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INTERNATIONAL JOURNAL OF INNOVATION IN ENGINEERING RESEARCH & MANAGEMENT ISSN :2348-4918

VOLUME :01 Issue 02 I Paper id-IJIERM-I-I I-1153 ,April 2014

1

SPIRAL BEVEL GEAR DESIGN AND DEVELOPMENT -

GENERATION AND SIMULATION OF MESHING AND TOOTH

CONTACT ANALYSIS (TCA)ASHOK KUMAR GUPTA

1

DR. VANDANA SOMKUWAR2

1Research Scholar (Ph D - Mechanical Engineering), AISECT University, Dist: Raisen, Near

Bhopal (M P) Email: [email protected], Mechanical Engineering Education Department, NITTTR, Bhopal (M P)

Email: vsomkuwar@nitttrbpl.ac.in---------------------------------------------------*****----------------------------------------------------------

ABSTRACT:Computer technology has touched all areas

of todays life, impacting how we obtainrailway tickets, shop online and receive

medical advice from remote location.

Computer-based design analysis is nowadaysa common activity in most developmentprojects. When new software and

manufacturing processes are introduced,traditional empirical knowledge is

unavailable and considerable effort isrequired to find starting design concepts.

This forces gear designers to go beyond thetraditional standards-based design methods.

The results obtained are in agreement withexisting knowledge. The transformation has

had a vast influence on gear manufacturingas well, providing process improvements that

lead to higher gear quality and lowermanufacturing costs. However, in the case of

the gear industry, the critical process ofGeneration and Simulation of Meshing and

Tooth Contact Analysis (TCA) of SpiralBevel Gears remains relatively unchanged.

Spiral bevel gears are crucial to powertransmission systems, power generation

machines and automobiles. However, the

design and manufacturing of spiral bevelgears are quite difficult. Currently, the majorparameters of spiral bevel gears are

calculated, but the geometries of the gears arenot fully defined. The procedures needed to

develop spiral bevel gear sets for a new

product can require months of trial-and-errorwork and thousands of dollars. In view of

increasing global competition for lowerpriced products, bevel gears are a prime

target for the next generation of

computerization. Answering this challenge,it has realized a new modified methodthrough a shift in the way spiral bevel gear

development is performed.The Gleason

face hobbing process has been widelyapplied by the gear industry. But so far, few

papers have been found regarding exactmodelling and simulation of the tooth surface

generations and tooth contact analysis (TCA)of spiral bevel gear sets. The developed face

hobbing generation model is directly relatedto a physical bevel gear generator. A

generalized and enhanced TCA algorithm isproposed. The face hobbing process has two

categories, non-generated (Formate) andgenerated methods, applied to the tooth

surface generation of the gear. In bothcategories, the pinion is always finished with

the generated method. The developed toothsurface generation model covers both

categories with left-hand and right-hand

members. Based upon the developed theory,an advanced tooth surface generation andTCA program is developed and integrated

into Gleason CAGE forWindows Software. Most of the truck

manufacturers have been confronted with

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ever more increasing demands on their

products and on the development process.These demands are reflected in higher engine

power, lower vehicle noise, higher fueleconomy and shorter lead times in

development. In most of commercial vehicle,single stage spiral bevel gears are used in the

rear axles. In engineering, new productdevelopment (NPD) is the complete process

of bringing a new product to market.

KeywordsSpiral Bevel Gear, Hypoid Gear,TCA, Computer Technology, Tooth Surface

Generation.

