DESIGN, ANALYSIS AND OPTIMIZATION OF
HELICAL GEAR TO IMPROVE LIFE BY VARYING
DIFFERENT DESIGN PARAMETER USING ANSYS
WORKBENCH 15.0
A PROJECT REPORT
Submitted By
SHAH SMIT YOGESHKUMAR
En no.160350708007
GUIDED BY
An IDP SUBMITTED TO
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GUJARATTECHNOLOGICAL UNIVERSITY, AHMEDABAD
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This is to certify that User Defined Problem/Project work embodied in this report entitled
“DESIGN, ANALYSIS AND OPTIMIZATION OF HELICAL GEAR TO IMPROVE
LIFE
BY
VARYING
DIFFERENT
DESIGN
PARAMETER
USING
ANSYS
WORKBENCH 15.0.”was carried out by your name 1. At for partial fulfilment of Master of
Engineering degree to be awarded by Gujarat Technological University. This research work has
been carried out under my supervision and is to my satisfaction.
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thanks to all StaffMembers of Organization for their support, guidance and advice.
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ABSTRACT
Gears are one of the most critical components in mechanical power transmission systems. The
bending and surface strength of the gear tooth are considered to be one of the main
contributors for the failure of the gear in a gear set. Thus, analysis of stresses has become
popular as an area of research on gears to minimize or to reduce the failures and for optimal
design of gears. This project investigates finite element model for monitoring the stresses
induced of tooth flank, tooth fillet during meshing of gears. The involute profile of helical gear
has been modeled and the simulation is carried out for the bending and contact stresses and the
same have been estimated. To estimate bending and contact stresses, 3D models are generated
by modeling software creo parametric3.0 and simulation will done by finite element software
package ANSYS 15.0. Analytical method of calculating gear bending stresses uses Lewis and
AGMA bending equation. For contact stresses Hertz and AGMA contact equation are used.
Study will conducted by varying the face width to find its effect on the bending stress of
helical gear. The stresses found from ANSYS results are compared with those from theoretical
and AGMA values.
TABLE OF CONTENT
Title
Page
No
I
Title Page
College Certificate
II
Industry Certificate
V
Acknowledgement Verify The Page No.
VI
Abstract
VII
Table of Content
VIII
List of Figures
X
List of Table
X
Chapter 1
1.1
1.1.1
Chapter 2
1
Introduction
Introduction of area
1
Problem definition
2
Literature Review
2.1
pg
2.2
2.3
Chapter 3
CONCEPTS & WORKDONE
3.1
Modelling
3.2
Methodology
pg
pg
Work Plan
Conclusion
References
LIST OF FIGURES
Figure
no.
Figure Name
Page
no.
pg
INTRODUCTIONChapter-1
1.1 Introduction of area
One of the best methods of transmitting power between the shafts is gears. Gears are mostly
used to transmit torque and angular velocity. The rapid development of industries such as
vehicle, shipbuilding and aircraft require advanced application of gear technology. Under
contact conditions,
gear
teeth
are
subjected
to
Hertzian contact
stresses
and
elastohydrodynamic lubrication. Excessive loading and lubrication breakdown can cause
combinations of abrasion, pitting and scoring. In the case of helical gear, the resultant load
between mating teeth is always perpendicular to the tooth surface. Hence bending stresses are
computed in the normal plane, and the strength of the tooth as a cantilever beam depends on
its profile in the normal plane. Designing highly loaded
helical
gears
for power
transmission systems that are good in strength and low level in noise necessitate suitable
analysis methods that can easily be put into practice and also give useful information on
contact and bending stresses. Gears are used to change the speed, magnitude, and direction
of a power source. Gears are being most widely used as the mechanical elements of
power transmission.
When two gears with unequal numbers of teeth are combined, a productive output is
realized with both the angular speeds and the torques of the two gears differing through a
simple relationship. AGMA and ISO standards generally are being used as the strength
standard for the design of spur, helical, and worm gears. The strength determined from the
AGMA and ISO standards is valid under the assumption that the load is uniformly
distribute along the line of contact. In actuality, the load per unit length varies with the point
of contact. The finite element method is proficient to supply this information but the time
required to generate proper model is large amount.
