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4、Fax: 724-776-0790 Email: CustomerServicesae.org SAE WEB ADDRESS: http:/www.sae.orgJ2817 AUG2008 SURFACEVEHICLERECOMMENDEDPRACTICEIssued 2008-08Definition and Measurement of Torque Biasing Differentials RATIONALENot applicable. 1. SCOPE This SAE Recommended Practice covers passive torque biasing axle
5、 and center differentials used in passenger car and light truck applications. Differentials are of the bevel gear, helical gear and planetary types although other configurations are possible. 1.1 Purpose To provide a common means to define, measure and quantify the operating characteristics of torqu
6、e biasing differentials.2. REFERENCES There are no referenced publications specified herein. 3. DEFINITIONS 3.1 Torque Bias Ratio Given a differential where one full turn of a first output shaft results in one full turn in the opposite direction of a secondoutput shaft (1:-1 ratio across outputs): T
7、orque bias ratio is defined as the ratio of the output torques when differentiating under load.Torque Bias Ratio (TBR) = Torque high / Torque low (Eq. 1) (expressed as N:1) SAE J2817 Issued AUG2008 - 2 -ThighTlowFIGURE 1 - DIFFERENTIAL OUTPUTS SHOWING HIGH AND LOW TORQUE 3.2 Locking Effect Locking e
8、ffect (LE) is an alternate means of expressing torque imbalance supported by the differential. It is the relationship between torque difference and input (total) torque. It is useful when defining the performance of a torque split differential (ratio across outputs other than 1:-1). The relationship
9、 between locking effect and bias ratio is shown in Figure 2. % Locking Effect = 100 X T / Ttotal (Eq. 2) % LE = 100 X (Torque High - Torque Low) / (Torque High + Torque Low) % LE = 100 X (TBR -1) / (TBR + 1) TBR = (1 + %LE) / (1 %LE) (Eq. 3) 02040608010012345678910TBR%LEFIGURE 2 - PLOT OF LOCKING EF
10、FECT VERSUS TORQUE BIAS RATIO SAE J2817 Issued AUG2008 - 3 -3.3 Torque Splitter TinputTrearTfrontFIGURE 3 - DIAGRAM OF TORQUE SPLITTER T input = T front + T rear (Eq. 4) Torque Split Ratio (TSR) is the gear ratio of the two output shafts where Nf = number of teeth on front output gear and Nr = numbe
11、r of teeth on rear output gear TSR = Nf / Nr (Eq. 5) Example:12 teeth on front output gear 18 teeth on rear output gear TSR = Nf / Nr = 12 / 18 = 0.667 Torque distribution (Front: Rear) assuming a “frictionless” open differential is always fixed at a certain ratio determined as follows: % Torque to
12、front output Tf = 100 X Nf / (Nf + Nr) % Torque to rear output Tr = 100 X Nr / (Nf + Nr) Example #1: 12 teeth on front output gear 18 teeth on rear output gear %Tf = 100 X 12 / (12 + 18) = 40% %Tr = 100 X 18 / (12 + 18) = 60% This is normally expressed as a 40/60 (Front / Rear) nominal torque split.
13、SAE J2817 Issued AUG2008 - 4 -When biasing capability is added, torque is distributed over a range around the nominal split ratio. Torque Distribution Ratio (TDR) is the ratio of the output torques when biasing. It is expressed as the ratio of the high torque output to the low torque output and may
14、also be shown as percent torque to front and rear. It is a combined effect of TSR and TBR. When biasing to the front, TDR = TBR * TSR When biasing to the rear, TDR = TBR / TSR Example #2: 12 / 18 tooth combination gearing, 30% Locking effect TSR = Nf / Nr = 12 / 18 = 0.667 LE = 0.3 TBR = (1 + 0.3) /
15、 (1 0.3) = 1.86 When biasing to front, TDR = 1.86 * 0.667 = 1.24 (1.24:1 ratio front to rear) %Tf = 100 X TDR / (TDR + 1)%Tf = 100 X 1.24 / (1.24 + 1) = 55.4% (55% front, 45% rear) When biasing to rear, TDR = 1.86 / 0.667 = 2.78 (2.78:1 ratio rear to front) %Tr = 100 X TDR / TDR + 1) %Tr = 100 X 2.7
16、8 / (2.78 + 1) = 73.5% (74% rear, 26% front) In Example #2, the nominal 40:60 torque split will send up to 55% of the torque to the front or 74% to the rear due to the biasing capability. Within the defined limits of torque distribution, differential gearing remains static relative to the differenti
17、al housing in a vehicle application. When torque distribution reaches either the bias to front or bias to rear limit,differentiation will occur with torque distributed at the limit. Torque distribution is shown graphically in Figure 4.1.0Torque Bias RatioInfinite50 / 5040 / 60100 % Rear100%Front1.86
18、 TBR30% Locking EffectNo differentiation within this rangeBias to Front(55 / 45)Bias to Rear(26 / 74)TorqueDistributionFIGURE 4 - TORQUE DISTRIBUTION AT 30% LE SAE J2817 Issued AUG2008 - 5 -Example #3: 18 / 12 tooth combination gearing, 30% Locking effect TSR = Nf / Nr = 18 / 12 = 1.50 LE = 0.3 TBR
