Lateral analysis, also referred as critical speed analysis, is the study of when rotational speed meets or exceeds the shaft natural frequency. This is important since not knowing the critical speed can lead to instability, unbalance or even cause unknown forces to alter the functionality of rotating machinery. Since a rotating machinery consists of many components (rotor, bearing, motor, seals, etc), lateral analysis is made up of three categories: undamped critical speed analysis, steady state synchronous analysis (also known as damped unbalance response analysis) and stability analysis.
Types of Unbalances
The three types of unbalances to consider are static, couple and dynamic. Static unbalance (Figure 1) occurs when a mass at a certain radius from the axis of rotation causes a shift in the inertia axis. Couple unbalance, usually found in cylindrical shapes, occurs when two equal masses positioned at 180 degrees from each other cause a shift in the inertia axis, leading to vibration effects on the bearings. Lastly and most common, dynamic unbalance occurs when you have a combination of both static and couple unbalance.
Not only was W.J.M Rankine a prestigious theoretical scientist and educator, he was a main contributor in the development of rotordynamics and he contributed to thermodynamics and the development of heat engines throughout his lifetime. During his spinning shaft experiment, he concluded that beyond the shaft’s first critical speed, the shaft would be unstable simply because its shape had been bent. By not taking into consideration support damping and Coriolis force in his analysis, many engineers were left confused for almost two centuries, until Gustaf de Laval, a Swedish engineer, ran a steam turbine to supercritical speeds in the late 1880’s. Laval also introduced the use of bearings to oppose absolute motion in his machinery. As the years went by, many other engineers discovered and investigated additional phenomenons (FEM for example) that have an influence in today’s practices.
It is because of these previous innovators that companies like SoftInWay have been able to develop the advanced rotodynamics modules that we use today.