Analysis of the dynamics of bearings and rotors in vertical and horizontal pumps

Problems with rotor bearing systems are one of the major factors in pump failure. Today, pumps are often designed to operate at increased speeds and loads to improve their efficiency. These operating requirements require that particular attention be paid to the analysis of the rotor dynamics during the design phase. This includes simulations of bearings, seals and other pump components.

There are many types of pumps available for industrial applications. These pumps can be classified based on design, operating principles, special features, working fluid characteristics, configuration (centrifugal, axial, screw, helical, positive displacement) and much more. With each type of pump there are challenges in terms of modeling and analyzing the rotor-bearing system. On the other side of the coin, many methods and principles of rotor dynamics are similar for all rotating machines.

This article will focus on two basic pump types: horizontal and vertical, with no further design specification, to describe common approaches and differences with respect to rotor dynamics, bearings, and seal simulations.

IMAGE 2: Multistage Vertical Turbine Pump

Vertical vs. Horizontal Pumps: Design Differences

The main difference between vertical and horizontal pumps is the orientation and shape of the shaft. A horizontal pump has a shaft that is placed horizontally (Top Image), between the bearings or cantilevered. The vertical pump shaft is positioned vertically. The most common type of vertical pump is the vertical turbine pump (VTP) — Image 2. Vertical pumps (like VTPs) usually have long spaghetti-shaped shafts that are connected to the motor (above or below) via the coupling and supported by a thrust bearing at the top or bottom. Another design feature of vertical pumps is the column casing which influences the dynamic characteristics of the pump. These design specifications make a difference in how to approach rotor dynamics modeling and vertical pump analysis.

What makes rotor dynamics different from the vertical pump?


Vertical pumps have long shafts which provide more flexibility. These flexible shafts have closely spaced modes and a dense range of frequencies. In this case, resonant vibrations with high amplitudes may occur, especially if the pumps operate in a wide range of rotational speeds.

The casing structure of vertical pumps (pipe) is also flexible. With this in mind, the flexibility of the pipe casing, as well as the cup assembly, must be considered when calculating the stiffness characteristics of the intermediate radial shaft supports. In addition, the casing structure of a vertical pump can experience strong vibrations due to its flexibility, so the frequencies of the pipe must also be analyzed.

Axial forces

Vertical cantilever pumps supported by a thrust bearing at the top of the machine are loaded with axial pulling force resulting from gravity loads. Conversely, if the stopper is placed at the bottom of the machine, a compression force acts along the shaft. The pushing force of the paddle wheels further contributes to the tension and stiffening of the shaft. All of these forces change the rotor’s bending stiffness, natural frequencies, and critical speeds. It is therefore important to take these factors into account through a dynamic analysis of the rotor before a machine is put into service.

IMAGE 4: A horizontal centrifugal pump (dynamic rotor FE model)
IMAGE 4: A horizontal centrifugal pump (FE rotor dynamic model)

Bearings and seals

The bearing is one of the most critical parts of any pump. Bearings support the shaft and reduce friction on moving pump parts by maintaining smooth rotor rotation. Bearings also provide stiffness and damping to the rotor bearing system. Bearings used for pumps can be classified as radial (support the shaft laterally) and axial (suitable for axial loads). The most common types of bearings used for pump applications are ball and roller bearings, hydrodynamic oil film plain bearings (regulators) and swivel pad bearings (axial thrust load bearing).

In the context of pumps, seals are no less important. Like bearings, pump seals are the source of stiffness, damping and additional “mass” coefficients for the rotor-bearing system, which change the dynamics of the whole system. The natural frequencies of a pump for systems with bearings and seals differ from systems on rigid supports.

The modeling of the bearing-seal system differs in vertical pumps compared to horizontal pumps. One difference is a potentially large number of radial bearings that support long shafts in vertical pumps. In many cases, a high number of stages (e.g. helical/spiral stages) in a pump increases the number of bearings and seals – the total number of bearings and seals can reach into the tens. Image 4 gives an idea of ​​the number of elements that will need to be modeled to obtain accurate rotor dynamic results. The combination of a long shaft, increased tolerances and misalignments with what is objectively a large number of radial bearings can result in a rapid and non-linear change in bearing stiffness in bearings where the shaft line approaches the supporting wall.

The second difference, and potentially even more important than the previous one, is that the radial bearings of vertical pumps are lightly loaded (no gravity force in the radial direction), which complicates the estimation of dynamic bearing coefficients. Unloaded cylindrical bearings are a cause of stability problems in vertical pumps. Thus, nonlinear analysis is essential for an accurate assessment of the rotor behavior of vertical pumps with long shafts and unloaded bearings.

Finally, in submersible pumps, which are mostly VTPs, the bearings are in a pressurized environment and lubricated by the process fluid, often with contaminations. In addition, the working fluid mixture can change composition and the operating conditions of a pump (speed of rotation) are often variable. Thus, these radial bearings undergo accelerated wear, and the prediction of their characteristics is complicated given the random characteristics of the applied conditions. A worst-case model approach can be used to predict dynamics and reliability to avoid critical failures.

What effects must be taken into account regardless of the type of pump?

There are areas where the analysis is similar. Some other effects that are important and must be taken into account in the analysis of the rotor dynamics of vertical and horizontal pumps are:

  • static and dynamic radial loads occurring at the location of the impeller due to uneven distribution of the clearance between the impeller and the volute
  • the inertias and hydraulic imbalance forces that must be introduced at the location of the wheel
  • effective added mass at the wheels and along the shaft
  • dry, wet and process fluid conditions, as well as “as new” and “worn” clearances considered during bearing and seal analyzes
  • the Lomakin effect: a force created at wear rings and throttle rings in a centrifugal pump
  • other similar general and technical effects for most rotating machinery and presented in American Petroleum Institute (API) 684 standards2

Although the approaches and methods for modeling and analyzing horizontal and vertical pumps are often similar, vertical pumps have their own set of features that make rotor dynamics analysis and bearing and seal simulations more complex. The main challenges encountered in vertical pumps relate to construction and operating specifications, including:

  • long shafts
  • a lot of steps
  • its bearings and seals
  • unloaded radial bearings
  • axial forces due to gravity

Due to these design features, vertical turbine pumps are more prone to vibration issues and structural/life issues. This can cause headaches for the rotor dynamics analyst dealing with these types of pumps. Fortunately, today’s engineers have access to digital tools that can be used to solve these headaches. Using advanced simulation software, dynamic standards and technical publications (e.g. References 1 and 2 below), these effects can be modeled and analyzed to ensure safe and reliable operation.


  1. API, 684, 2019. API Standard Paragraphs. Rotordynamic Tutorial: Critical Lateral Speeds, Imbalance Response, Stability, Train Torsion, and Rotor Balancing, American Petroleum Institute, Washington, DC, USA.
  2. API, 610, 2010. Centrifugal Pumps for the Petroleum, Petrochemical, and Natural Gas Industries, American Petroleum Institute, Washington, DC, USA.
  3. SoftInWay Rotor Dynamics and Bearings User Manual:

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