A project report on
Finite Element Analysis of Plastic Shredder Shaft
by
Muhammad Sameer Sajid
BME193087
Gul Nawab Ahmad
BME193062
A Project Report submitted to the
DEPARTMENT OF MECHANICAL ENGINEERING
in partial fulfillment of the requirements for the Course of
FINITE ELEMENT METHOD
of the degree of
BACHELOR OF SCIENCE MECHANICAL ENGINEERING
Faculty of Engineering
Capital University of Science and Technology
Islamabad
June 2022
1
Copyright © 2022 by CUST student
All rights reserved. Reproduction in whole or in part in any form requires the prior written
permission of Muhammad Taha, Sameer Sajid, and Gul Nawab.
2
DECLARATION
It is declared that this is an original piece of our own work, except where otherwise acknowledged
in text and references. This work has not been submitted in any form for another degree or diploma
at any university or other institution for tertiary education and shall not be submitted by us in future
for obtaining any degree from this or any other University or Institution.
Sameer Sajid
BME193087
Gul Nawab
BME193062
June 2022
3
CERTIFICATE OF APPROVAL
It is certified that the project titled “Design of wheat thresher” carried out by Muhammad Taha
BME193066, Sameer Sajid BME1930 and Gul Nawab BME1930 under the supervision of Ma’am
Shumaila Rasheed, Capital University of Science and Technology, Islamabad, is fully adequate,
in scope and in quality, as a semester project for the degree of BS of Mechanical Engineering.
Supervisor:
HOD:
-------------------------Dr. Waqas Lugmani
Lecturer
Department of Mechanical Engineering
Faculty of Engineering
Capital University of Science and Technology, Islamabad
-------------------------Dr. Mahabat Khan
Professor
Department of Mechanical Engineering
Faculty of Engineering
Capital University of Science & Technology, Islamabad
4
Table of Contents
1
INTRODUCTION .................................................................................................................. 9
1.1
Overview .......................................................................................................................... 9
1.2
Purpose of this Project...................................................................................................... 9
1.3
Applications of this project .............................................................................................. 9
1.4
Report Organization ......................................................................................................... 9
2
LITERATURE REVIEW ..................................................................................................... 11
3
PROJECT DESIGN AND CALCULATIONS ..................................................................... 12
3.1
Project Design ................................................................................................................ 12
3.2
Calculations Overview ................................................................................................... 13
3.3
Basic Measurements ....................................................................................................... 15
3.3.1
Constraints for Shaft ............................................................................................... 15
3.3.2
Constraints for Gear ................................................................................................ 15
3.4
4
Calculations .................................................................................................................... 15
3.4.1
Design Based on Strength ....................................................................................... 16
3.4.2
Design based on Stiffness ....................................................................................... 16
3.4.3
Principle stresses and Maximum stresses on Shaft ................................................. 17
3.4.4
Von-misses effective stresses ................................................................................. 18
3.4.5
Frequency and RPM relation .................................................................................. 18
PROJECT SIMULATIONS.................................................................................................. 19
5
4.1
Engineering Data ............................................................................................................ 19
4.2
Model ............................................................................................................................. 19
4.3
Meshing .......................................................................................................................... 20
4.3.1
Coarse Mesh............................................................................................................ 20
4.3.2
Fine Mesh................................................................................................................ 20
4.4
4.4.1
For Bending Test..................................................................................................... 21
4.4.2
For Torsional Test ................................................................................................... 21
4.5
Solution .......................................................................................................................... 22
4.5.1
Bending Stress ........................................................................................................ 22
4.5.2
Torsional Test ......................................................................................................... 25
4.6
5
Boundary Conditions...................................................................................................... 21
Mesh Convergence ......................................................................................................... 27
RESULTS AND DISCUSSION ........................................................................................... 28
5.1
Results ............................................................................................................................ 28
6
CONCLUSION ..................................................................................................................... 29
7
