Design procedure for dts (revised)

DEPARTMENT OF MECHANICAL ENGINEERING
FORMULA SHEET
SUBJECT CODE & NAME: ME 6601 – DESIGN OF TRANSMISSION SYSTEMS
Year /Sem: III / VI (Even sem 2016-17)
UNIT –I: DESIGN OF FLEXIBLE ELEMENTS
1.1 Design Procedure for Flat Belt Selection - Using PSG Design Data Book
Step:1- Selection of standard pulley diameters
Calculate the diameters of the smaller and larger pulley using the relation
Then select the standard pulley diameters from PSG 7.54
- Diameter of larger pulley
(mm)
- Speed of the larger pulley
(rpm)
- Diameter of small pulley
(mm)
- Speed of the small pulley
(rpm)
- velocity ratio
Step:2- Calculation of design power
For calculating design power select,
1. The load correction factor from PSG 7.53
2. The arc of contact factor from PSG 7.54 using the arc of contact
value
3. Small diameter factor from PSG 7.62
Calculate the design power using the formula
Design Power - (kW)
Rated power - Power of motor
(kW)

Step:3- Selection of belt
Select the type of belt from PSG 7.52
Step:4- Load Rating and Number of plies
Load Rating
Calculate the velocity of belt / belt speed using the formula
Then calculate the load rating using the formula in PSG 7.54
Number of plies
Select the number of plies required from PSG 7.52
- Diameter of small pulley
(mm)
- Speed of the small pulley
(rpm)
-Velocity of belt of speed of
belt (m/s)
Load rating - (kW/mm/ply)
Step:5- Belt Width
Calculate the belt width using the formula
Select the standard belt width from PSG 7.52
Design Power - (kW)
Load rating - (kW/mm/ply)
Width of belt - (mm)
Step:6- Pulley Width
Calculate the pulley width using the condition in PSG 7.54
Pulley width - (mm)
Step:7- Length of Belt
Calculate the belt length using the condition in PSG 7.53
Belt length - (mm)

1.2 Design procedure for V Belt Selection - Using PSG Design Data Book
Step:1- Belt cross section
Select standard v-belt cross section from PSG 7.58 based
on motor power(kW)
Step:2- Pulley diameters
Calculate the diameters of the smaller and larger pulley
using the relation
- Diameter of larger pulley (mm)
- Speed of the larger pulley (rpm)
- Diameter of small pulley (mm)
- Speed of the small pulley (rpm)
- velocity ratio
Step:3- Center distance
Calculate center distance value based on velocity
ratio/speed ratio from PSG 7.61
C - Center distance (mm)
Step:4- Nominal pitch length
Calculate nominal pitch length using formula from PSG
7.61
- Diameter of larger pulley (mm)
Step:5- Maximum power capacity of belt
Calculate the power capacity of belt using formula in PSG
7.62 for the selected belt cross section.
Calculate the velocity of belt / belt speed using the
formula
- Speed of the small pulley (rpm)
S - Velocity of belt of speed of belt (m/s)
Power capacity - (kW)
Step:6- Number of Belts
Calculate the number of belts required using the formula
in PSG 7.70
For,
- Refer PSG 7.69
- Refer PSG 7.58, 7.59 and 7.60
- Refer PSG 7.68

Step:7- Actual center distance
Calculate the center distance using the formula in PSG
7.61
1.3 Design procedure for Chain Drive - Using PSG Design Data Book
Step:1- Type of Chain
Roller Chain is selected for the application
Step:2- Determination of Transmission Ratio
Calculate transmission ratio (i) from PSG Design Data Book P. No: 7.74
Select the Preferred transmission ratio from PSG Design Data Book P.
No: 7.74 based on the calculated (i) value
Pinion : small sprocket
Wheel : large sprocket
Step:3- Standard Number of Teeth on Pinion Sprocket (Z1)
For the preferred transmission ratio (i) from PSG Design Data Book P.
No: 7.74 select recommend number of teeth on sprocket (Z1)
Choose odd number of teeth
Step:4- Standard Number of Teeth on Wheel Sprocket (Z2)
From the preferred transmission ratio (i) and recommend number of
teeth on sprocket (Z1) calculate number of teeth on wheel (Z2) using the
formula in PSG. Design Data Book P. No. 7.74
Choose even number of teeth
Step:5- Selection of standard pitch (p)
Using the formula of optimum centre distance in PSG. Design Data
Book P. No. 7.74 and calculate pitch value (
After calculating pitch value, from PSG Design Data Book P. No: 7.74
select standard pitch value
Select a random value between
30 to 50 or take average value
for calculating "p"
if "a" value is not given assume
a value(say 500 mm or 1000
mm)

