8

Effect of Tooth Profile Modification In Asymmetric Spur Gear Tooth on

vibration Analysis with FEM

Wasan ibraheem mansoor

Misan University/college of Edecation/math Dep.

Abstract :-

The current research presents a theoretical study for the effect of the form of

the edge side or what is known as (profile) of spur gear on the response of

vibration .in order to achieve this goal,a study is mad for two different models

first model (I) with (straight edge) and second (II) (curved profile)for model was

constructed for each of the three-dimensional models using the application of

ANSYS v11.0, and element (solid 45). The finite element method( FEM) was

used to analyze the theoretical part with the same amount of load had been

applied at the same locations (nodes) for both models. The results shown an

increase in the values of the first five responses of the first model than in the

second model and therefore less vibration and noise in the second model. The use

of technology specific elements gives high-quality results for the adoption of best

designs, reducing and reduces the time and effort and economic costs of these

minute parts in machines and structures.

تأثير تعديل شكل منحني السن ترس من النوع المهماز على تحليل

االهتزاز باستخدام طريقة العناصر المحددة

م.وسن إبراهيم منصور

لتربية األساسية/ قسم الرياضياتجامعة ميسان / كلية ا

-الخالصة:

( لتار profileيقدم البحث الحالي دراسة نظرية عن تأثير شكل حافة السن الجانبية او ماا يعارب با

( على استجابة االهتزاز ضامن األواوار الترددياة ال ماو األولىحولتحقيا spur gearمن النوع المستقيم

straight( بجاناام مسااتو Iلساان بجااانبين م تلاااين النمااو األو هاا ا الفاادب تاام دراسااة نمااو جين

profile والثاني )II بجانام منحناي )carved profile تام بناان نماو ث ثاي األبعااد لكا النماو جين )

FEM( . اسات دم وريقاة العنا ار المحادد solid 45ح وبعنصر ANSYS v11.0باست دام تطبي

لجانم النظر حوتم تسليط ناو مقدار الحمل عند ناو المواقا العقاد(. هرفارت النتاا الحتضان وتحليل ا

تزايد في قيم االستجابة لل مو ترددات األولى للنمو األو عنفا في النمو الثاني وبالتالي قيم االهتزاز

عالياة الجاود العتمااد والضوضان في النمو الثاني اقل . ان است دام تقنية العنا ر المحدد يعطاي نتاا

9

التصاميم األفضل مما ي تصر ويقلل في الجفد والوق والكلف االقتصادية لف ه األجزان الدقيقة فاي المكاا ن

والتراكيم .

1-1 Introduction :-

A Gear is a rotating machine part having cut teeth, or cogs , which mesh with

another toothed part in order to transmit torque . Two or more gears working in

tandem are called a transmission and can produce a mechanical advantage

through a gear ratio and thus may be considered a simple machine(1)

.

1.1.1 Spur gears:- which known also as straight - cut gears are one of

type of gear. They consist of a cylinder or disk and with the teeth projecting

radially as shown in fig (1-1)(2)

, and although they are not in form, thus the edge

of each tooth is straight and aligned parallel to the axis of rotation . These gears

can be meshed. Together correctly only if the ate fitted to parallel axis(3),(4),(5),(6)

.

1 Gears, Wikipedia, the free encyclopedia,7/9/2010, pag(1),http//en.Wikipedia.org/Wiki/Gear.

2 Gears, Wikipedia, the free encyclopedia,same refrence.

3 R.S.Khurmi & J.K.Gupta;'Theory of Machines',S.chand TECHNICAL,PUBLISHING,First

Multicolour Revised &updated edition ,2010,cha.12 ,pag(384).

4 R.S.Khurmi & J.K.Gupta; 'A Text book of Machine Design', S.chand ,RAMNAGAR, New Delhi-110

055,2010,chap.28,pag.(1203).

