"Axle ratio" is the common term for the reduction in the gear ratio of most implementations of mechanical differential drive axles in cars, trucks and tractors. These drive axle mechanisms receive driving torque from a driveshaft or transmission output, multiply it by the axle ratio, and transmit the final driving force to the axle shafts, and thus to the drive wheels. The higher the numerical ratio, the higher the output torque, but the lower the speed, in an inverse proportion. If torque doubles, the speed will be half of the driveshaft parameters.
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Calculating an Axle Ratio for a Payloader Tractor

Define the tractor axle application: In this case, a payloader tractor is used to jump train tracks in order to move railroad freight cars into place for unloading. It has been determined that this rail car movement is most efficient and manageable at about 3 mph. If the tractor has 6foothigh tires, a diesel engine with a maximum 200horsepower (hp) rating at 1800 RPM (revolutionsperminute), and a 12 : 1 reduction transmission, you can calculate the axle ratio that will deliver the most power to the wheels at the 3mph operating speed.

Calculate the diesel engine's torque at its 1800 RPM peak power speed. Using the motor equation, Torque = hp X 5252/RPM = 200 hp X 5252/1800 RPM = 583.56 footpounds.

Calculate the drive axle speed (in RPM) necessary to achieve 3mph. If the drive wheel is 6feet high, then the circumference = 6 feet X pi = 6 X 3.1416 = 18.85 feet; 3 mph = 3 mph X 5280 feet/mile/60 min/hr = 264 feet per minute; if each turn of the wheel provides 18.85 feet of movement, then the wheel needs to turn 264 feet/min/18.85 feet/revolution = 14 RPM axle speed to provide the 3mph speed.

Calculate the final axle drive ratio needed to deliver the 3mph speed: If the engine speed is 1800 RPM at peak power output, then the transmission output is 1800 RPM/12; the reduction transmission ratio = 150 RPM drive shaft speed; the axle ratio = 150 RPM driveshaft speed/14 RPM axle (wheel) speed or 10.714 : 1. Axle torque will be 583.56 X 12 X 10.714 = 75,027 footpounds, and 75,027 footpounds/3foot wheel radius = 25,009 pounds drive thrust available to push heavy freight cars.
Calculating an Axle Ratio for a Rally Car

Define the rally car operational scenario: An open class rally car has a 4speed transmission with a final 1 : 1 output ratio. The engine reaches its peak power at 5800 RPM and has a redline of 6600 RPM. If it is statistically determined that the car spends most of its race time centered at 89 mph in top gear, and tire diameter is 23 inches, you can calculate the optimal axle ratio to keep the car racing at maximum power most of the time.

Determine the axle RPM at the car's 89 mph optimal range with the 23inch diameter tires: Tire circumference = 23 X pi = 23 X 3.1416 = 72.26 inches/12 inches/foot = 6.021 feet; 89 mph X 5280/3600 seconds/hr = 130.53 feet/second; 130.53feet/sec speed/6.021 feet per revolution = 21.68 revolutions per second.

Calculate the axle ratio that allows the engine to operate at its peak power speed of 5800 RPM at 89 mph: 5800 RPM/60 seconds/minute = 96.67 revolutions/second. If the engine requires 96.67 revolutions to turn the rear wheels 21.68 revolutions, then the axle ratio = 96.67/21.68 = 4.46 : 1.
Tips & Warnings
 Always select axle ratios that allow peak power to be delivered at the intended operational speed.
 Automotive engines that continually operate at maximum power output wear out or blow up quickly, while heavy duty diesel engines are intended to operate at maximum output continually.
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 Photo Credit gears image by steve dimitriou from Fotolia.com loader 1 image by Jim Parkin from Fotolia.com dozer image by Inger Anne HulbÃ¦kdal from Fotolia.com voitures de course image by JeanMichel POUGET from Fotolia.com