A

uwcbs©

K

1

tcghntWtiipAttidi

rc

0d

Available online at www.sciencedirect.com

Wear 265 (2008) 81–87

Gear tooth wear in sintered spur gears under dry running conditions

S. Dhanasekaran, R. Gnanamoorthy ∗Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India

Received 28 December 2006; received in revised form 4 July 2007; accepted 31 August 2007Available online 18 October 2007

bstract

In this study, a wear prediction methodology for spur gears is employed to investigate the influence of material properties on gear tooth wear undernlubricated conditions. The methodology employs a single point observation-based gear contact mechanics in conjunction with the Archard’s

ear formulation to predict the tooth wear and wear pattern in spur gears. A MATLAB program is developed to account the changes in the gear

ontact per mesh cycle as the wear occurs. The material containing 3% MoS2 is found beneficial in improving the wear resistance. Wear is moreoth in addendum and dedendum tooth surfaces, and that the highest wear occurs at the dedendum of tooth surface. Results of the experimentaltudy are presented for validation of wear prediction methodology.

2007 Elsevier B.V. All rights reserved.

n

csmtip

gfaicpiatoda[

eywords: Spur gear; Wear; Sintered steels; Molybedenum di sulphide additio

. Introduction

Gear tooth wear causes an increased sound and vibration inhe system. In many applications, gears operate under unlubri-ated conditions and efforts are made to improve the life of theseears against wear. In order to reduce the wear, materials with aigh hardness, good strength and less coefficient of friction areeeded. Many sintered materials containing additives in ordero improve the strength and wear resistance were developed [1].

ear of a spur gear is not uniform throughout the surface ofeeth. Wear on the face side is low whereas that on the flank sides high. This is due to varying rolling sliding conditions betweennteracting gear teeth along the tooth profile. At the pitch point,ure rolling occurs with a less coefficient of friction and wear.t every other contact point, there is a relative sliding between

he mating gear teeth, and therefore, sliding occurs in additiono rolling component. Presence of the sliding component resultsn an increased friction coefficient and wear. Continuous wearuring service changes the tooth profile, affects the meshing andncreases the noise and vibration.

Gears during service experience a high stresses at the toothoot and contact zones. Tooth bending causes high stress con-entration at the root region and this region is more prone for

∗ Corresponding author. Tel.: +91 44 2257 4691; fax: +91 44 2257 0545.E-mail address: gmoorthy@iitm.ac.in (R. Gnanamoorthy).

etutbfb

043-1648/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.wear.2007.08.025

racking. In addition gear tooth experiences, a high contacttresses at the profile surfaces that leads to surface damage. Inetal spur gears, wear depends on the contact pressure distribu-

ion and shear stresses induced. The contact pressure distributions a function of contact width and shear stress changes with theresence of sliding component.

The unlubricated wear characteristics of En 8 and coatedears were reported [2]. Wu and Cheng [3] derived a formulaor quantifying the equivalent wear rate and tooth wear profileslong the line of action. A model for spur gear wear predictions developed by Andersson and co-workers [4] and the effect ofontact pressure, sliding distance, wear coefficient and materialroperties on the gear performance is reported. Wear simulations carried out by Brauer and Andersson [5] using finite elementnd analytical tools. The tooth profile changes during service andhe amount of wear that is acceptable depends on the required lifef the system [6]. Gear tooth stiffness is a key parameter in gearynamics. Tooth damage causes a reduction in tooth stiffnessnd affects the load bearing capacity [7]. Yuksel and Kahraman8] reported that the wear of tooth profile alters the gear meshxcitations in the form of kinematic motion errors and affecthe dynamic loads. Pit formation and life prediction of gearssing numerical tools are reported [9,10]. Tooth wear changes

he gear tooth contact pattern such that the altered load distri-utions and contact stresses accelerate the occurrence of otherailure modes [11]. In gear systems, excessive wear increasesacklash, leading to a loss in contact between the teeth and may

8 oorthy / Wear 265 (2008) 81–87

c[gtw

pbwre

2

oswatltbevcbR

wptt

taipa

2 S. Dhanasekaran, R. Gnanam

ause a non-uniform transmission of motion [12]. Lundvall et al.13] reported that the wear of tooth profile alters the geometry ofear pair and causes non-uniform rotation of gear pair. Unevenooth wear results high dynamic loads and accelerate the toothear [14].This paper describes the prediction of spur gear tooth wear

attern under unlubricated conditions. The wear model isased on the empirical relation, which includes the effect ofear coefficient, sliding velocity, contact pressure and mate-

ial combinations. The predicted wear depth is compared withxperimental results.