5 Joseph Edward Shigly & John Joseph Ulcker,JR;'Theory of Machines and Mechanisms', 2

nd

edition,McGraw-Hill,Inc,1995,chap.6, pag.(250-251)

6Budynas-Nisbett:Shigley

,s; "Mechanical Engineering Design", McGraw-Hill companies,2008 8

th

edition, chap.13,pag.(653-666).

Fig. (1-1) Spure gear and the terms used

with(1)

10

1.1.2 Vibration:-is one of the pre-dominate factors for the failures in rotating

machineries, especially, in the spur gear power transmission system ,for a heavy

load transmission, vibration is one of the important parameter to be maintained

within the limit of control ,a vibration in spur gear happens due to several reasons

such as errors (i.e,composite errors which includes static and dynamic

transmission error)(1)

. The prime source of vibration and noise in a gear system is

the transmission error between meshing gears. Transmission error is a term used

to describe or is defined as the differences between the theoretical and actual

positions between a pinion (driving gear) and a driven gear. It has been

recognized as a main source for mesh frequency excited noise and vibration. With

prior knowledge of the operating conditions of the gear set it is possible to design

the gears such that the vibration and noise is minimized(2)

1.1.3 Tooth Profile:-

A profile is one side of the tooth in a cross section between the addandum

circle and the root circle, usually a profile is the curve of intersection of the tooth

surface and a plane or surface normal to the pitch surface , such as the transverse ,

normal , or axial plane as shown in fig (1-2)(3),(4

).

1 Ramesh Babu.S. & Dr.Srinivasan K.;" Analysis of Influence of Tooth Depath in Spur Gear Vibration

" , International Journal of Scientific &Engineering Research ,vol.3,ISSUe 3,March 2012,http://

www.ijser.org.pag.1. 2 Zeping Wei;"STRESSES AND DEFORMATIONS IN INVOLUTE SPUR GEARS BY FINITE

ELEMENT METHOD ",A Thesis Submitted to the College of Graduate Studies and Research in Partial

Fulfillment of the Requirements for the Degree of Master of Science in the Department of Mechanical

Engineering,University of Saskatchewan,© Copyright Zeping Wei, October, 2004. All rights reserved."

3 Vishwjeet V. Ambade, Prof. Dr. A.V.Vanalkar, Prof. P. R. Gajbhiye;' FEM Analysis Of Spur Gear

Tooth ', International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622

www.ijera.com Vol. 3, Issue 4, Jul-Aug 2013, pp.2210-2216 2210.

4 G.mallesh,VB .Math,A.Shwij,Sai Dull and Rajendra Shanbhag;'Effect of tooth profile modification in

asymmetric spure Gear tooth Bending Stress by finit element

analysis',(NaCoMMo9),NIT,Durgapur,India,December 17-18,pag.63,2009.

11

Fig (1-2) the tooth profile(9),(10)

So ,in actual practice there are two type of teeth commonly used:-

1) Cycloidal teeth.

2) Inveloute teeth .

The standard gear profile in an involute that keeps the meshing gears in contact

as the gear teeth are revolved(1)

.In this paper the concerned with Involute one

which is a plane curve generated by a point on a tangent and had been compared

with another one which had sort of straight profile ,which rolls on the circle

without slipping or by a point on the taut string which in unwrapped from a

reed(2)

.

Using the present method ANSYS can solve three-dimensional and an

asymmetric model were built. First, parameter definitions were given and then

many points of the involute profile of gear were calculated to plot an involute

profile using a cylindrical system. The equations of an involute curve below were

taken from Zeping(3)

.

= radius of the base circle Where r=radius to the involute form ,

=vertorial angle at the pitch circle

= vertorial angle at the top of the tooth

𝜙=pressure angle at the pitch circle

One spur tooth profile was created using equation (1-1) of the first type (I) , as

are the outside diameter circle, the dedendum circle, and base circle of the gear.

