Pump Rotor Dynamics – from Residential Pools and Human Hearts to Heavy Duty Industry Applications

You rarely find a rotary machine with a wider range of applications than pumps. These machines acting in a single role can be installed both to supply the water to a garden pool and move the crude oil in pipelines.

And even more, the same simple pump can substitute the functions of the human heart by moving the blood through it.

Fig. 1 - Left ventricular assist device - a tiny pump moving the blood in the human body
Fig. 1 – Left ventricular assist device – a tiny pump moving the blood in the human body [1]
Although the heavy duty industry applications of pumps are less delicate at first sight, they can still generate similar effects of this unique nature which is inherent only to this type of machine and should be studied carefully when executing rotor dynamics calculations.

As industrial multistage pumps move various liquids through their passages, the leakage of these liquids is critical for two reasons: 1)  the undesired, and possibly dangerous, entrance of the fluid into the environment; and 2) the decrease of the pump efficiency. As a result of these concerns, the seals in pumps play a crucial role.

The typical liquid annular seal is a tool with a design which is pretty close to a regular fluid film journal plane in a cylindrical bearing. Depending on the location, seals can be of interstage, impeller eye, balance piston types, and so on [2].

Fig. 2 - The pump design which includes seals of various types
Fig. 2 – The pump design which includes seals of various types

The similar nature of seals and fluid film journal bearings results in similar influences on the rotors as they introduce stiffness and damping resistance of rotor lateral vibrations. Even though this property of seals is not the main property they are designed for, the seal stiffness and damping properties can not be neglected. Keeping this in mind, the rotor then can be considered installed not in two, but in a dozen or more radial bearings.

Fig. 3 – Pump rotor models including shaft Timoshenko beam finite-elements, impeller and coupling point masses and taking into account only radial bearings (top) and both radial bearings and seals (bottom)

On top of seals and fluid film journal bearings considerations, engineers must also take into account the stator parts of the seals as these must be compliant and heavy enough when modeling the pump lateral rotor dynamics. This can by done by introducing additional spring-damper-mass elements of supports in the series of modeling the spring-damper elements of seals themselves.

The total force generated by each liquid annular seal (LAS) is dependent on the stiffness mentioned above; damping and mass coefficients and on rotor deflections; and velocities and accelerations in their locations. Black [3] and Childs [4] developed the formulas for calculation of stiffness and damping coefficients of liquid seals. These formulas include a bunch of parameters such as rotor rotational speed, inlet swirl ratio, fluid viscosity, liquid annular seal radius, axial and circumferential Reynolds numbers, etc..  These calculations are quite complicated. The rule of thumb is to make the fastest and most accurate determination of seal rotor dynamics properties requires using the high-quality quality materials and validated codes.

Fig. 4 - Results of liquid annular seal calculations for different rotational speeds
Fig. 4 – Results of liquid annular seal calculations for different rotational speeds

In addition to seals, a lot of other unique effects happen in a pumps. Some of these are static forces generated in impellers due to uneven clearance distribution along the circumference of volutes, hydrodynamic cross-coupling forces and hydrodynamic imbalance. All of the unique features of pumps makes them a continuing source of scientific research and a challenging task for engineers who need to calculate for a rotor dynamics analyses which require a high level of experience and a deep understanding of the many processes taking place during lateral vibrations of the pump rotors.

Pump rotor dynamics models differ from the rest of finite-element representations of rotating machine rotors significantly, and require determining and applying liquid annular seal stiffness, damping and mass coefficients, as well as impeller hydrodynamic static and cross-coupling forces and imbalances. AxSTREAM Bearing and AxSTREAM RotorDynamics provides its users with this comprehensive calculation of bearing, seal and aerodynamics cross-coupling coefficients; and modelling of rotor operation including all these coefficients, forces and unbalances on the basis of recognized approaches and API standards. Learn more about AxSTREAM RotorDynamics here or request a demo by filling out this form 


  • Roehm, A.R. Vest and D.E. Weiner, “Left ventricular assist devices, kidney disease, and dialysis,” In Practice, vol. 71, is. 2, pp. 257-266, 201, doi: 10.1053/j.ajkd.2017.09.019
  • San Andrés, “Introduction to pump rotordynamics,” NATO RTO Educational Notes Paper. 2006. 26 p. doi: 10.14339/RTO-EN-AVT-143-09-pdf
  • F. Black and D.N. Jenssen, “Dynamic hybrid bearing characteristics of annular controlled leakage seals,” Proc. Inst. Mech. Eng. Conf. Proc., vol. 184, no. 14, pp. 92–100, Sep. 1969, doi: 10.1243/PIME_CONF_1969_184_427_02.
  • W. Childs, “Dynamic analysis of turbulent annular seals based on hirs’ lubrication equation,” J. Tribol., vol. 105, no. 3, pp. 429–436, 1983, doi: 10.1115/1.3254633.