Gear analysis can be performed using analytical methods which required a number
of assumption and simplifications which aim at getting the maximum stress values only but
gear analyses are
multidisciplinary including calculations related to the tooth stresses. In this work, an
attempt will been
made to analyse bending stress to resist bending of helical gears, as both affect transmission
error. Due to the progress of computer technology many researchers tended to use
numerical Methods to develop theoretical models to calculate the effect of whatever is
studied. Numerical methods are capable of providing more truthful solution since they
require very less restrictive assumptions. However, the developed model and its
solution method must be selected attentively to ensure that the results are more acceptable
and its computational time is reasonable. The dimension of the model have been arrived at by
theoretical methods. The stress generated of the tooth have been analysed for materials.
Finally the results obtained by theoretical analysis, AGMA calculations and finite element
analysis are compared to check the corrections.
Therefore, Finite element analysis which can involve complicated tooth geometry,
is now a popular and powerful analysis tool to determine tooth deflections and stress
distributions. Many
researchers have applied FEA to tooth deflection and stress
distribution for various gear drives. Several researchers have analysed line-contact involute
helical gears using three-dimensional Finite
element stress
analysis. However, these
researchers applied loads directly to the contact ellipses and contact lines obtained from tooth
contact analysis. FE contact analysis for deformable bodies is complex and non-linea
1.2 Problem Definition
Gears are one of the most critical components in mechanical power transmission systems.
The bending and surface strength of the gear tooth are considered to be one of the main
contributors for the failure of the gear in a gear set. Thus, analysis of stresses has become
popular as an area of research on gears to minimize or to reduce the failures and for optimal
design of gears. This project investigates finite element model for monitoring the stresses
induced of tooth flank, tooth fillet during meshing of gears. The involute profile of helical
gear has been modelled and the simulation is carried out for the bending and contact stresses
and the same have been estimated. To estimate bending and contact stresses, 3D models are
generated by modelling software creo parametric3.0 and simulation will done by finite
element software package ANSYS 15.0.
LITERATURE REVIEWChapter-2
 The research papers published in many aspects as follow:
2.1Finite Element Analysis of Helical Gear Using Three-Dimensional Cad
Model.[1]
BabitaVishwakarma*1, Upendra Kumar Joshi2
Parametric modeling allows the designengineer to let the characteristic parameters of
aproduct drive the design of that product. During thegear design, the main parameters that
would describethe designed gear such as module, pressure angle,and root radius, and tooth
thickness, number of teethcould be used as the parameters to define the gear. In this paper
work, module, pressure angle,numbers of teeth of both the gears are taken as
inputparameters. CATIA V5 uses these parameters, incombination with its features to
generate thegeometry of the helical gear and all essentialinformation to create the model. By
using therelational equation in CATIA V5, the accurate threedimensional helical gear models
are developed. CADsoftware packages allow for modeling and simulationof 3D parametric
modeling of helical gear. It also agood interface with Finite Element software. CATIAhas
model the involute profile helical gear geometryperfectly. For helical gear in CATIA, relation
andequation modeling is used. Relation is used toexpress dependencies among the dimension
neededfor defining the basic parameters on which the modelis depends. The assembly of gear
is done by considerthe left hand Helical gear and right hand helicalpinion. Then the file is
saved as IGES format.
It is observed that The strength of helical gear tooth is a crucialparameter to prevent failure.
In this work, itis shown that the effective method toestimate the root bending stress using
threedimensional model of a helical gear and toverify the accuracy of this method theresults
with different face width of teeth arecompared with theoretical and AGMAformulas.
In helical gear the engagement betweendriver gear and driven gear teeth beginswith point
contact and gradually extendsalong the tooth surface. Due to initial point contact in helical
gear the bending stressesproduced at critical section (root of tooth)are maximum as compared
to spur gear,which has kinematic line contact. The face width is an important geometrical
parameterin design of helical gear as it is expected in this workthe maximum bending stress
decreases withincreasing face width.
-
CONCEPTS& WORKDONEChapter-3
3.1 Initial Concepts
Bending Stress - Lewis Formula
Bending failure and pitting of the teeth are the two main failure modes in a transmission
gearbox. The bending stresses in a helical gear are another interesting problem. When loads
are too large, bending failure will occur. Bending failure in gears is predicted by comparing
the calculated bending stress to experimentally-determined allowable fatigue values for the
given material. This bending stress Equation (1) was derived from the Lewis formula.