Step:6- Calculation of Breaking Load (Q)
Rearrange the formula for Power Transmitted in PSG Design Data Book
P. No: 7.77 and calculate breaking load in kgf
 For calculating ks - use formula in page no. 7.76 & 7.77
 Calculate speed "v" using formula
v
 Select minimum factor of safety "n" based on the values of pitch
and speed of small sprocket in PSG Design Data Book P. No:
7.77
Step:7- Selection of Chain
Based on the calculated breaking load and pitch value select the Roller
chain from PSG Design Data Book P. No: 7.71 to 7.73
Step:8- Check for factor of safety
Using the formula in PSG Design Data Book P. No: 7.78 actual factor of
safety
If the calculated actual factor of safety is greater than minimum
factor of safety, then the design is safe
w - select it based on the chain
selected from PSG Design Data
Book P. No: 7.71 to 7.73
k (coefficient of sag) - select it
from PSG Design Data Book P.
No: 7.78
Step:9- Check for bearing stress
Using the formula of power transmitted in PSG Design Data Book P.
No: 7.77 calculate bearing stress
Select the allowable bearing stress from PSG Design Data Book P. No:
7.77 based on speed of small sprocket and pitch value
If the calculated bearing stress is less than allowable bearing stress,
then the design is safe
A - select it based on the chain
selected from PSG Design Data
Book P. No: 7.71 to 7.73
Step:10- Calculation of actual length of chain
Using the formula in PSG Design Data Book P. No: 7.75 calculate actual
length of chain
lp - calculate it using the
formula in PSG Design Data
Book P. No: 7.75
ap- calculate it using the
Book P. No: 7.75
Step:11- Calculation of exact centre distance
Using the formula in PSG Design Data Book P. No: 7.75 calculate exact
center distance.
e - calculate it using the
Book P. No: 7.75

m- calculate it using the
Book P. No: 7.75
Step:12- Calculation of pitch diameter of sprockets
Using the formula in PSG Design Data Book P. No: 7.78 calculate pitch
diameter of sprockets
1.4 Design procedure for Selection of Wire ropes - Using PSG Design Data Book
Step:1- Selection of wire rope type
Select a wire rope (6 x 19 or 6 x 37) from PSG Design Data Book P. No:
9.1 based on the type of application
Step:2- Calculation of design load
Design Load = 2.5 x Load to be lifted x Assumed factor of safety
Select factor of safety from PSG Design Data Book P. No: 9.1 based on
the rope application.
Step:3- Selection of wire rope diameter (d)
Assuming the design load as breaking load select the wire rope diameter
from PSG Design Data Book P. No: 9.4 to 9.5
Step:4- Calculation of sheave diameter or Drum Diameter (D)
Using the selected type of wire rope select D/d ratio from PSG Design
Data Book P. No: 9.1 and calculate D
Step:5- Selection of useful cross sectional area (A)
Using the formula for "A" in PSG Design Data Book P. No: 9.1 calculate
cross sectional area.
Step:6- Calculation of wire diameter (dw)
i = Number of strands x number of wires in each strand

Step:7- Selection of weight of rope (Wr)
For the selected diameter of wire rope in PSG Design Data Book P. No: -
9.4 to 9.5 select the weight of rope.
Step:8- Calculation of Various type of Load and Effective
Load (Wea)
Wd = W + Wr
Wst = 2. Wd
Effective Load
Wen = Wd + Wb
Wea = Wd + Wb + Wa
West = Ws + Wst
Wea - Effective Load
Wd - Direct Load (load to be
handled)
Wb- Bending Load
Wa - Acceleration Load
Wst – Starting Load
E' - Take it from PSG Design
Data Book P. No: 9.1 (Youngs
Modulus of wire 0.84 x 105
N/mm2)
v1 = 0 (initial velocity)
Wen = Effective Load on rope
during normal working
Wea = Effective load on the
rope during acceleration of
the load
West = Effective load on the
rope during starting
Step:9- Calculation of factor of safety
If the working factor of safety is greater than the recommended
factor of safety then the design is safe.
If its not safe calculate how many wires can be used to handle the load
using the next step.
Step:10- Calculation of number of wires

