Course project on "Topology Optimization of Spur Gears"

1. “Topology Optimization of Spur Gears”
PROJECT REPORT
Submitted for the course Design of Transmission Systems
(MEE4007)
By
16BME0086 ADARSH AGARWAL
16BME0701 ANURAG PURBEY
Slot: C1 + TC1
Name of faculty: Prof. NARENDIRANATH BABU T
(SCHOOL OF MECHANICAL ENGINEERING)
October, 2019

2. VIT UNIVERSITY, VELLORE
DEPARTMENT OF MECHANICAL ENGINEERING
CERTIFICATE
This is to certify that the project entitled “Topology Optimization of
Gears” is submitted by Adarsh Agarwal and Anurag Purbey bearing
reg. no. 16BME0086 and 16BME0701 in partial fulfillment of the
requirement of the J-component for the course “MEE4007 - Design of
Transmission Systems” for academic year 2019-20.
Adarsh Anurag Prof. Narendiranath
Place: Vellore
Date: 23/10/2019

3. ACKNOWLEDGEMENTS
I would like to thank everyone who played a role in our project component
accomplishments. First of all, our parents who supported us with their love and
their understanding.
Also, I would like to express my sincere gratitude to our course faculty Prof.
Narendiranath Babu T for providing his invaluable guidance, comments and
suggestions throughout the courseof the project.
I would specially thank lab assistants for constantly motivating us to work
harder and Ravi Sir for getting us the samples.

4. INDEX
SL. NO. TOPIC PAGE NO.
1 Abstract 5
2 Introduction 6
3 Literature Review 7
4 Project 8
a. Methodology Implementation 9
b. Components and Specifications 10
c. Model 10-11
d. Analysis 12-13
5 Results 14
6 Conclusion 15
7 References 14

5. ABSTRACT
The purpose of this experiment was to determine which type of design is the
optimal one among various structures.
The topology optimization of the gears will facilitate lesser material use. It is more
of a project based on the design factors which will reduce the scrap. The stress
induced areas on the gears are found by running simulation. The used software is
set to standards for keeping intact to the norms followed by the industries. The
different gear tooth profiles are studied and all the materials suitable for such gear
designs. The different results of models is snapped and put up in this report for
acceptance. The various factors which play a role are also discussed so as to avoid
such reluctance in future product development.
The result comprises the optimized and not optimized static structural analysis of
the materials – Aluminum, Stainless steel and Carbon fiber. The color variations
from less to more stress prone area help us figure out which all material to remove.
This project also shows the result variation in 3 different types of materials but one
major disadvantage is computational time since topology optimization works on
repetitive iterations it requires a powerful system to run it for a finer mesh since our
system was not powerful enough the results may vary if this same experiment is
performed in a high performance computer with a finer mesh.

6. INTRODUCTION
Gears are the most commonly used positive drive transmission systems. It will be a project
based on optimization methods for different types of gears like bevel and helical. The
different components which do not bear much load while the gear is working can be
secluded. We are looking forward to avoid the overdesigning via mathematical approach
A gear or “gear wheel” is a rotating machine part having cut teeth, or cogs, which mesh with
another toothed part in order to transmit power. Two or more gears working in tandem are
called a transmission and it produces mechanical advantages through a gear ratio and thus
may be considered a simple machine. Gears are mostly used in the mechanical field for
power transmission.
A gear is different from a pulley in that a gear is a round wheel. Mesh with other gear teeth,
allowing force to be fully transferred without slippage. Depending on their construction and
arrangement, geared devices can transmit forces at different speeds, torques, or in a different
direction, from the power source. Gears are a very useful simple machine. The most common
situation is for a gear to mesh with another gear, but a gear can mesh with any device having
compatible teeth, such as linear moving racks.
Gears can be classified by shape as involute, cycloidal and trochoidal gears. Also, they can be
classified by shaft positions as parallel shaft gears, intersecting shaft gears, and non-parallel
and non-intersecting shaft gears. The history of gears is old and the use of gears already
appears in ancient Greece in B.C. in the writing of Archimedes.
Spur gears are the simplest and most common type of gear. Their general form is a cylinder
or disk. The teeth projects radially and with these straight-cut gears, the leading edges of the
teeth are aligned parallel to the axis of rotation. These gears can only mesh correctly if they
are fitted to parallel axles. The torque ratio can be determined by considering the force that a
tooth of one gear exerts on a tooth of the other gear.
Optimization is a mathematical approach. The papers focused on the ideas related to topology
optimization i.e. modifying the design and weights of gears. Followed by the results of
various analyses it was shown to be feasible. The software used and various 3d models were
also studied to accumulate them in our project.
Structure optimization methods are basically classified into three categories: sizing
optimization, shape optimization and topology optimization. Sizing optimization is a classical
method and easy to conduct by choosing cross-sectional dimensions of trusses, beams and
frames, or the thicknesses of membranes, plates and shells as design variables. Sizing
optimization can be regarded as a detailed design procedure of the structural model involving
a large number of design variables. It has been developed maturely and is becoming the most
popular method in engineering community.
In all the cases the problem is to determine the position of the tooth’s weakest or critical
section. In reality, two methods are actually used for the determination of the critical section
at the fillet and to calculate the nominal stress. One is based on Lewis’ formula and another
on AGMA standard.

