The force of a helical gear splits into three primary components: tangential force, radial force, and axial force. These forces work simultaneously during operation, creating complex loading patterns that distinguish helical gearboxes from their spur gear counterparts. The tangential force drives the torque transmission. The radial force pushes gear teeth apart. The axial force creates thrust along the shaft axis due to the helical tooth angle.
Tangential Force (Circumferential Component)
The tangential force is the primary working force in any helical gearbox. It acts perpendicular to the gear radius and creates the torque that drives your machinery.
This force directly relates to the power being transmitted. A 100 HP motor driving a helical gear with a pitch diameter of 200mm generates approximately 14,300 N of tangential force at 1750 RPM.
The calculation is straightforward:
Ft = 2T/d
Where T is torque and d is pitch diameter.
Tangential force determines your gear tooth strength requirements. Standard industrial helical gears handle tangential forces ranging from 1,000 N in light-duty applications to over 50,000 N in heavy industrial drives. The force remains constant regardless of helix angle, making it the most predictable component in your design calculations.
Radial Force (Separating Component)
The radial force pushes gears apart, acting directly toward the gear center. In a helical gearbox, this force typically equals 35-40% of the tangential force.
For a standard 20-degree pressure angle, the radial force:
Fr = Ft × tan(20°) = 0.364 × Ft.
A helical gear transmitting 10,000 N of tangential force creates approximately 3,640 N of radial load on the bearings.
The radial force increases shaft deflection. A 50mm diameter shaft under 5,000 N radial load deflects approximately 0.05mm over a 200mm span. This deflection affects gear mesh alignment and can reduce efficiency by 2-3% if not properly managed.
Axial Force (Thrust Component)
The axial force is unique to helical and spiral gear designs. It acts parallel to the gear axis, creating thrust that must be properly supported.
The magnitude depends on your helix angle:
Fa = Ft × tan(β)
Where β is the helix angle.
A typical 15-degree helix angle generates axial force equal to 27% of the tangential force. Increasing the helix angle to 30 degrees doubles this to 58%. Most industrial helical gearbox designs use 15-25 degree helix angles to balance smooth operation with manageable thrust loads.
