How to calculate thrust load in helical gear

Written by pauline gill
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How to calculate thrust load in helical gear
Helical gears and straight gears on the same transmission shaft. (rusty gear on the paper image by Dmitri MIkitenko from

Helical gears are spur gears that have their teeth set at an angle with respect to the axial centre line of the shaft supporting the gear, instead of parallel to it. They are used in most high-speed automotive and machine applications where quiet operation and high gear loads are key factors. Helical gears have higher sideways thrust loads (axial loads) and slightly lower efficiency than straight spur gears, however, which makes their integrations more costly to build and operate. Calculating thrust loads for helical gears is therefore essential to their proper design and implementation.

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  1. 1

    Define the helical gear application. In this case, a reduction gear set employing helical gears is used in a luxury inboard boat drive because of its smoothness and quiet operation. Engine torque at cruising speed is 360-foot-pounds. If the pitch diameter of the right-handed 22-tooth driving gear connected to the spinning engine shaft is 4 inches and the diameter of the 44-tooth driven gear connected to the propeller shaft is 8 inches and their helical angle, B, is 18 degrees, you can calculate the axial thrust created by the driven helical gear while the boat is cruising.

    How to calculate thrust load in helical gear
    Transmissions use helical gears because they are quiet. (old gearbox dumped in a rest area on the side of the road image by Undy from
  2. 2

    Consult a helical gear right-hand, left-hand gear sense diagram to obtain the direction in which the thrust will be directed and a sense for the numbers you will be calculating. In this case, (all looking from the rear of the boat), the engine is rotating counter-clockwise, the propeller shaft is clockwise, the driving gear is helical right-hand, and the driven gear is helical left hand. Therefore, the driven helical gear will impart its thrust to the front of the gear case.

    How to calculate thrust load in helical gear
    Bevel gears by comparison to helical gears, change motion direction. (gears image by steve dimitriou from
  3. 3

    Calculate the instantaneous torque applied to the propeller shaft. Since the smaller 22-tooth gear is driving the larger 44-tooth gear, torque is doubled and speed is halved on the propeller shaft. Therefore, the driving torque applied to the propeller shaft is 360-foot-pounds x 2 = 720-foot-pounds.

  4. 4

    Calculate the instantaneous tangential gear force Kt imparted to the teeth on the driven gear. The radius of the driven gear is 8 inches/2 = 4 inches. However, the torque transmitted is 720-foot-pounds. Therefore the torque must be multiplied by 1 foot(12 inches)/4 inches = 3 x 720-foot-pounds = 980 Kilogram of tangential force against the gear at the point where its pitch circumference intersects the helical gear mesh.

  5. 5

    Calculate the axial thrust on the driven helical gear. The helical gear thrust equation is Ka (axial force) = Kt (tangential force) x tangent of angle B = 980 Kilogram x 0.3249 (tangent value of 18-degrees) = 318 Kilogram, directed toward the front of the gear case. This would also be the axial thrust imparted to the smaller driving gear because their respective Kt values are the same, although the direction of the force for the smaller gear would be in the opposite direction, toward the rear of the boat and the common gear case.

Tips and warnings

  • Many helical gear designers put both left- and right-hand sense helical gear width sections on both driving and driven gears to resolve the thrust forces within the individual gears themselves thus eliminating complex thrust bearing arrangements.
  • Gear trains, spinning shafts, fans, wheels and belt pulleys of any kind are notorious finger-crushers and necktie trappers---always exercise extreme caution around any open drive mechanism or machinery to avoid serious injury or death.
  • Always use protective eyewear around machinery.

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