SAE-TPS-701999-01-0787.pdf
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1、400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A.Tel: (724) 776-4841 Fax: (724) 776-5760 SAE TECHNICAL PAPER SERIES 1999-01-0787 New Parameters for Comparing Tire Rolling Resistance Parmeet S. Grover and Sid H. Bordelon Michelin Americas Research measurements made in the same lab) () RRP Zab
2、Vc V=+ 2 0.0 10.0 20.0 30.0 40.0 50.0 60.0 -20020406080100120 Speed (kph) RR (N) Tire 1Tire 2 180 kg, 2.5 bar 238 kg, 2.75 bar 356 kg, 2.0 bar 536 kg, 3.0 bar 536 kg, 2.0 bar Curve Set B Curve Set A Author:Gilligan-SID:1178-GUID:17436714-141.213.232.87 3 MERF - THE CONCEPT The motivation behind defi
3、n- ing a new parameter, MERF, is to be able to capture a tires rolling resistance performance over a range of speeds of interest. This is important because the rolling resistance of a tire is a function of its speed. A well known and often used approximation of the range of speeds encountered by an
4、automobile during service is a stan- dard driving cycle. Well known examples are the EPA urban and highway cycles in the US and their European or Japanese equivalents. Mean Equivalent Rolling Force (MERF) for a tire, at a given load/pressure condition, is defined as the average of all rolling resist
5、ance values corresponding to every sin- gle speed-time point in a fixed driving cycle. This implic- itly weights the rolling resistance at each speed by the length of time spent at that speed during the cycle. For the purpose of SAE J2452, MERF is calculated using the standard EPA urban and highway
6、driving cycles. It is noted that the basic concept of MERF remains unaf- fected by the choice of the reference driving cycle. Hence, for markets other than the U.S., it would be per- fectly acceptable to use the corresponding cycles. Mathematically, MERF is defined as: (2) where MERFU/H is the mean
7、equivalent rolling force over any standard urban (U) or highway (H) cycle. The term to is the time corresponding to the start of the cycle and tf corresponds to the end of the cycle. RR is given by Eq. (1), wherein the coefficients for a tire are known. Hence, MERF can be expressed in terms of the i
8、ndepen- dent variables (load pressure and speed) (3) Note that for a given load(Z)/pressure(P) condition, only speed(V) is a function of time. This functionality depends on the driving cycle chosen. For J2452, the EPA urban and highway driving cycles have been used. However, MERF may be calculated o
9、n any driving cycle that repre- sents the service conditions of interest. Since RR = f (V), and V = f (t) for a given driving cycle is known, V in Eq. (3) can be expressed as a function of time. Hence, the integral can be solved by standard numerical integration methods, such as the trapezoidal rule
10、5 used here. Since V = 0 at t0 and tf, Eq. (3) can be simplified to: (4) Selecting a unit time interval (t = ti-ti-1 = 1 sec) between successive speed points on the speed vs. time curve for a driving cycle (5) where, tf now represents the duration of the cycle (because t0 = 0). It is noted that Eq.
11、(5) can be used to calculate a MERF for any cycle. Hence, it would yield one value for the EPA Urban Cycle - FTP Schedule and a different one for the EPA Highway Fuel Economy Cycle. For the North Ameri- can market, the final MERF for a tire is a weighted aver- age of these two MERFs: (6) Thus, Eq. (
12、6) yields the MERF, at a given load/pressure, for average driving conditions as represented by the EPA urban and highway cycles. SMERF - Definition and Application Standard Mean Equivalent Rolling Force (SMERF) for any tire is the MERF for that tire under standard load/ pressure conditions defined i
13、n SAE J2452. For SAE J2452, the final SMERF is also calculated by weighting the SMERF obtained for the EPA urban cycle and that for the highway cycle, as discussed for MERF. The primary advantage of calculating a standard MERF (SMERF) is that it could be used to compare rolling resis- tance performa
14、nce of tires at the same standard condi- tion of load and pressure, over the range of speeds in a driving cycle. This standard condition should be such that it is most representative of tire operation in the market and market segment of interest. For example, there would be separate standard conditi
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