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ISSN 2278 – 0149 www.ijmerr.com

Vol. 3, No. 4, October, 2014

© 2014 IJMERR. All Rights Reserved

Research Paper

DESIGN AND ANALYSIS OF CROWN PINION OF ADIFFERENTIAL GEAR BOX FOR REDUCED NUMBER

OF TEETH TO IMPROVE TORQUE TRANSMITTED

Santosh S Bagewadi1*, I G Bhavi2 and S N Kurbet3

*Corresponding Author: Santosh S Bagewadi � kf.sant@gmail.com

Bevel gears are widely used because of their suitability towards transferring power betweennonparallel shafts at almost any angle or speed. Spiral bevel gears, in comparison to straight orzerol bevel gears, have additional overlapping tooth action which creates a smoother gearmesh. This smooth transmission of power along the gear teeth helps to reduce noise and vibrationthat increases exponentially at higher speeds. Currently the bolero pickup vehicle of MahindraCompany is running with a pinion present in the differential gear box having 11 numbers ofteeth. By reducing number of teeth on pinion, we can increase the torque. So we carried out thiswork to design a new pinion suitable to fit in the bolero pickup vehicle. Only the number of teethare reduced by keeping all other dimensions same to fit the new pinion in the same housing.

Keywords: Spiral bevel gear, Pinion, Differential gear box

INTRODUCTION

When the car is taking a turn, the outerwheels will have to travel greater speeddistance as compared to the inner wheels inthe same time, if therefore, the car has a solidrear axle only and no other device, there willbe tendency for the wheels to skid. Hence ifthe wheel skidding is to be avoided, somemechanism must be incorporated in the rearaxle, which should reduce the speed of theinner wheels and increase the speed of theouter wheels when taking turns; at the same

1 PG Scholar, Mechanical Department (Machine Design), B.L.D.E.A’S V.P Dr. P.G.H CET, Bijapur, India.2 Professor, Automobile, Department (Machine Design), B.L.D.E.A’S V.P Dr. P.G.H CET, Bijapur, India.3 Mechanical Department, Basaveshwar Engineering College, Bagalkot, India.

time it should keep the speed of all the wheelssame when going straight ahead. Such adevice which serves the above function iscalled a Differential. In differential gearassembly, crown wheel and pinion are thecritical components.

A gear is a mechanical device often usedin transmission systems that allows rotationalforce to be transferred to another gear ordevice. Throughout the mechanical industry,many types of gears exist with each type of

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gear possessing specific benefits for itsintended applications. Bevel gears are widelyused because of their suitability towardstransferring power between nonparallelshafts at almost any angle or speed.

standards. As a result, the stresses producedin the gear teeth were acceptable, mitigatingthe risk of failure to the designed gear teeth.

S H Gawande et.al

In this paper mechanical design of crownwheel and pinion in differential gear box ofMFWD (FWA) Axle (of TAFE MF 455) is done.Detailed modeling, assembly and analysis oftooth of crown gear and pinion is performedin Pro-E. Finite element analysis is performedto analyse the crown gear tooth for workingload. Induced equivalent stress is less thanallowable stress. From this it is concludedthat design is safe.

A Bensely et.al

In this paper failure investigation of crownwheel and pinion has been done. A fracturedgear was subjected to detailed analysis usingstandard metallurgical techniques to identifythe cause for failure. The study concludesthat the failure is due to the compromisemade in raw material composition by themanufacturer, which is evident by thepresence of high manganese content andnon-existence of nickel and molybdenum.This resulted in high core hardness (458 HV)leading to premature failure of the pinion.

D. Lewicki et.al

An experimental program to test the feasibilityof using face gears in a high-speed and high-power environment was conducted. Fourface gear sets were tested, two sets at a time,in a closed-loop test stand at pinion rotationalspeeds to 19,100 rpm and to 271 kW (364hp). The test gear sets were one-half scaleof the helicopter design gear set. Testing thegears at one-eighth power, the test gear set

In this work, spiral bevel pinion present inthe differential assembly is redesigned. Theselected pinion is the existing part of thebolero pickup vehicle. The material used tomanufacture the existing pinion is SAE 4130steel. To provide the same or higher marginof safety to the redesigned pinion, SAE 9310steel material is chosen.

