How will the size and cost of a rotating electric machine be if it is designed with greater speed?

When designing a rotating electric machine (such as a motor or generator) for greater speed, the resulting size and cost implications can be understood by considering several factors related to the design and operational aspects of these machines:

### Size Implications:

1. Reduced Size for Same Power Output: Higher speed designs typically allow for a reduction in the size of the machine for a given power output. This is because power (P) is the product of torque (T) and angular velocity (ω), as in the equation P = Tω. For a given power output, as the speed (reflected in angular velocity) increases, the required torque decreases. Therefore, components like the rotor can be made smaller, leading to a more compact machine overall.

2. Stator and Rotor Dimensions: While the machine might be more compact, particular attention needs to be paid to the design of the stator and rotor to ensure they can handle the higher speeds mechanically. This might mean using specific materials or designs to withstand centrifugal forces, which could influence the dimensions slightly differently than simply scaling down for power output would suggest.

### Cost Implications:

1. Material and Fabrication Costs: Higher speed machines may require more expensive materials or sophisticated fabrication techniques to handle the mechanical stresses and to maintain performance standards. Special alloys or composites might be necessary for the rotor, and tighter manufacturing tolerances could increase production costs.

2. Cooling Systems: High-speed operations often lead to increased heat generation,