Second, in ANSYS from the toolbars using “CREATE”, “COPY”, “MOVE”, and

1 R.S.Khurmi & J.K.Gupta;,pag(387).aformer refrence.

2 Dr. A. Tolga Bozdana Assistant Professor ;" ME 114 – Engineering Drawing II",Mechanical

Engineering University of Gaziantep, pag.

3 Zeping Wei.,same refrence.

12

“MESH” and so on, any number of teeth can be created, an FEM gear contact

model was generated as shown in Figure (2-2)(1)

.

1-2 Literature review :-

A number of researchers have worked on gear tooth vibration and used

experimental , analytical and numerical techniques to solve the problem , and the

most commonly experimental techniques include photo elastic and strain

gages,and FEM the most numerical technique .Used by , Ravichandra & Yesh in

2006 to develop and determine the effect of gear rim thickness on tooth bending

stress in large spur gears using ANSYS parametric Design Language (APDL) to

generated 2-D and 3- D model of 1,3 and 5 teeth segment with user defined rim

thickness value(1)

.The teeth of circular and involute crowned external spure gear

are modeled for the same crowning magnitude, based on the theory of gearing

,mathematical model of tooth generation and studied the effect of major

1 Ravichandra patchingolla & Yesh P.Singh; 'Finite Element Analysis of Spure gear tooth and rim with

and without web effects –part-I', American Society for Engineering Education,ASEE Gulf – South west

Annual conference Southern University and A & M college ,2006,session T1A6 .

Fig.(2-2) Involutometry of a spur gear(14)

13

performance characteristics of uncrowned spur gear teeth using the FEM analyses

from Ansys were presented (1)

.

Natural frequencies and dynamic response of a spur gear sector were

investigated using 2-D FEM and the gear teeth were analyzed for different

operating speeds ,ANSYS software has been used on proposetred model to find

the natural frequencies by block Lanczos technique and displacements and

dynamic stresses by transient mode super position method (2)

. To estimate

transmission error in a gear system, the characteristics of involute spur gears were

analyzed using FEM , the contact stresses were examined by 2-D models in

ANSYS and results indicated that combined torsional mesh stiffness increases at

double pair of teeth and decreased in single pair teeth due to mesh cycle and the

change in torsional mesh stiffness leads to change in (Tr.) that causes noise and

vibration(3)

. Analysis of experimental data of gear rattle in Roots Blower Vacuum

Pumps reveals that the source of the noise and vibration problem is the backlash

nonlinearity due to gear teeth losing and re – establishing contact(4)

. FEM used to

developed the real model of the geared set using the self developed the software

and the vibration mode shapes show the relation to the moving center of masses

of the gear that carries the moving mass and show the vibration sensitivity of the

gear set to design parameters (5)

.A tooth depth is increased to identify the

reduction of vibration in a spur gear with two model descried and analyzed by

FEA software under harmonic analysis to identify the displacement and

acceleration of the gear tooth due tooth due to transmitted and radial load(6)

.

1 -Ramalingam Gurumani*, Subramaniam Shanmugam* ;'MODELING AND CONTACT ANALYSIS

OF CROWNED SPUR GEAR TEETH', Engineering MECHANICS, Vol. 18, 2011, No. 1, p. 65–78 .

2 ali H.Al-Wazir & Amal A.Abdulah; "NON-LINEAR ANALYSIS SPUR GEAR MESH BY FEM",

Journal of Kerbala University , vol.5,No.4,Scientific, December,2007.

3 Joanna Mason, Mart Homer & R.Eddie Wislon; "MATHEMATICAL MODELS OF GEAR RATTLE

IN ROOTS BLOWER VACUUM PUMPS", University of Bristol ,BS81TR.

4 Joanna Mason, Mart Homer & R.Eddie Wislon; "MATHEMATICAL MODELS OF GEAR RATTLE

IN ROOTS BLOWER VACUUM PUMPS", University of Bristol ,BS81TR.

