Influence of rotor diameter and length on the rating of induction motors

The outputs of electrical machines are generally assumed to vary as the product of the square of the diameter and the length of the machine, although an examination of the outputs of ranges of machines for industrial use reveals that it is common to obtain significantly greater increases of output with diameter than would be expected from the square-law relationship. The basis upon which the classical output equation is founded is examined and an alternative equation based on conductor current density rather than ampere-conductors/unit-periphery is developed which indicates that an output varying with the cube of the diameter might be achieved. Effects on the electrical and thermal performance of ranges of machines based on a cube-law relationship are compared with that obtained assuming a square law, and conclusions are drawn which would support the adoption of the intermediate relationship approximating to the 2.5th power commonly found to occur in ranges of commercially produced machines. The paper also considers factors which influence the choice of machine `shape¿¿, i.e. the diameter to length ratio, and shows that though simple consideration of costs will yield a long thin machine, there are other factors, notably the number of poles, which serve to limit the length to the so-called `square¿¿ configuration where the length is approximately equal to the outer diameter of the stator core, and indicates how the diameter/length ratio affects the electrical performance.