Reciprocating machines fall into many categories. Despite different applications and designs, e.g. pumps or internal combustion engines with a varying number of pistons, a simple approach to determine torsional modes of regardless which crankshaft assembly can be investigated. The resulting natural frequencies are required by ISO 3046 for rotor dynamic analysis.
Below, a common way to express a crankshaft assembly with massless shaft and mass-inertia elements is presented, whereas the reciprocating and revolving mass around the crack can be expressed as follows: