1. The core of DYNAMICS R4 includes the following modules:
1.1 Graphics user interface
The graphic editor allows easy modeling and control of dynamical models of multi-shaft space rotor systems.
1.2 Simulation Command Interface
The Command interface extends the user’s capabilities in model creation and during its parametric analysis. It is possible to use converters integrated in DYNAMICS R4 to operate with data from external sources to gather it in form of table and perform its conversion automatically for further usage for model. DYNAMICS R4 program system also allows to create small “calculators” or user-defined scripts for preliminary simulations for further usage of the obtained data in computational dynamic model.
- Converters. Sometimes the input data are given in a table form. This may be data from an external system, or drawing review results, or results of stiffness matrix calculations. The command simulation interface helps to input these data.
- Calculators. Sometimes the input data need preliminary calculations, for example support stiffness, or flange flexibility. This calculation may be done in the script and resulting values may be used for an element insertion. For details see DYNAMICS R4 reference.
- Parameterization. The user may create calculations of a complicated function values or describe a complicated parameter variation.
1.3. Matrix Calculator
When an engineer simulates complex design units, the necessity in matrix calculations may arise. For example, as a result of calculation in FEM programs for common purposes the flexibility matrixes of engine structural elements were obtained. Compliance matrix inversion may be required in order to input data about the received elastic characteristics in a model using links. Another example – matrix of rotation.
1.4 Basis (natural frequencies of undamped and non-rotating rotor system)
The natural frequencies calculations and dynamic response of linear and nonlinear rotor structures are based on finite element and modal analysis methods (no transfer matrix method). These methods use the preliminary calculated basis that consists of the set of natural frequencies and mode shapes in given range of the rotor speed. The basis frequencies and shapes are calculated under assumptions of zero damping and zero rotors speeds. The basis includes the set of the frequencies and mode shapes for all types of vibration that are two-planes lateral, axial and torsional.
2. Optional elements for linear analyses
2.1 Natural frequencies and mode shapes of rotor system with damping and rotation
The algorithm computes damped natural frequencies and mode shapes of a rotor system. Natural frequencies can be computed taking into account the rotation speed of the rotor. Also the distribution of potential and kinetic energy over rotor model elements can be computed.
2.2 Critical speeds
The algorithm computes damped rotor critical speeds and mode shapes. Also the distribution of potential and kinetic energy over rotor model elements can be computed.
2.3 Natural frequencies and stability maps
A natural frequencies map shows the natural frequencies of rotor model versus the rotational speed.
2.4. Parametric analysis
This option provides influence of user defined parameters upon the natural frequencies, critical speeds etc. It is possible to study influences of one or two groups of verified parameters. This option may be used for a preliminary optimization, for example verifying critical speeds by changes in supports’ flexibilities.
2.5. Unbalance response
The algorithm allows to compute the response of the dynamic system caused from excitation load induced by unbalances on the rotor. User can obtain results in any point of rotor model. In one-time user can obtain magnitude-frequencies curves in all points of subsystem by means of 2D or 3D plots.
2.6 Nonsymmetric link
The element transmits loads between nodal stations of two subsystems. The element properties are defined with 6×6 stiffness and damping nonsymmetrical matrixes with all coefficients versus time and rotational speed.
2.7 Gear element
This element simulates different types of gear transmissions – spur and helical gears, conical gears and hypoid gears.
2.8 Aerodynamic excitation (Alford’s and Wachel’s formula)
Aerodynamic excitation caused by forces generated in labyrinth seals or forces generated in stages of the turbomachine may bring to instability of the rotor system. DYNAMICS R4 algorithm for aerodynamic excitation allows to compute aerodynamic cross-coupling for axial or centrifugal compressors and turbine stages in matrix form for further automatic integration in dynamic model.