UNIT -2: SPUR GEARS AND PARALLEL AXIS HELICAL GEARS
2.1 Design Procedure for Selection of Spur Gear Drive - Using PSG Design Data Book
(Manufactures Catalogue)
Step : 1.Calculation of gear ratio
From PSGDB page no: 8.6
𝑖 =
𝑵 𝟏
𝑵 𝟐
=
𝒛 𝟐
𝒛 𝟏
𝑁1,𝑧1 - Speed, No of teeth of driving gear 𝑁2, 𝑧2-
Speed, No of teeth of driven gear
If number of teeth in smaller pulley is not
given in problem, Assume
Number of teeth on driving wheel for both
14.50 involute system and 200 involute system
of gears (pinion) z1 = 20
Step : 2. Selection of Materials
Choose the suitable material for pinion and
wheel from
PSG Data Book page no: 1.9, 1.40, 8.4, and 8.5
using the i value.
If the pinion and wheel are same design only for
pinion.
If they are made of different material design for
both pinions and wheel.
Most cases C45 for pinion and C.I grade 20
for wheel (If material is not specified)
When selecting the material for gears
following parameters taken from the PSGDB.
1.IS Specification of Gears
2. Tensile Strength (σu)t in N/mm2
3. Brinell Hardness Number (BHN)
Step : 3. Selection of Gear Life
Calculate the gear life based on given data. Gear
life in (hours) Gear life in (min)
Life in number of cycles = (gear life in min) x N
N- speed of gear
If gear life is not specified assume Gear Life
as 20,000 hrs
Step : 4. Calculation of Initial design torque
[Mt]
From PSGDB Page No: 8.15 – Table: 13
Design torque [Mt] = Mt .k.kd
Mt=
60 ∙𝑃
2∙𝜋∙𝑁
P = Power Transmitted in W
N = N1 Speed of pinion
From PSGDB Pg.No 8.15 Initially assume
(k.kd)= 1.3
Step : 5.Determination of Equivalent Young’s
Modulus (Eeq) of gear pairs
Calculation of (Eeq) From PSGDB page no.
8.14, Table: 9
1.If both Gear and Pinion is made by same
material
E =Eeq taken from the PSGDB
2.If Gear and Pinion made by different

for the given gear material choose Equivalent
young's modulus (kgf/cm2) Convert the unit to
N/mm2
material use (Eeq)formula from PSGDB
Pg.No 8.14 determine the Equivalent Young’s
Modulus (Eeq)
Step: 5 (a). Calculation of DesignContact
Stress [𝝈 𝒄 ]
From PSGDB Page no: 8.16, Table:15;
Based on the available data for the gear material
select the formula for design contact stress
select CR or CB Valve based on the material and
its properties From PSGDB page no: 8.16,
table:16
Select the life factor for surface strength
(kcl)based on the material and its properties from
page no:8.17, Table :17
If Material of pinion is steel select CR.HRC
values
If Material of pinion is cast iron select CB.HB
values from PSGDB Pg.No 8.16 Table 16.

Step: 5 (b).Calculation of Designbending
stress [𝝈 𝒃]
From PSGDB page no:8.18,
Table:18, assuming the rotation is in one
direction unless specified, choose the formula
.
Select the 𝑘 𝜎 value from PSGBD page no:8.19,
Table:21; assuming addendum modification
factor as 0.
Select the 𝜎−1value from PSGDB page no:8.19,
Table:19 based on the material of pinion.
Calculate 𝜎−1value in kgf/cm2 and then convert
it toN/mm2
Select the ‘n’value from PSGDB page no:8.19,
Table:20 based on the material of pinionand its
properties
Select Kbl PSGDB page no:8.20,
Table :22, select the life factor bending kbl based
on the material

Step : 6. Calculation of centre distance (a)
From PSGDB Page no: 8.13
Assume the value of 𝛹 from Page no: 8.14,
Table 11. (or take it as 0.3)
Step : 7. Selection of z1,z2
If the number of teeth is not provided
Assume z1=17 for 200 pressure angle
Assume z1=32 for 14.50 pressure angle
Calculate the value for z2 = 𝑖 x𝑧1
Step : 8. Calculation for module (m)
From Page no 8.22, Table:26
From Page no:8.2, Table 1; choose the std value
of module
Step : 9. Revisionof centre distance(a)
From PSGDB Page no: 8.22,Table 26; calculate
the new centre distance
Step: 10. Calculation of b, d1, v, 𝜳 𝒑
Face width From PSGDB Page no: 8.1 b= .a
Pitch diameter of pinion (d1) From PSGDB Page
no: 8.22, Table :26
Pitch line velocity (v)
𝜐 =
𝜋.𝑑1.𝑁1
60
Calculation of 𝛹𝑝From PSGBD Page no: 8.15,
Table:14
d1 = m.z1
𝛹𝑝 =
𝑏
𝑑1
Step :11. Selection of Quality of Gear
From Page no: 8.3, table:2
Form the calculated pitch line velocity choose
the IS quality of gear
12. Revision of design torque
Revised [Mt] From PSGDB Page no:8.15
Design torque [Mt] = Mt.k.kd Mt=
60 ∙𝑃
2∙𝜋∙𝑁

Use the revised k,kdvalues
Revised k From PSGDB Page no:8.15 for the
𝛹𝑝value choose k value
Revised kd From PSGDB Page No:8.16
using the IS quality, pitch line velocity and
surface hardness value choose kd
Step : 14. Check for contact stress ( 𝝈 𝒄)
Calculation for induced contact stress From Page
no: 8.13
The value ( 𝝈 𝒄)of (induced contact stress) should
be less than [𝝈 𝒄] (design contact stress) then the
design is safe
Checking
If, [𝝈 𝒄]> ( 𝝈 𝒄) the Designis Safe.
Step :15. Check for bending stress ( 𝝈 𝒃)
Calculation for induced bending stress From
Page no: 8.13A
The value of (induced bending stress) should be
less than [𝜎𝑏] (design bending stress) then the
design is safe.
From PSGDB page no:8.18 – Table 18;
for the number of teeth z1value and assuming X
as 0, choose the y (form factor) value.
Checking
If, [𝝈 𝒃]> ( 𝝈 𝒃) the Designis Safe.
Select form factor y from PSGDB Pg.No 8.18
Table 18
Step: 15. Calculation of basic dimensions of
pinion and gear.
Calculate the following values from Page no:
8.22; Table:26
Module (m), Face width (b) ,Height factor (f0)
Bottom clearance (c) ,Tooth depth (h) Pitch
circle diameter (d1,d2),

