# What is the Formula for Sizing a Shaft at 150,000rpm?

• max11
In summary, the conversation is about sizing a shaft for a turbocharger that needs to transmit 9Nm at 150,000rpm and is 200mm in length. The shear stress of the material is 457MPa and the formula used is D = 1.72 (Tmax/σmax)1/3. However, the resulting diameter of 0.46mm seems too small and help is requested to verify the calculation.
max11
Hiya

I was hoping that somebody would be able to help me.

I need to size a shaft coming from a turbocharger spinning at 150,000rpm the shaft needs to transmit 9Nm and 200mm in length, the shear stress of the material is 457MPa.

I need to size the diameter of the shaft and know that it is going to be very small but can't seem to find a formula that gives me a sensible answer, right now I am using a formula from engineering toolbox (http://www.engineeringtoolbox.com/torsion-shafts-d_947.html)

D = 1.72 (Tmax/σmax)1/3

But this give me a diameter of 0.46mm which seems so small that it would just twist and break.

an y help greatly appreciated.

Cheers

Hi Max. Check your work again. I'm getting 4.65 mm.

## 1. How do you determine the appropriate diameter for a shaft operating at 150,000rpm?

The appropriate diameter for a shaft at 150,000rpm is typically determined by considering factors such as the material strength, rotational speed, and load requirements. This can be calculated using various equations and formulae, taking into account the desired safety factor and allowable stress limits.

## 2. What is the maximum speed at which a shaft can safely operate?

The maximum speed at which a shaft can safely operate depends on several factors, including the material strength, size and shape of the shaft, and the type of load it is subjected to. In general, a higher rotational speed will require a larger diameter shaft to maintain structural integrity and prevent failure.

## 3. What materials are commonly used for high-speed shafts?

Materials commonly used for high-speed shafts include steel, stainless steel, titanium, and various alloys such as aluminum and carbon fiber. The selection of material will depend on the specific application and the required strength and durability at high speeds.

## 4. How do you account for factors such as vibration and heat in determining shaft size?

In sizing a shaft for high-speed operation, factors such as vibration and heat must be taken into consideration. These can be accounted for by using appropriate safety factors, selecting materials with high fatigue resistance, and ensuring proper lubrication and cooling systems are in place.

## 5. Can the size of a shaft at 150,000rpm be reduced by using higher-grade materials?

Using higher-grade materials may allow for a smaller diameter shaft to be used at 150,000rpm, but this will depend on the specific material properties and the overall design requirements. It is important to carefully consider all factors and perform thorough calculations before determining the optimal shaft size for high-speed operation.

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