------------------------------------------------
C_load =
1
C_size =
0.8810
C_surf =
0.8969
C_temp =
1
C_reliab =
1
S_prime =
32
-------------------------------
----- Corrected strengths -----
-------------------------------
Se_i, Corrected strength for input shaft (psi)
Se_i =
2.5283e+004
Se_o, Corrected strength for output shaft (psi)
Se_o =
2.4620e+004
-------------------------------
----- Notch Sensitivities -----
-------------------------------
r, notch radius - assumed.
r =
0.0100
a_b, Neubers constant for bending stress (in).
a_b =
0.0100
q_b, Notch Sensitivity for bending stress in keyway.
q_b = 1 / (1 + sqrt(a_b/r))
q_b =
0.5000
a_t, Neubers constant for torsion stress (in).
a_t =
0.0056
q_t, Notch Sensitivity for torsion stress in keyway.
q_t = 1 / (1 + sqrt(a_t/r))
q_t =
0.5714
------------------------------------------------
----- Fatigue Stress Consentration Factors -----
------------------------------------------------
Kf, Fatigue Stress Consentration Factors for bending stress in keyway.
Kf = 1 + q_b*(Kt - 1)
Kf =
2
Kfs, Fatigue Stress Consentration Factors for tortion stress in keyway.
Kfs = 1 + q_t*(Kt - 1)
Kfs =
2.1429
Kfm = Kf
Kfsm = Kfs
---------------------------------
----- Diameter Calculations -----
---------------------------------
d_output, output diameter (in)
d_output =
1.1423
Tm_in, mean tourque for inner shaft (lbf*in)
Tm_in = 0.4*Tm
Tm_in =
110
Ta_in, alternating tourque for inner shaft (lbf*in)
Ta_in = 0.4*Ta
Ta_in =
210
d_input, input diameter (in)
d_input =
0.8686