1.INTRODUCTION:

Gearing is one of the most criticalcomponents in a mechanical power

transmission system, and in most industrialrotating machinery. A gear is a mechanical

device often used in transmission systemsthat allows rotational force to be transferred

to another gear or device. The gear teethallow force to be fully transmitted without

slippage and depending on theirconfiguration, can transmit forces at different

speeds, torques, and even in a differentdirection. Throughout the mechanical

industry, many types of gears exist with eachtype of gear possessing specific benefits for

its intended applications. Bevel gears arewidely used because of their suitability

towards transferring power betweennonparallel shafts at any required angle or

speed. Spiral bevel gears have curved andslope gear teeth in relation to the surface of

the pitch cone. As a result, an oblique surface

is formed during gear mesh which allowscontact to begin at one end of the tooth (toe)and smoothly progress to the other end of the

tooth (heel), as shown in Fig 1a.

Fig 1a: Spiral bevel gear mesh

Spiral bevel gears, in comparison to straightor zerol bevel gears, have additional

overlapping tooth action which creates asmoother gear mesh. This smooth

transmission of power along the gear teethhelps to reduce noise and vibration that

increases exponentially at higher speeds.Therefore, the ability of a spiral bevel gear to

change the direction of the mechanical load,coupled with their ability to aid in noise and

vibration reduction, make them a primecandidate for use in the automobile industry

and others. The American GearManufacturing Association (AGMA) has

developed standards for the design, analysis,and manufacture of bevel gears. The first step

in any general design employing gears is tofirst predict and understand all of the

conditions under which the gears willoperate. Most importantly are the anticipated

loads and speeds which will affect the designof the gear. Additional concerns are the

operating environment, lubrication,anticipated life of operation, and assembly

processes, just to name a few. The twoprimary failure modes of gears are, one by

tooth breakage from excessive bending stressand other by surface pitting or wear from

excessive contact stress. The driving anddriven gears are the most important

components of the Gear box of anyautomotive. Modelling allows the design

engineer to let the characteristic parametersof a product drive the design of that product.

Toe

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During the gear design, the main parameters

that would describe the designed gear such asmodule, pressure angle, root radius, tooth

thickness and number of teeth could be usedas the parameters to define the gear.

DefinitionsIt is important that certain terms be defined

before any testing and developmentprocedure for bevel gears is presented.

Gear- of two gears that run together, the onewith the larger number of teeth is called the

gear. It is the driven member of a pair ofgears.

Pinion - the member with the smallernumber of teeth. With miter gears it is the

driving member.

Toe- the portion of the tooth surface at theinner end.Heel- the portion of the tooth surface at the

outer end.Top- the upper portion of the tooth surface.

Flank - the lower portion of the toothsurface.

Top Land - the non-contacting surface at thetop of the tooth.

Root Land - the non-contacting surface atthe bottom of a tooth space.

Top Side and Bottom Side- in conventionalmachines for producing both straight and

curved tooth bevel gears, the cutter or cuttingtools always operate on the left hand side of

the gear blank as viewed from the front. Theterm top refers to the upper side of the tooth

in this position, and the term bottom refers tothe lower side.

Top Side of ToothLeft hand spiral - convex side of tooth.

Right hand spiral - concave side of tooth.

Bottom Side of ToothLeft hand spiral - concave side of tooth.Right hand spiral - convex side of tooth.

The terms bottom side or top side wouldalways apply to a specific side, regardless of

the hand of spiral, and also with straight

bevel gears. When the forward side in the

testing machine is running, the rotation of thepinion spindle is clockwise when viewed

from the source of power, and the bottomside of the pinion will contact the bottom side

of the gear. When the pinion is running in thereverse direction, the rotation is

counter-clockwise, and the top side of thepinion will contact the top side of the gear. It

would, therefore, be better to refer to bottomside orforward side, and top side or reverse

side.

When referring to a specific side of the tooth,the terms drive side or coast side are quite

often used, but, unless a full knowledge ofthe application is available, these terms

would not be specific. Normally the concave

side of the pinion is called the drive side andthe convex side of the pinion is called theCoast side,but in many cases either side may

drive. Also, with straight bevel gears, there isno concave or convex side, so it again would

be difficult to correctly specify by drive sideor coast side.