. Wear modeling

Gear contact involves combined rolling and sliding motionf two mating gear teeth surfaces. The wear model used in thistudy is based on the model proposed by Andersson and co-orkers [4]. The wear model employs Archard’s wear equation

nd determines the wear depth based on single point observa-ion method. The spur gear contact always lies in a straightine (line of action) tangential to both base circles and passinghrough pitch point. Therefore, the wear depth per revolution cane quantified locally along the line of action during one singlengagement (Fig. 1). The line of contact consists of several indi-idual points of contact, and each point is represented by contactharacteristics. The gear contact at each one of these points cane assumed similar to two meshing cylinders with radius R1 and2 and surface velocities U1 and U2.

The computational methodology employed to predict the

ear of sintered steel gear is shown in Fig. 2. A MATLABrogram was developed to calculate the wear depth. The ini-ial geometry, wear coefficient, material properties and appliedorque of the actual gear tooth surfaces serve as the initial condi-

pa

w

Fig. 1. Meshing points on t

Fig. 2. Methodology used for wear depth computation.

ions for wear prediction. The number of points on a test gear isssumed. The sliding speed, time increment of each point (slid-ng time), contact width and the contact pressure at the definedoints during one single mesh cycle is calculated in the singlend double tooth contact zones. Thereafter, the wear depth at a

oint was determined and the cumulative wear depth is predictedfter a defined number of cycles.

The gear wear model employs Archard’s wear equation,hich can be expressed for a point on one of the contacting

he gear teeth surface.

oorthy / Wear 265 (2008) 81–87 83

s

h

wdadr

c

h

wawop

c

v

wanc

t

wp

u

p

wsgatl

Table 2Details of gear pair

Pinion Mating gear

Manufacturing process Sintering HobbingNumber of teeth 14 57Module (mm) 1.5 1.5Pressure angle (◦) 20 20Pitch circle diameter (mm) 21 85.5Face width (mm) 11 20Centre distance (mm) 53.25Applied torque on pinion (N m) 1, 1.5, 2, and 2.5P

3

3

ToCidtiwa60 ± 2 HRc.

TS

S

FFF

S. Dhanasekaran, R. Gnanam

urface for a sliding duration as [4]:

p =∫ t

0kpv dt (1)

here hp is the wear depth at a point on the pinion in mm, k theimensional wear coefficient in m2/(N m), p the contact pressuret the point N/m2, ν the sliding speed in m/s and t is the slidinguration in s at a single point. The small increment of time stepepresents the small increment of points in the pinion.

The wear depth of the pinion after a particular number ofycles can be computed using

p,n = hp,(n−1) + kpvt (2)

here hp,n is the wear depth at a particular point on the pinionfter running the defined number of cycles and hp,(n−1) is theear depth at the same point one cycle before. The second termn the right-hand side of the equation defines the wear of theinion at the same point in the final mesh.

The sliding speed between the points on the test gear can bealculated using

= (ω1 + ω2)Yi (3)

here ω1 and ω2 are the angular velocities of the pinion and gearnd Yi is the distance between the pitch point and the instanta-eous contact point. The sliding duration for each point can bealculated using [3]:

=[

1

up

]sec α Yi (4)

here up is the pitch line velocity of the pinion and α is theressure angle of the pinion.

The contact pressure at each point in contact is predictedsing

= 2Ft∏a2 (a2 − Y2

i ) (5)

here Ft is the transmitted load at a particular point and a is theemi-Hertizian contact width. For spur gears, the contact ratio isreater than one, i.e., two pairs of teeth share the load for a partnd single teeth contact takes place for the remaining period. Athe beginning of contact and end of contact, two teeth takes fulload whereas in middle single pair takes the full load.

able 1intered density, porosity, hardness, strength and Young’s modulus of test gear mater

intered gear composition (wt.%) Sintered density(g/cm3)

Inter-connectedporosity (%)

e–0.6% C–2.5% Cu 6.32 16.5e–0.6% C–2.5% Cu–3% MoS2 6.52 9.1e–0.6% C–2.5% Cu–5% MoS2 6.57 8.8

inion speed (rpm) 800

. Test material and gear test details

.1. Material

Sintered steel spur gears are used in the current study.he material processing details, microstructure, pore morphol-gy and mechanical properties are described in Ref. [15].hemical composition, sintered density, interconnected poros-

ty, hardness, compressive strength and Young’s modulus of theeveloped sintered steel are listed in Table 1. Dimensions ofhe sintered and mating gears are given in Table 2. The mat-ng gear was made of En 31 [AISI 52100]. The mating gearas heat treated at 1118 K (845 ◦C) followed by oil quenching

nd tempering at 423 K (150 ◦C) for 1 h to attain a hardness of

Fig. 3. Power absorption gear test machine.