LITERATURE REVIEW

Matthew D Brown

This paper gives a detailed approach to spiralbevel gear design and analysis. Key designparameters are investigated in accord withindustry standards and recommendedpractices for use in a medium class heli-copter. A final gear design is proposed andanalyzed to show that proper margins ofsafety have been included in the design.Upon completion of the design phase of thegear, analysis was conducted to ensureappropriate margins of safety had beenimplemented into the design. Calculatedvalues of Hertz stress and bending stress areless than the allowable stresses as per AGMA

Figure 1: Spiral Bevel Gear Mesh

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had slightly increased bending and compre-ssive stresses when compared to the fullscale design. The tests were performed inthe NASA Lewis spiral bevel gear test facility.All four sets of gears successfully ran at 100percent of design torque and speed for 30million pinion cycles, and two setssuccessfully ran at 200 percent of torque foran additional 30 million pinion cycles. Theresults, although limited, demonstrated thefeasibility of using face gears for high-speed,high-load applications.

Robert F Handschuh

Experimental and analytical studies havebeen conducted with respect to the thermalbehavior of spiral bevel gears. Theexperimental effort was conducted onaerospace quality spiral bevel gears atrotational speeds to 14400 rpm and 537 kW(720 hp). The experimental results indicatedthat load, jet location, flow rate, and oil inlettemperature all can affect the steady stateoperating temperature of the spiral bevelpinions that were instrumented. Also ananalytical modelling method was developedto analyze the thermal behavior via the finiteelement method.

MATERIAL SELECTION

The specific application of a gear determinesthe necessary material properties andadditional treatments that may be required.Additional treatments typically considered arethrough hardening and surface hardening,which includes but is not limited tocarburization, nitriding, induction hardening,and flame hardening. Specifically, the desiredloading and desired design life are integralin selecting the proper material and anyadditional treatment that may be required.

Many years of gear industry experiencehas led the design community to rely oncarburized, case-hardened steel for bevelgears. Therefore, spiral bevel gear materialsare limited to only those which are easilycarburized and case-hardened. Table 1below, generated from AGMA recommen-dations of associated steel grades and theirtypical heat treatments displays the sevenpotential steel grades which are recognizedto be well suited towards carburization inbevel gear applications. To better understandthe steel grades above and their metallurgicalcompositions, Table 2 below shows thecommon steel designations and their nominalalloy contents.

Table 1: Heat Treatments andAssociated Steel Grades

Carburizing

Heat Treatment Steel Grade

1020

4118

4320

4820

8620

8822

9310

18CrNiMo7-6

Table 2: Steel Designations andAlloy Contents

Carbon Steels

10xx No intentional alloying

15xx Mn 1.00 - 1.35%

Alloy Steels

41xx Cr 1%, Mo 0.25%

43xx Ni 1.75%, Cr 0.75%, Mo 0.25%

86xx Ni 0.5%, Cr 0.5%, Mo 0.2%

93xx Ni 3.25%, Cr 1.25%, Mo 0.12%

Note: “xx” = (nominal percent carbon

content x 100)

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Steels under consideration also must havesufficient case hardenability in order to obtainadequate hardness below the depth of thecarburized case. Figure 1 below shows thecase hardenability for the alloy steels shownin Table 1 and Table.

pursuit of higher and higher properties inmaterials, heat treatment plays a veryimportant role.

In summary, the ultimate goal of a heattreatment procedure is to convert weakermetallurgical grain structures such as pearliteand bainite to a stronger structure likemartensite. This process is typicallyperformed using two essential steps; heatingthe steel to some temperature above itstransformation point such that it becomesentirely austenitic in structure, and thenquenching the steel at some rate faster thanthe critical rate in order to produce amartensitic structure. The resultingmartensitic structure is mainly dependent onthree factors (1) the composition of the alloy(austenite grain size and prior micro-structure), (2) the type and character of thequenching medium (time and temperatureduring austenitizing), and (3) the size andshape of the specimen. Water, oil and air canbe used to increase the rate of cooling, butoil is by far the most effective quenchingmedium when attempting to form a fullymartensitic structure. Geometry and shapeof a specimen can also affect the resultingmicrostructure after quenching, and thereforeit is important to investigate the rate at whichhardness drops off with distance into theinterior of a specimen as a result of dimini-shed martensite content.