References ............................................................................................................................. 30
6
List of Figures
Figure 1: CAD Model of the Shaft ............................................................................................... 12
Figure 2: Dimensions of the Shaft ................................................................................................ 12
Figure 3: Given properties of the shaft ......................................................................................... 13
Figure 4: Shear force and bending moment diagram .................................................................... 14
Figure 5: Failure Theory Graph .................................................................................................... 18
Figure 6: Engineering Data of Ansys............................................................................................ 19
Figure 7: Model of Shaft in Design Modeler ................................................................................ 19
Figure 8: Coarse Mesh in Ansys Mechanical ............................................................................... 20
Figure 9: Coarse Mesh in Ansys Mechanical ............................................................................... 20
Figure 10: Boundary Conditions (Bending Test).......................................................................... 21
Figure 11:Boundary Conditions (Torsional Test) ......................................................................... 21
Figure 12: Bending Test Total Deformation ................................................................................. 22
Figure 13: Bending Equivalent Stress........................................................................................... 22
Figure 14: Normal Stress along a path .......................................................................................... 23
Figure 15: Fine Mesh Bending Test Total Deformation ............................................................... 23
Figure 16: Fine mesh Bending Equivalent Stress ......................................................................... 24
Figure 17: Fine Mesh Normal Stress along a path ........................................................................ 24
Figure 18: Torsional Test Total deformation ................................................................................ 25
Figure 19: Torsional Test Maximum Shear Stress ....................................................................... 25
Figure 20: Torsional Test Equivalent Stress ................................................................................. 26
Figure 21: Torsional Test Equivalent Elastic Strain ..................................................................... 26
7
LIST OF TABLES
Table 1: Shear Stress Value for different plastics ......................................................................... 15
Table 3: Test Results of Bending Test in coarse mesh ................................................................. 23
Table 4: Results of Torsional Test on ANSYS Workbench ......................................................... 26
8
CHAPTER 1
1
INTRODUCTION
1.1 Overview
A plastic shredder is a very important recycling unit as it breaks down the large plastic pieces into
smaller pieces which can be then recycled into different things such as plastic tiles etc. Therefore,
it is of most important to develop a system which can recycle plastic easily and effectively. This
report emphasis on development of shaft for this plastic shredder. In this mechanical analysis of
plastic shredder shaft, all the stresses and strain analysis will be done on the shaft using FEA.
1.2 Purpose of this Project
The main purpose of this project is
1. To understand how problem-solving works in complex engineering problems.
2. To get a know how about how the stresses are acting on different elements of the body.
3. How to use software to solve real life examples using software simulations
1.3 Applications of this project
This mechanical analysis is not just restricted to this case. These calculations and assumptions
can be applied on various things such as
•
Determining forces acting on common chairs and tables.
•
Stresses and strains acting on a body under deformation.
•
Determining the proper failure criteria on basically anything which is under any sort of
stress.
1.4 Report Organization
•
In this report, the reader will firstly come across chapter 1. This chapter provides the most
basic information and an overall review about the whole report. How it will be analyzed
and the industrial uses that are associated with it.
•
Moving forward, there comes Chapter 2. This part of the entire context focuses more on
the literature review. This chapter will help the readers to have better concepts of the
project. It will focus on the work done by different individuals around the world.
9
•
Further into the report, Chapter 3 will be having the most essential content. It will include
the schematic and free body diagrams along with the forces the specimen will be
undergoing. It will also include all the necessary calculations.
•
Moving on, there will come chapter 4. In this chapter, the calculations will be evaluated to
proceed to the results.
•
Lastly, the reader will come to chapter 5. It is the concluding chapter. It will be a short
summary of all the analysis done through-out the report.
10
CHAPTER 2
2
LITERATURE REVIEW
Since their advent over a century ago, plastic has become an essential component of our daily lives.
It is currently one of the most used materials in the planet. They are available in five different
types. The Polyethylene Terephthalate (PET), the High-Density Polyethylene Terephthalate
(HDPE), and the High-Density Polyethylene Terephthalate (HDPE) , PVC (polyvinyl chloride),
and Low-density polyethylene (LDPE) and polypropylene (PP). These plastic categories, which
are now being offered in large quantities, will be phased out. They eventually make their way to
landfills which is causing problems. Due to the large amount of garbage generated, waste products
are an issue. Because of its short life cycle, a greater amount of material is required used in its
manufacture, as well as the trash generated [1].
