Gear transmission is a widely used form of transmission in mechanical transmission. How is the gear ratio calculated?

1、 Calculation of gear transmission ratio

Formula transmission ratio=number of driven wheel teeth/number of driving wheel teeth=driving wheel speed/driven wheel speed

I=z2/z1=n1/n2

1. Transmission ratio of gears:

Transmission ratio size:

I12=N1/N2=Z2/Z1

Turn to external meshing and take the "-" sign for opposite direction

Take the "+" sign for the same internal meshing direction

For cylindrical gear transmission, the steering relationship between the driven wheel and the driving wheel can be directly expressed in the transmission ratio formula, that is:

I12=± z2/z1

The "+" sign indicates that the main and driven wheels have the same direction of rotation and are used for internal meshing; The "-" symbol indicates that the main and driven wheels have opposite directions of rotation and is used for external meshing; For bevel gear transmission and worm gear transmission, since the motion of the master and slave wheels is not in the same plane, they cannot be determined by the "±" sign method. Cone gear transmission, worm gear transmission, and gear rack transmission can only be determined by drawing arrows.

For gear rack transmission, if ω 1 represents the angular velocity of gear 1, d1 represents the pitch circle diameter of gear 1, and v2 represents the moving speed of the gear rack, the following relationship exists: V2=d1 ω 1/2

2. Calculation of transmission ratio of planetary gear system

Relative rotational speed of the original component speed

Center wheel 1 n1 n1=n1 nH

Planetary gear 2 n2 n2=n2 nH

Center wheel 3 n3 n3=n3 nH

Planetary carrier H nH nH=nH nH=0

Transform the wheel system into a fixed axis wheel system

In the conversion gear train, gears 1 and 3 rotate in opposite directions.

General formula:

In the formula, m is the number of external meshing between gear G and K revolutions.

(1) Drive wheel G and driven wheel K are arranged in a master-slave relationship in order.

(2) The formula is only applicable when the axes of gears G, K, and planet carrier H are on a straight line.

(3) Two of the three quantities nG, nK, and nH need to be given; And it is necessary to assume that a certain turn is in the opposite direction and substitute negative values into the calculation.

Example 8-3: In the planetary gear system shown in the figure, the known motor speed n1=300r/min (clockwise rotation)

When z1=17 and z3=85, calculate nH when n3=0 and n3=120r/min (clockwise rotation).

2、 Characteristics of gear transmission

1) In commonly used mechanical transmissions, gear transmission has the highest efficiency, with closed transmission efficiency ranging from 96% to 99%. This has great economic significance for high-power transmission.

2) The compact structure requires less space than belt and chain drives.