DESIGN OF PINION

The process of designing gear teeth issomewhat arbitrary in that the specificapplication in which the gear will be useddetermines many of the key designparameters. Recommended design practices

Figure 2: Case Hardenability ofCarburizing Grades of Steel

SAE 9310 will provide the most adequatecase hardenability, according to Fig 2, andtherefore will be selected as the material fromwhich this pinion will be manufactured.

HEAT TREATMENT

Heat treatment is an operation or combinationof operations involving heating at a specificrate, soaking at a temperature for a period oftime and cooling at some specified rate. Theaim is to obtain a desired microstructure toachieve certain predetermined properties(physical, mechanical, magnetic or electrical).

Heat treatment is considered to be a veryimportant tool of the metallurgist by which hecan alter the properties of steel easily. Thesame steel can have a very wide range ofmechanical properties if subjected to differentheat treatment. Today, when science andtechnology are advancing very rapidly in

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are published in the AGMA standard 2005-D03, Design Manual for Bevel Gear Teeth.Spiral angle and pressure angle are twodesign parameters that help determine theshape of a spiral bevel gear tooth. Commondesign practices have determined that forspiral bevel gears, a pressure angle of twentydegrees and a spiral angle of thirty fivedegrees should be used. Following thiscommon practice for selection of spiral angleestablishes a good face contact ratio whichmaximizes smoothness and quietness duringgear mesh. In regards to the selection of apressure angle, a lower pressure angleincreases the transverse contact ratio, abenefit which results in increased bendingstrength, while also increasing the risk ofundercut which is a major concern. Lowerpressure angles also help to reduce the axialand separating forces and increase the toplands and slot widths.

In addition, spiral bevel gears are designedsuch that the axial thrust load tends to movethe pinion out of mesh. This helps to avoidthe loss of backlash, defined as the clearancebetween mating components. While a lot ofbacklash is not desirable, small amounts ofbacklash are required to allow for properlubrication, manufacturing errors, deflectionunder load, and differential expansionbetween the gears and housing.

As previously mentioned, the gear addre-ssed throughout this paper is replacing asimilar gear that operated in the fleet for manyyears. The main difference between the twogears is the number of teeth on the pinionwhich helps to achieve the proper gearreduction ratio. Minimal changes were madeto the values for diametral pitch, pitch dia-

meter, pitch angles, and face width, whichare the basis for calculating the necessarygeometric design parameters.

LOADING

Torque application to a spiral bevel gear meshinduces tangential, radial, and separatingloads on the gear teeth. For simplicity, theseloads are assumed to act as point loadsapplied at the mid-point of the face width ofthe gear tooth. The radial and separatingloads are dependent upon the direction ofrotation and hand of spiral, in addition topressure angle, spiral angle and pitch angle.The tangential loads are defined as

Wtp = –––––––––

for the pinion with T equal to the torque,dp equal to the pitch diameter, F equal to theface width, γ equal to the pitch angle of thepinion.

The radial and separating loads arecalculated as a percentage of the tangentialloads calculated above. For a right hand ofspiral rotating counter clockwise, the axialthrust load for a driving member (pinion) isdefined as

Wa = –––––– (tanφ sinγ + sinψ cosγ

And the separating load is defined as,

Wr = –––––– (tanφ cosγ – sinψ sinγ

Where φ is the pressure angle and ψ isthe mean spiral angle. Figure 2 belowdisplays the line of action through which thetangential, axial and separating loads act.

2 Tpdp–F sin γ

Wtpcos ψ

Wtpcos ψ

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Bending strength capacity ratings in bevelgear teeth are developed using a simplifiedapproach to cantilever beam theory.Calculating the bending strength rating willdetermine the acceptable load rating at whichtooth root fillet fracture should not occurduring the entirety of the life of the gear teethunder normal operation.

The basic equation for bending stress in abevel gear is given by

fb = Wtp –––––––––––––

where Wt is the tangential tooth loadpreviously discussed, PITCH is the diametralpitch, F is the face width, Ks is the size factor,Km is the load distribution factor, and j is thegeometry factor. Finally fatigue margin ofsafety, M.S, can be calculated using theformula.