5 Dejan Dimitrijević, Vera Nikolić-Stanojević;" Eigenfreuqency Analysis of the Spur Gear Pair with

Moving Excentric Masses on the Body of One of the Gears ", © Faculty of Mechanical Engineering,

Belgrade. All rights reserved FME Transactions (2007) 35, 157-163.

6Ramesh Babu.S* and Dr.Srinivasan.K; " Analysis of Influence of Tooth Depth in Spur Gear Vibration

", International Journal of Scientific & ineering Research, Volume 3, Issue 3, March-2012 1ISSN 2229-

5518.

14

2-1Finite Element Modeling :-

A program is developed using ANSYS parametric Design Language (APDL)

ver.11,to model the gear tooth involute profile of two type with different edge

shape as shown in figures shown to note the effect on vibration .The analysis is

preformed on 3-D finite element models in this paper the element is of the type

(solid 45) of solid structures and the element is defined by eight nodes having

three degrees of freedom at each node viz. Translation in the nodal X,Y and Z

direction. The material is assumed to be isotropic and homogeneous. The finite

element models are analyzed for the case of entire load acting at the HPSTC

(Highest Point of Single Tooth Contact). The edge length of the element along the

profile is calculated and the load is applied as a pressure on the profile edge each

time the same value on same nod for both design (involute profile model I and

involute profile model II ) .

3.1 Case illustrations :-

Table (1) provides the design and operating parameters of the standard spure

gear considered for two shape of profile (circular & straight profile) (1)

Table (1)Design and operating parameters of the standard spure gear

Description The value

Material 40 Ni2Cr Mo28(En24)

high strength

Ultimate tensile strength,Mpa 1550

Yield strength , Mpa 1300

Modulus of elasticity , Mpa 2.07*105

Density , Kg/m3

7840

Pitch circle diameter ,mm 180

Root diameter ,mm 175

Outsid diameter ,mm 184

Base diameter ,mm 169.15

Number of teeth 90

Radius of curvature at pitch point , mm 30.782

1 Ramalingam Gurumani*, Subramaniam Shanmugam* ;'MODELING AND CONTACT ANALYSIS

OF CROWNED SPUR GEAR TEETH', Engineering MECHANICS, Vol. 18, 2011, No. 1, p. 65–78 .

15

Fillet radius , mm 0.3 modula

Top land thickness 0.4 modula

Face wideth ,mm 30

Addendum ,mm 1 modula

Dedendum ,mm 1.25 modula

Poisson's ratio 0.25

Pressure angle ,deg 20

Contact pressure , N/mm2

1238

4.1 Results and Conclusions :-

4.1.1 results and figures :-

As mentioned above the results showed that when the involute gear profile of

straight edge had higher values at first five natural frequencies as in table (5-1)

compared with modal II(the modified one),the figures showed that modified

involute profile of modal II have lower vibration at the first five natural

frequencies as in (5-1),(5-2),(5-3)and (5-4) which shown the response of lower

value in modified modal (II) than modal( I) .

Table (5-1) the first five natural frequencies of two involute gear profile

types

Set Tim/ FREQ

Modal I (straight involute

gear profile)

Modal II (carved involute

gear profile)

1 0.29733 0.279425

2 0.29751 0.280485

3 0.29904 0.281367

4 0.30340 0.291083

5 0.30478 0.291555

16

Modal I Modal II

Fig. (5-1) The response at first natural frequencies for both Modal ( I and II)

Modal II Modal I

Fig. (5-2) The response at second natural frequencies for both Modal ( I and II)

17

Modal I Modal II

Fig. (5-3) The response at Third natural frequencies for both Modal ( I and II)

Modal II Modal I

Fig. (5-4) The response at fourth natural frequencies for both Modal ( I and II)

18

4-2 conclusions :-

As shown in tables (5-1) and (5-2) , and in figures above we notes that :-

1- The natural frequencies and vibration responses values had a relation with the

involute gear profile design ,that we had lower value for responses in modal(II)

the modified one with carved edge than modal(I) which had sort of straight edge .