19、= (1 + 0.3) / (1 0.3) = 1.86 When biasing to front, TDR = 1.86 * 1.50 = 2.78 (2.78:1 ratio front to rear) %Tf = 100 X TDR / (TDR + 1) %Tf = 100 X 2.78 / (2.78 + 1) = 73.5% (74% front, 26% rear) When biasing to rear, TDR = 1.86 / 1.50 = 1.24 (1.24:1 ratio rear to front) %Tr = 100 X TDR / TDR + 1) %Tr
20、 = 100 X 1.24 / (1.24 + 1) = 55.4% (55% rear, 45% front) 3.4 Preload Torque biasing properties of bevel, helical and planetary gear differentials are commonly achieved by using gear thrust forces to generate friction within the differential, and thereby resistance to differentiation. Spring thrust m
21、ay also be addedto generate additional friction.Without the addition of spring thrust, there is generally negligible resistance to differentiation when input torque is equal tozero. With the addition of spring thrust, an initial preload is generated which creates resistance to differentiation when i
22、nput torque is equal to zero.The effect of preload can be seen in Figure 5 by examining Torque versus Total Torque: +- +- T = Thigh- TlowTtotal= Thi gh+ TlowNo preloadPreloaded, gear thrust compresses springPreloaded, spring adds to gear thrust t0 t0= preload torque across outputs with no input torq
23、ueNote that with no input torque, there is no torque difference across the outputs with a non-preloaded differentialFIGURE 5 - PLOT OF TORQUE VERSUS TOTAL TORQUE In the typical case where spring preload adds to gear thrust, torque created by spring preload increased torque on the highly loaded outpu
24、t and decreases torque on the opposite output.Example #4: 2.5 TBR + 100 N*m Preload in an axle differential Thigh = Ttotal * TBR / (TBR + 1) + 100 Tlow = Ttotal * 1 / (TBR + 1) 100 SAE J2817 Issued AUG2008 - 6 -Figure 6 shows a comparison of output torques in an axle differential having 2.5 TBR with
25、 no preload and with 100 N*m preload.2.5 TBR + 100 N*m Preload-1500-1000-500050010001500-1500 -1000 -500 0 500 1000 1500TLTRPreload No PreloadFIGURE 6 - 2.5 TBR WITH AND WITHOUT PRELOAD 3.5 Backlash Backlash is normally found in any bevel, helical or planetary geared differential as a result of nece
26、ssary manufacturing tolerances and operating clearances between internal components. It is evident during a load reversal as a rotational movement of the input or outputs which occurs before torque is transmitted. It should be noted that preload (eg. spring) will increase the amount of input torque
27、required before this rotational movement can be detected.3.6 Modes of Operation Torque bias can be measured in four modes of operation as shown in Figure 7. These modes apply to both axle and center differentials.SAE J2817 Issued AUG2008 - 7 -Accelerate(High Torque) in 2 point test or braking in 3 p
28、oint testRotation RotationBraking(Low Torque)Reaction torque, fixture to housing (2 point test) or input torque (3 point test)Typical of drive mode, left turn in a rear axleTypical of coast mode, left turn in a rear axleAccelerate(High Torque)in 2 point test or braking in 3 point testRotationRotatio
29、nBraking(Low Torque)Reaction torque, fixture to housing (2 point test) or input torque (3 point test)Reaction torque, fixture to housing (2 point test) or input torque (3 point test)RotationRotationAccelerate(High Torque) in 2 point test or braking in 3 point testBraking(Low Torque)Typical of drive
30、mode, right turn in a rear axleFIGURE 7 - FOUR MODES OF OPERATION SAE J2817 Issued AUG2008 - 8 -Reaction torque, fixture to housing (2 point test) or input torque (3 point test)RotationRotationTypical of coast mode, right turn in a rear axleBraking(Low Torque)Accelerate(High Torque) in 2 point test
31、or braking in 3 point testFIGURE 7 - FOUR MODES OF OPERATION (CONTINUED) 4. PROCEDURES 4.1 Preload Measurement 4.1.1 Torque-To-Turn (TTT) Procedure (Low Bias / Output to Output Measurement) a. Lubricate all sliding surfaces with the application specific lubricant. Note certain clutch materials may n
32、eed to be soaked for an extended period of time. b. Assemble suitable output shafts to differential. c. Lock one output shaft from rotation. d. Allow input member to rotate freely e. Turn opposite output shaft a minimum of three full clockwise rotations f. Record peak (breakaway torque) reading as w
33、ell as average (rolling torque) reading. An example is shown in Figure 8. g. Repeat steps e. and f. in the reverse direction. Note this method can be used to measure an in-vehicle axle differential by raising one wheel off the ground and placing the transmission in Neutral. SAE J2817 Issued AUG2008
34、- 9 -Preload MeasurementRotationTorqueBreakaway TorqueRolling TorqueFIGURE 8 - EXAMPLE OF BREAKAWAY TORQUE AND ROLLING TORQUE 4.1.2 Torque-To-Turn (TTT) Procedure (High Bias / Output to Input Measurement) a. Lubricate all sliding surfaces with the application specific lubricant. Note certain clutch
