At present, various calculation methods of helical worm drive can be roughly classified into four categories:

1. Designed according to helical gear

The normal modulus of gears and worms are standard modulus, which is a relatively mature method and used more. However, the worm is machined according to the normal modulus:

Firstly, the normal modulus is concerned, but the axial modulus of the worm is ignored; It has lost the characteristic of axial modulus standard, and has become a helical gear with a stagger angle of 90 ° instead of a worm.

Second, it is impossible to process the standard modular thread directly on the lathe. Because there is no exchange gear on the lathe for you to choose. If the change gear is not correct, it is easy to cause problems. At the same time, it is also very difficult to find two helical gears with an intersection angle of 90 °. Some people may say that a CNC lathe can be used, which is another matter. But integers are better than decimals.

2. Orthogonal helical gear transmission with worm maintaining axial standard modulus

Helical gears are processed by making non-standard gear hobs according to the worm normal modulus data. This is the simplest and most normal method for calculation. In the 1960s, our factory used this method for military products. However, a pair of worm pairs and a non-standard hob have high manufacturing cost.

3. The design method of keeping the axial standard modulus of worm and selecting the tooth shape angle

The fault of this design method lies in the insufficient understanding of the meshing theory. It is mistakenly believed by subjective imagination that the tooth shape angle of all gears and worms is 20 °. Regardless of the axial pressure angle and the normal pressure angle, it seems that all 20 ° are the same and can be meshed. It is just like taking the tooth shape angle of the normal straight profile worm as the normal pressure angle. This is a common and very confused idea. The damage to the helical gear of the worm helical gear transmission pair in the keyway slotting machine of Changsha Machine Tool Plant mentioned above is a typical example of product defects caused by design methods.

4. The design method of the principle of equal law base section

The normal base section is equal to the normal base section Mn of the hob × π × cos α N is equal to the normal base joint Mn1 of the worm × π × cos α n1

In the 1970s, I wrote the article “design, processing and measurement of spiral gear type worm gear pair”, and proposed this algorithm, which is completed by summarizing the lessons of processing helical gears with non-standard gear hobs and keyway slotting machines in military products.

(1) Main calculation formulas of the design method based on the principle of equal basic sections

Calculation formula of meshing parameter modulus of worm and helical gear
（1）mn1=mx1cos γ 1 (Mn1 is worm normal modulus)

（2）cos α n1=mn × cos α n／mn1（ α N1 is worm normal pressure angle)

（3）sin β 2j=tan γ 1（ β 2J is the helix angle for helical gear machining)

(4) Mn=mx1 (Mn is the normal modulus of helical gear hob, MX1 is the axial modulus of worm)

(2) Formula characteristics

This design method is strict in theory and simple in calculation. The biggest advantage is that the following five indicators can meet the standard requirements. Now I will introduce it to the forum friends to share with you.

a. Principle up to standard It is designed according to the principle of equal base section of involute spiral gear transmission method;

b. Worm maintains standard axial modulus and can be machined on lathe;

c. The hob for processing helical gear is a gear hob with standard module, which meets the standardization requirements of the tool;

d. When machining, the helical angle of the helical gear reaches the standard (no longer equal to the rising angle of the worm), which is obtained according to the involute geometric principle;

e. The tooth shape angle of the turning tool for machining the worm reaches the standard. The tooth profile angle of turning tool is the rising angle of worm based cylindrical screw γ b， γ B is equal to the normal pressure angle (20 °) of the hob used.