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Helical Gear

Helical Tooth Gear

Helical gears are characterized by not having straight teeth, if not that they are in the form of a propeller, hence its name.

Advantages and disadvantages of helical gears

Although it may seem that helical teeth differ only in how teeth are positioned, the truth is that they are a great evolution over spur gears.


  • They can transmit much more power and speed.
  • They are quieter as the teeth slide together.
  • They can, if necessary, transmit movements between trees at an angle.


  • They have greater wear due to their sliding.
  • They need more lubrication to prevent excessive wear.
  • Due to their characteristic shape, they are more complex and expensive to manufacture.

As you have read, they have several very interesting advantages over spur gears. Being able to transmit more power and speed is a great advantage, which is why they are so widely used in the automotive industry. If, in addition, greasing is not a problem, practically all are advantages.

Helical Tooth Calculations

The formulas and calculations differ slightly from traditional gears. We only have to take into account the angle and the different steps that exist.

cálculos helicoidales

Helical Gears Calculation

  • Normal step (Pn): It is the step measured perpendicularly between the teeth.
  • Circumferential pitch (Pc): It is the measured pitch measured on the primitive circumference of the gear. See what a primitive circumference is.
  • Helical pitch (Ph): It is what a helical gear advances for each entire turn it rotates, that is, every 360º.
  • Angle (β): It is the angle that the teeth have with respect to the axis of rotation of the gear, it is measured in degrees, for example 30º.
  • Module (M): It is the relationship between the number of teeth and the original diameter. 2 gears of different module, do not work with each other.
  • Number of teeth (Z): They are the total number of teeth that the gear has.


Circumferential pitch: Pc = (π x Dp) / cosβ
Normal step: Pn = Pc x cosβ
Normal modulus: Mn = Mc x cosβ
Circumferential modulus: Mc = Mn / cosβ
Helical pitch: Ph = (Mn x Z x π) / sinβ
Tooth height: h = π x M
Tooth length: L = 10 x Mn
Primitive diameter: Dp = (H x tanβ) / π
Outside diameter: De = ((Mn x Z) / cosβ) + 2Mn

Gear carving

Conventional milling machines

The process of carving the helical teeth in conventional milling machines is very similar to that of straight teeth, but with an addition, in the dividing plate we must place a gear train that is coupled to the machine spindle so that when it advances, it makes also rotate the divider plate and thus get the angle on the teeth. The ratio in the gear train is one turn of the spindle equivalent to the pitch of the propeller to be machined.

CNC milling machines

As for the numerically controlled milling machines, we can do it in several different ways. With a strawberry of the necessary form, as in the conventional milling machine if we have a motorized dividing plate. Or with special milling cutters for helical gears.

With this last example it can also be done on CNC lathes if they have motorized tools and a C axis that controls the rotation of the part to be machined.

And this would be all for today’s class. I hope I have helped you, and if you want to learn and practice a little more, you can do the exercises that you will find shortly.