For a rotating shaft with a mounted disc and small eccentricity, according to classical whirling theory, which parameter(s) influence the critical (whirling) speed of the system?

Introduction / Context

Critical or whirling speed is the rotational speed at which a rotating shaft–disc system experiences resonance due to coincidence of the running speed with a natural frequency, leading to large lateral vibrations. Designers must understand the variables that set this speed.

Given Data / Assumptions

• Uniform shaft with a mounted disc.
• Small eccentricity between mass center and geometric center.
• Linear, classical whirling theory applies (small deflections).

Concept / Approach

The lateral natural frequency depends on shaft stiffness (a function of length, diameter, and boundary conditions) and the attached mass distribution. Eccentricity introduces a rotating unbalance force that excites the mode strongly near the natural frequency.

Step-by-Step Solution

Verification / Alternative check

Rayleigh or Dunkerley estimates show explicit dependence on stiffness (length) and mass; design charts account for unbalance via eccentricity.

Why Other Options Are Wrong

• Single-parameter answers ignore coupled dependence on stiffness (length), mass (disc), and excitation via eccentricity.
• None of these contradicts theory and practice.

Common Pitfalls

• Confusing effect on natural frequency (stiffness, mass) with excitation amplitude (eccentricity); both matter to practical critical speed operation.

Final Answer

All of these