# ENDLESS SCREW: DEFINITIONS AND FORMULAS This threaded element is never accompanied by a nut, and it does engage with a cogwheel, with which it forms a mechanism that allows a great reduction of speeds.

The screw can therefore be considered as a cogwheel with a number of teeth equal to the number of entries.

It can also be considered as a trapezoidal thread with an angle between flanks of 40 ° and with a pitch equal to the pitch of the wheel with which it will engage; that is, the step is modular or multiple of, therefore, its dimensions will be expressed as a function of the module and the primitive diameter dp.

# NOMENCLATURE AND DEFINITIONS

The main elements of an auger are the following:

ß = Angle of the propeller. It is the angle formed by the tagent to the fillet with a plane perpendicular to the axis of the screw

Ph = Propeller pitch. It is the distance between two threads belonging to the same fillet, measured in the axial direction. This step is the one that interests the turner to calculate the wheels to put in the lyre.

Px = Axial pitch. It is the distance between two consecutive threads, measured in the axial direction.

Pn = Normal step. It is the distance between two consecutive threads, measured according to a normal plane to the fillet. This step corresponds to a module m, which is considered for calculation purposes.

n = Number of entries. It is the number of carved steaks.

# FORMULAS RELATING TO THE ENDLESS SCREW

Taking as data:

The module m.
The number of entries n.
The primitive diameter dp (this value that depends mainly on the resistance of the auger, becomes equal to approximately 15 x m).

The calculation of the dimensions of an auger is done according to the following formulas:

• Head height-> h ’= m.
• Height of the thread foot-> h´´ = 1.25 m.
• Thread height or thread depth: h = h ’+ h´´ = 2.25 m.
• Outside diameter-> de = dp + 2m.
• Inner diameter -> di = dp - 2.5 m

# VALUES IN THE FLAT NORMAL PLANE

• Normal step-> Pn = .¶. m.
• Where ¶ = 3.1416.
• Thickness of the wire in the primitive diameter-> e = Pn / 2 = 1.57 m.
• Angle between flanks-> 2 = 40º.
• Propeller angle-> sin ß = {Pn x n} / {dp x ¶} = m x n / dp.