Tip diameter (da1,da2), Root diameter (df1,df2)
16. Check for wheel
If the material for wheel is different then this
step is needed •
Calculate N2 • Gear life based on N2 •
Calculate the design values of [𝛔 𝐛]wheel
,[𝝈 𝒄]wheelfor wheel •
Calculate the induced values of ,𝛔 𝐛 , 𝝈 𝒄for
wheel
Check the induced bending and contact
stresses of wheel less than the permissible
values
Verify that the wheel design is safe • Then
calculate the basic dimensions of wheel.
Note: If design is not safe [𝛔 𝐜]wheel< ( 𝝈 𝒄)pinion
Increases the design contact stress by
increasing the HB value further check both
stresses.
N2 =
𝑁1
𝑖
N2 = Speed of wheel in rpm.
Life of wheel (N)wheel = PSGDB Pg.No
8.17
N = 60.N2.T T = Life in number of cycles.
Find [𝛔 𝐛] wheel, [𝝈 𝒄] wheelby using same
formulas which we have to use for pinion
design. (PSGDB Pg.No 8.18 and 8.16
respectively).
Checking
Check for bending (Plastic Deformation)
Calculation of induced bending stress for
wheel ( 𝜎𝑏)wheel
𝜎𝑏 𝑝𝑖𝑛𝑖𝑜𝑛 × 𝑦1
= 𝜎𝑏 𝑤ℎ𝑒𝑒𝑙 × 𝑦2
𝑦1 and 𝑦2 form factors for pinion and wheel
Select 𝑦2 from PSGBD Pg.No 8.18 based on
number teeth on wheels 𝑧2 , and calculate
induced bending stress for wheel ( 𝜎𝑏)wheel
( 𝜎𝑏)wheel< [σb]wheel therefore design of wheel
is satisfactory.
Check for wear (contact) stress for wheels
Since the contact area of both gear and pinion
is same so the induced contact stresses in
pinion and gear is same ( 𝜎𝑐)pinion= ( 𝜎𝑐)wheel
Checking
( 𝜎𝑐)pinion<[σc]wheel there for the design of
wheel is satisfactory.

2.2 Design Procedure for Selection of Helical Gear Drive - Using PSG Design Data Book
𝑖 =
𝑵 𝟏
𝑵 𝟐
=
𝒛 𝟐
𝒛 𝟏
wheel from
using the i value.
pinion.
both pinions and wheel.
Most cases C45 for pinion and C.I grade 20
for wheel (If material is not specified)
N- speed of gear
If gear life is not specified assume Gear Life
as 20,000 hrs
[Mt]
Mt=
60 ∙𝑃
2∙𝜋∙𝑁
(k.kd)= 1.3
8.14, Table: 9
N/mm2
1. If both Gear and Pinion is made by same
material
2. If Gear and Pinion made by different
material use (Eeq)formula from PSGDB
Pg.No 8.14 determine the Equivalent Young’s
Modulus (Eeq)

Step: 5 (a). Calculation of Design Contact
Stress [𝝈 𝒄 ]
From PSGDB Page no: 8.16, Table:15;
Based on the available data for the gear material
select the formula for design contact stress
select CR or CB Valve based on the material and
its properties From PSGDB page no: 8.16,
table:16
Select the life factor for surface strength
(kcl)based on the material and its properties from
page no:8.17, Table :17
If Material of pinion is steel select CR.HRC
values
If Material of pinion is cast iron select CB.HB
values from PSGDB Pg.No 8.16 Table 16.

Step: 5 (b).Calculation of Designbending
stress [𝝈 𝒃]
From PSGDB page no:8.18,
Table:18, assuming the rotation is in one
direction unless specified, choose the formula
.
Select the 𝑘 𝜎 value from PSGBD page no:8.19,
Table:21; assuming addendum modification
factor as 0.
Select the 𝜎−1value from PSGDB page no:8.19,
Table:19 based on the material of pinion.
Calculate 𝜎−1value in kgf/cm2 and then convert
it toN/mm2
Select the ‘n’value from PSGDB page no:8.19,
Table:20 based on the material of pinion and its
properties
Select KblPSGDB page no:8.20,
Table :22, select the life factor bending kbl based
on the material

