1、_ SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising there
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4、SA) Fax: 724-776-0790 Email: CustomerServicesae.org SAE WEB ADDRESS: http:/www.sae.orgSAE values your input. To provide feedbackon this Technical Report, please visit http:/www.sae.org/technical/standards/J2789_201008SURFACEVEHICLERECOMMENDEDPRACTICEJ2789 AUG2010 Issued 2010-08 Inertia Calculation f
5、or Single-Ended Inertia-Dynamometer Testing RATIONALE The validity of the results of a single-ended inertia-dynamometer test depends heavily on the inertia values. The objective of this Recommended Practice is to provide a common methodology for determining the inertia values for single-ended brake
6、dynamometer testing. The test loads, energy levels, and rotational speeds during single-ended inertia-dynamometer testing are a function of the vehicle under evaluation. Since the majority of dynamometer tests use a single-ended configuration, a standardized methodology to determine the test inertia
7、 is necessary to ensure the consistency and usefulness of the test results. When using this Recommended Practice the value for the test inertia can be determined as a function of vehicle type, braking system configuration, vehicle parameters available, chassis dimensions, vehicle weights, center of
8、gravity location, and deceleration level. TABLE OF CONTENTS 1. SCOPE 21.1 Purpose . 22. REFERENCES 22.1 Related Publications . 22.1.1 ISO Publications 23. DEFINITIONS . 23.1 ANTILOCK BRAKING SYSTEMS - ABS 23.2 ELECTRONIC BRAKE DISTRIBUTION - EBD 23.3 GROSS VEHICLE WEIGHT RATING - GVWR 23.4 LIGHTLY L
9、OADED VEHICLE WEIGHT - LLVW 33.5 TIRE DYNAMIC ROLLING RADIUS - RR 34. TEST INERTIA CALCULATION METHODS 34.1 Default Method 54.2 Torque Index Method 74.3 Dynamic Weight Transfer Method 85. CALCULATION REPORTS 95.1 Vehicle description: make or manufacturer, model year, brand or platform, trim level 95
10、.2 Gross Vehicle Weight Rating 95.3 Lightly Loaded Vehicle Weight 95.4 Brake proportioning type (fixed or electronic) . 95.5 Hydraulic system split (diagonal or front-to-rear) for tests with partial circuit failure sections 95.6 Specific method used to calculate inertia 95.7 Tire size and its corres
11、ponding dynamic RR used for the calculations 9SAE J2789 Issued AUG2010 Page 2 of 95.8 Front and rear inertia value calculated for each vehicle loading (LLVW or GVWR) . 95.9 Any loss factor applied to the effective inertia values for the test . 96. NOTES 96.1 Marginal Indicia . 9FIGURE 1 WORKFLOW TO
12、SELECT THE INERTIA CALCULATION METHOD . 4TABLE 1 INERTIA SPLIT FOR FULLY-OPERATIONAL SYSTEMS WITH FIXED BRAKE PROPORTIONING 6TABLE 2 INERTIA SPLIT FOR FULLY-OPERATIONAL SYSTEMS WITH ELECTRONIC BRAKE DISTRIBUTION 61. SCOPE This procedure provides methods to determine the appropriate inertia values fo
13、r all passenger cars and light trucks up to 4540 kg of GVWR. For the same vehicle application and axle (front or rear), different tests sections or brake applications may use different inertia values to reflect the duty-cycle and loading conditions indicated on the specific test. 1.1 Purpose The pur
14、pose of this procedure is to provide a common methodology to calculate test inertia (wheel load and tire rolling radius). The use of common inertia values allows the comparison of test results from different inertia-dynamometers or different testing facilities. This makes the overall testing activit
15、ies more cost-effective and repeatable. 2. REFERENCES 2.1 Related Publications The following publications are provided for information purposes only and are not a required part of this SAE Technical Report.2.1.1 ISO Publications Available from American National Standards Institute, 25 West 43rd Stre
16、et, New York, NY 10036-8002, Tel: 212-642-4900, www.ansi.org.ISO 611 Road vehicles Braking of automotive vehicles and their trailers Vocabulary 3. DEFINITIONS 3.1 ANTILOCK BRAKING SYSTEMS - ABS Closed-loop control device which prevents wheel lock when braking and, as a result, retains the vehicles s
17、teering ability and stability. 3.2 ELECTRONIC BRAKE DISTRIBUTION - EBD Closed-loop technology that automatically varies the amount of pressure applied to the rear brakes to maximize tire-to-road adhesion utilization while maintaining the vehicle stability. This condition typically happens at or near
18、 the wheel lock-up condition. 3.3 GROSS VEHICLE WEIGHT RATING - GVWR Maximum vehicle weight indicated by the manufacturer. kg SAE J2789 Issued AUG2010 Page 3 of 93.4 LIGHTLY LOADED VEHICLE WEIGHT - LLVW Unloaded vehicle weight plus 180 kg including driver and test instrumentation. kg 3.5 TIRE DYNAMI
