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Summary:
Can Rotor Bars be "Too Long"? With
trilingual summary
By
Richard L. Nailen, EA Engineering Editor
Material cost, full-load slip, internal ventilation, acceleration characteristics, and manufacturing methods all influence the length of squirrel-cage rotor bar extensions between the core ends and the rings joining the bars together.
Those extensions are stressed by expansion and contraction of the rings under thermal and centrifugal forces. Some authorities have claimed that the stress increases with bar extension length, warning against making the extensions "too long."
Such a misunderstanding probably arises from the general knowledge that the maximum stress caused by a given force increases as the distance of that force from the stressed location. We multiply the effect of a force by using a longer lever arm.
In the rotor, however, the force is not a constant. Rather, the deflection of the bars--the amount of end ring expansion--is the constant, and will be the same regardless of extension length. The greater that length for a given deflection, the lower the force on the bar associated with that deflection.
Therefore, within rather broad limits, the longer the extension, the lower the bar bending stress caused by ring expansion.
That is true only if the bars can be treated as cantilever beams, subject only to purely bending forces. When the extension length becomes quite short, that is no longer true, and the relationship changes. In the extreme case (almost never encountered except with some aluminum rotor cages) of zero extension length, no bending takes place. Ring expansion subjects each bar to shearing stress only, in the plane of the core end, which must be calculated differently.
Can the stiffness of the bar ends themselves exert enough restraining force to prevent thermal or centrifugal ring expansion? No. Calculations show that this cannot happen until extension length becomes extremely short. The rings can therefore be expected to expand freely to the extent consistent with the temperature rise and centrifugal force (normally a concern only in large, high-speed machines).
n the more commonly encountered range of design dimensions, greater extension length means bar stress reduction, not increase. Hence, no particular length can be described as "too long" from the standpoint of bar stress. Unusually long extensions increase rotor cage cost and electrical resistance, but are desirable in designs requiring high slip or subject to severe load cycling.
Copyright 2003, Barks Publications, Inc., Chicago.
Reproduction by any means prohibited.
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