Experimental Tooth Contact Analysis and Life Prediction

SAE Paper Mo. 2003-26-0014

Experimental Tooth Contact Analysis and Life Prediction Methodology for Truck Axles Hypoid Gears

A n o o p Jain Eicher Motors Ltd., Pithampur, India

A B S T R A C T

This paper describes the methodology followed for experimental prediction of tooth contact patterns of Truck Axle Hypoid Gear sets in loaded state. Effort has been m a d e to establish Hypoid Gear Life based on Duty Cycle simulation on a pair of Test Axles an in-house developed n e w closed loop Axle Test Machine. Service Load Data is acquired on loaded truck to establish sustained torque levels on the Drive Axles. Loaded Tooth Contact pattern (LTCA) is generated using Gleason Program and Deflection Test analysis is carried out on the Four Square Axle Test Machine. Typical tooth contact patterns at a series of loads from no load to max imum load are generated on the axle test machine. Variation of tooth contact patterns as a function of applied torque is compared with the predicted L T C A . Methodology for accelerated testing has been concluded and correlation with the service data is being established.

I N T R O D U C T I O N

Extensive study of the performance of truck axle gears has indicated that axle gears are more dependent on the m a x i m u m sustained loads rather than the occasional peak loads which occur during the anticipated life of the vehicle. The stresses resulting from the sustained loads cannot safely exceed the endurance limit of the gear material. On~Highway truck axle gears are sized based on performance torque based on equivalent grade and road conditions. Hypoid gears having pinion offset with respect to the gear centre line permit a larger, stronger pinion with more tooth contact area and are popular on highway truck application as compared to spiral bevels.

According to the classic design, gear sets have three principal types of tooth contact pattern. The type of tooth contact depends to the highest degree on the possible flank form modifications versus the conjugate flank form.

The intent of flank modifications is to provide a limited contact area under no load or light load which provides insensitivity to gear housing tolerances, inaccuracies in the gear members and assembly, as well as deflections.

For cutting bevel gears there are three mechanisms to create modifications known as "crowning'" that have the intent to locate the bearing contact inside the boundaries of the teeth and therefore, prevent edge contact.

The first element is lengthwise crowning which is a circular modification along the face width. The second element to generate crowning is a profile modification on the tool. The third element of flank crowning Is flank twist from toe to heel. All real bevel and hypoid gear application used in power transmissions use a combination of all three types of crowning. (Refer Fig.1)

The fatigue life of bevel and hypoid gear has been known to be a function of length, width and position of the "no load" tooth contact pattern. Careful positioning of the tooth contact pattern relative to the gear m e m b e r can produce dramatic increases in bending fatigue life.

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Symposium on international Automotive Technology 2003

it has been established that there is a two fold increase in bending fatigue life obtained by positioning the tooth contact pattern toward the toe of the gear tooth rather than at a central toe position.

HYPOID GEAR DEVELOPMENT AND EVALUATION METHODOLOGY

Fig. 2 outlines the methodology of Gear Development process followed.

Objective is to sign off the acceptable tooth contact pattern and asses the acceptable range of tooth contact patterns on a finally applied hypoid pair by making use of a variety of theoretical analysis outputs obtained through T 9 0 0 and T 2 0 0 0 Gleason Program in consultation with gleason.

Efforts are on to establish the influence of contact patterns on bending and contact fatigue life of truck axle hypoid gears by conducting a series of constant duty cycle tests on a specific ratio of hypoid gear pair on an in-house developed Axle Test machine.

CORRELATION B E T W E E N EXPERIMENTAL A N D LOADED TCA

As torque is applied to a gear set the area of contact

between the gear and pinion teeth changes as the tooth surfaces deform and the gear housing deflects. These changes are usually observed as a growth in the contact pattern along with a movement of the contact area. The exact nature of the growth and movement of the contact pattern has a profound effect on the strength performance of the gear set.

L O A D E D T C A T H R O U G H F E A : In order to visualize the change in contact pattern as a function of applied torque, Gleason program T900 was used to display the loaded TCA plots at the no-load position and for three non zero torque loads. Four panels are shown in Fig, 3.

The loaded T C A plot shows the growth and movement of the tooth contact pattern as a function of applied torque. The upper left hand panel is the bench (no -load) tooth contact pattern. The bench tooth contact pattern corresponds to the tooth contact pattern predicted by the Gleason T C A program and is a function of the developed settings for the gear and pinion contained in a special analysis file. The three non-zero torque positions shown in Fig. 3 correspond to three different percentage torques.

Program T900 uses E P . G to describe the rigid body motions of the pinion relative to the gear as torque is

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applied to the pinion. The tooth contact patterns were calculated using the values of E,P,G determined from the experimental axle deflection tests as described in section "Deflection testing".

In T900 program, gear blanks are rendered as finite element models. Gear geometry is constructed using special analysis files obtained by Gleason T 2000 program.