35、materials may need to be soaked for an extended period of time. b. Assemble suitable output shafts to differential. c. Lock input member from rotation. d. Turn one output shaft a minimum of three full clockwise rotations while allowing the opposite output to rotate freely. e. Record peak (breakaway)
36、 reading as well as average (rolling torque) reading. f. Repeat steps d. and e. in the reverse direction. g. Repeat steps d. through f. with the opposite output shaft. Note this method can be used to measure an in-vehicle axle differential by raising both wheels off the ground and placing the transm
37、ission in Park. 4.2 Backlash Measurement (applies to differentials without preload) 4.2.1 Measurement at One Output a. Lubricate all sliding surfaces with the application specific lubricant. Note certain clutch materials may need to be soaked for an extended period of time. b. Assemble output shafts
38、 equipped with expanding arbors to differential. This is intended to measure backlash of the differential assembly only and does not include splines.c. Lock one output shaft from rotation. d. Lock input member from rotation. SAE J2817 Issued AUG2008 - 10 -e. Turn opposite output shaft in both clockw
39、ise and counterclockwise directions under a torque load of 15 Nm. f. Measure and record total rotational movement of the output shaft to which torque was applied.NOTE: If testing a differential in an assembly (such as an axle), be aware that other components will contribute to measured backlash. 4.2
40、.2 Measurement at Input (high torque) a. Lubricate all sliding surfaces with the application specific lubricant. Note certain clutch materials may need to be soaked for an extended period of time. b. Assemble output shafts equipped with expanding arbors to differential. This is intended to measure b
41、acklash of the differential assembly only and does not include splines.c. Lock both output shafts from rotation. d. Rotate the input in one direction to a torque of 100 Nm. e. Rotate the input in the opposite direction to a torque of 100 Nm. f. Rotate the input back to the original position (zero to
42、rque). g. Referring to Figure 9, draw the best-fit lines (labeled) tangent to the curves. This separates wind up from lash. +Lash A to CC D0A BLash B to D- 0 +Degrees rotationTypical Rotational Lash GraphTorqueFIGURE 9 - ROTATIONAL LASH h. Measure the distance between lines A and C and B and D. i. A
43、verage the distance. j. Multiply this value by the graph scale to determine rotational lash value. SAE J2817 Issued AUG2008 - 11 -To eliminate variability due to interpretation of best fit lines, it is recommended to use a curve fitting technique. 4.3 Component Level Torque Bias Test 4.3.1 Equipment
44、 Requirements Measurement at component level can be performed on a vertical or horizontal axis bench stand with two motor-brakes with the test differential secured to a fixture and provisions for lubricant flow to the differential. Temperature control is typically not required, however, temperature
45、must remain below the maximum operating level as defined by the lubricant supplier. It should be noted that lubricant temperature may affect torque bias ratio. A provision to ensure removal of lubricant contaminants is required. Motor / BrakeMotor / BrakeTorquemeterTorquemeterBiasing device grounded
46、 to fixture plateFIGURE 10 - TWO POINT TEST RIG A diagram of the two point test rig is shown in Figure 10. Torque and speed capabilities are to be appropriately sized for the differential application. Torquemeter accuracy is to be within 0.5% of full scale. Output speed measurement is to be accurate
47、 within 1% of actual speed. SAE J2817 Issued AUG2008 - 12 -4.3.2 Test Conditions 4.3.2.1 Break-in Break-in is not specified as part of this document. It is assumed that the differential will be tested in the “as-shipped” condition recognizing that a change in bias ratio may be observed with extended
48、 operation at differentiation under load. This typically appears as a knee in the bias curve after which bias becomes stable as shown in Figure 11. 2.002.202.402.602.803.003.203.403.603.800 500 1000 1500 2000 2500 3000 3500Differential LifeBiasRatioKnee in break-in curveFIGURE 11 - TYPICAL BREAK-IN
49、CURVE 4.3.2.2 Backlash and Preload If applicable, record differential preload and rotational backlash prior to testing.4.3.2.3 Operating Parameters for Test Maximum total torque for the test to be controlled to 5 30 percent of vehicle skid torque as measured across the differential outputs. Torque is to be either continuously ramped or incrementally stepped from 0 to the maximum (30% of ski