2.9 Fluid bearing calculation
Calculation of stiffness and damping properties of fluid bearings using finite difference method for solving of Reynolds equation for incompressible fluids. Among supported bearings types are Partial Arc bearing, Multi axial groove bearing, Elliptical bearing, Offset Half bearing, Multilobe bearing, Tapered land bearing, Pressure dam bearing, Multi pocket bearing, Tilting Pad bearing.
2.10 Gas bearing calculation
Calculation of stiffness and damping properties of gas bearings using finite difference method for solving of Reynolds equation for compressible fluids. Among supported bearings types are Air Foil Bearing, Cylindrical gas bearing with rigid case, Multilobe gas bearing with rigid case.
3. Non-linear dynamics
Behavior of a linear or a non-linear system is calculated by direct integration of the motion equations. This algorithm is used for analysis of rotor models with non-linear elements, unsteady loads, unsteady operating regimes, etc. The integration methods are user tuned depending upon specific requirements to the solution. The waveform post-processing includes also the following algorithms:
Mean value
Two possible algorithms are:
Peak-to-Peak is the total maximum to minimum distance of the vibration signal over the sometime interval. RMS of a signal is computed by squaring the instantaneous magnitude, integrating over the desired time, and taking the square root.
Orbit (Transient response)
Algorithm allows to compute and output time waveform signal and orbits while performing transient response analysis. User can obtain orbits in any time interval and at any section of the dynamic model by means of 2D and 3D plots.
Waterfall diagram
This algorithm allows obtaining cascade and waterfall plots. Waterfall– is a series of spectra at several different times. Cascade diagram – a series of spectra at several speeds.
Fast Fourier Transform
The Fast Fourier Transform (FFT) is an efficient mathematical algorithm that derives the frequency domain signal from the time domain signal. It is assumed that signals in given time interval are stable in frequency (stationary signal).
4. Optional elements for non-linear and transient analysis
4.1 Elastic Damping Lateral Restraint element (clearance)
This element is represented by link of special kind (clearance link) and allows to model different cases of contact and rubbings of rotating and non-rotating structures. This allows modeling most cases of instability in rotating systems with clearances. It takes into account any kinds of contact with external and internal damping, with friction in contact point, weight and circumferential irregularity of clearance.
4.2 Dry bush element
The element simulates dry bush support. Point or line contact type can be selected. In case of point contact this element can be used as fast substitution element for Clearance element.
4.3 Squeeze-film damper element
This element models two well-known cases of hydrodynamic damper: the “short” damper and the “long” damper. Different kinds of fluid film cavitations are considered: uncavitated (2-π film) damper and cavitated (π-film) damper. Laminar flow. It allows computing dynamical systems in steady-state and non-steady state conditions. FDM solution by request.
4.4 Journal bearing element
This element allows computing the rotating system with two notable cases of plain bearing: “short” bearing and the “long” bearing. Different kinds of cavitation of fluid film are considered: uncavitated (2-π film) bearing and cavitated (π-film) bearing. It allows computing dynamical systems in steady-state and non-steady state conditions. Inlet oil pressure can be considered.
4.5 Rolling bearings elements (2DOF)
The elements are represented by link between two subsystems. They model ball and roll bearings mounted between rotor and stator. The bearing models take into account a radial clearance, number of rolling elements under radial load and contact stiffness in loading area. A damping also can be considered for bearings.
4.6 Rolling bearings elements (5 DOF)
The element is represented by a link between two subsystems. It models a ball bearing mounted between a rotor and a stator/rotor. The ball bearing model takes into account a radial clearance, curvature radiuses of inner and outer race, number of rolling elements under radial load, their inertia and contact stiffness in loading area. Contact stiffness in dependence on the Kp_input parameter may be assigned or calculated automatically. The system may be considered without balls inertia and with it. The element takes into account 5 degrees of freedom of inner race: 3 translational and 2 rotational.
4.7 Non-linear support element
The element is represented by link between two subsystems. It models nonlinear links between subsystems (for example, rolling bearings mounted between rotor and stator/rotor). The model takes into account a radial clearance, and radial stiffness which is given by polynom Ax2+Bx=F(x). A damping also can be considered.
