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 ther
2、efrom, is the sole responsibility of the user.” SAE reviews each technical report at least every five years at which time it may be revised, reaffirmed, stabilized, or cancelled. SAE invites your written comments and suggestions. Copyright 2015 SAE International All rights reserved. No part of this
3、publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. TO PLACE A DOCUMENT ORDER: Tel: 877-606-7323 (inside USA and Canada) Tel: +1 724-776-49
4、70 (outside USA) Fax: 724-776-0790 Email: CustomerServicesae.org SAE WEB ADDRESS: http:/www.sae.org SAE values your input. To provide feedback on this Technical Report, please visit http:/www.sae.org/technical/standards/J2188_201510 SURFACE VEHICLE RECOMMENDED PRACTICE J2188 OCT2015 Issued 1996-03 R
5、evised 2015-10 Superseding J2188 JUL2012 Commercial Truck and Bus SAE Recommended Procedure for Vehicle Performance Prediction and Charting RATIONALE A user reported an error in Eq. 17. The Constant in the original equation (0.0024) has been replaced by the corrected value, 0.0025565. FOREWORD This
6、procedure is the recommended replacement for SAE J688 Truck Ability Procedure. It includes recommended graphic representations of vehicle steady-state performance, with mathematical equations and recommended constants for various configurations of commercial vehicle components, systems, and vocation
7、al environments. It may also be used instead of SAE J688, as a standardized form for summarizing and presenting comparative vehicle steady-state performance in bids and tenders. A proposed worksheet for bids and tenders is included (see Appendix A). 1. SCOPE This SAE Recommended Practice takes into
8、account modern standardized methods for collecting and summarizing data that has an effect on vehicle steady-state performance, such as engine output (gross and net), transmission losses, drivetrain efficiency, vehicle aerodynamic devices for various vehicle and body configurations, as well as road
9、surface variations and air density variations resulting from altitude and barometric effects. The procedure does not address vehicle transient performance (acceleration, braking, and cornering), because of the considerable amount of additional data required such as moment of inertia of all the rotat
10、ing parts. Nor does it address vehicles with torque converters and automatic transmissions. This document is, therefore, intended for vehicles having fixed-ratio type transmissions and positive engagement clutches. Metric and ISO unit conversions are provided in the metric conversion tables at the e
11、nd of this procedure (see Appendix B). Some modern vehicles with electronic engine controls have the ability to vary the maximum engine revolutions for each gear, as well as permitting the power or rpm to increase if more time is spent in the lower gears, as when climbing a grade. These special case
12、s can be handled by this procedure, just by customizing the data for each transmission ratio and superimposing the long-term data on top of the instantaneous data. All of the equations are written in a form suitable for programming into a mainframe or desk-top computer, using a spreadsheet/database
13、or a higher level language, such as Basic, Fortran, Pascal, C or Unix, etc. However, they are simple enough, to be performed on a hand-held calculator. SAE INTERNATIONAL J2188 OCT2015 Page 2 of 16 2. REFERENCES 2.1 Applicable Documents The following publications form a part of this specification to
14、the extent specified herein. Unless otherwise indicated, the latest issue of SAE publications shall apply. 2.1.1 SAE Publications Available from SAE International, 400 Commonwealth Drive, Warrendale, PA 15096-0001, Tel: 877-606-7323 (inside USA and Canada) or 724-776-4970 (outside USA), www.sae.org.
15、 SAE J688 Truck Ability Prediction Procedure SAE J1489 Heavy Truck and Bus Retarder Downhill Performance Mapping Procedure 2.2 Other Publications Tables and Formulas for the Automotive Engineer (reference 6-67 - BCR 10M), Clark Equipment Company 3. TECHNICAL DATA The following diagrams represent a r
16、ecommended standard format for illustrating vehicle performance with tables and graphs. They also represent a recommended standardized form for presenting vehicle performance in a general manner. It should be recognized that there are special vehicles, powertrains, and operating conditions that may