19、C ROLLING RADIUS - RR Tire radius that equates to the Revolutions Per Mile (RPM) published by the tire manufacturer for the specific tire size. If unknown, the rolling radius can be calculated from the RPM value using Equation 1. Use the tire dynamic rolling radius to calculate test inertia and the
20、dynamometer rotational speed in revolutions per minute (r/min) for a given linear vehicle speed. 44 L5 : 4 = 7 8 86 (Eq. 1) where: 44 = tire dynamic rolling radius m = tire manufacturer specification for revolutions per mile. Typically shown for the tire size on the manufacturers website. 4. TEST IN
21、ERTIA CALCULATION METHODS There are three methods available to calculate the test inertia depending upon the amount of information available, the vehicle type, and the deceleration level for the specific test section or brake application. The inertia values are required to determine the amount of en
22、ergy imposed on the brake during testing. Also, the inertia value is required to determine the torque level for a given deceleration value or set-point. The minimum information required to run an inertia-dynamometer test is: a. Vehicle description: make or manufacturer, model year, brand or platform
23、, trim level b. Gross Vehicle Weight Rating c. Lightly Loaded Vehicle Weight d. Tire size description e. Brake proportioning type (fixed or electronic) Use the flowchart in Figure 1 to determine the appropriate method as a function of: availability of vehicle information, type of front-to-rear brake
24、 proportioning, and target deceleration. Follow the steps on the flowchart, answer the questions and then proceed to the corresponding section using the information available for the specific vehicle application. SAE J2789 Issued AUG2010 Page 4 of 9FIGURE 1 - WORKFLOW TO SELECT THE INERTIA CALCULATI
25、ON METHOD There are three main methods to determine the corresponding inertia level for the test as a function of the brake system configuration and the level of information available at the time of testing: a. Default method for front-to-rear inertia split when there is no detailed vehicle informat
26、ion available. Refer to item 4.1. b. Torque index method using nominal brake torque output for the front and rear brake as a function of known friction values and the corresponding brake dimensions. This method applies to fixed brake proportioning or for ABS/EBD system at vehicle decelerations below
27、 0.65 g. Refer to item 4.2. c. Dynamic weight transfer method for all vehicle decelerations above 0.65 g when there is detailed vehicle information available. For vehicles with fixed proportioning, use the LLVW values for all weight conditions. Refer to item 4.3. The test inertias follow the front-t
28、o-rear braking force distribution. Equations 2 and 3 provide the calculation for the front and rear inertias. + L56 : 9 446(Eq. 2) + L56 ; 9 446(Eq. 3) Vehicle Description, Vehicle GVWR, Vehicle LLVW,Tire Size, Brake proportioning type, Hydraulic split typeDo you have additional vehicle data?Default
29、 Chart ValuesNoDefault methodusing Tables 1 = percentage of brake torque provided by the front or rear axle respectively. Reference items 4.1 and 4.2 for different methods to obtain them based on default values, nominal torque calculations, or actual dynamometer testing. 9 = vehicle test weight as s
30、pecified by the requestor: GVWR or LLVW kg 44 = tire dynamic rolling radius per item Equation 1 m NOTE: Verify with the test requestor if there is a loss factor required to adjust the calculated inertia from Equations 2 and 3 to account for engine braking, transmission losses, or aerodynamic drag. F
31、or brake applications under hydraulic circuit failure use one of the two following calculation depending upon the type of brake system split: a. For diagonal hydraulic circuit split use twice the inertia calculated for the corner under testing b. For front-to-rear hydraulic circuit split use half th
32、e inertia for the total vehicle (LLVW or GVWR) 4.1 Default Method Use the values provided in Tables 1 or 2 for fixed or electronic brake proportioning respectively. These values are not appropriate for final brake system sizing, performance prediction using dynamometer test results or for investigat
33、ing brake performance for a specific vehicle configuration when the brake system, weight distribution, and location of the center of gravity are known. Since the late 1980s, all full-size pickup trucks manufactured in the U.S. have at least a rear wheel antilock brake system. Therefore, use the elec
34、tronic proportioning work split table and calculations for these vehicles. The sum of the front and rear inertias adds to more than 100% to take into account the variation in vehicles within the same category. The default table uses the following boundary conditions for fixed proportioning (includin
