## SOUTHWEST RESEARCH INSTITUTE ®

6220 CULEBRA ROAD  POST OFFICE DRAWER 28510  SAN ANTONIO, TEXAS, USA 78228-0510  (210) 684-5111  www.swri.org ENGINE, EMISSIONS, AND VEHICLE RESEARCH DIVISION HTTP://ENGINEANDVEHICLE .SWRI.ORG
FAX: (210) 522-3950 ISO 9001 Certified ISO 14001 Certified

SAN ANTONIO, TEXAS

HOUSTON, TEXAS  WASHINGTON, DC  ANN ARBOR, MI February 8, 2011

Mr. Joseph Bachman USEPA Headquarters Ariel Rios Building 1200 Pennsylvania Avenue, N. W. Mail Code: 6406J Washington, DC 20460

SUBJECT: SwRI ® Final Report 03-15194.02 Titled, "Heavy-Duty Wheel and Tire Combination Rotational Inertia Study”

1.0 INTRODUCTION

Chassis dynamometers attempt to reproduce th e forces acting on vehicles as they are operated on the road. The two major loads imparted on vehicles are typically referred to as road load and inertia. Road load is force created by the force associated with aerodynamic drag, tire deflection, and driveline components. Inertia is the resistance to changes in acceleration and is the primary load on vehicles during transient operation.

Chassis dynamometer testing of heavy-duty ve hicles has historical ly been conducted to compare two different components or technologies on the same ve hicle chassis. However, new regulations have been proposed to measure the absolute value of fuel economy and emissions. This means that more accurate values of road load and inertia are required to meet the expectations of chassis dynamometer results.

Vehicles are typically mounted on a chassi s dynamometer by locating the driven tires on the dynamometer rolls and using chocks and straps on the non-driven tires to keep the vehicle positioned during testing, as shown in Figure 1. Since the steer tires are not rotating during testing, the linear mass of their rotational inertia mu st be added to the test weight of the vehicle for accurate results. Rotational inertia of stationary wheel/tire combinations has typically been assumed to be between three and five percent of the equivalent linear inertia of a typical vehicle. However, this estimation does not accurately refl ect the effect of a c hosen wheel and tire combination on fuel economy or the number of stat ionary wheels. For example, taller, heavier wheels and tires have more inertia than lighter, s horter combinations. Therefore, the benefits of lower inertia combinations would not be reflected in chassis dynamometer testing if their inertia estimation was based on a percenta ge of vehicle test weight. In addition, the estimation does not consider the number of stationary wheels. Figure 2 is a diagra m of a Class 8 tractor-trailer equipped with eighteen wheels, resulting in ten st ationary wheels compared to two stationary wheels for vehicles without a trailer. This st udy is intended to both provide a more accurate calculation of rotational inertia and provide the ability to more accurate ly reflect the fuel economy benefit of reduci ng rotational inertia.Mr. Joseph Bachman Environmental Protection Agency February 8, 2011 Page 2 of 9

Report 03.15194.02 FIGURE 1. DIAGRAM OF HEAVY- DUTY VEHICLE INSTALLED ON A CHASSIS DYNAMOMETER

FIGURE 2. DIAGRAM OF CLASS 8 TRACTOR-TRAILER INSTALLED ON A CHASSIS DYNAMOMETER S

D

D D

D

S S

Simulated Drive D D

R R

D

D D

D Dynamometer
Rolls

S

S S

S

D

D D

D

D

D D

D

S S

Simulated Simulated Drive D D S S S

R R Dynamometer
Rolls

S

S S

S Note: Trailer not present during dynamometer testingMr. Joseph Bachman Environmental Protection Agency February 8, 2011 Page 3 of 9

Report 03.15194.02 2.0 TESTING

Five of the most common wheel and tire co mbinations were purchased from a local supplier for the purpose of measuring each combin ation’s inertia. A description of each combination is listed in Table 1.