Bending Stress is given by,
Y is called the Lewis form factor. The Lewis equation considers only static loading and does
not take the dynamics of meshing teeth. The maximum stress is expected at the point which is
a tangential point where the parabola curve is tangent to the curve of the tooth root fillet
called parabola tangential method. Two points can be found at each side of the tooth root
fillet. The stress on the area connecting those two points is thought to be the worst case.
Lewis equation is derived from the basic beam bending stress equation It treats the gear tooth
using a factor called “Lewis from factor,”Y”. It also includes a correction for dynamic effects
“KV”(due to rotation of the gear).Lewis equation forms the basis of the AGMA bending
stress equation used nowadays.
Where Wt = Tangential load
F = Face Width
AGMA Bending Stress Equation
Above stress formula must be modified to account different situations like stress
concentration and geometry of the tooth. Therefore, Equation as shown as below is the
modified Lewis equation recommended by AGMA for practical gear design to account for
variety of conditions that can be encountered in service. The AGMA equation for bending
stresses given by,
This analysis considered only the component of the tangential force acting on the
tooth and doesn’t considered the effects of the radial force, which will cause in compressive
stress over the cross-section on the root of the tooth.
Hertz Contact Stress
One of the main gear tooth failure is pitting which is a surface fatigue failure due to repetition
of high contact stresses occurring in the gear tooth surface while a pair of teethes transmitting
power. Contact failure in gears is currently predicted by comparing the calculated Hertz
contact stress to experimentally determined allowable values for the given material. The
method of calculating gear contact stress by Hertz’s Equation originally derived for contact
between two cylinders. In machine design, problems frequently
occurs when two members with curved surfaces are deformed when pressed against one
another giving rise to an area of contact under compressive stresses. Of particular interest to
the gear designer is the case where the curved surfaces are of cylindrical shape because they
closely resemble gear tooth surfaces. The surface compressive stress (Hertzian stress) is
found from the equation,
Where, where r1 and r2 are the instantaneous values of the radii of curvature on the pinionand gear-tooth profiles, respectively, at the point of contact.
AGMA Contact Stress Equations
Where, an elastic coefficient
Cp = 190.3 (MPa) for steel (Bhandari, 2012)
V is the pitch line velocity or the velocity of rotation. Ko is the overload factor which reflects
the degree of non-uniformity of driving and load torques. Km is the load distribution factor
which accounts for non- uniform spread of the load across the face width. It depends on the
accuracy of mounting, bearings, shaft deflection and accuracy of gears. Thus, using the above
theory contact stress will be calculated and be used to verify the FEA results.
The Hertz equations discussed so far can be utilized to calculate the contact stresses
which prevail in case of tooth surfaces of two mating helical gears. Though an
approximation, the contact aspects of such gears can be taken to be equivalent to those of
cylinders having the same radii of curvature at the contact point as the load transmitting gears
have. Radius of curvature changes continuously in case of an involutes curve, and it changes
sharply in the vicinity of the base circle.
Table 1 : Dimensions of Helical Gear
Sr. No.
Parameters
1.
Number of teeth
2.
Pressure angle,
normal
3.
Helix angle
4.
Face width (mm)
5.
Normal module
(mm)
6.
Material
7.
Input speed (rpm)
(A)
8.
Input power (KW)
(A)
9.
Input speed (rpm)
(B)
10.
Input power (KW)
(B)
11.
Diameter of pitch
circle (mm)
12.
Diameter of base
circle (mm)
13.
Diameter of
Addendum circle
(mm)
14.
Diameter of
Dedendum circle
(mm)
15.
Circular Pitch
(mm)
16.
Young’s modulus
(MPa)
17.
Poisson’s ratio
18.
Torque (N-m)
Pinion
18
200
150(RH)
40
4
Gear
36
150(LH)
Grade 1 Steel
720
Grade 1 Steel
…………..
5
…………..
1500
…………..
35
…………..
72
144
67.4
135.2
80
152
62.8
134
12.56
2.1x105
0.3
594
3.2Methodology
Here first of all we have made a model in modelling software Creo 3.0 and after that we are
going to analyse it in Ansys 15.0 with respect to different loads to fatigue life.
(Fig 3.1 :stp file imported in Ansys 15.0)
After getting model in Ansys we are going to analyse it with respect to various design
concideration of helical gear.