35、g proportioning valves): a. The brake work distribution is based under the assumption that the proportioning valve setting ensures front-bias at LLVW. b. Since the proportioning valve has fixed settings, the pressure distribution at GVWR will be the same as at LLVW. c. At low deceleration, the line
36、pressure is typically below or close to the split point of the proportioning valve. Hence, thevalve will have little or no effect; and the vehicle will be less front-biased than above the split point. The default table uses the following boundary conditions for Electronic Brake Distribution systems
37、a. Vehicles with EBD usually have a g-critical at LLVW between 0.6 and 0.8 g. Compared to vehicles that are not equipped with EBD, there will be a higher percentage of braking work done by the rear brakes at GVWR and at low decelerations at the LLVW condition. b. At low decelerations, the EBD would
38、probably not be active so the LLVW and GVWR brake force distributions would be the same. SAE J2789 Issued AUG2010 Page 6 of 9TABLE 1 - INERTIA SPLIT FOR FULLY-OPERATIONAL SYSTEMS WITH FIXED BRAKE PROPORTIONING Percent of brake force done by each axle (X and Y values)Vehicle type Fixed Proportioning
39、Low deceleration 0.65 g GVWR LLVW GVWR LLVW Front XRear YFront XRear YFront XRear YFront XRear YPassenger car - FWD 78 28 78 28 80 25 80 25 Passenger car - RWD 78 28 78 28 75 30 75 30 Minivan and crossover 78 28 78 28 75 30 75 30 Pick-up trucks 68 38 63 45 80 25 80 25 SUV-RWD 73 33 73 33 75 30 75 30
40、TABLE 2 - INERTIA SPLIT FOR FULLY-OPERATIONAL SYSTEMS WITH ELECTRONIC BRAKE DISTRIBUTION Percent of brake force done by each axle (X and Y values) Vehicle type Electronic brake distribution Low deceleration 0.65 g GVWR LLVW GVWR LLVW Front XRear YFront XRear YFront XRear YFront XRear YPassenger car
41、- FWD 70 35 70 35 70 35 80 25 Passenger car - RWD 68 38 68 38 68 38 75 30 Minivan and crossover 70 35 70 35 70 35 80 30 Pick-up trucks 55 50 60 45 60 45 80 25 SUV-RWD/AWD 65 40 65 40 65 40 75 30 SAE J2789 Issued AUG2010 Page 7 of 94.2 Torque Index Method If there is information available from the re
42、questor regarding the friction or effectiveness values for both axles, in additionto the brake sizes, calculate the values for : and ; required for Equations 2 and 3 using the values obtained from the torque index BD and Equations 6 and 7. Use Equation 4 to calculate the torque index for all-disc br
43、ake system configurations. Use Equation 5 to calculate the torque index for disc-drum brake system configurations: $ L 5 (Eq. 7) where: $ total wheel cylinder area for drum brakes mm2N = radial distance from centerline of the piston to the axis of rotation for disc brakes; internal drum diameter div
44、ided by 2 for drum brakes, unless other dimensions are provided by the requestor mm = apparent friction for disc brakes unitless %= effectiveness for drum brakes unitless If there is no information available from the requestor regarding the friction or effectiveness values for both axles, conduct pa
45、rtial inertia-dynamometer testing per SAE J2784 to calculate the values for : and ; as follows: a. Perform separate inertia dynamometer testing on the front and the rear brakes b. Obtain apparent friction or effectiveness (C* values) from the test results c. Calculate the corresponding value for BD
46、using Equation 4 or 5 for disc-disc or disc-drum configuration respectively d. Calculate the corresponding values for X and Y using Equations 6 and 7 e. Calculate the values for the front and rear inertias using Equations 2 and 3 respectively Detailed steps are as follows: a. Determine the appropria
47、te burnish section from the SAE J2784 Recommended Practice as a function of the Gross Vehicle Weight Rating: for vehicles 3500 kg or below GVWR use Table 2; for vehicles above 3500 kg GVWR use Table 3. b. Setup the test inertia for the front brake. Unless indicated by the requestor, setup the test i
48、nertia per the values provided in Table 1 or Table 2 corresponding to low deceleration. c. Perform one complete burnish sequence on the front brake and compute the average apparent friction value from the last 10 burnish stops. d. Change over brake fixture and test inertia to the rear brake. Unless
49、indicated by the requestor, setup the test inertia per the values provided in Table 1 or Table 2 corresponding to low deceleration. SAE J2789 Issued AUG2010 Page 8 of 9e. Perform one complete burnish sequence on the rear brake and compute the average apparent friction or effectiveness (C* values) the last 10 burnish stops. Using