Right Hand Spiral- when viewed from thefront, above center, the spiral angle of a bevel

gear curves to the right.Left Hand Spiral - when viewed from the

front, above center, the spiral angle of a bevelgear curves to the left.

Clockwise Rotation - the pinion rotatesclockwise when viewed from the back.

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Fig 1b: Face Milling v/s Face Hobbing

Fig 1c shows a configuration of a bevelpinion generation, which consists of a virtual

generating gear, a cutter head with blades,

and the work piece (the pinion). Therotational motion of the virtual generatinggear is implemented by the cradle

mechanism of a bevel gear generator.Generally, the tooth surfaces of the

generating gears are kinematically formed bythe traces of the cutting edges of the blades.

In practice, in order to introduce mismatch ofthe generated tooth surfaces, modification is

applied on the generating gear tooth surfaceand on the generating motion.

Fig 1c Configuration of a Bevel Pinion

Generation

In the spiral bevel and hypoid gear

generation process, two sets of related

motions are generally defined. The first set of

related motion is the rotation of the tool

(cutter head) and rotation of the work piece,

namely,

Equation 1

Here tand cdenote the angular velocities

of the tool and the work piece; Nc and Nt

denote the number of the blade groups and

the number of teeth of the work piece,

respectively. This related motion provides

the continuous indexing between the tool and

the work for the face hobbing process. Theindexing relationship also exists between the

rotation of the tool and the generating gear

as,

Equation 2

Where c andNc denote the angular velocity

and the number of teeth of the generating

gear respectively. In the face hobbingprocess, the indexing motion between the

tool and the generating gear kinematically

forms the tooth surface of the generating gear

with an extended-epicycloid lengthwise

tooth curve.

However, Equations 1 and 2 are not

applicable for the face milling process where

the cutter rotates independently at its selected

cutting speed and forms a surface ofrevolution for the generating gear teeth with

a circular lengthwise curve as shown in Fig.

The second set of related motions is the

rotation of the generating gear and rotation of

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the work piece. Such a related motion is

called rolling or generating motion and is

represented as

Equation 3

Where Ra is called the ratio of roll. The

generating motion is provided for both face

milling and face hobbing processes when the

gear or pinion is cut in the generating

method. In the non-generating (FORMATE)

process, which is usually applied to the gear,

both the generating gear and the work piece

are held at rest, and only the cutter rotation is

provided. Therefore, the gear tooth surfaces

are actually the complementary copy of the

generating tooth surfaces, which are formed

by the cutter motion described above.

Kinematical model of a spir al bevel &

hypoid gear generator

(Dr. Qi Fan and Dr. Lowell Wilcox, 2005)

CAD Model:Attempt has been made to create spiral tooth

profile of gear in a robust way using

parametric equation as below:

X (t) = Dg *t* cos (t)

Y (t) = Dg *t* sin (t)

Z (t) = k*t

Where, Dg = Diameter of gear, k = Root

angle in turns of radians.

Fig 2: Computer Model of Spiral Bevel

Gear Tooth

EPG

Tooth contact of mating gear teeth can be

positioned by manipulation oftester machineadjustments. The directions of these

movements and their designating letters areshown

in FIG. This sketch is of a hypoid pair, butthe directions of the movements are equally

applicable to spiral, or straight bevel gears.

(E) = movement perpendicular to the gearand pinion axes. A change in offset (E) can

be made by moving the pinion relative to thegear. Or, it can be made by moving the gear

relative to the pinion, depending upon thedesign of the testing equipment used.

(P)= pinion axial movement. A change in the

pinion axial distance (P) can be made by

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moving the pinion relative to the gear. Or, it

can be made by moving the gear relative tothe pinion, depending upon the design of the

testing equipment used. (P) is commonlyknown as a pinion cone change or a pinion

mounting distance change.

