The cross-section of a turbine rotor disc is designed for uniform strength under rotational conditions. The disc is keyed to a 60 mm diameter shaft at which point its thickness is a maximum. It then tapers to a minimum thickness of 10 mm at the outer radius of 250 mm where the blades are attached.

Question

The cross-section of a turbine rotor disc is designed for uniform strength under rotational conditions. The disc is keyed to a 60 mm diameter shaft at which point its thickness is a maximum. It then tapers to a minimum thickness of 10 mm at the outer radius of 250 mm where the blades are attached. If the design stress of the shaft is[latex] 250 MN/m^{2} [/latex]at the design speed of 12000 rev/min, what is the required maximum thickness? For steel [latex]p = 7470 kg/m^{3}[/latex]

Accepted Answer

From eqn. (4.22) the thickness of a uniform strength disc is given by

[latex]t=t_{0}e^{(- ho \omega ^{2}r^{2} )/(2\sigma )}[/latex] (1)(4.22)

where [latex] t_0 [/latex] is the thickness at r =0

Now at r = 0.25

[latex]\frac{ ho \omega ^{2}r^{2}}{2\sigma } =\frac{7470}{2 imes 250 imes 10^{6} } (12000 imes \frac{2\pi }{60} )^{2} imes 0.25^{2}=1.47[/latex]

and at r = 0.03

[latex]\frac{ ho \omega ^{2}r^{2}}{2\sigma } =\frac{7470}{2 imes 250 imes 10^{6} } (12000 imes \frac{2\pi }{60} )^{2} imes 0.03^{2}[/latex]
[latex]=1.47 imes \frac{9 imes 10^{-4} }{625 imes 10^{-4} } =0.0212[/latex]

But at r = 0.25, t = 10 mm

Therefore substituting in (1)

[latex]0.01=t_{0}e^{-1.47}=0.2299 t_{0}[/latex]
[latex]t_{0}=\frac{0.01}{0.2299} =0.0435m=43.5 mm[/latex]

Therefore at r = 0.03

[latex]t = 0.0435e^{-0.021}=2 0.0435 × 0.98[/latex]
[latex]= 0.0426 m = 42.6 mm[/latex]

Question 4.3: The cross-section of a turbine rotor disc is designed for un...

Related Answered Questions

An initially unstressed short steel cylinder, internal radius 0.2 m and external radius 0.3 m, is subjected to a temperature distribution of the form T =a + b loge r to ensure constant heat flow through the cylinder walls. With this form of distribution the radial and circumferential stresses at ...

Verified Answer:

Verified Answer:

Verified Answer:

A steel rotor disc which is part of a turbine assembly has a uniform thickness of 40 mm. The disc has an outer diameter of 600 mm and a central hole of 100 mm diameter. If there are 200 blades each of mass 0.153 kg pitched evenly around the periphery of the disc at an effective radius of 320 mm, ...

Verified Answer: