There are essentially two strategies for vibration analysis of non-linear rotor-bearing-foundation systems, such as systems with hydrodynamic journal bearings:

  1. Linearization in the vicinity of a stable equilibrium position. This approach is very effective if the Rotor-Bearing-Foundation (RBF) system equilibrium is stable and vibrations are sufficiently small. Please see TURBINE-PAK for more information about this strategy.
  2. Direct solution of the non-linear differential equations of motion in the time domain. This approach, although computationally very intensive, is necessary for the non-linear transient motion analysis, studying of large vibration as well as for analysis of unstable rotor systems. TURBINE-PAK NON-LINEAR is an advanced software tool that implements this approach for practical and effective engineering use.

TURBINE-PAK NON-LINEAR solver formulates and computes numerical solutions of non-linear equations of motion of the Rotor-Bearing-Foundation system in the time domain - step by step. Results of computations are communicated using animated graphic user interface.

TURBINE-PAK NON-LINEAR is designed to study transient responses of RBF systems, including the loss of stability of the rotor equilibrium position and the development of the limit cycle vibrations that follow the loss of stability.

  • Designed for practical and effective NON-LINEAR analysis of vibration transients and limit cycles in multi-bearing rotor systems with up to 50 bearings on elastic foundation (hyperstatic system analysis).
  • Extensive hydrodynamic and hydrostatic bearing support (including multi-pad, elliptical, fixed pad, rolling pad and pivot pad journal bearings).
  • Optimized real-time Computational Fluid Dynamics (CFD) calculations for hydrodynamic bearings (no databases) - enabling almost an infinite number of bearing configurations.
  • Comprehensive treatment of machine alignment. (In multi-bearing systems with non-linear hydrodynamic bearings vibration response depends on bearing alignment).
  • Modelling vibration of a non-straight (pre-bent) shaft in hydrodynamic bearings.
  • Modelling vibration of machines with a vertical shaft in hydrodynamic bearings.
  • High computational efficiency on Pentium class computers running Win98 - up to several steps per second are achievable for a RBF system with 5 journal bearings.
  • Visualization. Solutions can be animated.
  • Open style, fully documented ASCII type input and output files, enabling the user to access, process and/or generate data practically without restrictions.
  • Mobile computing. TURBINE-PAK NON-LINEAR can be installed on a portable computer (laptop) to assist in field diagnostics and field troubleshooting without any loss of performance.
  • Sharing the RBF input data files with TURBINE-PAK.
  • Tested and verified by leading Turbine Manufacturers, academics and Research Laboratories
  • Developed and maintained by scientists (PhD) with over 25 years of research and consulting experience in the field of rotordynamics and vibration analysis. If you find a feature that is missing, we can customize TURBINE-PAK NON-LINEAR to meet your particular requirements.

Rotor-Bearing-Foundation (RBF) System Vibration response computation

TURBINE-PAK NON-LINEAR computes the transient RBF system vibration response as a function of:

  • the system configuration (static load and alignment)
  • bearings (types, geometry, lubricant properties etc.)
  • shaft (geometry, pre-bending, material properties, temperature distribution etc.)
  • foundation and casings dynamic properties (general FEM superelement model)
  • rotor speed
  • excitation forces and unbalance

TURBINE-PAK NON-LINEAR solver uses variable order, variable step, adaptive predictor-corrector procedure based on the 4-5-th order Runge-Kutta-Fehlberg method. 

Modelling changes in transient vibration due to parameter change

User can modify, among other parameters, bearing alignment, unbalance, bearing types, bearing geometry or other properties, rotor speed, foundation properties etc., and observe resulting changes in the transient vibration response of the system. Response to step changes in any parameter (such as step change in unbalance, alignment or rotating speed for example) can be evaluated. Various cases can be conveniently compared.