TABLE 1. DESCRIPTION OF EACH COMBINATION CONSIDERED FOR THIS PROJECT

Combination Number

1 2 3 4 5

Wheel Material Aluminum Steel Alumi num Steel Aluminum

Wheel Size, Diameter X Width (in) 24.5 X 8.25 24.5 X 8.25 22.5 X 8.25 22.5 X 8.25 22.5 X 14

Tire Size R675/11R24.5 R67511R 24.5 295/75R22.5 295/75R22.5 445/50R22.5

2.1 Test Stand Description

The test stand that was used for this testing is one of SwRI’s Virtual Vehicle Transmission Test Cells (VVTTC). The continuous power rating of this motor is 310 kW from 6000 rpm to a maximum speed of 9000 rpm. The motor can produce a maximum continuous torque of 493 N-m from zero to 6000 rpm. For th e purposes of this testing the dynamometer was operated in torque control mode. Operating the dynamometer in this mode allows the user to deliver a constant torque up to a specified speed limit. The VV TTC provides excellent control accuracy when operating in this manner. Custom fixtures were designed and fabricated to allow the wheel/tire combination to be mounted to a headstand. The headstand was driven by a driveshaft connected to an HBM T10FS tor que meter mounted directly to the input dynamometer. Figure 3 shows Combin ation 5 installed on the test stand.Mr. Joseph Bachman Environmental Protection Agency February 8, 2011 Page 4 of 9

Report 03.15194.02 FIGURE 3. TEST STAND SETUP

2.1 Measured Combination Inertia

The inertia of the drive assembly was measur ed by accelerating it at various rates without a combination mounted. Each combination wa s then mounted on the drive assembly and accelerated to a desired speed limit using a cons tant command torque. This test method produces data showing constant torque and constant accelerat ion over a significant period of time allowing inertia to be calculated as torq ue divided by acceleration. Figure 4 shows an example of the data generated during one of the tests. Table 2 is a summary of each Combination’s mass and measured inertia.

FIGURE 4. SPEED AND TORQUE PROFILE Ramped Speed @ Constant Torque for Tire/Wheel

0 20 40 60 80 100 120 140 160 180 200

0 5 10 15 20 25 Time (s) Tire Speed (RPM) Torque (N-m)Mr. Joseph Bachman Environmental Protection Agency February 8, 2011 Page 5 of 9

Report 03.15194.02 TABLE 2. MASS AND MEASURED IN ERTIA OF EACH COMBINATION

Combination Number

1 2 3 4 5

Mass (kg) 77.1 88.5 77.1 63.5 107

Inertia (kg-m 2 ) 13.2 14.8 12.4 9.97 18.9

2.3 Calculated Combination Inertia

The wheel inertia was treated as two separate pieces, with the outer rim treated as a thinwalled cylinder and the inner wheel portion treated as a hollow cylinder, as shown in Figure 5. The weight of each portion of the wheel was a ssumed to correspond to its surface area, the weight was assumed to be spread evenly upon the surface, and all design details were ignored. The inertia can be calculated from the mass and ra dii of each element using Equations 1 and 2. The calculated inertia values for each wheel are shown in Table 3.

FIGURE 5. DIAGRAM OF WHEEL ELEMENTS USED TO CALCULATE WHEEL INERTIAMr. Joseph Bachman Environmental Protection Agency February 8, 2011 Page 6 of 9

Report 03.15194.02 TABLE 3. WHEEL PARAMETERS USED TO ESTIMATE THEROTATIONAL INERTIA OF EACH COMBINATION

Wheel
Parameters Combination Number

1 2 3 4 5
Mass (kg) 27.3 40.8 34.5 20.7 32.4

Width (m) 0.254 0.254 0.254 0.254 0.381

Outer Diameter (m) 0.610 0.610 0.572 0.572 0.572

Inner Diameter (m) 0.222 0.222 0.222 0.222 0.222

Equation 1. Inertia of a Thin-Walled Cylinder

I= m r 2 m= mass of hollow cylinder r = distance between axis and cylinder mean radius

Equation 2. Inertia of a Hollow Cylinder

I=(1/2) m (r i + r o ) 2 m= mass of hollow cylinder

r i = distance between axis and inside hollow cylinder

r o = distance between axis and outside hollow cylinder

The tire inertia was calculated as hollow cylinder using three elements, the tread and each sidewall, as shown in Figure 4. The density and thickness of th e tire was assumed to be uniform throughout each element. Table 4 lists the values used for calculating the inertia of each tire. The sidewalls were assumed to be identical; therefore, the mass listed in Table 4 is the mass of both sidewalls.Mr. Joseph Bachman Environmental Protection Agency February 8, 2011 Page 7 of 9

Report 03.15194.02 FIGURE 4. DIAGRAM OF TIRE ELEMENTS USED TO CALCULATE WHEEL INERTIA

TABLE 4. TIRE PARAMETERS USED TO ESTIMATE THE ROTATIONAL INERTIA OF EACH COMBINATION

Tire Parameters Combination Number

1 2 3 4 5

Tread
Mass (kg) 22.7 22.7 20.4 20.4 49.4 Outer radius (m) 0.550 0.550 0.506 0.506 0.506 Inner radius (m) 0.526 0.526 0.482 0.482 0.474