Given that the shaft is mounted on bearings at both ends and rotates freely, the torque experienced
by the shaft is anticipated to be caused by the plastic materials that will be shredded in the
shredding chamber. The bearing reactions, pulley, flywheel, cutting drum, and belt tension weights
operate as the shaft's primary loads. Because the shaft will experience varying torque and bending
moments, combined shock and fatigue considerations are taken into consideration[2].
11
CHAPTER 3
3
PROJECT DESIGN AND CALCULATIONS
3.1 Project Design
Figure 1: CAD Model of the Shaft
Figure 2: Dimensions of the Shaft
12
3.2 Calculations Overview
Figure 3: Given properties of the shaft
13
Figure 4: Shear force and bending moment diagram
14
3.3 Basic Measurements
Following table shows the ultimate shear stress value for different plastic materials we will be
working on
Table 1: Shear Stress Value for different plastics
Material
Kg/m2
Polyethylene (PE)
880000 - 3.3e+6
Polypropylene (PP)
4e+6
Polystyrene (PS)
2.8e+6 - 4.8e+6
PVC
2.8e+6 - 5.04e+6
3.3.1 Constraints for Shaft
Material chosen for shaft = Mild Steel
Yield Strength (Sy) = 250 MPa
Motor Power rating = 3 Hp
Motor Rpms = 50 rpms
Factor of Safety = 2.80
Length of Shaft = 1 ft = 304.8 mm
Shear Modulus (G) = 75 GPa
3.3.2 Constraints for Gear
Pressure Angle α = 20°
No. of teeth = 25
Rotor Diameter = 220 mm
Angle of twist (Φ) = 0.3̊ /mm
3.4 Calculations
Using the above properties and value we will calculate the diameter of the shaft using following
assumptions
15
Now we will find diameter
3.4.1 Design Based on Strength
𝝅
× 𝝉 × 𝒅𝟑
𝟏𝟔
Rearranging the equation
𝑻=
First, we will find the torque acting on shaft
𝝉=
𝟎. 𝟓
× 𝑺𝒚
𝑭. 𝑺
Putting values
𝝉 = 𝟒𝟒. 𝟔𝟒 𝑴𝑷𝒂
Torque produced by the motor
𝑷 × 𝟔𝟎
𝑻=
𝟐𝝅𝑵
𝟑
𝒅= √
𝟏𝟔 × 𝑻
𝝉
Putting values
𝒅 = 𝟑𝟗. 𝟐𝟕 𝒎𝒎 or 𝒅 = 𝟒𝟎 𝒎𝒎
3.4.2 Design based on Stiffness
Which comes out to be
Using the formula for angle of twist
𝑻 = 𝟒𝟐𝟕. 𝟐𝟑 𝑵𝒎
𝜱=
𝑻𝑳
𝑱𝑮
……. (1)
Force produced due to torque
First, we will find polar moment of inertia
𝑭𝒕 =
𝟐𝑻
𝑫
𝑭𝒕 = 𝟑𝟖𝟖𝟑. 𝟗𝟏 𝑵
For Gear
𝝅
× 𝑫𝟒
𝟑𝟐
𝑱=
𝑱 = 𝟎. 𝟎𝟗𝟖 × 𝑫𝟒
Putting in eq (1)
Load acting on spur gear
𝟒
𝑭𝒕
𝒘=
𝐜𝐨 𝐬(𝜶)
Putting values
𝑫= √
Putting values
𝑫 = 𝟖 𝒎𝒎
𝒘 = 𝟒𝟏𝟑𝟑. 𝟏𝟕 𝑵
Moment produced
𝑴=
𝒘 ×𝑳
𝟒
𝑻𝑳
𝟎. 𝟎𝟗𝟖 × 𝑮
3.4.2.1 For fluctuating shaft (Based on
Strength)
From table
𝑴 = 𝟑𝟏𝟒. 𝟗𝟓 𝑵𝒎
Torque due to moment
𝑻𝒆 = √𝑴𝟐 + 𝑻𝟐