M.S. = ––––––––

Where Fen is the endurance limit

CONCLUSION

Currently the existing pinion is manufacturedby SAE 4130 steel material. The existingbevel pinion is redesigned by consideringSAE 9310 steel as the pinion material.Decrease in the number of teeth on pinionleads to the increase in torque at the output.Calculating the design parameters for SAE4130 steel material gives the margin of safetyvalue of 0.57 for 11 teeth. Similar calculationsare done for SAE 9310 steel material whichgives margin of safety value of 0.68 for 10teeth. From this we can conclude that marginof safety is high even though after reducing1 tooth on pinion. Reduction of teeth also

Figure 3: Loads Acting on Pinion

The loads in Figure 3, labeled Rba, Rbh,Rbv, Raa, Rav, and Rah, are reaction loadsgenerated by the two tapered roller bearingsthat support the gear shaft. It is theresponsibility of these bearing reaction loadsto counteract the forces generated by themesh of the gear teeth, shown in the fig 2 asWap, Wtp and Wrp.

ANALYTICAL METHODOLOGY

Spiral bevel gear teeth are primarily designedfor resistance to pitting and for their bendingstrength capacity. Design for pittingresistance is primarily governed by a failuremode of fatigue on the surface of the gearteeth under the influence of the contact stressbetween the mating gears. Design forbending strength capacity is based on afailure mode of breakage in the gear teethcaused by bending fatigue.

The basic equation for compressive stressin a bevel gear tooth is given by

fc = Cp ––––––––––––

Where Cp is the elastic coefficient, Wt isthe tangential tooth load, Co is the overloadfactor, Cv is the dynamic factor, F is the facewidth, dp is the pitch diameter, Km is the loaddistribution factor, and I is the geometryfactor.

WtxCox1xKmCvxFxdpx1

PITCHx KsxKmFxj

Fen

Kt xfb

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reduces the weight of the pinion. So the newlydesigned pinion can be installed in theexisting gear box with the existing bearing,housing and other accessories.

REFERENCES

1. A Bensely, S Stephen Jayakumar, DMohan Lal, G Nagarajan and A Rajadurai(2006), “Failure Investigation of CrownWheel and Pinion”, Engineering FailureAnalysis, Vol. 13, pp. 1285–1292.

2. Askeland, Donald R and Pradeep P Fulay(2005), “The Science and Engineering ofMaterials. New York: CengageEngineering”.

3. Callister, William D Jr (2003), “MaterialsScience and Engineering anIntroduction”, New York: John Wiley &Sons Inc.

4. G González Rey, R J García Martín andP Frechilla Fernández (2007),“Estimating Gear Fatigue Life Using theStrength-life Theory”, Gear Solutions.

5. Hemanshu D Joshi, K D Kothari (2014),“Mode and Cause of Failure of a Bevelgear-A Review”, International Journal ofAdvance Engineering and ResearchDevelopment (IJAERD, Vol. 1, No. 2, pp.2348-4470.

6. Horton, Holbrook L, Franklin D Jones,Erik Oberg and Henry H Ryffel (2008),

Machinery’s Handbook, 28th Edition.New York: Industrial Press.

7. Matthew D Brown (2009), “Design andAnalysis of a Spiral Bevel Gear”,Rensselaer Polytechnic Institute Hartford,Connecticut.

8. R Handschuh, D Lewicki and R Bossier(1992), “Experimental Testing ofPrototype Face Gears for HelicopterTransmissions”, NASA TechnicalMemorandum 105434, Prepared forGcearbox Configurations of the 90’s,sponsored by the Institute of MechanicalEngineers, Solihull, West Midlands,United Kingdom.

9. Robert F Handschuh and Thomas PKicher (1995), “Experimental andAnalytical Assessment of the ThermalBehavior of Spiral Bevel Gears”,Prepared for the 1995 Fall TechnicalMeeting, sponsored by the AmericanGear Manufacturers Association,Charleston, South Carolina, pp. 16-18.

10. S H Gawande, S V Khandagale, V TJadhav, V D Patil and D J Thorat (2013),“Design, Manufacturing & Analysis ofDifferential Crown Gear and Pinion forMFWD Axle”, (Department ofMechanical Engineering, M.E.S. Collegeof Engineering, Pune).