E X P E R I M E N T A L L O A D E D T O O T H C O N T A C T T E S T A P P R O A C H A N D M E T H O D O L O G Y : This test was performed on completely processed gears. Typical Tooth contact check was conducted at a

series of loads from no load to maximum load; the tooth contact photographs show how the tooth contact pattern shifts and lengthens as the load is increased. (Refer Table - I for input torque load simulation for carrying out the test)

Under peak torque load the contact pattern should extend to the tooth boundaries without showing a concentration of the contact pattern at any point on the tooth surface.

Any tooth contact pattern which shows a concentration of load near tooth boundaries indicates

that there is either an excessive displacement of the gears in their mounting or an unsatisfactory tooth contact pattern development for this application.

To determine what action is required, the second phase of the deflection test should be performed.

This test is conducted on a 4 Square Axle test machine described below. (Refer Fig. 4)

TESTING E Q U I P M E N T , F O U R S Q U A R E A X L E T E S T M A C H I N E : This is a back to back or closed loop type Dynamometer where the basic arrangement includes two automotive drive axles positioned one above the other. The output shafts of the Axles are connected by a spur gear box at each end. Input to Axles goes via a spur gear box which is driven by a D C Drive with step less speed control. This in - house developed axle test machine features a dynamic torque transducer to measure the re-circulating torque in the system. (Refer Fig. 4) Torque is twisted into the system to impose a load throughout, by a unique torque mechanism, in the direction to place the load on the desired side of the teeth, and then the entire system is rotated by the drive motor in the direction counter to the twist (in the drive direction). The power demand is small, being only the amount needed to overcome the friction in the system.

Drive motor is placed at the input end of the test component to add power here and relieve the load on the slave component. In this set up the bottom axle is the test piece and the top one is the slave axle.

This machine is capable of carrying out Loaded Tooth contact test, Deflection Test, Accelerated Stress (AST) and Accelerated Life Test (ALT) to stimulate and simulate various modes of Drive Axle Gear failures, which include Bending Fatigue, Pitting, Scuffing tests.

R E S U L T S A N D ANALYSIS : Variation of tooth contact pattern for a 15.5 inch Hypoid gear design versus applied gear torque as predicted by Finite Element model are depicted in Fig. 3. The Four panels correspond to the

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bench contact pattern and at 25%, 50% and 100% pinion input torque.

Corresponding tooth contact patterns obtained from the experimental tests carried out on 4 Square Axle Test Machine on a 15.5 inch Hypoid Pair are depicted in Fig. 5.

O n comparing Fig. 3 and 5 it can be seen that there is good agreement between the predicted and measured tooth contact patterns as a function of applied torque. The lengths at each value of gear torque are within five percent of each other while the shape characteristics are in close agreement, it can be also observed that the tooth contact spread is uniform and contained within the tooth boundaries which suggest that the tooth contact development is acceptable.

L O A D E D A X L E DEFLECTION T E S T A P P R O A C H A N D M E T H O D O L O G Y

The deflection test is essential in determining the suitability of the gear mountings. The purpose of this test is to determine the displacements of the hypoid gear pair and their mountings under various load conditions. This test is carried out subsequent to the loaded tooth contact check.

The axle deflections (E,P,G) measurements are as per the Gleason Works recommended procedure. E,P,G are the linear components of the rigid body motions of the gear and pinion relative to the axle housing. Drive and Coast tests are performed at 10%, 25% ,50% ,75% and 100% of input torque in the axle.

TESTING E Q U I P M E N T : Testing was conducted with the Gear unit installed in a device capable of applying

load in increments of 25 % of full torque up to 100%. Desirable speed is approximately 2-3 r/min of the output shaft, to permit accurate readings of the deflections. Experimental setup for carrying out the deflection test is shown below in Fig. 6.

MEASUREMENT OF DISPLACEMENTS : The measurement of displacements w a s accomplished by attaching a series of linear displacement transducers (Dial indicators) which are appropriately located to measure the displacement of the gears, shafts, bearings and the differential housing itself in all the three principal directions; along the pinion axis (P), along gear axis (G) and perpendicular to these axis (E). Fig. 7 shows a typical placement of the indicators on the Axle housing to measure the displacements. O n c e the indicators were mounted, the displacements were recorded at various input torque levels as indicated in the Input torque simulation matrix (Table - I)

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DEFLECTION S U M M A R Y A N D ANALYSIS : Dial indicator readings were recorded for further

analysis. A completed Indicator / Displacement diagram (refer Fig. 8) was prepared where the maximum readings were posted at each indicator position.

Using dial indicator readings, calculations were made along each of the three principal axis E,P,G and also the relative displacements were calculated. (Refer Table - I!)

Although the combination of deflections exceeded the recommended limits as specified below, these deflections are tolerable as contact behavior was found satisfactory. (Refer Table - III)

E N D U R A N C E TESTING

The Endurance testing is frequently identified as the "acceptance" test because it establishes the working life of the product and thus its acceptability. The purpose of endurance test is to determine the life of a gear design under actual or simulated conditions of test operation. The endurance tests include : Bending Fatigue (Tooth root fillet breakage) a Contact Fatigue (Pitting and Case crushing) Scoring Wear Repetitive shock loading breakage

And the test procedures include : Field Testing in Normal service Field Testing under controlled conditions Laboratory Testing, using a closed-loop Axle test

Dynamometer.