Unit System
Metric (mm, kg, N, s, mV, mA) Degrees rad/s Celsius
Angle
Degrees
Rotational Velocity
rad/s
Temperature
Celsius
Model (D4) > Geometry
Object Name
Geometry
State
Fully Defined
Definition
Type
Iges
Length Unit
Meters
Element Control
Program Controlled
Display Style
Body Color
Bounding Box
Length X
40. mm
Length Y
157.08 mm
Length Z
236.56 mm
Properties
Volume
8.4102e+005 mm³
Mass
6.602 kg
Scale Factor Value
1.
Statistics
Bodies
2
Active Bodies
2
Nodes
62525
Elements
18951
Mesh Metric
None
Basic Geometry Options
Solid Bodies
Yes
Surface Bodies
Yes
Line Bodies
No
Parameters
Yes
Parameter Key
DS
Attributes
No
Named Selections
No
Material Properties
No
Advanced Geometry Options
Use Associativity
Yes
Coordinate Systems
No
Reader Mode Saves Updated File
No
Use Instances
Yes
Smart CAD Update
No
Compare Parts On Update
No
Attach File Via Temp File
Yes
Analysis Type
3-D
Mixed Import Resolution
None
Decompose Disjoint Geometry
Yes
Enclosure and Symmetry Processing
Yes
(Fig 3.2 :Model (C4) > Mesh )
Model (C4) > Mesh
Object Name
Mesh
State
Solved
Defaults
Physics Preference
Mechanical
Relevance
0
Sizing
Use Advanced Size Function
Off
Relevance Center
Coarse
Element Size
Default
Initial Size Seed
Active Assembly
Smoothing
Medium
Transition
Fast
Span Angle Center
Coarse
Minimum Edge Length
1.28460 mm
Inflation
Use Automatic Inflation
None
Inflation Option
Smooth Transition
Transition Ratio
0.272
Maximum Layers
5
Growth Rate
1.2
Inflation Algorithm
Pre
View Advanced Options
No
(Fig 3.3 :Model > Applicable Force)
(Fig 3.4 :Model > Force Characteristics)
Model (C4) > Static Structural (C5) > Solution (C6) > Results
Object Name
Maximum Principal Stress Total Deformation
State
Solved
Scope
Scoping Method
Geometry Selection
Geometry
All Bodies
Definition
Type
Maximum Principal Stress Total Deformation
By
Time
Display Time
Last
Calculate Time History
Yes
Identifier
Suppressed
No
Integration Point Results
Display Option
Averaged
Average Across Bodies
No
Results
Minimum
-2.9721 MPa
0. mm
Maximum
22.33 MPa
2.0531e-003 mm
Minimum Value Over Time
Minimum
-2.9721 MPa
0. mm
Maximum
-2.9721 MPa
0. mm
Maximum Value Over Time
Minimum
22.33 MPa
2.0531e-003 mm
Maximum
22.33 MPa
2.0531e-003 mm
Information
Time
1. s
Load Step
1
Substep
1
Iteration Number
1
Analysis For Bending Stress
(Fig 3.5 :Model >Model (C4) > Static Structural (C5) > Solution (C6) > Total Deformation )
(Fig 3.5 :Model (C4) > Static Structural (C5) > Solution (C6) > Total Deformation)
Analysis For Contact Stress
(Fig 3.6 :Assambly Of helicasl gear in Ansys 15.0))
(Fig 3.7 :Meshing in Two Contacting Gear)
(Fig 3.8 :Model (D4) > Static Structural (D5)
Model (C4) > Static Structural (C5) > Solution (C6) > Results
Object Name
Maximum Principal Stress Total Deformation
State
Solved
Scope
Scoping Method
Geometry Selection
Geometry
All Bodies
Definition
Type
Maximum Principal Stress Total Deformation
By
Time
Display Time
Last
Calculate Time History
Yes
Identifier
Suppressed
No
Integration Point Results
Display Option
Averaged
Average Across Bodies
No
Results
Minimum
-2.9721 MPa
0. mm
Maximum
22.33 MPa
2.0531e-003 mm
Minimum Value Over Time
Minimum
-2.9721 MPa
0. mm
Maximum
-2.9721 MPa
0. mm
Maximum Value Over Time
Minimum
22.33 MPa
2.0531e-003 mm
Maximum
22.33 MPa
2.0531e-003 mm
Information
Time
1. s
Load Step
1
Substep
1
Iteration Number
1
(Fig 3.9 :Model (D4) > Static Structural (D5) > Solution (D6) > Equivalent Stress)
(Fig 3.10 :Model (D4) > Static Structural (D5) > Solution (D6) > Total Deformation)
Material Data
Density
