Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
MAE 4342- Mechanical Design II (Fall 2020)
Hoist Reducer: Gear-Box Design Project
Team Members: Sandesh Amgai, Ayush Thapa, Rupak Luitel, Prince Agrawal, Mukunda Thakali
Client
Designers
D. Ratan Kumar
Metal Gear Solid Inc.
500 W 1st St,
634 Nedderman Hall 416, Yates St,
Arlington, TX 76010
Arlington, TX 76019
United States
United States
Phone: (817) 272-0740
Phone: (817) 272-2571
Email: ratan.kumar@uta.edu
Email: rd@metalgear.com
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Problem Statement
We propose a gear reducing system consisting of three gear sets, which is powered by a 15HP
motor rotating the input shaft at 1800 rpm. The output of the gear box can lift 7.5T of load at
maximum speed of 30 ft/min. According to the problem specification, the gear ratio of each set
must be in between 3:1 to 10:1, with our chosen ratio for each set at 4:1. The pressure angle for
each gear/pinion is 25-deg. Overall work period of the gear box is for 10 years at an average use
of 5 hour/day for 200 days in a year. With lowed safety factor in fatigue being 1.2 (surface) and
1.5 (bending), this gear set includes four shafts able to host gear and pinion sets.
Members
Details
Ayush Thapa
Contribution
Shaft Design/Analysis, Report Writing
ayush.thapa@mavs.uta.edu
Mukunda Thakali
Shaft Design/Analysis, Report Writing
mukunda.thakali@mavs.uta.edu
Prince Agrawal
CAD, Report Writing
prince.agrawal@mavs.uta.edu
Rupak Luitel
Gear/Pinion Design, Report Writing
rupak.luitel@mavs.uta.edu
Sandesh Amgai
sandesh.amgai@mavs.uta.edu
Gear/Pinion Analysis, Report Writing
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Introduction
Gear are important mechanisms that are prevalent in our real life to make our task easier. A rotating
circular machine part consisting of teeth (gearwheel) which meshes with other set of teeth (teeth
of pinion) to transmit torque is called gears. Geared devices are capable to change the speed,
torque, and direction of a power source. A set of gear and pinion is called gear drives which can
be of different types.
Figure 1. Types of gear drives.
Parallel Axis gear drives are discussed and analyzed in this project with specification on Spur
gears. In spur gear the teeth are parallel to the axis and it is easily disengaged. The least expensive
type of gear has a disadvantage of being noisy than other gear types. Few popular gear types in
parallel axis group are helical, herringbone and internal (planetary).
Figure 2. Types of gear within parallel axis gear set.
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
The scope of this project falls under spur gear sets. The gear box designed consists of three gear
sets according to the problem specification mentioned. Each gear set: consisting of a pinion and
gear has its gear ratio. The overall requirement was to reduce the speed and increase torque when
a certain torque is passed through the input pinion shaft.
Design Procedure
The main target of the gear box is to reduce the speed and increase the torque. To begin with the
analysis, we started with the overall gear ratio of the train. With the ratio of input angular velocity
and output angular velocity we were able to get the overall train ratio for the system. Dividing the
train ratio into three gearset components allowed us to obtain gear ratio for each gear set. The
known gear ratio was used to guess the number of teeth in gears and pinion. Pressure angle for
each gearset was mentioned in the problem statement allowing us to perform stress analysis and
determine appropriate size of the gears and pinions.
To find the diameter for shaft 2, the forces and moment that act on the shaft were identified. The
shaft is subjected to tangential and radial forces during operation. After drawing the analytical free
body diagram, the moment acting on the shaft was calculated using the singularity function. The
code used for calculating the moment is shown in XXXX. The maximum moment values were
then inputted in the ASME equation to find the diameter of the shaft. The shaft with the lowest
diameter than satisfy our requirement was chosen for our project.
Key is an integral part of a gear system which is used to connect the transmission shaft to gear. It
is also a safety component and must be of brittle material with less strength than the gear material.
Whenever the stress in the system increases, key must be the first component to fail to prevent
other expensive and important components like shaft, gears from failure. As the shaft of the fourth
system was provided, we used that length to obtain the parameters of the cross section of a square
key. With the cross-section it was essential to calculate the length of the key with the safety factor
being less than that of the gear-pinion.
