 Gear Ratio Concepts When troubleshooting, maintaining, or designing a gear drive system, it is necessary to understand the concept of gear ratios. A simple gear train consisting of two spur gears is shown here. Notice how one gear turns slower than the other. Also notice that there is a different number of teeth on each of the gears. There is a relationship of the ratios of the output gears and the input gears number of teeth, circumference, diameter, radii, torque, and velocity. The pinion gear has a 1-inch diameter and the output gear has a 5-inch diameter. Pi can be considered a constant because the diameter ratio, 5 inches to 1 inch, equals 5 to 1, which equals the circumference ratio 15.7 inches to 3.14 inches, which equals 5 to 1. The diameters and the circumferences of these two gears have the same relationships. The linear lengths illustrate the relationship between the distances traveled as the gears rotate one revolution. The ratio of the diameters of the output gear to the input gear is 5 to 1. The ratio of the circumferences of the output gear to the input gear is 5 to 1. The distance traveled by the smaller gear during one revolution is less than the distance traveled by the larger gear. The same number of teeth have made contact, but there are more teeth on the larger gear because of its larger circumference. When the larger output gear rotates one revolution, the smaller pinion gear will rotate five revolutions. This gives an angular displacement ratio of 5 to 1. If the pinion is driven by a motor at 100 revolutions in one minute, the output gear will rotate 20 revolutions during that same minute. Remember that the ratio of the diameters and the ratio of the number of teeth are the same ratio. Note that the ratio of the diameters and the ratio of the revolutions per minute are also the same ratio. 100 rpm to 20 rpm equals 5 to 1. Note the velocity ratio is inverse that of the diameter ratio or the number of teeth ratio. Since the ratio of the number of teeth and the ratio of the diameters are the same, you can use either ratio to find the unknown velocity. What is the output rpm of the gear train shown if the input is driven at 1,750 rpm? To find a velocity of a gear, set up a basic linear equation and cross-multiply and divide. Set up your formula as follows. Input rpm over output rpm equals output diameter over input diameter. 1750 times 1 equals output rpm times 5. Solve for the output gear rpm. 1750 over 5 equals 350 rpm. Remember you can use either the ratio of the diameters or the ratio of the number of teeth since they are the same to find an unknown velocity. Cross-multiply 1750 times 8 equals output rpm times 40. Solve for the output gear rpm. 14,000 over 40 equals 350 rpm. Congratulations! You have completed this learning activity on gear ratio concepts.