4.8 Active Magnetic Bearing
The element is represented by a link between two subsystems. It models active magnetic bearing (AMB). Three main types of AMB are modeled: radial, cone and axial. The model takes into account: radial clearance, maximal current and current density, electromagnetic poles number, control pole number, coil remove option. Pole control is the axis coincides with direction of the resultant force from the closest to it electromagnet. Current to these electromagnets is calculated from the displacements along the axis of the pole control. Electromagnets are evenly distributed at the control poles. Two control options are present – [PD – controller] and [PID – controller].
4.9 Kinematic excitation [Seismic excitation]
At the [Transient response] algorithm calculation, the link allows modeling of kinematic excitation of the installation foundation and transient processes appearing at it. One of the frequent cases is the installation work under earthquake conditions. The element allows adjusting stiffness of the basement link with the installation in three directions and assigning spectrum of seismic excitation response from the part of the basement. Excitation is defined as a poly harmonic signal acting simultaneously along three directions. Time range of excitation is divided into several ones. They are the ranges of divergent, constant and decaying amplitudes.
4.10 Annular seal element
This element models interaction between a rotor and a stator in case of incompressible fluid with constant viscous flowing through small clearance under pressure. The mathematical model of this element takes into account: the algorithm which describes the bulk flow with centering force (Lomakin effect), inlet whirl factor, entrance loss factor. The rotor dynamic coefficients are calculated in the centered rotor position.
4.11 Floating ring seal
This element models an interaction between rotor and stator in case of incompressible fluid with constant viscous flowing between small clearance under pressure. Mathematical model of this element takes into account: the algorithm which describes the bulk flow with centering force (Lomakin effect), inlet whirl factor, entrance loss factor. The mean axial velocity is defined by an iterative process. The rotor dynamic coefficients are calculated in the centered rotor position.
4.12 Floating ring bearing (not included in current user version, available by request)
The element is represented by link between two subsystems. Allows modeling high speed rotors supported on fully-floating ring bearings as well as for a shaft supported on semi-floating ring bearings. The element lets calculation of ring rotating speed, journal and bush reactions, stiffness and damping coefficients etc. Inlet oil pressure can be considered.
4.12 Crack
The element is represented by link between two subsystems. Allows to model nonlinear effects for rotating shafts with cracks. “Breathing” and “open” crack models is implemented.
4.13 Unbalanced magnetic pull
It is the link modeling the effect of unbalanced magnetic pull (UMP) in electric machines. In case of appearance of air clearance irregularity between a rotor and a stator, as a result of static and dynamic rotor eccentricity, electromagnetic field provokes a one-sided radial force applied to the rotor centre and directed at the part of the minimum air clearance. UMB works to increase the rotor stiffness. Unbalanced magnetic pull is inherent in hydro generators and electric motors.
4.14 User link (user’s nonlinear algorithms, Python, C++)
It allows to use the user’s own algorithms of nonlinear effects in rotating machinery to program new link between subsystems (float ring seals, cracks, joints, spline couplings etc) and also to integrate them into program system. The new element can be of any complexity and it can be used in a rotor model in combination with other non-linear elements. The language of programming is the script language Python (www.python.org) built-in in program system or C++.
For example, a user can develop new models of journal bearings, joints, seals, dampers, spline couplings, etc. The new element can be of any complexity and can be used in a rotor model in combination with any algorithms and elements of DYNAMICS R4. By the user’s request the new element can be adapted and included in program system by DYNAMICS R4 developer.
4.15 Misalignment (shafts)
The element models a link between two rotor subsystems (the shaft parts) coupled together with misalignment. It reproduces cyclic variation of the coupling stiffness matrix during rotation accounting for relative parallel and angular misalignment.
5. Software maintenance and support
During the support period, Developer shall correct any defects or malfunctions in the Software and Documentation discovered during such support period and provide Customer with corrected copies of same, without additional charge. Developer’s obligations hereunder shall not affect any other liability which it may have to Customer.
