Question

how to calculate a shaft diameter of horizontal wind turbine

Answer 1

When any shaft is transmitting the power from the driver equipment to the driven equipment, It is very necessary to calculate the feasible shaft diameter from the torque based on the maximum torque that can be uninterruptedly transferred through the shaft or the maximum amount of twist in the shaft. Failing this, the shaft may not satisfy the functions of the designed equipment.

Actually, the shaft is one of the most important constituents in most engines (wind turbine also); it is a revolving or static component that generally has a cylindrical shape, but can be in square or cross-shape. In addition, they can be made solid or hollow. The power is supplied to the shaft over the tangential force and then transmitted to different elements that are connected to the shaft (thanks to the subsequent torque or twisting moment). For instance, we can find gears, cranks, cranks, and rolling-elements attached to the shafts resulting in bending moment together with the forces applied over them. In other words, its purpose is the transmission of loads to the stationary system of the nacelle in case of a wind turbine. Thus, the shaft is subjected to many external forces that should be taken into consideration while making its design.

Inputs that we need to calculate shaft diameter

As we know Torsional equation is given as

Where

τ = Torsional stress induced on the outer surface of the shaft (Maximum Shear stress).

r = Radius of the shaft.

T = Twisting Moment or Torque applied.

J = Polar moment of inertia.

C = Modulus of rigidity of the shaft material.

l = Length of the shaft.

θ = Angle of twist in radians on a length.

From Torsion Equation we can consider that

It can be written as

Polar moment of inertia will be calculated from the following equation.

Polar moment of inertia for a circular cross-section is as

From this, the maximum torque that can be transferred through the shaft can be written as

From the above equation, we are able to calculate the unknown factors. In our case, the shaft diameter is the unknown factor.

So we need the following input data

• The maximum torque that would be transferred through the shaft (We can calculate torque from the Power and the speed also)
• The torsional shear stress of the material.

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