ials

Hardness (HV) Compressivestrength (MPa)

Young’s modulus(GPa)

91 497 113136 1006 151126 840 153

8 oort

3

pp[rrAtw

wGmtp

4

FM

4 S. Dhanasekaran, R. Gnanam

.2. Gear test details

Wear tests of the sintered spur gears were carried out on aower absorption type gear test machine (Fig. 3). The details ofower absorption type gear test rig used are described elsewhere1]. The sintered gears were subjected to different test torquesanging from 1 to 2.5 N m under dry running condition and the

otational speed of the pinion was maintained constant, 800 rpm.t least three specimens were tested at each torque level. Gear

ests were conducted until tooth breakage or 20 × 104 cycleshichever is earlier. After every 2 × 104 cycle, the test machine

Fa

ig. 4. Wear depth in the test gear after 2 × 104 cycles (wear cycles 2000–2 × 104 roS2 (1 N m), (d) Fe–C–Cu–3% MoS2 (2.5 N m), (e) Fe–C–Cu–5% MoS2 (1 N m), a

hy / Wear 265 (2008) 81–87

as stopped for observation and tooth thickness measurement.ear tooth images were taken using a high resolution videoicroscope. Gear tooth wear was quantified on the three marked

eeth. Initial and final tooth profiles were observed using a profilerojector.

. Results and discussion

Fig. 4 shows the predicted wear depth and wear contour ofe–C–Cu, Fe–C–Cu–3% MoS2, and Fe–C–Cu–5% MoS2 gearsfter 2 × 104 cycles. The gear wear pattern is quite different for

epresented): (a) Fe–C–Cu (1 N m), (b) Fe–C–Cu (2.5 N m), (c) Fe–C–Cu–3%nd (f) Fe–C–Cu–5% MoS2 (2.5 N m).

S. Dhanasekaran, R. Gnanamoort

Fc

tWapcwpppi

cmr

dsgmtctrgmiOoiososawaa

iWt

ig. 5. Gear tooth contact mechanics: (a) beginning of contact and (b) end ofontact.

he base and MoS2 containing gears at the each meshing cycle.ear depth quantified in every mesh cycle along the line of

ction in the MoS2 containing gear composition is lower com-ared to that in a base composition gears. During each meshingycle, the wear contour changes along the line of action and highear occurs at the root and tip side. Furthermore, at the pitchoint all the curves have a minimum or zero wear. At the pitchoint, where the sliding velocity is zero and minimum wear takeslace. The wear depth is high at the rest of contact where slidings more.

Fig. 5 shows the gear tooth at the beginning and at the end ofontact. At the beginning of contact, the root of the sintered geareshes with the tip of mating gear and there is a combination of

olling and sliding (Fig. 5(a)). Due to the difference in deden-

bAaf

Fig. 6. (a) Sliding velocity of sintered spur gear an

Fig. 7. Pitting formation in the failed gear tooth surfaces tested at

hy / Wear 265 (2008) 81–87 85

um and addendum dimensions in the sintered and mating gear,liding occurs between the root of sintered gear and tip of matingear. The sliding velocity changes continuously throughout theesh and is zero only at pitch point (Fig. 5(b)). Sliding is posi-

ive in the addendum and negative in the dedendum resulting inompressive friction force above the pitch point and tensile fric-ion force below the pitch point. Fig. 6(a) shows the schematicepresentation of sliding velocity along the line of action in spurears. As seen from the figure, the sliding velocity increases asesh progresses from points A to B. That is, the sliding velocity

ncreases along the flank and face side of gear tooth surface.nly at the pitch point pure rolling (point C) occurs. At everyther contact points, towards or away from the pitch point, theres a relative sliding velocity between the gear teeth and slidingccurs between teeth surfaces. For the above reasons, it can bepeculated that pitting takes place in the dedendum flank portionr root portion of a test gear where severe conditions in terms ofliding contact, namely a maximum slippage, prevails (Fig. 7(a)nd (b)). Simulated wear pattern of the test gear shows maximumear at the root portion and minimum wear at the face side. In

ddition, high dedendum surface deformation in the tested gearslso supports the above statement [1] (Fig. 8(a) and (b)).