Both Sidewalls
Total mass (kg) 23.7 23.7 20.4 20.4 23.8 Outer radius (m) 0.508 0.508 0.464 0.464 0.457

Inner radius (m) 0.305 0.305 0.279 0.279 0.273Mr. Joseph Bachman Environmental Protection Agency February 8, 2011 Page 8 of 9

Report 03.15194.02 Table 5 lists the calculated inertia for each wh eel and tire and the total calculated inertia for each combination. The total m easured inertia values are show n to compare to the empirical values. The difference between the empirical and calculated values was between 13 and 10 percent for Combinations 1 and 2, the 24.5 inch wheel sets. The difference was much less for Combinations 3 through 5, 22.5 wheel sets, includ ing the “Super Single.” The difference ranged between 5.9 and 1.3 percent.

TABLE 5. ESTIMATED ROTA TIONAL INERTIA VALUES COMPARED TO EMPIRICAL VALUES

Combination Number

1 2 3 4 5 Calculated Tire Inertia, kg-m 2 10.1 10.1 7.49 7.49 14.1 Calculated Wheel Inertia, kg-m 2 4.62 6.82 5.17 3.10 5.04 Total Calculated Inertia, kg-m 2 14.8 17.0 12.7 10.6 19.1

Total Measured Inertia, kg-m 2 13.2 14.8 12.4 10.0 18.9

Percent Difference 10% 13% 2.2% 5.9% 1.3%

4.0 SUMMARY

Five different wheel and tire combinations acquired for the purpose of determining the linear equivalent mass of each combination in or der to accurately simulate the non-drive tires’ inertia during chassis dynamomete r testing. Each combination was mounted on an electric dynamometer and accelerated by a constant torque, resulting in constant acceleration value used to directly calculate inertia.

The purpose of the study was to determine whet her or not the estimate of three percent of vehicle test weight was appropriate. Vehicl e test weights are depe ndent on the vehicle’s purpose. For instance, the test we ight for a bus is the bus’s empty weight plus half the passenger load plus driver multiplied by 68 kg. However, a utility truck is typically always loaded to its Gross Vehicle Weight Rating (GVWR) due the boom and associated equipment mounted on the truck. Class 8 tractor-trailers are typically lo aded to seventy percent of their fully loaded weight.

Table 6 lists the GVW for Classes 5 through 8, for which the wheel and tire combinations tested are normally used, along w ith the test weight of seventy percent of GVW for each class. The number of wheels that must ha ve inertia simulated is shown in the third line of Table 6. Most Class 5 through Class 7 vehicles do not norma lly pull trailers, so only the front tires must be simulated, but Class 8 tractor-trailers typically have eight trailer tires in addition to the two front tires. The table shows the additional inerti a added using the estimation of three percent of test weight and the empirical values after being converted to linear mass. The linear mass equivalent of each combination is calculated by dividing the rotational inertia value by the effective radius, which is the outer radius of the tire, in this case.Mr. Joseph Bachman Environmental Protection Agency February 8, 2011 Page 9 of 9

Report 03.15194.02 TABLE 6. COMPARISON OF STANDA RD THREE PERCENT ASSUMPTION

VALUES AND MEASURED INERTIA VAL UES USED FOR ESTIMATING INERTIA OF STATIONARY WHEELS DURING CHASSIS DYNAMOMETER TESTING

Class 5 Class 6 Class 7 Class 8

Gross Vehicle Weight (GVW), kg 8840 11800 15000 36000

Test Weight (70 percent of GVW), kg 6190 8250 10500 25400
Number of stationary wheels 2 2 2 10
3% of test weight, kg 186 248 314 762 Empirical values

, kg 49.0 49.0 49.0 245

Net difference

, kg 137 199 265 517

Percent difference vs. test weight 2.2% 2.4% 2.5% 2.0%

The net differences, in this example, for Classes 5 through 8 are 137 kg, 199 kg, 265 kg, and 517 kg, respectively. The percent differe nce between the standard assumption and the measured values compared to test weight vary between 2.0 and 2.5 percent. The difference between the previous three percent of test weight assumption and the measured values show that for A-B comparisons of a techno logy on the same vehicle is clos e enough to the actual inertia values for valid experiments, however, for ab solute fuel economy and emission tests, the measured values will likely produce more accurate results.

Prepared by: Reviewed by:

Joseph W. Anthony Vlad Ulmet Senior Research Engineer Manager Emissions Research and Development Emissions Research and Development Department Department

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