Gear Ratio and Torque Calculation

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Gear Ratio

            The gear ratio of a gear train is the ratio of the angular velocity of the input gear to the angular velocity of the output gear, also known as the speed ratio of the gear train. The gear ratio can be computed directly from the numbers of teeth of the various gears that engage to form the gear train.

            In simple words, the gear ratio defines the relationship between multiple gears.

 

Gear Ratio= Output gear # teeth / Input gear # teeth

 

            For example, if our motor is attached to gear with 60 teeth and this gear is then attached to a gear with 20 teeth that drives a wheel, our gear ratio is 60:20, or more accurately 3:1

            If you do not want to count a gear's teeth (or if they do not exist), gear ratios can also be determined by measuring the distance between the center of each gear to the point of contact.

            For example, if our motor is attached to a gear with a 1" diameter and this gear is connected to a gear with a 2" diameter attached to a wheel,

  • From the center to the edge of our input gear is 0.5"
  • From the center to the edge of our output gear is 1"
  • Our ratio is 1/0.5 or more accurately 2:1

How Does a Gear Ratio Affect Speed?

            The gear ratio tells us how fast one gear is rotating when compared to another.

            If our input gear (10 teeth) is rotating at 5 RPMs, and it is connected to our output gear (50 teeth), our output gear will rotate at 1 RPMs.                                          

Why?

Our gear ratio is 50:10... Or 5:1

            If our small gear rotates 1x, our large gear only rotates 1/5. It takes 5 rotations of our small gear to = 1 rotation of our large gear. Thus our large gear is rotating at 1/5 the speed = 1rpm.

            What if our gear ratio where 1:3?

            In this case, our input gear is 3x larger as large as our output gear.

            If our input gear were rotating at 20 RPMs.... each rotation, would result in 3 rotations of our output gear. Our output would be 60 RPMs.

How Does Gear Ratio Affect Torque


First....What is torque?

            Torque is a twisting force- (it doesn't do any 'work' itself- it is simply an application of energy).

            Work (or 'stuff') happens, when torque is applied and movement occurs.

            "Torque is a force that tends to rotate or turn things. You generate a torque any time you apply a force using a wrench. Tightening the lug nuts on your wheels is a good example. When you use a wrench, you apply a force to the handle. This force creates a torque on the lug nut, which tends to turn the lug nut.

            English units of torque are pound-inches or pound-feet; the SI unit is the Newton-meter. Notice that the torque units contain a distance and a force. To calculate the torque, you just multiply the force by the distance from the center. 

            In the case of lug nuts, if the wrench is a foot long, and you put 200 pounds of force on it, you are generating 200 pound-feet of torque. If you use a two-foot wrench, you only need to put 100 pounds of force on it to generate the same torque."

In summary:

Torque equals Force multiplied by Distance


How does gear ratio affect Torque?

        Simply put, torque at work (such as at a wheel) is your motor's torque times your gear ratio.

    Motor Torque x gear ratio = torque at the wheel

        Let’s say we have a 10rmps motor that is capable of 5 oz. Torque (we know this from our motor spec.)

        Let’s say we have 2 gears. Our input gear (attached to our motor) has 10 teeth our output gear has 50 teeth

Our Gear ratio is 5:1

        Motor Torque x gear ratio = torque at the wheel

                                   5oz x 5:1 = 25 oz.

What if our gear ratio were 1:3?

                                   5oz x 1:3 = 1.6oz

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