Design of Shafts

3
Power, P = 40Kw = 40 x 10 W
N = 1500 rpm

P 1=2 P2 ( horizontal )

Q 1=2 Q2 (vertical)
Pulley D – Driver
Pulley C – Driven

Rc=170 mm , Rd=130 mm
In the design process of a shaft, several critical considerations come into play to ensure its
structural integrity and functionality:
1. Dual Loading Conditions: The shaft is subject to both twisting and bending moments.
This dual loading necessitates a careful analysis of the material properties and dimensions
to withstand these forces effectively.
2. Key Design: Four keys are essential for transmitting the required torque. The design of
these keys is crucial to ensure efficient power transmission without compromising the shaft's
strength or introducing potential weak points.
3. Equivalent Torque and Bending Moment: Determining the equivalent torque (T) and
equivalent bending moment (Me) is pivotal in establishing the overall diameter of the shaft.
These calculations are essential for accurate sizing and material selection to meet the
operational requirements.
4. Muff-Coupling Connection: The presence of a muff-coupling, connecting two long
shafts, necessitates the design of both shafts. Coordination between the coupling and shaft
design is crucial to maintain a seamless power transmission system.
5. Bearing Considerations: When designing shafts, careful attention must be paid to the
bearings. Factors such as lubrication, housing design, and heat dissipation need
consideration. Adequate measures should be taken to ensure efficient lubrication, proper
housing support, and effective heat management to prevent bearing failure.
6. Variable Diameter: The shaft diameter is not constant but varies across the axial
direction (AD). This variable diameter design may be essential to optimize material usage
and account for varying stress and loading conditions along the shaft's length.

Here are the properties of ASTM A36 Steel

 Tensile strength: 399 MPa

 Yield strength:248.225 MPa
 Modulus of elasticity: 200 GPa
 Shear modulus: 76.91GPa
 Poisson's ratio: 0.3 ul
 Density: 7.85 g/cm³

These are the standard sizes and lengths for transmission shafts:

Standard sizes of transmission shafts:

  110 mm to 140 mm with 15 mm steps
 140 mm to 500 mm with 20 mm steps

Standard lengths of transmission shafts:

 5m
 6m
 7m
The maximum permissible working stresses for transmission shafts are as follows:

 Tension or compression:

o 112 MPa for shafts without allowance for keyways

o 84 MPa for shafts with allowance for keyways
 Shear:

o 56 MPa for shafts without allowance for keyways

o 42 MPa for shafts with allowance for keyways
 Shaft Calculations
60 P 60 x 40 x 103
P=50 x 10 W N = 1000rpm T =
3
 =
2 πN 2 x 1000 x π
 = 254.65N-m or 254.65 x 103 N-mm
 ( Q 1−Q 2 ) Rc=254.65 x 10 3 Nmm
 ( Q 1−Q 2 ) 170=254.65 x 103 Nmm
 ( 2 Q2−Q 2 ) 170=254.65 x 103 Nmm
3
170 254.65 x 10
 Q 2= =2995.88 N (Vertical Force)
170 170
 P 1=2 P2
 ( P 1−Pc ) rD=254.65 x 103 Nmm
( P 2 ) 130 254.65 x 103
 = =1958.58 N (Horizontal force )
130 140
 P 1=3917.69 N
 P 1+ P2=1958.58 N + 3917.69 N =5876.27 N ( Horizontal force )
 ¿
 Horizontal Forces;
 RA+ RB=W ,W =5876.27 N
 RB=2 x 5876.27 N
 RB=1175254 N
 RA+1175254=5876.27 N −1175254=−5876.27 N

Maximum bending moment

 WL 5876.27 x 2000
¿ = =11752540 Nmm
2 2

Me=√ ( 0 ) +11752540 =11752540 Nmm

2 2

Twisting moment

3
T =254.65 x 10 Nmm
16
3√
2 2
shear stress= (Cbm × M ) +(Ct × T )
πd
16
3√
2 3 2
42 MPa= (1.5 × 11752540) +(1 ×254.65 x 10 )
πd
D=128mm
Design of key

Here are the properties of carbon steel:

 Density: 7.85 g/cm³

 Ultimate tensile strength: 420 MPa
 Yield strength: 350MPa
 Young's modulus: 200 GPa

The key of choice for a mild steel shaft is a sunk key rectangular.

The measurements of a rectangular sunk key are taken from the table.

Hence for d= 128mm :

w= 36mm t= 20mm

a) Considering shearing of the key

Since the key material is the same as that of the shaft, then:
l=L/2=448/2=224 mm
Length of the key = 224 mm
d
T =lxwxτx
2
3
3 128 254.65 x 10 Nmm
254.65 x 10 =224 mm x 36 mm x → 3
2 516096 mm
2
τ =0.4934 N /m m
b) Crushing Stress
 t d 3 20 128
T =lx x σc x 254.65 x 10 Nmm=224 mm x x
2 2 2 2
3
254.65 x 10 N
=1.7701 2
143360 mm
There are 4 keys to be designed.
Sleeve/muff coupling
Calculations
Outer diameter of sleeve, D=2d +13 mm=2 ( 128 ) +13=269 mm

Length of sleeve, ¿ 3.5 d=3.5 ( 128 )=448 mm

Induced Shear Stress
π d 128
xτcx D [ 1−k ] k = =
3 4
T= mm=0.2857
16 D 448
3
254.65 x 10
=τc=0.067 MPa
3796501.15