Assume the value of 𝛹 from Page no: 8.14,
Table 11. (or take it as 0.3)
Step : 7. Selection of z1,z2
Calculate the value for z2 = 𝑖 x𝑧1
Step : 8. Calculation for module (mn)
From Page no:8.2, Table 1; choose the std value
of module
mn =
𝟐𝒂
( 𝒁 𝟏 +𝒁 𝟐)
x cos β
From PSGDB Page no: 8.22,Table 26; calculate
the new centre distance
a =
𝒎 𝒏
𝐜𝐨𝐬 𝜷
× (
𝒁 𝟏 + 𝒁 𝟐
𝟐
)
Face width From PSGDB Page no: 8.1 b= a .ψ
Pitch diameter of pinion (d1) From PSGDB Page
no: 8.22, Table :26
Pitch line velocity (v)
𝜐 =
𝜋.𝑑1.𝑁1
60
Calculation of 𝛹𝑝From PSGBD Page no: 8.15,
Table:14
𝛹𝑝 =
𝑏
𝑑1
Step : 11. Selection of Quality of Gear

Design torque [Mt] = Mt.k.kd
Mt=
60 ∙𝑃
2∙𝜋∙𝑁
no: 8.13
design is safe
Checking
Step : 15. Check for bending stress ( 𝝈 𝒃)
Page no: 8.13A
design is safe.
Checking
Table 18
pinion and gear.
8.22; Table:26

Virtual number teeth Zv1 & Zv2
16. Check for wheel
step is needed •
Calculate the design values of [𝛔 𝐛]wheel ,[𝝈 𝒄]wheel
for wheel •
wheel
values
stresses.
N2 =
𝑁1
𝑖
Life of wheel (N)wheel = PSGDB Pg.No
8.17
Find [𝛔 𝐛] wheel, [𝝈 𝒄] wheelby using same
formulas which we have to use for pinion
design. (PSGDB Pg.No 8.18 and 8.16
respectively).
Checking
Calculation of induced bending stress for
wheel ( 𝜎𝑏)wheel
( 𝜎𝑏)wheel< [σb]wheel therefore design of wheel
is satisfactory.
Since the contact area of both gear and pinion
is same so the induced contact stresses in
pinion and gear is same ( 𝜎𝑐)pinion= ( 𝜎𝑐)wheel
Checking
( 𝜎𝑐)pinion<[σc]wheel there for the design of
wheel is satisfactory.

UNIT -3: DESIGN OF BEVEL,WORM AND CROSS HELICAL GEARS
3.1 DesignProcedure for Selection of Bevel Gear Drive - Using PSG Design Data
Book (Manufactures Catalogue)
𝑖 =
𝑵 𝟏
𝑵 𝟐
=
𝒛 𝟐
𝒛 𝟏
Speed, No of teeth of driven gear.
Calculation of reference angle
From PSGDB pg.no 8.39
𝛿2= tan−1.𝑖; 𝛿1= 90° − 𝛿2
i - Gear ratio
𝛿1, 𝛿2 - Reference angle for both pinion and
gear.
If number of teeth in smaller pulley is not given
in problem, Assume
wheel from
using the i value.
pinion.
both pinions andwheel.
Most cases C45 for pinion and C.I grade 20 for
wheel (If material is not specified)
When selecting the material for gears following
parameters taken from the PSGDB.
N- speed of gear
If gear life is not specified assume Gear Life as
20,000 hrs
[Mt]
Mt=
60 ∙𝑃
2∙𝜋∙𝑁

(k.kd)= 1.3
8.14, Table: 9
N/mm2
1. If both Gear and Pinion is made by same
material
2. If Gear and Pinion made by different
material use (Eeq)formula from PSGDB Pg.No
8.14 determine the Equivalent Young’s
Modulus (Eeq)

Step : 6. Calculation of cone distance (R)
From PSGDB Page no: 8.13 Table no 8.
Assume the value of Ψyfrom Page no: 8.15,
Table 13. Based on i value.
Step : 7. Selection of z1,z2 and 𝑧 𝑣1, 𝑧 𝑣2)
Calculate the value for z2 = 𝑖 x 𝑧1
Calculation of virtual number of teeth
Calculation of virtual number of teeth(𝑧𝑣1,
𝑧𝑣2) from PSGDB Pg.No 8.39
𝑧 𝑣1 = 𝑧1 . cos𝛿1
𝑧 𝑣2 = 𝑧2 .cos𝛿2
𝛿1, 𝛿2 - Reference angle 𝑧1, 𝑧2 - Number of
teeth
8. Calculation for transverse module (mt)
Rearranging it;
𝑚𝑡 =
𝑅
0.5 √𝑍1
2+ 𝑍2
2
From Page no:8.2, Table 1; choose the std. value
of module
Step : 9. Revisionof Cone distance (R)
From PSGDB Page no: 8.38, Table-31;
calculate the new Cone distance
𝑅 = 𝑚𝑡 . 0.5 √𝑍1
2 + 𝑍2
2
From Page no: 8.15, Table-13
𝑅 𝑦 Average or mean module From Page no:
8.38, Tble:31 ; rearranging it
𝑚𝑚 = 𝑚𝑡−
𝑏sin𝛿
Reference diameter (d) From Page no: 8.38,
Table:31
Pitch line velocity
𝛹𝑝 =
𝑏
𝑑1