7. LITERATURE REVIEW
Topology Optimization in Engineering Structure Design explores the recent advances and
applications of topology optimization in engineering structures design, with a particular focus
on aircraft and aerospace structural systems.
PINAKNATH PEWANJI., This paper analyses the bending stresses characteristics of an
involute spur gear tooth under static load condition s. The tooth profile is generated using
catia and analysis is carried out by ANSYS software. The stresses on the tooth root are
evaluated analytically using existing theoretical models.
ANUJ NATH ET., This paper modeled the spur gear using pro-e software. The impact
analyses for cast steel and composite materials are studied. Finally comparing and analyzing
the composite gears with existing cast steel gear is to be done using ANSYS 13.0.
To meet the increasingly complex engineering challenges provided by rapid developments in
these industries, structural optimization techniques have developed in conjunction with them
over the past two decades. The latest methods and theories to improve mechanical
performances and save structural weight under static, dynamic and thermal loads are
summarized and explained in detail here, in addition to potential applications of topology
optimization techniques such as shape preserving design, smart structure design and additive
manufacturing.
S.MAGENDRAN, K.M.EAZHIL., This paper modeled the spur gear using solid works
software. The weight reduction and stress distribution for cast steel and composite materials
are studied. Finally compare and analyzing the spur gear using ANSYS software.
DEVENDRA SINGH ., In this paper modeled the spur gear and study about gear drive
design and analysis is carried out with the help of pro-e and ANSYS and improve the static
and dynamic characteristics of gear drive.
It should be mentioned that alternating solid and void elements over the design domain often
occurs in topology optimization. This phenomenon behaves in a checkerboard fashion and is
mesh dependent. According to Jog and Haber, it was due to the finite element approximation
or design optimization criteria. From this viewpoint, Rodrigues and Fernandes improved the
interpolation accuracy by means of high-order elements in thermoelastic optimization
problems. However, the computing cost increases dramatically together with the number of
degrees of freedom of the structural system. Later, Sigmund and Petersson developed the
filtering scheme to smooth the sensitivities of the objective functions over the considered
element and its eight neighbors based on image filtering techniques. However, this sensitivity
filter is not appropriate for the searching strategies because the modified sensitivities do not
completely correspond to the objective function and may lead to some divergence problems.
As a result, further developments are being made on the density filter by Bruns and Tortorelli
and Bourdin. The modifications are directly implemented on the updated design variables.