(G)= gear axial movement. A change in thegear axial distance (G) can be made by

moving the pinion relative to the gear. Or, itcan be made by moving the gear relative to

the pinion, depending upon the design of thetesting equipment used. (G) is commonly

known as a backlash change, a gear conechange or a gear mounting distance change.

EPG Sign ConventionsThe readings on all dials on testing machineE, P and G adjustments should be considered

"zero" readings, when the gears are mountedat the mounting distances and hypoid offset

specified on the Summary.(E+) indicates an increase in offset.

(E -) indicates a decrease in offset.(P +) indicates an increase in pinion axial

distance.(P -) indicates a decrease in pinion axial

distance.(G +) indicates an increase in gear axial

distance.(G -) indicates a decrease in gear axial

distance.

V&HThe E & P check accomplishes the same

thing as the former V & H check. "V" isequivalent to (E) and "H" is equivalent to (P).

Testing Procedures

A. The E & P CheckThe E & P (offset and pinion axial) check is

used as a method of measuring the axialdisplacement movement required in the test

machine, to move the contact from a central

profile contact shading out at the toe to a

central profile contact shading out at the heel.The following can be determined by analysis

of the E & P check:1. The total length of contact.

2. The amount and the direction of bias (biasin or bias out).

3. Position of the tooth contact in relation tocorrect testing machine centers.

4. By visual observation of the tooth contact,when the heel and the toeE & P checks are

on the tooth at the same time, the relativelength of the heel and toe contact is

determined and the width of profile can beobserved.

5. The approximate amount of displacement

that the gear will withstand without causingload concentration.

E &P Check (Left Hand Spiral, Pinion)Increase the gear offset and decrease the

pinion axial distance to move the contact tothe toe on the concave side of the pinion or to

the heel on the convex side of the pinion.When moving the contact to the heel on the

concave side of the pinion or to the toe on theconvex side of the pinion, the gear offset is

decreased and the pinion axial distance isincreased.

E & P Check (Right Hand Spiral Pinion)To move the contact to the toe on the convex

side of the pinion or to the heel on theconcave side of the pinion, the gear offset is

increased, and the pinion axial distance isincreased. To move the contact to the heel on

the convex side of the pinion or toe on theconcave side of the pinion, the gear offset

and the pinion axial distance are decreased.

The preceding example refers to the bottom

sidebecause decreasing the offset of the gear

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Bias out is often required, in developing the

tooth contact, due to the normal changes thattake place during hardening, and to allow for

the deflections in the mountings when thegears are in operation. A slight amount of

bias in is desirable after lapping inautomotive gears to give a quieter operating

pair of gears. The line of contact as the toothrolls into and out of engagement on the

concave side of the pinion, starts in the flankat the heel and rolls out at the top at the toe,

therefore, bias in increases the line ofcontact, but it will also decrease the amount

of pinion mounting adjustment if the amountof bias in is too great.

Figs. 4 and 5 illustrate bias contacts.

Regardless of the hand of spiral on thepinion, bias in will always run from the flankat the toe to the top at the heel on the convex

side, and from the top at the toe to the flank atthe heel on the concave side.

2. PROFILE TOOTH CONTACT

The width of the contact (tooth profile) is asimportant as the length of the contact. A wide

profile contact, Fig. 6, shows a contact

covering the full depth of the tooth. Quiteoften there is a heavier concentration at the

top of the tooth and in the flank of the toothwith the center of the tooth profile showing a

lighter contact.Too wide a profile contact is not desirable

because even a slight amount of change inmounting distance would cause a definite

concentration of load either high or deep onthe tooth and may result in noisy gears which

might also scuff or score along the area ofconcentration.

An extremely narrow profile contact. Fig. 7,

shows a narrow concentration of contact in

the center of the working depth. Thiscondition permits a greater variation inmounting distance, hut results in a noisier

pair of gears which will also have a tendencyto scuff or score at the concentrated contact

points.In general, gears which have a wide profile

before hardening will show a narrowerprofile after hardening. However r lapping

will generally widen the profile, therefore anattempt should be made to obtain a profile

width in cutting that will result in thehardened and lapped gears having a good

profile adjustment and still be quiet inoperation.