Design of journal bearing

Considering transmission shafts;
From the table
l/d=2.5
l/128=2.5
l=320mm

p=w/ld
=Z*N/4.75*10^6*(d/c)^2*(l/d+l)
From the table;
c/d=0.001
0.001*128=0.128
c=0.128

p=7.66 N/mm^2

p=W/L*d=7.66=W/128*320

W=314KN

Z*N/P=0.034*1500/7.67
=6.667

3K= Z*N/P K=2.33 ,Since 6.667>2.33 hence in hydrodynamic condition

=33/10^8*6.65*1/0.001+0.002

= Qg= μ.W.VN

dN 0.1× 1500
V= π =π
60 60

Qg=0.0042*314000*7.85=10352.58W

Qd=CA(ta-to)

=1232*0.25*0.1*15

=455W

Amount of cooling required

Qg-Qd=10352-455=9997W

CAD DRAWINGS

ASSEMBLY DRAWING
EXPLODED DRAWING

Stress Analysis Report

 Analyzed File: Assembly1.iam
Autodesk Inventor 2023 (Build 270158000,
Version: 158)
Creation Date: 18/11/2023, 19:22
Study Author: USER
Summary:

Static Analysis:2
General objective and settings:

Design Objective Single Point

Study Type Static Analysis
Last Modification Date 18/11/2023,
19:19
Model State [Primary]
Design View Default
Positional [Primary]
Detect and Eliminate Rigid Body No
Modes
Separate Stresses Across Contact No
Surfaces
Motion Loads Analysis No

i
P
r
o
p
e
r
ti
e
s

S
Author USER
u
m
m
a
r
y

Project
 Part Assembly
Number 1
Designer USER
Cost Ksh0.00
Date 17/11/202
Created 3

Status
Design Status WorkInProgress

Physical

Mass 644.724 kg
Area 4259470 mm^2
Volume 81758100
mm^3
x=-1195.64
Center of mm y=-
Gravity 1510.93 mm
z=2169.47
mm
Note: Physical values could be different from Physical values used by FEA reported
below.

Mesh settings:
Avg. Element Size (fraction of model 0.1
diameter)
Min. Element Size (fraction of avg. size) 0.2
Grading Factor 1.5
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PM Report
Max. Turn Angle 20
deg
Create Curved Mesh Elements No
Use part based measure for Assembly Yes
mesh

Material(s)

Name Stainless Steel

Mass Density 8 g/cm^3
General Yield Strength 250 MPa
Ultimate Tensile 540 MPa
Strength
Young's Modulus 193 GPa
Stress Poisson's Ratio 0.3 ul
Shear Modulus 74.2308
GPa
Part bearing.ip
Name(s) t
journal.ipt
Name Steel ASTM A36
Mass Density 7.85
General g/cm^3
Yield Strength 248.225
MPa
Ultimate Tensile 399.9 MPa
Strength
Young's Modulus 199.959
Stress GPa
Poisson's Ratio 0.3 ul
Shear Modulus 76.9073
GPa
SHAFT
2.ipt
Part pulley.ipt
Name(s) MUFF.ipt
SHAFT
1.ipt
KEY.ipt
pulley 2.ipt
Name Steel, Carbon
Mass Density 7.85
General g/cm^3
Yield Strength 350 MPa
Ultimate Tensile 420 MPa
Strength
Young's Modulus 200 GPa
Stress Poisson's Ratio 0.29 ul
Shear Modulus 77.5194
GPa
Part KEY 1.ipt
Name(s)

Operating conditions

Force:1

Load Force
Type
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Magnitud 3479.000
e N
Vector X 0.000 N
Vector Y 0.000 N
Vector Z 3479.000
N

Selected Face(s)

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0N 0Nm

Result Summary

Name Minimum Maximum

Volume 81758100 mm^3
Mass 644.724 kg
Von Mises Stress 0 MPa 0.615813 MPa
1st Principal -0.14029 MPa 0.271707 MPa
Stress
3rd Principal -0.698234 MPa 0.0281253 MPa
Stress
Displacement 0 mm 0.000021299 mm
Safety Factor 15 ul 15 ul
Stress XX -0.201985 MPa 0.0449758 MPa
Stress XY -0.168013 MPa 0.153698 MPa
Stress XZ -0.0606314 MPa 0.0672685 MPa
Stress YY -0.647137 MPa 0.0792711 MPa
Stress YZ -0.0897176 MPa 0.223071 MPa
Stress ZZ -0.262507 MPa 0.126614 MPa
X Displacement -0.0000203289 mm
0.0000203914
mm
Y Displacement -0.0000212988 mm 0.0000204112
mm
Z Displacement -0.00000740761 0.00000727063
mm mm
Equivalent Strain 0 ul 0.00000278512 ul
1st Principal -0.0000000172621 0.00000151967 ul
Strain ul
3rd Principal -0.00000323937 ul 0 ul
Strain
Strain XX -0.000000689415 0.000000424893
ul ul
Strain XY -0.00000108368 ul 0.000000991352
ul
Strain XZ -0.000000391073 0.000000433882
ul ul
Strain YY -0.0000029098 ul 0.000000341321
ul
Strain YZ -0.000000578679 0.00000143881 ul
ul
Strain ZZ -0.000000869353 0.00000106041 ul
ul
Contact Pressure 0 MPa 0.606912 MPa
Contact Pressure -0.247204 MPa 0.172911 MPa
X
Contact Pressure -0.491037 MPa 0.157945 MPa
Y
Contact Pressure -0.255367 MPa 0.356115 MPa
Z

Figures

Von Mises Stress

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