8. PROBLEM DESCRIPTION
The weight of different components of the gear and the design of gear is to be studied. The
different components in gear which doesn’t bear much load while the gear is working can be
secluded. The forces on the different parts of gears are analyzed to find where no impact of
load is developed. The structural analysis will be done with loads on various points on the
gears to find the least deformation.
In recent decades, structural optimization methods have gained great progress with the
increasing performances of computers and computing algorithms. Solutions of practical and
complicated optimization problems undergoing complex loading conditions are made
possible to satisfy severe multidisciplinary design performances. Among others, topology
optimization has become one of the most promising techniques.
The main purpose of gear mechanisms is to transmit rotation and torque between axes. The
gear wheel is a machine element that has intrigued many engineers because of numerous
technological problems arises in a complete mesh cycle. In order to achieve the need for high
load carrying capacity with reduced weight of gear drives but with increased strength in gear
transmission, design, gear tooth stress analysis, tooth modifications and optimum design of
gear drives are becoming major research area. Gears with involute teeth have widely been
used in industry because of the low cost of manufacturing.
METHODOLOGY - SOLUTION APPROACH
CAD model for the gears will be created using Solid works 2016
Later the model will be analyzed using the topology optimization feature of ANSYS 16.0
The efficiency will be calculated so as to make it feasible in real-time as in prototype
Calculation of various forces and optimization results will be done
The idea will be supported by a simulation model. We chose material like steel, cast iron and
carbon fiber to put forth our results
Analytical calculations –
The formulae were derived using various research papers and the values were checked
corresponding to another paper but the answers did not match
Solidworks model to figure out the structure of gear profile for spur gear and the various
sections to be checked for stresses
Gear parameters were determined using data book and the optimized conditions such as:
Pitch circle diameter; Module; Clearance; Torque; Boundary constraints are provided
COMPONENTS AND SOFTWARE REQUIRED
 Solid works 2018
 ANSYS 18.0

9. SOLIDWORKS MODEL
Material
Aluminum
Steel
Carbon fiber
RESULTS
MATERIAL STRESS
1
(x10^7)
STRESS
2
(x10^7)
%
CHANGE
DEFLECTION
1 (x10^-6)
DEFLECTION
2 (x10^-6)
%
CHANGE
MASS
1
MASS
1
%
CHANGE
STEEL 2.75 2.77 0.73 4.16 4.52 8.6
ALUMINIUM 2.75 2.81 2.18 11.9 12.1 1.6
CARBON FB 6.72 6.92 3.24 69.9 73.05 4.5

10. Optimized for steel Result from ANSYS steel
Not Optimized Deformation for steel Not Optimized Stress for steel
Optimized Stress for steel Optimized Deformation for steel

11. Not Optimized Deformation for Aluminum Not Optimized Stress for Aluminum
Ansys optimized refineddesign
‘
Optimized Stress for aluminium Optimized Deformation for aluminium

12. OptimizedStressfor aluminium OptimizedStress for aluminium Optimized Stress for aluminium
Optimized Stress for aluminium Optimized Stress for aluminium
CONCLUSION
The results and discussions help us conclude that the spur gear has certain sections
which are subject to less stress and the material there can be optimized to obtain
modified design. The results identified and presented via the different analyses models
present the topology optimization for spur gears. Also, from the results we can see that
the total change in stress is around 3-4% on average for the materials and 3-4% for
deflection also. The average change in mass is _____ %. From these results it has
many advantages and disadvantages, the advantage is that it can give us an
approximate idea for how to change the gear design. This project also shows the result
variation in 3 different types of materials but one major disadvantage is computational
time since topology optimization works on repetitive iterations it requires a powerful
system to run it for a finer mesh since our system was not powerful enough the results
may vary if this same experiment is performed in a high performance computer with a
finer mesh.

13. REFERENCES
1. B.Sivakumar1, I. Joe michael2 – “Design And Stress Analysis Of Spur
Gear”, May 2018
2. Jihong Zhu Tong Gao – “TopologyOptimization in Engineering
Structure Design”, October2016
3. TheodoreCostopoulos, V. Spitas – “Analytical Mechanics of Spur
Gears”, June 1995
4. Hock, Willi, and Klaus Schittkowski – “Journal of Optimization Theory
and Applications”, January 1980
5. Ahmed Kadhim Zarzoor, Nabeel Almuramady – “Stress Analysis for
Spur Gears Using Solid Works Simulation”, November 2018