𝜐 =
𝜋 𝑑 𝑁 60
𝑏 𝑑
11. Selection of Quality of Gear
Step : 11. Selection of Quality of Gear
Mt=
60 ∙𝑃
2∙𝜋∙𝑁
no: 8.13
design is safe
Checking
Step : 15. Check for bending stress ( 𝝈 𝒃)
Page no: 8.13A
design is safe.
Table 18

Checking
pinion and gear.
8.22; Table:26
Virtual number teeth Zv1 & Zv2
16. Check for wheel
step is needed •
Calculate the design values of [𝛔 𝐛]wheel ,[𝝈 𝒄]wheel
for wheel •
wheel
values
N2 =
𝑁1
𝑖
Life of wheel (N)wheel = PSGDB Pg.No 8.17
Find [𝛔 𝐛] wheel, [𝝈 𝒄] wheelby using same formulas
which we have to use for pinion design.
(PSGDB Pg.No 8.18 and 8.16 respectively).
Checking
Calculation of induced bending stress for wheel
( 𝜎𝑏)wheel
( 𝜎𝑏)wheel< [σb]wheel therefore design of wheel is
satisfactory.
Since the contact area of both gear and pinion is
same so the induced contact stresses in pinion
and gear is same ( 𝜎𝑐)pinion= ( 𝜎𝑐)wheel

stresses.
Checking
( 𝜎𝑐)pinion<[σc]wheel there for the design of wheel
is satisfactory.

3.2 Design Procedure for Selection of worm gears - Using PSG Design Data Book
𝑖 =
𝑵 𝟏
𝑵 𝟐
=
𝒛 𝟐
𝒛 𝟏
Choose the suitable material for worm and worm
gear from PSG Data book page no: 8.45
Most cases steel is selected for worm and
bronze is selected for worm wheel
[Mt]
From PSGDB Page No: 8.44
Mt=
60 ∙𝑃
2∙𝜋∙𝑁
Step : 4 Selection of z1 & z2
Based on required efficiency choose the number
of starts in worm gear from PSGDB page no:
8.46
Calculate the value for z2
𝑖 =
𝒛 𝟐
𝒛 𝟏
*

Step: 5. Selection of [𝝈 𝒄 ] , [𝝈 𝒃]
Calculation of [𝜎𝑐 ]
From PSGDB page no. 8.45, select the value for
[𝜎𝑐 ]
Initially assuming the sliding velocity as 3 m/s
Calculation of [𝝈 𝒃]
From PSGDB page no:8.45, assuming the
rotation is in
One direction.
*Initially choose diameter factor q = 11
Step : 7. Calculation for axial module (mx)
From PSGDB Page no 8.43
mx =
2𝑎
( 𝑞 + 𝑧2)
From Page no:8.2, Table 1; choose the std
value of module
From PSGDB Page no 8.45
a = 0.5 mx (q + z2)
Step: 9. Calculation of d, v, 𝜸, vs
Pitch diameter From PSGDB Page no: 8.43
d1= 𝑞. m𝑥
d2= z2 . m𝑥
Pitch line velocity
𝜐 = 𝜋 𝑑 𝑁/ 60

Lead angle 𝜸
From Page no: 3.43
𝜸 = 𝑡𝑎𝑛−1
𝑧1
𝑞
Calculation of vs
From Page no: 8.44
Vs =
𝑣1
cos 𝛾
Step: 10 Revisionof [𝝈 𝒄 ]
For the actual value of choose the [𝜎𝑐 ] value
Step : 11 Revisionof design torque
Mt=
60 ∙𝑃
2∙𝜋∙𝑁
k = 1,load correction factor, when load is
almost constant
kd = 1, dynamic load factor, for v2 < 3 m/sec.
Step : 12 . Check for bending stress ( 𝝈 𝒄)
Calculation for induced bending stress
Checking
Step :13. Check for surface contact stress
( 𝝈 𝒄)

Step: 14 . Check for efficiency
PSGDB Pg.no 8.49
ή =
tan 𝛾
tan( 𝛾 + 𝜌)
𝛾 = 𝑡𝑎𝑛−1 (𝜇)
If 𝜂calculated ≥ ηdesired ; otherwise increase the lead
angle 𝛾
Step : 15 . Calculate the power loss and the area
required to dissipate the heat
(1 – η) × input power = Kt.A.(to – ta)
Step : 15. Calculation of basic dimensions
8.43; Table:33
Axial Module
Number of starts
Number of teeth on worm wheel
Length of worm
Centre distance
Face width
Height factor
Bottom clearance
Pitch diameter
Tip and Root diameter