17、require a different form of presentation, such as those presented in SAE J1489 Vehicle Downhill Performance Mapping Procedure. 4. ENGINE SPEED VERSUS ROAD SPEED (See Figure 1.) Figure 1 - Engine speed versus road speed SAE INTERNATIONAL J2188 OCT2015 Page 3 of 16 For vehicles having stepped transmis
18、sions with positive engagement friction clutches, the co-ordinate of the point of rated engine speed (or full power governed engine speed) versus the maximum vehicle speed for each gear ratio is defined by Equation 1: (Eq. 1) The co-ordinates of the interception point or downshift engine speed are d
19、efined as follows in Equation 2: (Eq. 2) 5. PERCENT GRADEABILITY VERSUS VEHICLE SPEED (See Figure 2 and Equations 3 and 4.) Figure 2 - Percent gradeability versus vehicle speed VGNma x( )NRA60M RG-=VG 1( )Nma x( )NR A60MxRG 1( )-NSNRARGRG 1( )-=SAE INTERNATIONAL J2188 OCT2015 Page 4 of 16 (Eq. 3) (E
20、q. 4) 1 hp = 0.7457 kW 1 kW = 1.1341 hp where: 6. LIMITING GRADE FOR WHEEL SLIP (See Figure 3.) Figure 3 - Limiting grade for wheel slip Figure 3 represents the maximum steady-state gradeability that can be achieved for a given vehicle combination and road surface. It can be represented by Equation
21、5: (Eq. 5) VGNN 60M RG-=( )+=GNARGNGNVWWPWPEHPP 375sintan1001WPRW RC1R C2V+( ) S C V375 1000-WPACDCAFA V3 0.0024375-=PSWDACT 100W-=SAE INTERNATIONAL J2188 OCT2015 Page 5 of 16 7. WHEEL POWER VERSUS VEHICLE SPEED (See Figure 4.) Figure 4 - Wheel power versus vehicle speed Figure 4 represents the whee
22、l power exchange on the vehicle. It can be broken down into two major components, as follows: a. Wheel Power available from the vehicle drivetrain in various gears and at specified engine speed. b. Wheel Power required for given speed, tire/road surface interaction, vehicle weight, aerodynamic drag,
23、 and grade conditions. The Wheel Power available is defined in Equation 6: (Eq. 6) The vehicle speed component is the same as for the previous chart, as follows in Equation 7: (Eq. 7) WPGNHPNEG100-=VGNN 60M RG-=SAE INTERNATIONAL J2188 OCT2015 Page 6 of 16 It is sometimes useful to define the engine
24、rpm point where engine peak torque occurs with a distinctive mark on the power available curves. The same equation can be used, substituting the engine peak torque rpm (NPT) for N. The Wheel Power required can be plotted for both positive and negative grades. The values of the positive grades plotte
25、d should increase in approximately logarithmic order. For trucks under 15 HP per ton GCW on the USA highway system, the following percent grade values are of most interest: Table 1 - Grade value percentages Uphill Grades 0.0 0.5 1.0 2.0 3.0 5.0 8.0 15.0 25.0 Downhill Grades -0.5 -1.0 -1.5 -2.0 -2.5
26、-3.0 The Wheel Power (WP) required is the sum of the following three functions: a. Power required to overcome wheel rolling resistance (WPR). b. Power required to overcome air drag (WPA). c. Power required to overcome the gradient (WPP). This can be represented by Equations 8 to 11. (Eq. 8) where: (
27、Eq. 9) (Eq. 10) (Eq. 11) The difference between Wheel Power Available and Wheel Power Required for a given grade is the Wheel Power available for acceleration or deceleration of the vehicle on this grade. WP WPRWPAWP+ +=WPRW RC1R C2V+( ) S C V375 1000-=WPACDCA FA V3 0.0024375-=WPPW V375-tan1 P100- s
28、in=SAE INTERNATIONAL J2188 OCT2015 Page 7 of 16 8. TRACTIVE EFFORT VERSUS VEHICLE SPEED (See Figure 5.) Figure 5 - Tractive effort versus vehicle speed Tractive effort is the “drawbar pull” available after all other parasitic loads have been taken into account. It can be plotted alone for each vehic
29、le gear ratio, or in combination with gradeability lines. As with the Wheel Power chart, the difference between Tractive Effort Available and Tractive Effort Required for a given grade is the Tractive Effort available for acceleration or deceleration of the vehicle on this grade. The Tractive Effort
30、 (lb) Available (TEGN) for each gear (G) and engine RPM (N), can be defined by Equations 12 and 13. (Eq. 12) or (Eq. 13) TEGNHPN5252N-EG100-RG2 M5280-=TEG NHPNEG100-375VG N-=SAE INTERNATIONAL J2188 OCT2015 Page 8 of 16 The vehicle speed component is the same as for previous charts, as follows in Equ
31、ation 14: (Eq. 14) The Tractive Effort Required can be defined by Equation 15: (Eq. 15) where: (Eq. 16) TEA= FA x V2x CDx CAx 0.0025565 (Eq. 17) (Eq. 18) 9. DESCRIPTION OF VARIABLES USED AND UNITS M = Tire revolutions per mile at 45 mph (see Table 2) RG = Total reduction (RA x Rl x RT) R(G-1) = Prev
