Gears help to change the rotation rate of a machinery shaft and the direction of the axis of rotation. This component can even alter rotary motion to linear motion. However, the magic of gears lies in their transferring of directional power. For that, they require a proper gear ratio that works concerning one another.

A gear ratio is the proportion of the number of teeth in the gear to the number of teeth in the pinion. The pinion is the smaller of the two components in a mesh. By dividing the input shaft's angular speed by the output shaft's rotational speed, one can calculate a gear ratio. 

The gear ratio might also apply to two sprockets attached by the same pulleys or chains connected by a drive belt. Therefore, a gear ratio is necessary to calculate the speed that a given gear chain will produce.

You can easily calculate the speed when you know how to calculate a gear ratio. So, the equation is as follows:

Speed (Gear 1) * Teeth (Gear 1) = Speed (Gear X) * Teeth (Gear X). 

When you assemble two gear wheels, their sizes determine the speed they will spin. Moreover, if the driving wheel is smaller than the driven wheel, it will rotate more than its component. This also means the driven wheel will spin fast if the driver wheel is larger. 

Here is a step-by-step guide to calculating the gear ratio:

Step 1: Begin with a two-gear train. To determine a gear ratio, you must have two gears connected. It is called a gear train. The first gear is a driving gear attached to the motor shaft, and the second is a driven gear connected to the load shaft. 

Step 2: Count the no. of teeth on the driving gear. An easy way to determine the gear ratio concerning two interlocking gears is to calculate the number of teeth they both have and compare them. You can count the number of teeth manually. However, check for this information labelled on the gear itself to refrain from manually calculating.

Step 3: Count the no. of teeth on the driven gear. Then, understand the number of teeth on the driven gear just as you did before for the driving gear.

Step 4: Now, divide one tooth count by another. As you know the number of teeth on each gear, you can determine a gear ratio easily. Divide the driven gear teeth by the driving gear teeth. You can count the no. of teeth on the driving and driven wheel and determine these numbers as a ratio or a fraction.

Follow this example to understand this calculation:

If a driving wheel has 20 teeth and a driven wheel has 40, evaluate the gear ratio as 40/20. It simplifies to 2/1 or 2:1. It means, for every rotation of the driven wheel, the driving wheel makes two spins. Similarly, a ratio of 1/2 means that the driven wheel spins twice for every rotation of the driving wheel. In other words, the driven wheel rotates faster than the motor shaft.

There might be several gears between a driving and a driven gear. It helps to transmit power from the drive gear to the driven gear. These are called idler gears. Below is a step-by-step guide to calculating gear ratio when there are more than two gears:

Step 1: Begin with a gear train. In these cases, the first gear is the driver gear, the last gear remains the driven gear, and the components in between become idler gears. Idler gears change the rotation direction or connect two gears when direct gearing makes them challenging.

Step 2: Now, divide the teeth of the driving and driven gears. Idler gears don't affect the gear ratio of the overall train.

Step 3: Find gear ratios for the intermediate gears. In such cases, begin from driving and work toward load gear. Use the preceding gear as if it were the driving gear. Then, divide the number of teeth on each driven gear by the number of teeth on a driving gear for every interlocking gear set. It will help you to calculate the intermediate gear ratio.

To calculate the velocity ratio of a gear, follow the below steps:

Step 1: Calculate the rotational speed of your driving gear by using the idea of gear ratios. Firstly, find the rotational speed of your driving gear by determining rotations per minute or RPM.

Step 2: Use the formula S1 × T1 = S2 × T2. In this formula, S1 stands for the rotational speed of the drive gear, T1 indicates the teeth in a driving gear, and S2 indicate speed while T2 point towards the teeth of a driven gear. Fill in the variables accordingly until you have only one left to be defined.

Step 3: Now, you can solve this equation. Calculate the remaining variable using algebra. You can simplify the rest of the equation and keep this variable aside from the equals sign, and you will have the answer. Ensure to label it with the correct units.

Here are some essential factors you must keep in mind when calculating gear ratios: 

• Gear Speed: You must calculate the amount of speeding up and down of a gear system by comparing the radii of the wheels.

• Compare Teeth Number: Ensure both wheels' teeth are the same size. They both interlock while functioning. It will enable you to compare the number of teeth on the two wheels.

• Tooth Count: Remember the tooth count on a driven wheel always goes on top of the fraction or first in the ratio.

• Gear Lubrication: Proper lubrication affects a gear ratio immensely. A properly lubricated gear will have a higher ratio than an improperly lubricated one.

• Idler Gears: When dealing with gear trains or idler gears, the driving and driven gears (usually the first and last ones) matter.

• Gear Size: The size of a gear affects the gear ratio. A larger component will spin slowly but with greater torque. However, a smaller one will rotate quickly but with less torque.

• Gear Teeth: The number of teeth on a gear defines its size. It, in turn, affects the gear ratio. If one component has more teeth than the other, it will spin slowly but with higher torque.

• Material: The material used to make a gear also affects a gear ratio. For example, a gear made of a softer material or aluminium will have a lower gear ratio than one made of a robust material or steel.

• Gear Efficiency: The efficiency of the gear system can also affect the gear ratio. A more efficient gear system will have a higher gear ratio than a less efficient one.

• Gear Load: Loading on a gear also affects a gear ratio. A gear carrying a heavy load will have a lower gear ratio than one carrying a lighter load.

Gears have teeth that are advantageous and contribute to your calculation of gear ratio:

• Gear tooth refrains slippage between gears. So, axles attached by gears are always synchronised adequately with one another.

• It helps to determine a gear ratio as you count the number of teeth in the two gears and divide them. So, if one component has 60 teeth and another has 20, the gear ratio as these two gears connect is 3:1.

• Small imperfections in the original circumference and diameter of two gears don't matter. A gear ratio is evaluated by the number of teeth, even if the diameters are inadequate.

The purpose of a gear ratio is as follows:

• Gear ratio reduces the torque by enhancing the speed, and vice versa. 

• It states that your car will not initially move at higher gear ratios, as it requires more torque than horsepower. 

• Lower gear ratios show the vehicle is unsuitable for highway driving as you require higher speed than torque.

• A worm gear is suitable for you if you want to get a high gear ratio. A threaded shaft contacts the gear’s teeth in a worm gear.

• Gear ratios are important in calculating the efficiency of an engine.

• Gear ratio helps measure various mechanical items, including farming machines and equipment, clocks, automobiles, and more. 

The main use of gear ratio and its calculation is in the automotive industries worldwide. The shift in speed of a vehicle corresponds to a shift in gears. It means the higher the gear, the higher the vehicle speed. Manufacturers calculate and consider gear ratios while designing gears.