Putting values
𝑻𝒆 = 𝟓𝟑𝟎. 𝟖𝟓 𝑵𝒎
Km = 1.5
Kt = 1
Calculating torque
𝑻𝒆 = √(𝑲𝒎 + 𝑴)𝟐 + (𝑲𝒕 + 𝑻)𝟐
Putting values
16
𝑻𝒆 = 𝟔𝟑𝟔. 𝟗𝟓 𝑵𝒎
Now calculating moment
𝑴𝒆
𝟏
= [𝑲𝒎 + 𝑴
𝟐
+ √(𝑲𝒎 + 𝑴)𝟐 + (𝑲𝒕 + 𝑻)𝟐 ]
Putting values
𝑴𝒆 = 𝟓𝟓𝟒. 𝟔𝟗 𝑵𝒎
Now,
𝝅
× 𝝉 × 𝒅𝟑
𝟏𝟔
Rearranging the equation
𝑻=
𝝈𝟏 =
𝟏
[(𝝈𝒙 + 𝝈𝒚
𝟐
𝟐
+ √(𝝈𝒙 − 𝝈𝒚 ) + 𝟒𝒛𝟐 )]
here
𝝈𝒙 = 𝟔𝒃 & 𝝈𝒚 = 𝟎
3.4.3.1 Minimum Principle Stress
The equation for minimum principle stresses
is given by
𝝈𝟏 =
𝟑
𝒅= √
𝟏𝟔 × 𝑻𝒆
𝝉
Putting values
𝒅 = 𝟒𝟏 𝒎𝒎
3.4.2.2 For fluctuating shaft (Based on
Stiffness)
Using formula for angle of twist
𝑻𝒆 𝑳
𝜱=
𝑱𝑮
Replacing J
𝟏
[𝟔𝒃 + √(𝟔𝒃)𝟐 + 𝟒𝒛𝟐 )]
𝟐
𝝈𝟏
𝟏 𝟑𝟐 𝑴
𝟑𝟐 𝑴 𝟐
𝟏𝟔 𝑻 𝟐
√
) +𝟒(
) ]
= [
+ (
𝟐 𝝅 𝒅𝟑
𝝅 𝒅𝟑
𝟏𝟔𝝅𝒅
Simplifying
𝟏
𝟑𝟐
𝝈𝟏 = 𝟐 × 𝝅𝒅𝟑 [ 𝑴 − √𝑴𝟐 + 𝑻𝟐 ]…….. (2)
𝟏𝟔
𝝈𝟐 = 𝝅𝒅𝟑 [ 𝑴 − √𝑴𝟐 + 𝑻𝟐 ]…… (3)
3.4.3.2 Maximum Shear Stress
𝟒
𝑫= √
𝑻𝒆 𝑳
𝟎. 𝟎𝟗𝟖 × 𝑮
𝝉𝟏 =
Putting values
𝑫 = 𝟖. 𝟒 𝒎𝒎 or 𝑫 = 𝟖 𝒎𝒎
3.4.3 Principle stresses and
Maximum stresses on Shaft
The equation for principle stresses is
𝝉𝟏 =
𝝈𝟏 − 𝝈𝟐
𝟐
𝟏 𝟏
𝟑𝟐
[ ×
[ 𝑴 − √𝑴𝟐 + 𝑻𝟐 ] ]
𝟐 𝟐 𝝅𝒅𝟑
𝟏𝟔
− [ 𝟑 [ 𝑴 − √𝑴𝟐 + 𝑻𝟐 ]]
𝝅𝒅
𝝉𝟏 =
𝟏𝟔
[ √𝑴𝟐 + 𝑻𝟐 ]
𝝅𝒅𝟑
As we have already calculated
D = 40 mm
17
M = 554.69 Nm
T = 636.95 Nm
Putting values in eq (1) and eq (2)
𝝈𝟏 = 𝟏𝟕𝟖𝟏𝟔𝟓. 𝟗𝟒 𝑵/𝒎
&
𝝈𝟐 = −𝟑𝟔𝟗𝟏𝟓. 𝟐𝟗 𝑵/𝒎
3.4.4 Von-misses effective stresses
There equation for Tresca failure theory is
given by
Figure 5: Failure Theory Graph
𝝈′ = √𝝈𝟏 𝟐 − 𝝈𝟏 𝝈𝟐 + 𝝈𝟐 𝟐
Putting values
𝝈′ = 𝟏𝟗𝟗𝟐𝟎𝟓. 𝟔𝟒 𝑵/𝒎
3.4.5 Frequency and RPM relation
As we know that
𝑷𝒐𝒘𝒆𝒓 = 𝑻𝒐𝒓𝒒𝒖𝒆 ×
𝑨𝒏𝒈𝒖𝒍𝒂𝒓 𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚
𝟐. 𝟐𝟑𝟐 × 𝟏𝟎𝟑 = 𝟒𝟐𝟕. 𝟐𝟑 × 𝝎
Formula for frequency is
ƒ=
𝝎
𝟐𝝅
Therefore,
ƒ = 𝟎. 𝟖𝟑𝟑𝟑 𝑯𝒛
18
CHAPTER 4
4
PROJECT SIMULATIONS
4.1 Engineering Data
Figure 6: Engineering Data of Ansys
4.2 Model
Figure 7: Model of Shaft in Design Modeler
19
4.3 Meshing
4.3.1 Coarse Mesh
Figure 8: Coarse Mesh in Ansys Mechanical
4.3.2 Fine Mesh
Figure 9: Coarse Mesh in Ansys Mechanical
20
4.4 Boundary Conditions
4.4.1 For Bending Test
Figure 10: Boundary Conditions (Bending Test)
4.4.2 For Torsional Test
Figure 11:Boundary Conditions (Torsional Test)
21
4.5 Solution
4.5.1 Bending Stress
4.5.1.1 Coarse Mesh
Figure 12: Bending Test Total Deformation
Figure 13: Bending Equivalent Stress
22
Figure 14: Normal Stress along a path
Table 2: Test Results of Bending Test in coarse mesh
4.5.1.2
Fine Mesh
Figure 15: Fine Mesh Bending Test Total Deformation
23