The contact pressure at a point depends on the load shar-ng. Fig. 6(b) shows the load distribution in spur gear contacts.

hen gear teeth contact commences at A1, there is another paireeth also in contact at A3. The load will continue to be shared

etween the two pairs until initial contact moves to contact point2. At the same time the preceding pair of teeth will disengage

t point A4. The full load is then taken by a single pair of teethor contacts between A2 and A3. Less wear occur near the pitch

d (b) load distribution of sintered spur gear.

2.51 N m torque: (a) Fe–C–Cu and (b) Fe–C–Cu–3% MoS2.

86 S. Dhanasekaran, R. Gnanamoorthy / Wear 265 (2008) 81–87

m tor

pasoctfBphzriTaTbo

decsiemratwTf

Fo

casswttamnvctwwg

rasaFsuiasing area and decreases the localization of strain. Presence of

Fig. 8. Dedendum damage of gears tested at 1 N

oint where the sliding velocities are small compared to the rootnd tip regions of the teeth. The distance between A and B, ashown in Fig. 4, is the single tooth-meshing zone. The amountf wear increases from pitch point towards A and B and afterrossing points A and B, there is a sudden drop in wear dueo the variation in the contact pressure as the contact changesrom single to double tooth. The distance between points A and

in the single meshing tooth are strained due to high contactressure. Near the pitch point, wear increases as a function ofigh contact pressure. In addition, in the single tooth contactone (points between A and B) wear depth is low in dedendumegion (point A in Fig. 4) compared to addendum region. Thiss mainly due to long and short addendum system employed.he long and short addendum system increase tooth thicknessnd relative sliding velocities between the meshing teeth flanks.hicker teeth and relative sliding velocity reduces the suscepti-ility to such damage. Tooth modification has a marked effectn the wear of meshing teeth.

The amount of material removal in one meshing cycleepends on the wear coefficient. The wear coefficient is not gen-rally a material property, but a variable that is determined byontact condition, and mating material properties. In the currenttudies, it is assumed that the tooth profile change is not signif-cant in one cycle and the amount of material removed duringach cycle is same. The values of wear coefficient can be deter-ined from the experimentally measured wear depth. Schematic

epresentation of profile change and wear depth measurementre shown in Fig. 9(a) and (b). Wear depth is the distance along

he radii between the worn and unworn surface. The measuredear coefficients at all tested torque levels are given in Table 3.he wear depth after a certain number of cycles was estimated

rom the maximum wear depth in the dedendum region. Surface

ig. 9. (a) Schematic representation of tooth profile change and (b) measurementf wear depth.

MsY

TS

T(

1122

que: (a) Fe–C–Cu and (b) Fe–C–Cu–3% MoS2.

ondition changes continuously during service and influence thectual wear process. The 3% MoS2 containing gear alloy compo-ition exhibited a lower wear coefficient. The computed resultshow that materials with low wear coefficient exhibited less toothear. Tooth profile loss or cycles to failure is therefore related

o mechanical properties of the material. The second phase par-icles are uniformly distributed and porosity is less in MoS2dded sintered steel [13]. The second phase particles in the steelatrix lead to an increase in the compressive strength and hard-

ess compared to base composition (Table 1). Presence of higholume fraction of second phase in 5% MoS2 containing gearompositions result in a lower strength and hardness comparedo 3% MoS2. The increased hardness and strength decreases theear coefficient in 3% MoS2 contained gear samples. The lowear coefficient decreases the wear depth in MoS2 containingears.

In the sintered steel gears, Young’s modulus and Poisson’satio were predicted from experimentally measured porositynd density. Table 1 shows the predicted Young’s modulus ofintered gear compositions investigated. The MoS2 added gearlloy has a high Young’s modulus and good wear resistance.or the porous materials Young’s modulus is a good measure oftrength, since for a given stress, an increase in Young’s mod-lus results in a low applied strain. A low applied strain resultsn a low degree of strain localization, which decreases the wearnd increases the life of gear. Particularly, in MoS2 added gearamples, an increase in Young’s modulus increases the load bear-

oS2 increases the compressibility and increases the part den-ity of gear specimen. Increased density results in an increase inoung’s modulus.

able 3intered gear wear coefficient

orqueN m)

Fe–0.6% C–2.5%Cu (m2/(N m))

Fe–0.6% C–2.5%Cu–3% MoS2

(×10−9 m2/(N m))

Fe–0.6% C–2.5%Cu–5% MoS2

(×10−9 m2/(N m))

5.10 × 10−9 1.24 2.05.5 1.55 × 10−8 2.07 4.46

2.03 × 10−8 5.34 8.26.5 2.78 × 10−8 5.38 9.21

S. Dhanasekaran, R. Gnanamoort

Ft

pTeiigdata

5

iswoiwrmdshct

R

[

[

[

[

[14] J. Wojnarowski, V. Onishchenko, Tooth wear effects on spur gear dynamics,Mech. Mach. Theory 38 (2) (2003) 161–178.