At E M L , Various Endurance tests are being conducted on a 4 Square Axle Test machine.

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SERVICE LOADING AND ENDURANCE TEST PRINCIPLE : Reproduction of realistic driveline loading warrants the need for multi-channel, phase related, recorded road load data. This has been achieved by carrying out Dynamic Service load data acquisition of strain, angular velocities and gear shift pattern on a truck operating at rated G V W using Q X -3 data gate system with a sampling rate of 205 samples on roads and under various events viz. highway, rough road, hilly section and on standard grade. Refer Fig. 9 for illustration of a sample data recorded on test vehicle.

TEST APPROACH and METHODOLOGY : Most automobile gear teeth are subjected to

repeated, one way bending for the major part of their lives. O n road vehicle gears are loaded in reverse which represents only 0.1 % to 1 % of their service life. So, in general, it is considered appropriate to test automobile gears in one way bending fatigue.

Bending fatigue tests are performed at loads that correspond to a life factor between 2.00 to 2.67 thus yielding an expected test life of between 20,000 and 1,000,000 pinion cycles (Fig. 10).

This is constant amplitude testing with increased frequency of cyclic loading (Accelerated test)

Test torque should produce a stress on the Gear and Pinion at s o m e value above the endurance limit to avoid a test that could continue indefinitely.

5 samples of each Gear pair of different type are being tested for bending fatigue in accordance to the Accelerated Test Simulation Matrix (refer Table - IV) at a life factor of 1.8, which yields an estimated Pinion life of 200,000 cycles or 18h approximately (Fig. 10).

S - N Curves are to be generated by approximating the Life scatter data as available from the test rig.

Failure m o d e s are to be recorded and analyzed.

LIFE C Y C L E S E V A L U A T I O N : Life cycle computation for the pair is done based on the Gleason method is briefly described below :

Life Factor, KL , is defined as the numerical ratio of the calculated tensile bending stress, St to the allowed tensile bending stress, Sat.

Equivalent Life cycles for pinion

Infinite life is assumed to be greater than 6 x 106 cycles for Pinion. Based on the calculated life cycles, equivalent test torque is computed for simulating the rupture cycles is determined using Gleason Dimension sheet of the

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particular Gear design under Bending fatigue test. This is summarized in a form of a test Simulation matrix (Table - IV). ACCELERATED TEST PROGRESS SUMMARY : Currently, Bending fatigue tests are being conducted on a particular Drive Axle Hypoid pair. Fatigue data for two samples have been recorded.

Efforts are on to establish experimental procedures which closely correlate the theoretical model which will cut short the future development cycle for establishing and proving a n e w pair.

Refer failure photographs in Fig. 11 and 12 of two failed samples where teeth uprooting took place after 36 and 2 8 h of Accelerated test respectively.

F U T U R E W O R K O N HYPOID G E A R LIFE PREDICTION

Correlation of field life data on proven designs with data obtained on Axle test machine.

To perform Weibull analysis of the fatigue data associated with the gear design. Weibull slopes and mean life for the gear design to be compared with

a second set of data for a different gear design. Weibull analysis calculates the slope and shape parameter for a given confidence value (usually 90%) and displays the upper limit estimates of the 50 percent mean life curve on the S-N curve for the gear design being analyzed.

To draw updated S-N Curve displaying the upper and lower confidence limits of the estimated mean life curve based on confidence limits along with gear and pinion failures plot.

Axle test machine will be upgraded to simulate the actual RLDA cycles by replacing the manual mechanical torque mechanism with a magnetic torque valve coupled with an Epicyclic Gear Box. Post Upgradation, variable dynamic torque loads can be simulated in the Axle test machine loop which will be controlled by a microprocessor.

S E L E C T E D B IBL IOGRAPHY

1. "Design and Manufacture of Spiral Bevel and Hypoid Gears for Heavy Duty Drive Axles", Gleason Works Publication

2. Theodore, J. K., "Tooth Contact Analysis of Spiral Bevel and Hypoid Gears under Load", S A E Paper No . 810688

3. "Understanding Tooth Contact Analysis", Gleason Works Publication, SD3139A, January 1978.

4. Lehrmann, J. R., "Development of Contact Patterns on Tractor Spiral and Hypoid Gears", S A E Paper No. 841091

5. Wilcox, L., "Analyzing Gear Tooth Stress as a Function of Tooth Contact Pattern Shape and Position", Gleason Works Publication

6. Wicox, L., "Improved Finite Element Model For Calculating Stresses in Bevel and Hypoid Gear Teeth", A G M A Paper, 1997

7. "Application Testing of Bevel and Hypoid Gears", Gleason Publication

8. "Bending and Contact Stresses in Hypoid Gear Teeth", Gleason Publication

C O N T A C T

Mr. Anoop Jain Manager, Product Design & Development Eicher Motors Limited Indore, India E-mail : [email protected]

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Experimental Tooth Contact Analysis and Life Prediction

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