The basic meshing principle of gears and racks

The basic meshing principle of gears and racks

Original Gear and Machine Tool Gear and Machine Tool 2024-04-15 07:55 Hunan

Gear rack meshing is an important mechanical transmission method, which is based on the principle of matching tooth profiles to achieve the conversion between linear motion and rotational motion.

Specifically, a rack is a linear gear with straight or helical teeth, whose tooth profile is straight and can be regarded as a cylindrical gear with an infinite radius of the indexing circle. The following is a detailed explanation of the meshing between gears and racks:

1. Basic characteristics of gears and racks

A gear is a component that transmits rotational motion through tooth meshing, and its tooth profile curve can be involute, cycloid, circular arc, etc. A rack is a special gear with a straight tooth profile, and its working principle is to transform the rotational motion of the gear into the reciprocating linear motion of the rack, or to transform the reciprocating linear motion of the rack into the rotational motion of the gear.

The basic parameters of gears include modulus (m) and pressure angle（ α） And the number of teeth (z). The modulus is the ratio of the diameter of the dividing circle to the number of teeth, the pressure angle is the angle between the normal tangent of the gear teeth and the horizontal plane, and the number of teeth determines the rotational speed of the gear. The characteristic of a rack is that each point on its tooth profile has the same pressure angle, which is equal to the inclination angle of the tooth profile. This angle is called the tooth profile angle, with a standard value of 20 °. The tooth pitch and modulus of the rack are the same as those of the gear, and it has a dividing line (centerline) parallel to the tooth crest line, which is the reference line for calculating the size of the rack.

2. Conditions for gear and rack meshing

The correct meshing of gears and racks requires certain specific conditions to be met. Firstly, the modulus and pressure angle must be equal, which is the most basic requirement. In addition, the helix angles of gears and racks are equal in size and opposite in direction, which is also an important condition to ensure correct meshing. In practical applications, the correct meshing condition for an external meshing helical cylindrical gear is that the normal surface modulus and normal surface pressure angle of the two wheels are equal, and the helix angles on the indexing cylinders of the two wheels are equal in size and opposite in direction.

3. Working principle of gear rack meshing

The working principle of gear rack meshing involves the concepts of instantaneous center line and pitch circle. The instantaneous center line refers to the trajectory of a point on two components that move in plane relative to each other and have an instantaneous relative velocity of zero. When the gear and rack mesh, the instantaneous center lines of the two will undergo pure rolling, which is the key to ensuring smooth meshing. The pitch circle is a reference circle used to determine the proportional dimensions of the gear tooth elements.

4. Application of gear rack meshing

Gear and rack meshing is widely used in various situations, especially in situations that require fast and accurate positioning mechanisms, as well as CNC machine tools, machining centers, cutting machinery, welding machinery, etc. with heavy loads, high precision, high rigidity, high speed, and long travel. In addition, it is also suitable for factory automation rapid transplanting machinery, industrial robot arm grasping mechanisms, and so on.