UNIT : 1 . Design of Flexible Machine Elements
Designof Belt Drives:
Law of Belting:
Law of belting states that the centre line of the belt, as it approaches the pulley, must lie in a plane
perpendicular to the axis of that pulley or must lie in the plane of the pulley, otherwise the belt will
run off the pulley.
Geometrical Relationship
For open belt drive:
D and d = Diameters of the larger and smaller pulleys respectively
C = Center distance between the two pulley in meters,
L = Total length of the belt in meters
Wrap angle for Larger pulley (αL) = (180 + 2α)
Wrap angle for Smaller Pulley (αS) = (180 − 2α)
Sin α =
𝐷−𝑑
2𝐶
For Cross belt drive:
Sin α =
𝐷+𝑑
2𝐶
; (αL) =(αS) = (180 + 2α)
Power Transmitted by Belt
P = ( 𝑇1 − 𝑇2). 𝑉 v =
𝜋.𝐷.𝑁
60.1000
Tensions on belt drive
T1 & T2 = Tight side and Slack Side tensions respectively
Tc = Centrifugal tension = m.𝑣2
; m= Mass per unit length of the belt in kg/m.
v = Linear velocity of belt in m/sec.
Initial Tension (T0) =
( 𝑇1 + 𝑇2)
2
(without considering centrifugal tension)
=
( 𝑇1 +𝑇2+ 2𝑇 𝐶)
2
(With considering centrifugal tension)

*Note
1. Maximum tension (T) to which belt is subjected to centrifugal tension ,
T = 𝑇1 + 𝑇𝐶
Maximum Tension (T) = Maximum stress (σ) × Cross sectional area of belt.
= σ × b.t b = Width of the belt
𝑡 = Thickness of the belt
2. If centrifugal tension is considered
Total tension on tight side = Tt1 = 𝑇1 + 𝑇𝐶
Total tension on slack side = Tt2 = 𝑇2 + 𝑇𝐶
3. Effect of power transmitted on centrifugal tension
P = ( 𝑇𝑡1 − 𝑇𝑡2) × v
= [( 𝑇1 + 𝑇𝐶 ) − ( 𝑇2 + 𝑇𝐶)]× v
P = ( 𝑇1 − 𝑇2). 𝑉
So, There is no effect on centrifugal tension on the power transmitted.
4. For a belt speed upto 10 m/sec the centrifugal tension is negligible But for belt speed
more than 10m/sec, centrifugal tension should be considered.
5. Ratio of belt tension for the open belt drive
𝑻 𝟏
𝑻 𝟐
= 𝑒 𝜇𝛼
(without centrifugal tension) α = Angle of wrap or Angle of contact
𝑻 𝟏− 𝑻 𝑪
𝑻 𝟐− 𝑻 𝑪
= 𝑒 𝜇𝛼
(with centrifugal tension)
Ratio of tension for ‘V’ belt drive
𝑻 𝟏
𝑻 𝟐
= 𝑒 𝜇𝛼/𝑠𝑖𝑛𝛽 (without centrifugal tension) α = Angle of wrap or Angle of
contact
2𝛽 = V –groove angle
𝑻 𝟏− 𝑻 𝑪
𝑻 𝟐− 𝑻 𝑪
= 𝑒 𝜇𝛼/𝑠𝑖𝑛𝛽
(with centrifugal tension)
6. Condition for transmission of maximum power
The power transmitted is maximum when the Tc is one third of the maximum belt
tension (T)
T = 3Tc
Maximum velocity Vmax = √
𝑇
3𝑚

7. For most efficient power transmission for belt, the belt speed is 17.5 to 22.5 m/sec.
8. Permissible Stresses for belt material
Leather belt= 2 to 3.45 Mpa
Rubber belt = 1 to 1.7 Mpa
Fabric belt = less than 1.5 Mpa

Terminology used in gears
Pitch : Pitch of the two mating gears must be same. It is defined as follows
(a). Circular Pitch (pc) =
𝜋.𝐷
𝑍
(b). Diametral Pitch (pd) =
𝜋
𝑝 𝑐
(c). Module Pitch (m) =
𝐷
𝑍
(d). Backlash = Tooth space – Tooth thickness
(e). Pressure angle or angle of obliquity (φ) : It is angle between the common normal to two gear
teeth at the point of contact and the common tangent at the pitch point. The standard pressure angle
are 14.5 and 200
Velocity ratio (i) =
𝑁1
𝑁2
=
𝑍2
𝑍1
Law of Gearing
The law of gearing states the condition which must be fulfilled by the gear tooth profile to maintain
a constant angular velocity ratio between two gears. This is the fundamental condition which must
be satisfied while designing the profile of the gear wheel.
Standard System of Gear Tooth
The American Gear Manufacturers Association (AGMA) and the American National Standard
Institute (ANSI) standardized the following four forms of gear teeth depending upon the pressure
angle.
1. 14.50 composite system
2. 14.50 full depth involute system
3. 200 full depth involute system
4. 200 stub involute system