2- The area of contact in modal (II) is slightly lower than that in modal (I) which

provide a less point of contact compared as a result lower vibration and noise.

3- It's evident from the result that vibration of spur gear can be modified by

modifying the involute gear profile design .

4- FEM is an acceptable method for study and analyzed and investigated the

effect of the involute gear profile design with vibration analysis .

5-1 Refrencess : 1- Ali H.Al-Wazir & Amal A.Abdulah; "NON-LINEAR ANALYSIS SPUR

GEAR MESH BY FEM", Journal of Kerbala University , vol.5,No.4,Scientific,

December,2007.

2- A.Tolga Bozdana Assistant Professor ;" ME 114 – Engineering Drawing

II",Mechanical Engineering University of Gaziantep

3-Budynas-Nisbett:Shigley,s;"MechanicalEngineeringDesign",McGraw-Hill

companies,8thedition,chap.13,pag.(653-666) ,2008.

4- Dejan Dimitrijević, Vera Nikolić-Stanojević;" Eigenfreuqency Analysis of

the Spur Gear Pair with Moving Excentric Masses on the Body of One of the

Fig. (5-5) The response at fifth natural frequencies for both Modal ( I and II)

Modal II Modal I

19

Gears ",©Faculty of Mechanical Engineering, Belgrade. All rights reserved FME

Transactions , 2007.

5- G.mallesh,VB .Math,A.Shwij,Sai Dull and Rajendra Shanbhag;'Effect of

tooth profile modification in asymmetric spure Gear tooth Bending Stress by finit

element analysis',(NaCoMMo9),NIT,Durgapur,India,December 17-18,2009.

6-Gears(1),http//en.,Wikipedia,thefreeencyclopedia,7/9/2010,

Wikipedia.org/Wiki/Gear.

7- Joanna Mason, Mart Homer & R.Eddie Wislon; "MATHEMATICAL

MODELS OF GEAR RATTLE IN ROOTS BLOWER VACUUM PUMPS",

University of Bristol ,BS81TR.vol.308, 4 December 2007.

8- Joseph Edward Shigly & John Joseph Ulcker,JR;'Theory of Machines and

Mechanisms', 2nd

edition,McGraw-Hill,Inc,chap.6,1995.

9- Ramalingam Gurumani*, Subramaniam Shanmugam* ;'MODELING AND

CONTACT ANALYSIS OF CROWNED SPUR GEAR TEETH', Engineering

MECHANICS, Vol. 18 , No. 1, 2011

10- Ramesh Babu.S. & Dr.Srinivasan K.;" Analysis of Influence of Tooth

Depath in Spur Gear Vibration " , International Journal of Scientific

&Engineering Research ,vol.3,ISSUe 3,http:// www.ijser.org.pag.1,March 2012.

11-

R.S.Khurmi&J.K.Gupta;'TheoryofMachines',S.chandTECHNICAL,PUBLISHIN

G,

First Multicolour Revised &updated edition,chap.12 ,2010.

12- Vishwjeet V. Ambade, Prof. Dr. A.V.Vanalkar, Prof. P. R. Gajbhiye;'

FEM Analysis Of Spur Gear Tooth ', International Journal of Engineering

Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3,

Issue 4, Jul-Aug, 2013.

13- Zeping Wei;"STRESSES AND DEFORMATIONS IN INVOLUTE SPUR

GEARS BY FINITE ELEMENT METHOD ",A Thesis Submitted to the College

of Graduate Studies and Research in Partial Fulfillment of the Requirements for

the Degree of Master of Science in the Department of Mechanical

Engineering,University of Saskatchewan,© Copyright Zeping WeiAll rights

reserved, October, 2004.