TURBINE-PAK NON-LINEAR animated graphical interface greatly enhances our understanding of machine dynamic characteristics and vibration response. TURBINE-PAK NON-LINEAR provides:

  • Global motion animation
  • Animation of the detailed behavior of the shaft in each bearing, showing foundation, shaft and relative motion, as well as bearing reactions and alignment
  • Accurate phase relationships is preserved in TURBINE-PAK NON-LINEAR animation.
  • Simultaneous animation of the  response to unbalance and other excitation
  • Rapid comparison of various animated systems/cases/conditions

nl.gif (14047 bytes)
Fig 1. Reaction in one of the hydrodynamic bearings during the development of a Limit Cycle vibration in the vertical pump


TURBINE-PAK NON-LINEAR is a practical, efficient and effective tool in investigating

  • transient vibration phenomena in rotating machinery
  • vibration behavior of  the rotor-bearing-foundation system following the loss of stability
  • imit cycles in non-linear systems and their development (see Fig 1 above)
  • limitations of linearized analysis approach implemented in TURBINE-PAK for large vibration amplitudes
  • solutions to vibration problems in rotating machinery that develop limit cycle vibrations. Using TURBINE-PAK NON-LINEAR, vibration problems can be simulated and tested using a computer model of a machine. Possible solutions and remedies can be tested on the computer model first, before they are implemented.
  • TURBINE-PAK can be used as an aid in machine monitoring and maintenance. Every machine operator can greatly benefit from having a reliable computer model of his particular machine that is capable of predicting its vibration as a function of the operating parameter change.


TURBINE-PAK NON-LINEAR comes with comprehensive documentation that includes the Theoretical Manual.


Technical support is available to registered users only and is normally limited to the assistance in use of all available features of TURBINE-PAK NON-LINEAR and solving problems preventing the user from using these features.

Access to our support is available 24 hours a day, most days in the year via email tjc@sci-e-research.com for the first 12 months after User registration. Customization of the program, as well as support for longer periods of time can be arranged at additional cost. The benefit of maintaining the User Support is receiving TURBINE-PAK NON-LINEAR software upgrades at no additional cost.

For the first time Users of TURBINE-PAK NON-LINEAR, SER will, on the basis of the User data, prepare a complete TURBINE-PAK data set for one set of rotor-bearing-foundation system. This free modeling service is designed to provide the User with a complete, ready to use system, immediately after installation.

If the User data is unavailable at the time of ordering TURBINE-PAK NON-LINEAR, SER will deliver the software with a complete example set of data, representing some hypothetical rotor-bearing-foundation system.

On-site User training is available on request in the following areas

  • theoretical rotordynamics
  • vibration analysis
  • machine modelling for vibration analysis - the fastest way from drawings to a computer model
  • effective using of TURBINE-PAK NON-LINEAR


TURBINE-PAK NON-LINEAR software updates are free of charge during the first 12 months after TURBINE-PAK NON-LINEAR registration as well as thereafter, providing that the User continues to maintain the Technical Support from SER after the initial 12 month period.

Scientific references

  • Chalko T.J., Li D.X., Modelling Turbine Vibration in Terms of its Load Variation, International Journal of Rotating Machinery, 1995, Vol 1, No 3-4, pp. 295-299
  • Chalko T.J., Li D.X., Bearing Alignment Estimation in Rotating Machinery,  Proceedings of 6-th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC-6) Honolulu, Hawaii, USA, Feb 23-28, 1996
  • Li D.X., Chalko T.J., Hydrodynamic Characteristics of Combination Pad Journal Bearing,  Proceedings of 6-th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC-6) Honolulu, Hawaii, USA, Feb 23-28, 1996
  • Chalko T.J., Li D.X., Estimation of Alignment and Transverse Load in Multi-Bearing Rotor Systems International Journal of Rotating Machinery, 1996, Vol. 1, No. 7-8, pp 593-602

Professional contact

Dr Tom J Chalko

Dr Thomas J. Chalko MSc, PhD
email: tjc@sci-e-research.com
Fax: +61 5681 6361
945 Gunyah Rd, Mt Best
Vic 3960, Australia

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