Basic Types of Gear Transmissions and Gear Ratio Calculation

I. Introduction A. What is a Gear Transmissions The basic definition of gear transmission is a mechanical system that transfers mechanical energy from one rotating shaft to another through the meshing of gear teeth. The gear transmission system facilitates the transfer of power and motion by ensuring that the teeth of the gears come into contact, enabling the conversion of rotational speed, direction, and torque. B. Purpose of this Article The purpose of this article is to explore the basic types of gear transmission systems and the methods for calculating gear ratios. By examining various gears such as spur,…

I. Introduction

A. What is a Gear Transmissions

The basic definition of gear transmission is a mechanical system that transfers mechanical energy from one rotating shaft to another through the meshing of gear teeth. The gear transmission system facilitates the transfer of power and motion by ensuring that the teeth of the gears come into contact, enabling the conversion of rotational speed, direction, and torque.

B. Purpose of this Article

The purpose of this article is to explore the basic types of gear transmission systems and the methods for calculating gear ratios. By examining various gears such as spur, helical, planetary, and worm gears, we will understand how these gears facilitate efficient mechanical energy transfer in different configurations. Additionally, understanding the calculation of gear ratios is crucial, as it helps engineers optimize the design and matching of gearboxes for specific applications.

II. Basic Types of Gear Transmissions in Small Gearbox

The gear structure inside a small gearbox includes spur gears, planetary gears, worm gears, and helical gears. Each type offers unique advantages for different applications due to their specific structural features. Analyzing these gear types helps us understand their essential roles in small gearbox design, enhancing the overall efficiency and stability of mechanical systems.

Gear Type	Advantages	Disadvantages
Spur Gear	Simple design, easy to manufacture	Noisy at high speeds, limited load capacity
Planetary Gear	High torque density, compact design	Complex design, high cost
Worm Gear	High reduction ratios, self-locking capability	Low efficiency, high friction,

Baisc Gear Transmission Types

A. Spur Gears

1. What is a Spur Gear

The tooth profile of the spur gear is parallel to the gear axis. When two spur gears are meshed, the transmission of power and motion is achieved through the contact of the tooth surfaces. Spur gear transmission is usually used for transmission between parallel axes.

2. Working principle of spur gear

M₁: Driving Gear (Input Gear)
M₂: Driven Gear (Output Gear)
W₁: Driving Gear Speed (Input Speed)
T₁: Driving Gear Torque (Input Torque)
W₂: Driven Gear Speed (Output Speed)
T₂: Driven Gear Torque (Output Torque)
r₁: Driving Gear Radius
r₂: Driven Gear Radius

The angular velocity of the driving gear (W₁) and its torque (T₁) are transmitted to the driven gear (W₂, T₂) through the gear ratio. Depending on the number of teeth on the gears, the output torque and speed can be altered.

Mathematically, this relationship can be expressed as:

$$W_1 \cdot T_1 = W_2 \cdot T_2$$

3. How to calculate the spur gear ratio

Formula

$$\text{Total Gear Ratio} = \frac{\text{Number of Teeth on Gear 1}}{\text{Number of Teeth on Gear 2}} \times \frac{\text{Number of Teeth on Gear 2}}{\text{Number of Teeth on Gear 3}}$$

Given Data

The data for the calculation is as follows:

Gear 1 (Driving Gear): 80 teeth
Gear 2 (Driven Gear 1 and Driving Gear 2): 40 teeth
Gear 3 (Driven Gear 2): 20 teeth

First Stage Gear Ratio

$$R_1 = \frac{\text{Number of Teeth on Gear 1}}{\text{Number of Teeth on Gear 2}} = \frac{80}{40} = 2:1$$

Second Stage Gear Ratio

$$R_2 = \frac{\text{Number of Teeth on Gear 2}}{\text{Number of Teeth on Gear 3}} = \frac{40}{20} = 2:1$$

Total Gear Ratio

$$R_{\text{total}} = R_1 \times R_2 = 2 \times 2 = 4:1$$

B. Planetary Gears

1. What is a Planetary Gear

The planetary gear system consists of a sun gear at the center, one or more planetary gears that rotate around it, and a fixed ring gear (external gear) that the planetary gears simultaneously mesh with.

2. Working Pinciple of Planetary Gear

Z_s: Sun Gear
Z_p: Planet Gear
Z_r: Ring Gear
F₁: Force between Sun Gear and Planet Gear
F₂: Force between Planet Gear and Ring Gear

3. How to calculate the Planetary Gear ratio

Formula

$$i = \frac{Z_r}{Z_s}$$

Given Data

Fixed Component: Planet Carrier
Sun Gear (Zs): 20 teeth
Ring Gear (Zr): 74 teeth

Gear Ratio

$$i = \frac{Z_r}{Z_s} = \frac{74}{20} = 3.7$$

Attention！

The total gear ratio of a multi-stage planetary gear system is the product of the gear ratios of each stage

$$i_{\text{total}} = i_1 \times i_2 \times i_3 \dots$$

• C. Worm Gears

1. What is a Worm Gear

The worm gear system is a transmission device composed of a worm wheel and a worm. Its working principle is to drive the worm wheel to rotate through the rotation of the worm, thereby achieving speed reduction and changing the direction of torque transmission.