Force Analysis of Spur Gear
Assumption Made in Force Analysis of Spur Gear
 Friction losses in the bearing and gears are negligible
 The gears mesh at the pitch circle
 The gear teeth have standard involute tooth profiles
 The shafts for pinion and gear are parallel
 The effect of the dynamic forces is neglected.
 As the point of constant moves, the magnitude of resultant force F changes. This effect is
neglected.
Formulae for Force Analysis of Spur gears
P = Power transmitted by gears
Mt = Torque transmitted by gears in N-mm
N1 and N2 = Speed of pinion and gear respectively in rpm
d1 and d2 = Pitch circle diameters of pinion and wheel respectively in m.
φ = Pressure angle
Torque Transmitted (Mt) =
60 𝑋 𝑃
2.𝜋.𝑁
The Tangential Component Force (Ft) =
2.𝑀𝑡
𝑑
The Radial Component Force (Fr) = Ft. tan𝜑

The power transmitted (P) = Ft . v v =
𝜋.𝑑 .𝑁
60
m/sec.
Helical Gears
Kinematics and Nomenclature of helical gears
1. Transverse circular pitch (Pt) = 𝜋. 𝑚 𝑡 =
𝜋.𝑑1
𝑧1
=
𝑝 𝑛
cos 𝛽
2. Circular Pitch (Pn) = Pt x cosβ
3. Axial Pitch (Pa) =
𝑃𝑡
tan 𝛽
=
𝑝 𝑛
sin 𝛽
=
𝜋.𝑚 𝑛
sin 𝛽
4. Normal Diametral pitch (pd) =
1
𝑚 𝑛
=
𝜋
𝑝 𝑛
Tooth Proportions for Helical Gears
There are no standard proportions for helical gears. The proportions recommended by American
Gear Manufacturer’s Association (AGMA) are as follows
 Normal Pressure angle (𝛼n) = 150 to 250
 Helix angle (β) = 80 to 250, for helical
o = 250 to 400, for herringbone
 Addendum , maximum = 0.8 mn
 Dedendum , maximum = mn
 Tooth depth = 2.25 mn
 Minimum Clearance = 0.2 mn
 Thickness of tooth = 1.5708 mn
Force Analysis of Helical Gears
F = Resultant or tooth force
Ft = Tangential or transmitted force
Fr = Radial force,
Fa = Axial or Thrust force
Mt = Transmitted torque
d = pitch circle diameter of gear
β = Helix angle
𝛼 𝑡 and 𝛼 𝑛 = Transverse and normal pressure angles respectively.

Tangential component of the resultant tooth force (Ft)
Ft =
2.𝑀𝑡
𝑑
Radial component of the resultant tooth force (Fr)
Fr = Ft x [
tan 𝛼 𝑛
cos 𝛽
]
Axial component of the resultant tooth force (Fa)
Fa = Ft x tan 𝛽

FORCE ANALYSIS OF BEVEL GEAR
In force analysis of bevel gears, it is assumed that the resultant tooth force between two meshing
gears is concentrated at the midpoint along the face width of the tooth. The forces acting at the
centre of the tooth
The component of the resultant force is:
1. Tangential or useful resultant force (Ft)
2. Separating force (Fs): It is resolved into two components. They are
(i). Axial force (Fa)
(ii). Radial force (Fr)
𝛿1, 𝛿2 - Reference angle for both pinion and gear.
Calculation of reference angle (if pinion and gear is intersects from angle 𝜽)
tan 𝛿1 =
sin 𝜃
(
𝑧2
𝑧1
+cos 𝜃)
; 𝜃 = ( 𝛿1 + 𝛿2)
(i). Components of the tooth force on the pinion
Ft =
2.𝑀𝑡
𝑑1𝑎𝑣
=
𝑀𝑡
𝑟 𝑚
rm = (
𝑑1
2
−
𝑏 sin 𝛿1
2
)
Calculation of reference angle (if pinion and gear is perpendicular)
From PSGDB pg.no 8.39
𝛿2= tan−1.𝑖; 𝛿1= 90° − 𝛿2
i - Gear ratio

Radial force (Fr) = Fs × cos 𝛿
Axial force (Fa) = Fs × sin 𝛿
Separating force (Fs) = Ft × tan 𝛼
Radial force (Fr) = Ft × tan 𝛼 × cos 𝛿1
Axial force (Fa) = Ft × tan 𝛼 × sin 𝛿1
(ii). Component of the tooth force on the gear
Ft (Pinion) = Ft(gear)
Separating force (Fs) = Ft × tan 𝛼
Radial force (Fr) = Ft × tan 𝛼 × cos 𝛿2
Axial force (Fa) = Ft × tan 𝛼 × sin 𝛿2

UNIT: 4 – Design of Gear Box

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