The gear box is designed in solid works which consists of gears, pinions, shafts, and gear box of
given dimension. Gear and pinions are made using spline function in solid works with critical
dimensions of addendum, dedendum, and pitch diameter. Most of the features of the gear box are
extruded instead of pinion which is extrude cut into the shaft. The given material is added into the
CAD to determine mass properties. The whole gear box is matted together to visualize the overall
assembly.
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Assumptions
Gears
•
•
•
•
•
•
Qv = 9 (Table 12-7)
Ka = 1 (uniform loading)
Bending Stress = 40000 psi (Table 12-20)
Jp = 0.34 (Table 12-13)
Jg = 0.37 (Table 12-13)
Kt = 1
Shaft
• Reliability of 50%
• Machined Surface Finish
Key
•
•
Square Key
Material (SAE 1040 CR Steel)
Calculations
-
MATLAB Script to calculate required angular speed for output shaft.
%calculation of required angular speed for output shaft
clc;
clear all;
Pin=15*6600;%lbfin/s
omegain=1800;%rpm
Pout=Pin;
Weight=7.5*2200;%lbf
vel=(Pout/Weight)*60/12; %velocity in ft/min
radius=2;%radius of shaft 4
omega_req==(Pout/Weight)/radius;
fprintf('The provided velocity for the output shaft is: %d ft/min.\n',vel)
fprintf('The required angular velocity for the output shaft is: %d rad/s.\n',omega_req)
The provided velocity for the output shaft is: 30 ft/min.
The required angular velocity for the output shaft is: 3 rad/s.
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
-
Hand Calculation for Gear Ratio
Figure 3. Compound Gear Train.
𝑚𝑣 (𝑜𝑣𝑒𝑟 𝑎𝑙𝑙 𝑔𝑒𝑎𝑟 𝑟𝑎𝑡𝑖𝑜) =
𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑡𝑒𝑒𝑡ℎ 𝑑𝑟𝑖𝑣𝑒𝑟 𝑔𝑒𝑎𝑟
𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑡𝑒𝑒𝑡ℎ 𝑜𝑓 𝑑𝑟𝑖𝑣𝑒𝑟 𝑔𝑒𝑎𝑟
𝑚𝑣 =
Win
𝑁𝑝1 𝑁𝑝2 𝑁𝑝3
𝑁𝑔1 𝑁𝑔2 𝑁𝑔3
=
(2*pi/60) *1800 rpm
=
Wout
60 * pi (rad/sec)
=
3 (rad/sec)
Total gear ratio (mv) =
=
(Approx.)
Wi / Wout
20 * pi
63: 1
𝑁𝑝1 𝑁𝑝2 𝑁𝑝3
1
=
63 𝑁𝑔1 𝑁𝑔2 𝑁𝑔3
We assumed the individual gear ratio for each pinion to be 4, and to avoid interference, we took
the gear teeth value of 14 and 55 using the Jp value for HPSTC full depth for pressure angle 25
degree (Table 12-13)
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
-
MATLAB Script for Gear Design (Bending)
%{
MAE 4342
12/04/2020
Gear Design
%}
clc
clear
close all
H =15*550*12; %hp to (lbf*in/s), input power
n = 1800; %rpm, input omega
R = 0.90; %reliability factor
N = 10*200*5*60*1800; %cycles
Nfb = 1.5; %factor of safety for bending
Nfs = 1.2; %factor of safety for surface
Ka =1; %application factor
Qv = 9; %quality index
GR = 4;
Ng = 55; %number of gear teeth
Jp = .34;
Jg = .47;
Satp = 40000;
Np = Ng/GR; %number of pinion teeth
pd = 1:1:20; %standard values of pd, in^-1