32、ious Gear total reduction RA = The axle ratio RI = The intermediate or auxiliary transmission ratio RT = The main transmission ratio EG = Powertrain efficiency (%), for gear G (see Table 3) N = Engine speed (RPM) NRA = Engine speed (RPM) at rated power (or the full power governed engine speed if gre
33、ater) NPT = Engine speed (RPM) at peak torque NS = Maximum theoretical instantaneous engine speed (RPM) before downshift or after upshift HPN = Net Engine power available at “N” RPM W = Vehicle actual Total Gross Combination Weight (lb) WDA = Gross actual Load on drive axle(s) (lb) CT = Traction coe
34、fficient between tire and road (see road surface Table 4) RC1 & RC2 are rolling constants for the tires (see Table 5) SC is a constant for the road surface (see Table 4) P = Gradient (%) (vertical climb/travel distance horizontal projection) VGNN 60M RG-=TE TERTEATEP+ +=TERW RC1RC2V+( ) S C1000-=TEW
35、 tan1 P100- sin=SAE INTERNATIONAL J2188 OCT2015 Page 9 of 16 PGN = Vehicle gradeability (%) for gear G at engine speed N PS = Limiting gradeability (%) at which wheel slip occurs CD = The air drag coefficient, calculated from total vehicle air drag, divided by the full frontal area (height x width)
36、ignoring ground clearance (see examples on Table 6) CA = Air Density Correction for altitude (see Table 7) FA = Frontal Area of vehicle (ft2), based on height x width, ignoring ground clearance (see Table 8) V = Vehicle speed (mph) VGN = Vehicle forward speed (mph) for selected gear G at engine spee
37、d N VGN(max) = Vehicle forward speed (mph) at rated engine speed (RPM) in gear G V(G-1)N(max) = Same as previous except for the previous gear TE = Tractive Effort (lb) TER = Tractive Effort to overcome rolling resistance (lb) TEA = Tractive Effort to overcome air resistance (lb) TEP = Tractive Effor
38、t to overcome P% Grade (lb) TEGN = The Tractive Effort Available (lb) for each gear ratio (G) and engine speed (N) WP = Wheel Power (HP) WPR = Wheel Power to overcome rolling resistance (HP) WPA = Wheel Power to overcome air resistance (HP) WPP = Wheel Power to overcome P% Grade (HP) WPGN = Wheel Po
39、wer Available (HP) for each gear ratio (G) and engine speed (N) SAE INTERNATIONAL J2188 OCT2015 Page 10 of 16 Table 2 - Typical values for tire revolutions per mile at 45 mph (M) Revs/Mile Rib Revs/Mile Lug Tire Type/Size Tube Type Tire Type/Size Bias Tubless Tire Type/Size Tube Type Tire Type/Size
40、Radial Tubeless Tire Type/Size Tube Type Tire Type/Size Low Profile Tubleless 651 647 225/70R19.5 629 624 245/70R19.5 626 626 8-19.5 8R19.5 571 564 255/70R22.5 561 557 245/70R22.5 558 551 7.50-20 8-22.5 7.50R20 8R22.5 558 554 235/80R22.5 542 538 8.25-20 8-22.5 8.25R20 9R22.5 541 540 255/80R22.5 537
41、537 265/75R22.5 519 513 9.00-20 10-22.5 9.00R20 10R22.5 515 513 275/80R22.5 514 512 275/75R22.5 503 13/80R20 13/75R22.5 503 496 285/75R24.5 501 500 275/80R24.5 501 497 10.00-20 11-22.5 10.00R20 11R22.5 491 315/80R22.5 491 15R22.5 385/65R22.5 485 18-19.5 14/80R20 486 483 11.00-20 12-22.5 11.00R20 12R
42、22.5 480 15-22.5 478 473 10.00-22 11-24.5 10.00R22 11R24.5 471 12.00-20 12.00R20 16R22.5 425/65R22.5 462 459 11.00-22 12-24.5 11.00R22 12R24.5 464 16.5-22.5 457 451 445/65R22.5 448 18-22.5 442 439 11.00-24 11.00R24 426 417 12.00-24 12.00R24 421 415 14.00-20 14.00R20 Tire type/size underlined are wid
43、e base. SAE INTERNATIONAL J2188 OCT2015 Page 11 of 16 Table 3 - Typical values for drivetrain efficiency (EG) G - DIRECT (through trans.) G - INDIRECT (single trans.) G = DOUBLE INDIRECT (auxiliary trans.) Single Drive 0.94 0.92 0.90 Tandem Drive 0.93 0.91 0.89 Table 4 - Typical values for highway s
44、urface coefficients (RC) Road Type Rolling Resistance lb per 1000 lb GCW SC Friction Coeff. CT Concrete, excellent 10 1 0.8 Concrete, good 15 1.5 0.7 Concrete, poor 20 2 0.6 Asphalt, good 12 1.2 0.6 Asphalt, fair 17 1.7 0.5 Asphalt, poor 22 2.2 0.4 Macadam, good 15 1.5 0.55 Macadam, fair 22 2.2 0.45
45、 Macadam, poor 37 3.7 0.35 Cobbles, ordinary 55 5.5 0.5 Cobbles, poor 85 8.5 0.4 Snow, 2 in 25 2.5 0.2 Snow, 4 in 37 3.7 0.15 Dirt, smooth 25 2.5 0.3 Dirt, sandy 37 3.7 0.2 Mud 37 to 3.7 to 0.15 150 15 Sand, level and soft 60 to 6 to 0.15 150 15 Sand, dunes 160 to 16 to 0.1 300 30 NOTE: Source is fr
46、om booklet titled: “Tables and Formulas for the Automotive Engineer,” published by: Clark Equipment Company (reference 6-67 - BCR 10M). SAE INTERNATIONAL J2188 OCT2015 Page 12 of 16 Table 5 - Typical values for the rolling resistance constants (RC1 and RC2) Static RC1 Additional Increment for Each mph (lb (resistance)/1000 lb GCW) RC2 Additional Increment for Each mph (lb (resitancy)/1000 lb GCW) Source Bias Ply Tires 7.6 0.090 SAE J688 6.6 0.046
