What is the MODULUS of a gear?

The modulus is what determines the size of the gear. The gear modulus is defined as a basic parameter of the modulus gear teeth, which is a number artificially abstracted to measure the size of the gear teeth. The aim is to standardize gear cutters and reduce costs. The modules of spur, helical and bevel gears can all refer to the standard module series table.The degree circle of the gear is the benchmark for designing and calculating the dimensions of each part of the gear, and the circumference of the gear indexing circle = πd=z p, so the diameter of the scoring circle is d=z p/π.

In some countries, different modules use the diameter pitch as the basic parameter of the gear, with inches as the unit of measurement, the diameter pitch is expressed as P, which refers to the ratio of the pi to the tooth pitch ρ, the diameter pitch P=π/ρ, with 1/ inches.

The circumference of the gear index circle = πd = z ρ, so the pitch of the index circle ρ = πd/z.

Diameter P=Z/d (d is in inches)

Modulus m=d/Z (the unit of d is mm)

As can be seen:

m=(1/P)*25.4=25.4/P

P=(1/m)*25.4=25.4/m

Therefore, the relationship between the modulus m and the diameter pitch P is the reciprocal of each other, and / is a different unit system.

That is: the product of the modulus and the diameter node is always equal to 1.

Corresponding to the conversion of the unit, there is the following relationship between the diameter pitch and the modulus

P=π/ρ=25.4/m where P is the diameter pitch (1/inch); ρ is the tooth pitch (inch); m is the modulus (mm).

The diameter of the pitch P is equivalent to the role of the modulus m in the metric system. In most inch gears, gear couplings and ratchets, the diameter pitch is an essential parameter. The larger the diameter pitch, the smaller the gear tooth size (tooth height and tooth thickness). Some countries have standard series values for diameter sections.

The dual-modulus system is another way to obtain a short tooth profile, which can improve the bending strength, but has poor stability, and is often used in the automobile and tractor industry.

The dual-module system stipulates that two modules of different sizes are used to calculate the size of each part of a gear, which is marked as the fractional form m1/m2, where the larger module m1 is used to calculate the diameter of the dividing circle, and the smaller m2 Used to calculate the size of the gear teeth.

The calculation formula of each dimension is as follows:

Dividing circle diameter: d=m1*Z

Addendum height: ha=ha*m2

Root height: hf=(ha1+c1)*m2

Addendum diameter: da=d+2*ha=m1*Z+2*ha*m2

Root diameter: df=d-2*hf=m1*Z-2*(ha1+c1)*m2

In addition, the pitch circle tooth thickness S, the tooth pitch P, the base circle diameter db and the center distance a are calculated according to m1.

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Double diameter control is another way to obtain short tooth profile in inch gears to improve flexural strength. It stipulates that the smaller diameter pitch P2 is used to calculate the diameter of the index circle, and the larger diameter pitch P1 is used to calculate the size of the gear teeth, marked as P2/P1, the smaller P2 is the numerator, and the larger P1 is the denominator. Just the opposite of the dual modulo system.

The calculation formula of each dimension is as follows:

Dividing circle diameter: d=Z/P2

Addendum height: ha=ha/P1

Root height: hf=(ha1+c1)/P1

Addendum diameter: da=d+2*ha=Z/P2+2*ha/P1

Root diameter: df=d-2*hf=Z/P2-2*(ha1+c1)/P1

In addition, the pitch circle tooth thickness S, the tooth pitch P, the base circle diameter db and the center distance a are calculated according to P2.

It means to use the smaller diameter pitch P2=10 (numerator) to calculate the pitch circle diameter, and use the larger pitch P1=20 (denominator) to calculate the tooth height.

Therefore, the dimensions of a 10/20 pitch double diameter pitch gear are calculated as follows:

Dividing circle diameter: d=Z/P2=Z/10 (d is in inches)

Addendum height: ha=ha/P1=1/20=0.05"=1.27mm

Root height: hf=(ha1+c1)/P1=1.25/20=0.625"=1.588mm

The center distance a is calculated according to the smaller diameter pitch 10 .

You can also convert the double-diameter control to the double-modulus system first, and then calculate the size:

The double-modulus system is marked as fractional form m1/m2. The larger modulus m1 is used to calculate the diameter of the index circle, and the smaller m2 is used to calculate the size of the gear teeth.

m1=1/P2*25.4=1/10"*25.4=2.54mm

m2=1/P1*25.4=1/20"*25.4=1.27mm

So, this gear is 2.54/1.27 expressed as a double modulo gear:

Dividing circle diameter: d=2.54*z

Addendum height: ha=ha*m2=1*1.27=1.27mm

Root height: hf=(ha1+c1)*m2=1.25*1.27=1.588mm

The center distance a is calculated according to the larger modulus m1=2.54mm

However, if the gear is to be designed according to the modulus, the standard value of the modulus should be selected, and the displacement should be used to meet the requirements of the center distance.

Since π is an irrational number in the above formula, it is not convenient to locate the reference circle as a reference. In order to facilitate calculation, manufacture and inspection, the ratio p/π is now artificially specified as some simple values, and this ratio is called the module (module), which is expressed in m, that is, its unit is mm. So get:

The modulus m is a basic parameter that determines the size of the gear. If the modulus of the gear with the same tooth p is larger, its size is also larger. The modulo values of the gears have been standardized for ease of manufacture, inspection and interchangeability.

The standardized value of modulus refers to GB1357-87.

The first series are: 0.1, 0.12, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.8, 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16 , 20, 25, 32, 40, 50. (The first series is preferred).

The second series are: 0.35, 0.7, 0.9, 1.75, 2.25, 2.75, 3.25, 3.5, 3.75, 4.5, 5.5, 6.5, 7, 9, 11, 14, 18, 22, 28, 36, 45. Unit mm.

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