%Gear Analysis for Bending
%gear analysis-bending
dgd = Ng./pd; %pitch diamter of gear, in
Vgd = 2*pi*((dgd.*n)/(12*2)); % pitch-line velocity, fpm
Wtgd = H./(Vgd*12/60); % transmitted load
B = 0.25*(12-Qv)^0.667; %dynamic load factor constant
A = 50 + 56*(1-B); %dynamic load factor constant
Kvgd = (A./(A+(Vgd.^0.5))).^B; %dynamic load factor
Km = 1.7; %mounting factor assumption for 2<F<6
Kl = 1.6831*N^(-0.0323); %life factor
Kr = 0.7-0.15*log10(1-R); %reliability
Kt = 1;
Sf = Satp*Kl/(Kt*Kr); %endurance strength
Fugd = 16./pd; %upper limit
Flgd = 8./pd; %lower limit
Fgd = (Ka*Wtgd.*pd*Km*Nfb)./(Kvgd.*Jg*Sf); %face width
Sbg = (Ka*Wtgd.*pd*Km)./(Kvgd.*Fgd*Jg); %bending stress
figure(1)
plot(pd,Fgd,'r',pd,Fugd,'b',pd,Flgd,'k')
title('The intersection plot for gear')
grid on
pdu=10;
pdl=8;
pd=pdl:0.5:pdu;
dgd = Ng./pd;
Vgd = 2*pi*((dgd.*n)/(12*2)); % pitch-line velocity, fpm
Wtgd = H./(Vgd*12/60); % transmitted load
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
B = 0.25*(12-Qv)^0.667; %dynamic load factor constant
A = 50 + 56*(1-B); %dynamic load factor constant
Kvgd = (A./(A+(Vgd.^0.5))).^B; %dynamic load factor
Fgd = 12./pd;
Sbg = (Ka.*Wtgd.*pd*Km)./(Kvgd.*Fgd*Jg); %bending stress
Nfbg = Sf./Sbg; %safety factor
if Nfbg(:)<1.5
error("THe desgin is unsafe");
end
%Pinion Analysis for Bending
%pinion analysis -bending
pd = 1:1:20;
dpd = Np./pd; %pitch diamter of pinion, in
Vpd = 2*pi*((dpd.*n)/(12*2)); % pitch-line velocity, fpm
Wtpd = H./(Vpd*12/60); % transmitted load
B = 0.25*(12-Qv)^0.667; %dynamic load factor constant
A = 50 + 56*(1-B); %dynamic load factor constant
Kvpd = (A./(A+(Vpd.^0.5))).^B; %dynamic load factor
Km = 1.7; %mounting factor assumption for 2<F<6
Kl = 1.6831*N^(-0.0323); %life factor
Kr = 0.7-0.15*log10(1-R); %reliability
Kt = 1;
Sf = Satp*Kl/(Kt*Kr); %endurance strength
Fupd = 16./pd; %upper limit
Flpd = 8./pd; %lower limit
Fpd = (Ka*Wtpd.*pd*Km*Nfb)./(Kvpd.*Jp*Sf); %face width
Sbp = (Ka*Wtpd.*pd*Km)./(Kvpd.*Fpd*Jp); %bending stress
figure(2)
plot(pd,Fpd,'r',pd,Fupd,'b',pd,Flpd,'k')
title('The intersection plot for pinion')
grid on
%after looking at the plot
% using standard pd to find the values
pdu=10;
pdl=8;
pd=pdl:0.5:pdu;
dpd = Np./pd;
Vpd = 2*pi*((dpd.*n)/(12*2)); % pitch-line velocity, fpm
Wtpd = H./(Vpd*12/60); % transmitted load
B = 0.25*(12-Qv)^0.667; %dynamic load factor constant
A = 50 + 56*(1-B); %dynamic load factor constant
Kvpd = (A./(A+(Vpd.^0.5))).^B; %dynamic load factor
Fpd = 12./pd;
Sbp = (Ka.*Wtpd.*pd*Km)./(Kvpd.*Fpd*Jp); %bending stress
Nfb = Sf./Sbp; %safety factor
if Nfbg(:)<1.5
error("THe desgin is unsafe");
end
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Figure 4. pd calculation for Gearset (Bending).
