Where does commutation collide?

In mathematics, commutativity is the property of an operation whereby the order of its operands does not affect the result, so that a + b = b + a; where it fails, the commutator measures by how much, as in ab − ba for two elements. Dummit and Foote's Abstract Algebra treats commutative structures and the commutator that quantifies non-commutativity in groups and rings. The referent is an algebraic property of an operation (or the element that measures its failure), and it is a different construct from switching current in a motor or reducing a prison sentence, sharing only the Latin root for interchange.[1]

Unit

Not applicable

Recovery means

Not applicable

Measured by

Established by proof that an operation satisfies a·b = b·a, or quantified by the commutator ab − ba (or aba⁻¹b⁻¹)

In electrical machines and power electronics, commutation is the controlled transfer of current from one conducting path to another at the correct instant, as the commutator and brushes of a DC machine reverse the current in each armature coil to keep torque unidirectional, or as switching devices hand off current in a converter. Umans's revision of Fitzgerald & Kingsley's Electric Machinery treats the timing and the sparking or losses that poor commutation causes. The referent is the timed hand-off of current between circuit paths, and it is unrelated to algebraic order or legal clemency, joined to them only by the shared idea of a switch-over.[2]

Unit

The commutation interval and the current transferred between paths

Recovery means

Not applicable

Measured by

Assessed by commutation timing, voltage/current waveforms at switch-over, and brush sparking or switching losses