Figure 16: Fine mesh Bending Equivalent Stress
Figure 17: Fine Mesh Normal Stress along a path
24
4.5.2 Torsional Test
Figure 18: Torsional Test Total deformation
Figure 19: Torsional Test Maximum Shear Stress
25
Figure 20: Torsional Test Equivalent Stress
Figure 21: Torsional Test Equivalent Elastic Strain
Table 3: Results of Torsional Test on ANSYS Workbench
26
4.6 Mesh Convergence
27
CHAPTER 5
5
RESULTS AND DISCUSSION
This section of the report discusses the results obtained from the calculations done in chapter 3
5.1 Results
Table 4: Results in Tabular form
Design Analysis
Diameter
1.
Design Based on Strength
𝑑 = 39.27 𝑚𝑚 or 𝑑 = 40 𝑚𝑚
2.
Design based on Stiffness
𝐷 = 8 𝑚𝑚
3.
For fluctuating shaft (Based on Strength)
𝑑 = 40 𝑚𝑚
4.
For fluctuating shaft (Based on Stiffness)
𝐷 = 8.4 𝑚𝑚 or 𝐷 = 8 𝑚𝑚
From the above analysis we can see that the maximum diameter achieved is through design based
on strength. Therefore, we will be using this diameter. To provide more strength and rigidity we
design a hexagonal shaft which allows the blades to rotate without any sort of welds. This cad
model has been tested and simulated on ANSYS workbench.
Moreover, in simulations we can see that our numerical and theoretical calculations are in
correlation we each other and they validate each other.
28
CHAPTER 6
6
CONCLUSION
As we can see that we have successfully designed a shaft which can bear the load of the shearing
plastic. We analyzed the shaft using different design aspects and concluded that design based on
strength provided us with the optimal diameter for the shaft. Also, this shaft was analyzed and
simulated on ANSYS, and it survived all the tests.
From the results obtained from the torsional and bending test we can see that the diameter we have
calculated is optimal. Maximum shear stress applied on the shaft was 20.42 MPa which shaft can
bear very easily. This shaft design can easily be put to real life test under the same conditions.
29
7
References
[1] A. Waleola Ayo, "Development of a Waste Plastic Shredding Machine," International
Journal of Waste Resources, vol. 07, no. 02, pp. 2-5, 2017.
[2] A. David, "Design and construction of a plastic shredding machine for recycling and
mangement of plastic waste," Journal of Multidisciplinary Engineering Science and
Technology (JMEST), vol. 9, no. 5, pp. 1379-1385, 2018.
30