Determining the Speed and the Turbine Speed and the Gear Ratio

The parameters of a wind turbine are the generator speed $N_g = 870 rpm$ and the wind speed $v_a = 6 m/s$ . The turbine has a fixed $TSR = 8$ and a sweep diameter $d = 12 m$ . Calculate (a) the low speed of the gearbox or turbine speed $N_t$ and (b) the gear ratio $GR_t$ .

Question

Determining the Speed and the Turbine Speed and the Gear Ratio

The parameters of a wind turbine are the generator speed [latex]N_g = 870 rpm[/latex] and the wind speed [latex]v_a = 6 m/s[/latex]. The turbine has a fixed [latex]TSR = 8[/latex] and a sweep diameter [latex]d = 12 m[/latex]. Calculate (a) the low speed of the gearbox or turbine speed [latex]N_t[/latex] and (b) the gear ratio [latex]GR_t[/latex].

Accepted Answer

[latex]N_g = 870 rpm, v_a = 6 m/s, TSR = 8, d = 12 m, r = d/2 = 6 m[/latex]

a. Equation (16.43)

[latex]TSR=\frac{\upsilon _{tip}}{\upsilon_a }[/latex] (16.43)

gives the tip speed

[latex]\upsilon _{tip}=TSR imes \upsilon_a= 8 imes 6 = 48 m/s[/latex]

Equation (16.44)

[latex]v_{tip} = \omega _r = 2\pi nr[/latex] (16.44)

gives the low speed of the gear

[latex]N_t=\frac{\upsilon_{tip} }{2\pi r}=\frac{48}{2\pi imes 6} imes 60=76.39 rpm[/latex]

b. Equation (16.48)

[latex]GR=\frac{N_g}{N_t}=\frac{60 imes f_s imes (1 - s) }{p imes N_t}[/latex] (16.48)

gives the gear ratio

[latex]GR_t=\frac{N_g}{N_t}=\frac{870 }{76.39}=11.39[/latex]

Question 16.6: Determining the Speed and the Turbine Speed and the Gear Rat...

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