Number of teeth z: The total number of teeth of a gear.

Modulus m: The product of the pitch and the number of teeth is equal to the circumference of the division circle, ie pz = πd, where z is a natural number and π is an irrational number. The condition for making d a rational number is that p/π is a rational number and is called a modulus. Ie: m=p/π

Index circle diameter d: The gear tooth size of the gear is determined based on this circle, d=mz

Tip circle diameter da and root circle diameter df:

The formula for calculating the diameter of the tip circle and the diameter of the root of the root can be derived from the calculation formula of the height of the crown and the height of the root:

da=d+2ha df=d-2hf

=mz+2m=mz-2×1.25m

=m(z+2)=m(z-2.5)

Modulus z: The index circle of the gear is the reference for designing and calculating the dimensions of each part of the gear, and the circumference of the gear index circle = πd=z p, so the diameter of the score circle

d=z p/π 

Since π is an irrational number in the above formula, it is inconvenient to locate the index circle as a reference. In order to facilitate calculation, manufacture and inspection, the ratio p/π is artificially specified as some simple values, and this ratio is called modulo. Module (module), expressed in m, that is,

Its unit is mm. So it is:

The modulus m is a basic parameter that determines the size of the gear. If the gear modulus of the same number of teeth is large, the size is also large. In order to facilitate manufacturing, inspection and interchangeability, the modulus value of the gear has been standardized.

Index circle diameter d: In the calculation of the gear, a circle must be specified as the reference circle for the dimension calculation, and the circle whose diameter is the product of the modulus multiplied by the number of teeth is defined. Actually does not exist in the gear, just a circle on the definition. The diameter and radius are represented by d and r, respectively, and the value is only related to the product of the modulus and the number of teeth, and the modulus is the end modulus. Independent of the coefficient of displacement. In the standard gear, the circle with the same groove width and tooth thickness (regardless of the flank clearance) is the index circle. The standard gear transmission coincides with the pitch circle. However, in the case of a displacement gear, the cogging and tooth thickness on the indexing circle will no longer be equal. If the index gear of the high-position gear transmission in the displacement gear transmission still coincides with the pitch circle. However, the angular displacement of the gear drive separates the index circle and the pitch circle.

Pressure angle α—the common normal of the two tooth profiles (ie the direction of the force of the tooth profile) and the common tangent of the two circles (ie the instantaneous direction of motion at point P) at the point tangential point P of the two gear pitches The acute angle of the clip is called the pressure angle, also called the engagement angle. For a single gear, it is a toothed angle. The standard gear has a pressure angle of 20".

The small pressure angle gear has a small load carrying capacity; while the large pressure angle gear has a higher load carrying capacity, the bearing load increases under the same transmission torque, and therefore is used only for special cases.

Basic parameters and expression of the tooth profile:

Bb%h[1]wFU, B-r0 According to the standard gear design rules, there is a reference map for calculating the contour of the groove as shown in Fig. 2. +e"A[|b0