-
MATLAB Script for Gear Design (Surface)
%Gear Analysis for Surface-Pinion
pd= [8:1:20];
phi = 25; %pressure angle
Ip= (sind(phi)*cosd(phi)/2) *Ng/(Np+Ng); %Surface geometry factor
dps = Np./pd; %pitch diamter of pinion, in
Vps = 2*pi*((dps.*n)/(12*2)); % pitch-line velocity, fpm
Wtps = H./(Vps*12/60); % transmitted load
Bps = 0.25*(12-Qv)^0.667; %dynamic load factor constant
Aps = 50 + 56*(1-Bps); %dynamic load factor constant
Cvps = (Aps./(Aps+(Vps.^0.5))).^Bps; %dynamic load factor
Cms = 1.7; %mounting factor assumption for 2<F<6
Cps = 2300^0.5; %elastic coefficient in psi
Caps = 1;
Fps = 16./pd;
Clps = 2.466*N^(-0.056); %life factor
Crps = 0.7 - 0.15*log10(1-R); %reliability factor
Ctps = 1;
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Sacp = 165000; %material surface strength, psi
Sfcp = Sacp*Clps/(Ctps*Crps);%endurance strength
Scps = Cps* ((Caps*Wtps*Cms)./(Cvps.*Fps.*dps*Ip)).^0.5; %surface stress equation
Fups
Flps
Nfcp
Fpds
= 16./pd; %upper limit
= 8./pd; %lower limit
= Sfcp./Scps; %safety factor for pinion surface
=1000*Nfs.*((Cms*Caps.*Wtps)./(Cvps.*dps*Ip))*((Cps/Sfcp)^2); %face width
figure()
plot(pd,Fups,'r',pd,Flps,'b',pd,Fpds,'g')
%Pinion Analysis for Surface-Gear
phi = 25; %pressure angle
Ip= (sind(phi)*cosd(phi)/2) *Np/(Ng+Np); %Surface geometry factor
dgs = Ng./pd; %pitch diamter of pinion, in
Vgs = 2*pi*((dgs.*n)/(12*2)); % pitch-line velocity, fpm
Wtgs = H./(Vgs*12/60); % transmitted load
Bgs = 0.25*(12-Qv)^0.667; %dynamic load factor constant
Ags = 50 + 56*(1-Bgs); %dynamic load factor constant
Cvgs = (Ags./(Ags+(Vgs.^0.5))).^Bgs; %dynamic load factor
Cmgs = 1.7; %mounting factor assumption for 2<F<6
Cgs = 2300^0.5; %elastic coefficient in psi
Cags = 1;
Fgs = 16./pd;
Clgs = 2.466*N^(-0.056); %life factor
Crgs = 0.7 - 0.15*log10(1-R); %reliability factor
Ctgs = 1;
Sacg = 165000; %material surface strength, psi
Sfcg = Sacg*Clgs/(Ctgs*Crgs);%endurance strength
Scgs = Cgs* ((Cags*Wtgs*Cmgs)./(Cvgs.*Fgs.*dgs*Ip)).^0.5; %surface stress equation
Fugs
Flgs
Nfcg
Fgds
= 16./pd; %upper limit
= 8./pd; %lower limit
= Sfcg./Scgs; %safety factor for pinion surface
=1000*Nfs.*((Cmgs*Cags.*Wtgs)./(Cvgs.*dgs*Ip))*((Cgs/Sfcg)^2); %face width
figure()
plot(pd,Fugs,'r',pd,Flgs,'b',pd,Fgds,'g')
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Figure 5. pd calculation for Gearset (Surface).
As the ‘pd’ range for surface analysis is higher than for gear analysis, the pd range of [8, 9, and
10] is chosen for analysis from bending.
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
-
Shaft Design Calculation in X-Y axis
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
-
Shaft Design Calculation in X-Z axis.
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
-
MATLAB Script for Shaft Design
%shaft design problem
%for yx plane
clc
clear
close all
x=0:0.1:6+(7/8);
%length of the shaft in inches
T=2100;
Ry1 =-287.43;
Wt =675.27;
W=10.82;
Ry2=298.25;
Rz1=-137.98;
Rz2=137.98;
Wr=314.88;
AB=2.1;
CD=1.765;
BC=3.015;
AC=AB+BC;
AD=6+(7/8);
My=Ry1*x+(Wt-W)*(x-AB).*(x>AB)-Wt*(x-AC).*(x>AC)+Ry2*(x-AD).*(x>AD);
Mz=Rz1*x+(Wr)*(x-AB).*(x>AB)-Wr*(x-AC).*(x>AC)+Rz2*(x-AD).*(x>AD);
figure(1)
plot(x,My)
grid on
title('Moment in xy plane')
xlabel('Distance along z axis(in)')
ylabel('Moment(lbf-in)')
figure(2)
plot(x,Mz)
grid on
title('Moment in xz plane')
xlabel('Distance along z axis(in)')
ylabel('Moment(lbf-in)')
M=sqrt(My.^2+Mz.^2);
figure(3)
plot(x,M)
grid on
title('Magnitude of the Moment')
xlabel('Distance along x axis(in)')
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
ylabel('Moment(lbf-in)')
%finding the diameter
sut=95000; %in psi
sys=60200; % in psi
see=0.5*sut;
Cload=1;
Csize=1;
Csurf=0.84;
Ctemp=1;
Crela=1;
%for bending load
N=2.5;
%saftey factor
%finished material Fig 6-26
%50% reliability
se=Cload*Csize*Csurf*Ctemp*Crela*see;
q=0.5;
kt=3.5;
kts=2;
kf=1+q*(kt-1);
kfs=1+q*(kts-1);
kfsm=kfs;
MC=670;
MB=580;
AA=(kf*MC/se);
BB=(kfsm*T/sys);
db=(32*N/pi*((AA)^2+0.75*(BB)^2)^0.5)^(1/3);
fprintf('The diameter of the shaft at B is %f in \n\n',db)
AA1=(kf*MB/se);
db1=(32*N/pi*((AA1)^2+0.75*(BB)^2)^0.5)^(1/3);
fprintf('The diameter of the shaft at C is %f in \n',db1)
The diameter of the shaft at B is 1.145328 in
The diameter of the shaft at C is 1.124813 in
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Figure 6. Moment on shaft in z axis.