7.85e-006 kg mm^-3
Coefficient of Thermal Expansion
1.2e-005 C^-1
Specific Heat
4.34e+005 mJ kg^-1 C^-1
Thermal Conductivity
6.05e-002 W mm^-1 C^-1
Resistivity
1.7e-004 ohm mm
Structural Steel > Alternating Stress Mean Stress
Alternating Stress MPa Cycles Mean Stress MPa
3999
10
0
2827
20
0
1896
50
0
1413
100
0
1069
200
0
441
2000
0
262
10000
0
214
20000
0
138
1.e+005
0
114
2.e+005
0
86.2
1.e+006
0
Compressive Yield Strength MPa
Tensile Yield Strength MPa
Tensile Ultimate Strength MPa
250
250
460
Structural Steel > Strain-Life Parameters
Strength
Coefficient
MPa
Strength
Exponent
Ductility
Coefficient
Ductility
Exponent
Cyclic Strength
Coefficient MPa
Cyclic Strain
Hardening
Exponent
920
-0.106
0.213
-0.47
1000
0.2
Relative Consideration And Calculations
(All the calculations are done manually as per the given eqations)
Comparison of Root Bending Stresses
Face Width
(b)
(mm)
Root Bending Stresses (MPa)
LEWIS
AGMA
ANSYS
40
20.86
29.40
22.33
Contact Stresses
Face
Width (b)
(mm)
Helix
Angle
Load(N)
Hertz
contact
stress
AGMA
contact
stress
FEA by
Ansys
15.0
40
150
850
1416.56
1309.70
1362.4
Work Plan
Conclusion
As per the given data of face width 40mm and helix angle 15o, currently we have the analysis
of the pair of helical gear which is generated in the modeling software Creo 3.0. After this
stage we are going to change the design for optimum result and we will try to increase the life
span in consideration of various design parameter.
Future Work
In the next semester we will go for changing the helix angle with appropriate face width also
using change in appropriate material as aluminum alloys. We will try to get optimum result
for design by reducing weight with increasing life of the helical gear.
References
1. Bhandari V B (2012), Design of Machine Elements, 2nd Edition, Tata McGraw Hill
Publishing Compan Limited.
2. “Design Data Book”, Central Techno Publications, Nagpur, India.
3. NegashAlemu (2009), “Analysis of Stresses in Helical Gears by Finite Element
Method”, pp. 1-55.
4. Venkatesh B, Kamala V and Prasad A MK (2011), “Parametric Approach to Analysis
of Aluminium Alloy Helical Gear for High Speed Marine Application”, pp. 173-178.s
5. Moorthy V., B.A. Shaw Contact fatigue performance of helical gears with surface
coatings Wear 276– 277 (2012) 130– 14.
6. AGMA standards, http://www.agma.org/.
7. ISO gear standards, http://www.iso.org/.
8. J.I. Pedrero, M. Pleguezuelos, M. Munoz, Critical stress and load conditions for
pitting calculations of involute spur and helical gear teeth, Mechanism and Machine
Theory 46 (2011) 425–437.
9. F.L. Litvin, Gear Geometry and Applied Theory, Prentice-Hall, U.S.A., New Jersey,
1994.
10. M.A.S. Arikan, M. Tamar, Tooth contact and 3-D stress analysis of involute helical
gears, ASME, International Power Transmission and Gearing Conference, De-Vol.
43, No. 2, 1992, pp. 461–468.
11. E. Buckingham, Analytical Mechanics of Gears, Dover, U.S.A., New York, 1949.
12. D.W. Dudley, Dudley’s Gear Handbook, 2nd Edition, McGraw-Hill, U.S.A., New
York, 1992.
13. R.F. Handschuh, G.D. Bibel, Experimental and analytical study of aerospace spiral
bevel gear tooth _llet stresses, ASME J. Mech. Des. 121 (1999) 565–572.
14. R.D. Cook, D.S. Malkus, M.E. Plesha, Concepts and Applications of Finite Element
Analysis, 3rd Edition, Wiley, U.S.A., New York, 1989.
15. Peter R.N. Childs, Mechanical Design, Second edition, Elsevier Butterworth
Heinemaan, 2004
16. Shigley, J.E., and Mischke, C.R., Standard Handbook of Machine Design, Mc-Graw
Hill, USA, 1996.