[15] S. Dhanasekaran, R. Gnanamoorthy, Dry sliding friction and wear char-acteristics of Fe–C–Cu alloy containing molybdenum di sulphide, Mater.

ig. 10. Predicted and experimental wear depth for the sintered steel gears inves-igated: (a) Fe–C–Cu, (b) Fe–C–Cu–3% MoS2, and (c) Fe–C–Cu–5% MoS2.

Wear predictions based on the described wear model are com-ared with the tooth wear measurements conducted in gear tests.he predicted wear depth using the above model along withxperimental results under different torque conditions are shownn Fig. 10. Predicted values are in good agreement with the exper-mentally measured wear depth for both base and MoS2 addedear compositions. The wear resistance of sintered steel gear

epends on the amount of MoS2 addition in the base compositionnd microstructure. Based on the both predicted and experimen-al results, it is clear that the material with high density, hardnessnd strength improves the wear resistance.

hy / Wear 265 (2008) 81–87 87

. Conclusions

The gear wear characteristics of sintered steel gears contain-ng MoS2 were investigated. Wear prediction model suitable forintered steels was described based on the existing approach forear prediction in gears and Archard’s wear equation. Additionf MoS2 improves the part density, hardness and strength andncreases the wear resistance. The progressive wear predictionsill enable the gear designers to evaluate the safe gear-operating

egime. Wear predictions and observations indicate the maxi-um wear in the dedendum and addendum regions. Gear wear

epends the materials hardness and strength. The results pre-ented show the progression of material removal and indicateow the wear varies from point to point over the gear meshingycle. The predicted wear depths are in close agreement withhe experimental results.

eferences

[1] S. Dhanasekaran, R. Gnanamoorthy, Abrasive wear behavior of sin-tered steels prepared with MoS2 addition, Wear 262 (5–6) (2007)617–623.

[2] D. Walton, A.J. Goodwin, The wear of unlubricated metallic spur gears,Wear 222 (2) (1998) 103–113.

[3] S. Wu, H.S. Cheng, Sliding wear calculation in spur gears, J. Tribol. 115(1993) 493–500.

[4] A. Flodin, S. Andersson, Simulation of mild wear in spur gears, Wear 207(1997) 16–23.

[5] J. Brauer, S. Andersson, Simulation of wear in gears with flankinterference—a mixed FE and analytical approach, Wear 254 (2003)1216–1232.

[6] H. Imrek, H. Duzcukoglu, Relation between wear and tooth width modifi-cation in spur gears, Wear 262 (3–4) (2007) 390–394.

[7] I. Yesilyurta, F. Gub, A.D. Ball, Gear tooth stiffness reduction measurementusing modal analysis and its use in wear fault severity assessment of spurgears, NDT&E Int. 36 (2003) 357–372.

[8] C. Yuksel, A. Kahraman, Dynamic tooth loads of planetary gear sets havingtooth profile wear, Mech. Mach. Theory 39 (2004) 695–715.

[9] S. Glodez, B. Abersek, J. Flasker, Z. Ren, Evaluation of the servicelife of gears in regard to surface pitting, Eng. Fract. Mech. 71 (2004)429–438.

10] K. Aslantas, S. Tasgetiren, A study of spur gear pitting formation and lifeprediction, Wear 257 (2004) 1167–1175.

11] L.K. Timothy, A. Kahraman, An Experimental Investigation of theInfluence of the Lubricant Viscosity and Additives on Gear Wear,NASA/TM—005-213956, 2005, pp. 1–25.

12] G. Litak, I. Michael, Friswell, Vibration in gear systems, Chaos SolitonFract. 16 (2003) 795–800.

13] O. Lundvall, N. Stromberg, A. Klarbring, A flexible multi-body approachfor frictional contact in spur gears, J. Sound Vib. 278 (3) (2004) 479–499.

Design 28 (4) (2007) 1135–1141.