Steady-state measurement of tire rolling resistance as a function of load, pressure.

The current EPA procedure (ref. 1) used by vehicle manufacturers in establishing alternative dynamometer power absorber settings is concerned with the 72 to 88 km/hr speed range. The intent is to adjust the dynamometer so that the vehicle exhibits the same coast down performance on the dynamometer as on a road or track at ambient conditions. The routine measurement and use of tire rolling resistance characteristics at 80 km/hr as a function of load and inflation allow the vehicle manufacturer engineers to calculate the required dynamometer absorbed power for combinations of vehicle/tire/weight for their entire product line, thus reducing the number of actual vehicle coast down tests that have to be performed.

In the near future, vehicle manufacturers will have a need for tire rolling resistance values in the range of 15 to 115 km/hr as well as at various loads and inflation pressures. This requirement results from the EPA need to respond to a U.S. Congressional mandate to develop a true road load matching procedure for all vehicle emissions testing. The vehicle manufacturers are working with the EPA to develop a new way of matching a vehicle's road force to a 48" electric dynamometer. In turn, they would like to be able to model rolling resistance as a function of load, speed and pressure.

Considerable investigation of rolling resistance measurement was conducted in the late 1970s and early 1980s. The need for a short duration test, while at the same time maintaining precision and accuracy, was identified (ref. 2). By properly selecting a matrix of loads and inflations, considerable reductions in test time could accrue (ref. 3). Measurements at various conditions of speed, load and inflation pressure were made during tire warm-up which demonstrated that tire stabilization time was relatively independent of the operating conditions (ref. 4). This work, and that of many others, ultimately led to the SAE J1269 and ISO 8767 rolling resistance measurement procedures which are used today.

The SAEJ1269 procedure defines a four point test matrix, for passenger car tires, of load and pressure to be run at 80 km/hr. This article covers work done to develop a five parameter model which may be used to predict steady-state rolling resistance of a tire over a range of load, pressure and speed using an eight point test matrix.

Experimental

The test program was designed to measure rolling resistance of each tire at 20 test points consisting of two loads, two regulated pressures and five different speeds as shown in table 1. Twenty test points were measured on each tire in order to validate the proposed eight point test method. A 1.7 m roadwheel having an 80 grit surface was used, with all tires being run at an ambient temperature of 24[degrees]C. The force method was utilized for all measurements and all alignment, control and instrumentation accuracies met or exceeded the requirements of SAE J1269.

Table 1 - actual test matrix
Load (% T&RA Max)       50 & 90
Pressure (kPa)          210 & 310
Speed (km/hr)           40, 60,80,100 & 120

Tires used for testing consisted of three brands representing seven different sizes as shown in table 2. Two or three tires of each size were tested.

Table 2 - tire profile
Group   Size          Brand          Design           Qty.

1       P175/70R13     Michelin      LX1                3
2       195/60R15      Michelin      MXV4               3
3       P205/70R15     Michelin      XW4                3
4       P255/50R16     Michelin      XGTZ               3
5       P215/70R15     Uniroyal      AWP                2
6       P215/70R15     BFGoodrich    Touring T/A        2
7       P215/65R16     Uniroyal      AWP                2
8       P225/60R16     BFGoodrich    Touring T/A        2

Results and discussion

Previous work (ref. 3) established the concepts pertaining to

the linearity of load and the reciprocal of inflation pressure with rolling resistance. Velocity squared terms were merged with the above to create a five parameter equation:

(1) [RR.sub.f] = [A.sub.0] + [A.sub.1]L + [A.sub.2]L/P + [A.sub.3][V.sup.2] + [A.sub.4][LV.sup.2]/P + [A.sub.5]/P where:

[RR.sub.f] = tire rolling resistance in Newtons at inflation pressure P, load L and velocity V; and

[A.sub.]...[A.sub.5] = constants for each tire.

Data from an eight point test matrix, shown in table 3, were fitted to equation 1 using least-squares regression. The coefficients and their standard error as shown in table 4 were calculated and analyzed for each parameter. The variables selected for the model were significant in most cases and the correlation coefficients ([R.sup.2]), shown in table 5, approached 1. A typical plot of the measured versus predicted rolling resistance is shown in figure 1.

Table 3 - proposed matrix
         Load              Pressure    Speed
            (% T&RA Max)   (kPa)       (km/hr)
Point 1           50        310          40
Point 2           90        210          40
Point 3           50        210          80
Point 4           50        310          80
Point 5           90        210          80
Point 6           90        310          80
Point 7           50        310         120
Point 8           90        210         120

[TABULAR DATA 4 OMITTED]

Table 5 - statistics
Group   Std. Err.   [R.sup.2]   No. of        [D.sub.f]
        of Y Est.              observations
1          .194     .9993         24              18
2          .412     .9979         24              20
3         1.275     .9811         24              21
4          .486     .9988         24              19
5          .441     .9996         16              10
6          .752     .9988         16              10
7          .401     .9995         16              10
8          .687     .9990         16              10

Although this model provides exceptionally good predictions of rolling resistance for other load, pressure and speed conditions within the bounds of the test matrix, there is more work to be done. Since limited brands and only two loads and two pressures were tested, the model is valid only over a relatively small range. Also, the variables selected for the model may not be optimum. For example, the effect of the reciprocal of the pressure squared was not evaluated. Finally, relationships to the 48" road wheel and a flat-surface, perhaps under transient conditions, must be explored.

Conclusions

A model which requires a limited amount of data input has been developed. This model provides exceptionally good predictions of steady-state rolling resistance for other load, pressure and speed conditions within the bounds of the test matrix. Additional investigation will be required on a broader range of tires, loads and pressures. Study of transient and roadwheel diameter effects will be needed in order to determine their significance and to finalize the model.

[Figure 1 ILLUSTRATION OMITTED]

(This article is based on an article first published in Tire Technology International 1996, by UK International Press, Dorking, UK)