Figure 7. Moment on shaft in y axis.
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Figure 8. Magnitude of Moment across the length of shaft.
-
MATLAB Script for Key Design
%key desgin
clc;
clear;
%material SAE 1040 CR steel*
Sut=586*145.0377;%MPA to PSI
Sy=490*1450.0377;
%desgining key for bending and check for surface
Nd=1.5;
OD=4; %in
%from table 10.2
w=1; %in width
v=30*12;%in/sec
dp1 = 1.5; %in
dg1 = 5.6; %in
dp2 = 1.667; %in
dg2 = 6.222; %in
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
dp3 = 1.875; %in
dg3 = 7.0; %in
rpm1
rpm2
rpm3
rpm4
=
=
=
=
1800; %rpm for shaft 1
rpm1*dp1/dg1;
rpm2*dp2/dg2;
rpm3*dp3/dg3;
Tmin =0;
omega=rpm4*2*pi/60;
P=15;%hp
Tmax=P*6600/omega;
Fa=(Tmax-Tmin)/OD;
Fm=(Tmax+Tmin)/OD;
L=1:0.5:5;
for i=1:length(L)
A_shear=w*L(i);
ta=Fa/A_shear;
tm=Fm/A_shear;
sig_vma=sqrt(3)*ta; sig_vmm=sqrt(3)*tm;
%determining key endurance limit
Sed=0.5*Sut;
Cload=1;
A=w*L(i);
deq=sqrt(A/0.0766);
Csize=1.189*deq^(-0.097);
Csurf=4.51*(Sut)^(-0.265);
Ctemp=1;
R=0.9;
Creliab=0.7-0.15*log10(1-R);
Se=Cload*Csize*Csurf*Ctemp*Creliab*Sed;
L1(i)=(sqrt(3)*Nd*(Sut*Fa+Se*Fm))/(w*Sut*Se);
if abs(L(i)-L1(i))<0.5
LL=L1(i)
end
end
LL =
2.3814
LL =
2.4051
The length of the key was taken as 2.5 inch and the cross-section being 1 inch.
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Drawings
Figure 9. Engineering Drawing for gear.
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Figure 10. Engineering Drawing for Pinion and Shaft.
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Figure 11. Exploded view of the Gearset.
Conclusion
The gear box requirement is to lift a 7.5T mass at speed of 30 ft/min. As the calculation of output
angular velocity is done using this consideration, we can verify that our system is according to the
requirement of the client. The safety factors consideration of greater than 1 ensures that our design
is safe to use. Conservation of energy shows that decrease in velocity results in increase in the
torque, which is clearly demonstrated by the reduction of angular speed from 188.5 rad/s (input)
to 3 rad/s (output) in the shaft. The material of key selected is a brittle material so that it fails first
whenever there is increased stress in the system. Overall, the design by Metal Gear Solid Inc. is in
accordance with the requirement of the client and is aesthetically pleasing and top notch efficient
in performing the designated task.
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Appendix
Figure 12. CAD Render for one gearset.
Figure 13. CAD Render for shaft and pinion.
Metal Gear Solid Inc.
Gears, Pulleys and Belt Drives
Figure 14. CAD Render for shaft with gear and pinion.
Figure 15. CAD Render for the gearbox.