Developer shall provide to Customer without additional charge, copies of Software and Documentation revised to reflect any enhancements to the Software made by Developer during the support period. Such enhancements shall include all modifications to the Software which increase the speed, efficiency or ease of operation of the software, or add additional capabilities to or otherwise improve the functions of the Software.
6. Aliases by support types
In the table below, it is shown which elements of DYNAMICS R4 may be used for different support types simulation.
| Type of the support | DYNAMICS R4 element | Comment |
| Rolling bearings | ||
| Radial ball bearing | Link1 Elastic nonsymmetric link2 Non-linear support Ball Bearing support3 Angular contact ball bearing4 | |
| Angular Contact Ball bearing | Link1 Elastic nonsymmetric link2 Angular contact ball bearing4 | |
| Cylindrical Roller bearing | Link1 Elastic nonsymmetric link2 Non-linear support Roll Bearing support3 | |
| Angular contact roller bearing Tapered Roller | Link1 Elastic nonsymmetric link2 | |
| Spherical bearing Spherical thrust bearing | Link1 Elastic nonsymmetric link2 | |
| Fluid bearings | ||
| Plain cylindrical bearing | Plain Journal bearing Elastic nonsymmetric link | Nonlinear |
| Multi axial groove bearing | Elastic nonsymmetric link | Integrated tool for K and C. |
| Elliptical bearing | Elastic nonsymmetric link | |
| Offset Half bearing | Elastic nonsymmetric link | |
| Multilobe bearing | Elastic nonsymmetric link | |
| Tapered land bearing | Elastic nonsymmetric link | |
| Pressure dam bearing | Elastic nonsymmetric link | |
| Multi pocket bearing | Elastic nonsymmetric link | |
| Tilting Pad bearing | Elastic nonsymmetric link | Integrated tool K and C |
| Thrust bearing | Elastic nonsymmetric link5 | |
| Floating ring bearing | 2x seq. Plain Journal bearing Elastic nonsymmetric link6 | |
| Hydrostatic bearing | Elastic nonsymmetric link5 | |
| Gas bearings | ||
| Air Foil Bearing | Elastic nonsymmetric link | Integrated tool K and C |
| Cylindrical gas bearing with rigid case | Elastic nonsymmetric link | |
| Multilobe gas bearing with rigid case | Elastic nonsymmetric link | |
| Magnetic bearings | ||
| Passive Magnetic bearings | Elastic nonsymmetric link5 | |
| Active Magnetic bearings | Active magnetic bearing Elastic nonsymmetric link6 | Nonlinear element. |
| Active Magnetic bearings (Thrust) | Elastic nonsymmetric link5 | |
| Damper Supports | ||
| Open- and Closed-End Squeeze Film Dampers | Damper support Elastic nonsymmetric link6 | Nonlinear element |
| Seals | ||
| Labyrinth seal | Elastic nonsymmetric link5 | |
| Annular seal | Annular seal Elastic nonsymmetric link6 | Nonlinear element Integrated tool K and C |
| Floating ring seal | Floating ring seal Elastic nonsymmetric link6 | Nonlinear element |
| Aerodynamic forces | ||
| Axial | Elastic nonsymmetric link | Integrated automation script is available. Alford |
| Centrifugal compressors | Elastic nonsymmetric link | Integrated automation script is available, Modified Alford , Wachel. |
1. Linear symmetrical stiffness and damping (constant versus rotating speed)
2. Quasi linear nonsymmetrical (if applicable) stiffness and damping (variable versus rotating speed)
3. Nonlinear 2DOF element. Available stiffness output
4. Nonlinear 5DOF element. Full stiffness matrix output. Extended post-processing functionality (Bearing info)
5. Stiffness and damping coefficients should be obtained from the external tools or from bearing manufacturer.
6. Stiffness and damping coefficients should be obtained from the external tools or from nonlinear element output.