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correct the shaft angle to obtain the proper

tooth contact. (Fig. 11, Fig. 12)

7. INCORRECT PINION MOUNTINGDISTANCEChanging the pinion mounting (axial)distance will cause the contact to move high

or deep on the tooth profile. (Figs. 13 and 14)Increasing the pinion mounting distance will

move the contact toward the flank of thepinion and high on the gear. In the case of

spiral bevel, or hypoid gears, the contact mayalso move toward the heel or toe.

8. DESIRED TOOTH CONTACT

A localized tooth contact is desirable becauseit allows for displacement of the gear under

operating loads without causing

concentration of the load at the ends of the

teeth. It also permits some variation in thefinal mountings without affecting the running

qualities.Fig. 15 shows a central toe contact. The

contact extends along approximatelyone-half the tooth length and is nearer the toe

of the tooth than the heel. The contact is alsorelieved slightly along the top and flank of

the tooth. Under light loads the contactshould be in this position on the tooth.

Fig. 16 shows the same tooth with a contactas it should be under full load. It should show

slight relief at the ends and along the top andflank of the teeth with no load concentration

at the extreme edges of the tooth.

A. Run outRun out is characterized by a periodic

variation in sound during each revolution andby the tooth contact shifting progressively

around the gear from heel to toe and toe toheel.

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CONCLUSION:The robust and computerized toothgeneration approach along with the tooth

contact analysis provides a better way toreduce the wear, noise and vibration

problems related to spiral bevel gears. Also,the optimization of tooth profile can be done

with greater proceedings to the calculations.Ultimately, we should think of automated

soft-wares for designing that would create an

optimized model of the gear tooth profile justby inputting the basic parameters. Theconventional spiral bevel gears are

continuously being investigated in order toreduce the failure or increase their

transmissible power level, either bydeveloping new composite materials or by

modifying the gear tooth geometry. Amathematical model of an ideal spiral bevel

and hypoid gear-tooth surfaces based on theGleason hypoid gear generator mechanism is

proposed. Using the proposed mathematicalmodel, the tooth surface sensitivity matrix to

the variations in machinetool settings isinvestigated. Surface deviations of a real cut

pinion and gear with respect to the theoreticaltooth surfaces are also investigated. An

optimization procedure for finding corrective

machinetool settings is then proposed tominimize surface deviations of real cut

pinion and gear-tooth surfaces. The resultsreveal that surface deviations of real cut

gear-tooth surfaces with respect to the idealones can be reduced to only a few microns.

Therefore, the proposed method forobtaining corrective machinetool settings

can improve the conventional developmentprocess and can also be applied to different

manufacturing machines and methods forspiral bevel and hypoid gear generation.

References:

1. LITVIN F L, LU Xianzhan, GAO

Yetian, et al. Theory of gearing[M].2nd ed. Shanghai: ShanghaiScientific & Technical Publishers,

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et al. Gear geometry and appliedtheory[M]. Shanghai: Shanghai

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3. LITVIN F L, GUTMAN Y. Methodsof synthesis and analysis for hypoid

gear-drives of formate andhelixform[J].ASME Journal of

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4. LITVIN F L, ZHANG Y.Localsynthesis and tooth contact analysis

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LITVIN F L, WANG A G,HANDSCHUH R F. Computerizedgeneration and simulation of meshing

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local synthesis[J].MechanicalScience and Technology, 1999, 18(6):956960.

12.CAO Xuemei, FANG Zongde,ZHANG Jinliang. Function-oriented

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offset[J].Journal of AerospacePower, 2008, 23(1): 189194

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Hao, et al. Design of pinion machinetool-settings for spiral bevel gears bycontrolling contact path and

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