# Output Torque of Gear Reducer

## 1. Concept of gear reducers torque :

(1). The concept of reduction ratio: namely the transmission ratio of the reduction gear, which is a kind of transmission ratio. It refers to the ratio of the instantaneous input speed to the output speed of the reduction mechanism, which is represented by the symbol “i”. If the input speed is 1500r/min and the output speed is 25r/min, then the reduction ratio is: i=60:1.

(2). The output torque of the speed gear reducer is calculated as follows:

- Speed ratio = output revolution of motor ÷ output revolution of gear reducer (“speed ratio” is also called “transmission ratio”)

(3). If the motor power, speed ratio and use coefficient is known, the torque of the motor reducer can be calculated as follows:

- Torque of gear reducer = 9550 * motor power ÷ motor input revolution * speed ratio * use coefficient

(4). If the torque and the output revolution of the reducer and the use coefficient are calculated, the motor power required by the reducer is obtained as follows:

- Motor power = torque ÷ 9550 × motor power input revolution ÷ speed ratio ÷ use coefficient

(5). The reducer is a relatively precise machine, and its purpose is to reduce the speed and increase the torque.

- Torque=9550*power (W)/revolutions (revolutions/min)=9550*0.75/(1440/15)=74.6N.m

## 2. Introduction of gear ratio

The concept of gear ratio: the transmission ratio of the reduction device, which is a kind of transmission ratio, which is a kind of transmission ratio. It refers to the ratio of the instantaneous input speed to the output speed of the reduction mechanism, which is represented by the symbol “i”. If the input speed is 1500r/min and the output speed is 25r/min, then the reduction ratio is: i=60:1.

### How to calculate the gear ratio of the reducer (also called reduction ratio):

(1).In a pair of gears, the gear with a lower number of teeth is called a small gear, and the gear with a higher number of teeth is called a large gear. When the number of teeth are the same, the driving gear is called a small gear, and the driven gear is called a large gear;

(2). In a pair of external gears, whose operation is reverse rotation, the small gear rotates to the right, and the large gear rotates to the left;

(3). In a pair of internal gears, the two gears run in the same direction;

(4). In a pair of gears, the number of revolutions and the number of teeth are inversely proportional, and the number of revolutions of the small gear is more than that of the large gear. The gear ratio and speed ratio of the speed gear reducer are as follows: (i means reduction ratio)

- Gear ratioⅰ= Number of teeth of large gear/Number of teeth of small gear
- Worm gear: Gear ratioⅰ= Worm gear teeth/worm

## 3. The concept of motor torque :

(1). Motor torque is the output torque of the motor, which is one of the basic parameters of the motor. The unit of measurement is N.M (Newton. Meter).

(2). The relationship between motor output torque and motor speed and power.

- Formula: T=9550*P/n. This formula is commonly used in engineering to calculate torque, power, rotational speed.
- In the formula: T–torque; 9550–constant (no need to investigate its source); P–power of the motor (KW); n–output speed (rev/min)
- Note: It should be noted that if you calculate the torque with this formula, the factor of gear transmission efficiency loss should be taken into consideration.

(3). Torque calculation formula for servo motor: T=F*R*reduction ratio. For example: To drive a 100kg object, R=50mm, and the reduction ratio is 1:50. What is the torque of the servo motor? Answer: 100 x 9.8 (gravitational acceleration) x 0.05 x 0.02=1.98N.M