Showing papers on "Critical speed published in 1990"

Earthquake-Induced Instability of a Rotor Supported by Oil Film Bearings

Abstract: The effect of seismic waves on the stability of a Jeffcott rotor supported by oil film bearings is investigated by calculating loci of the centers of the journal and the disk using the Runge-Kutta-Gill method. It will be shown that a linearly stable rotor can become unstable under a strong artificial shock and a real seismic wave, if it is running at speeds above twice the first critical speed, which is close to the natural frequency of the rotor

Optimum Weight Design of a Rotor Bearing System With Dynamic Behavior Constraints

Abstract: The constraints include restrictions on stresses, unbalance response, and/or critical speeds. The system dynamic behaviors are analyzed by the finite element method. The exterior penalty function method is used as the optimization technique to minimize the system weight. The system design variables are the cross-sectional areas of the shaft and the stiffnesses of the bearings. The example of a single spool rotor bearing system is employed to demonstrate the merits of the design algorithm

Nonstationary vibration of a rotating shaft with nonlinear spring characteristics during acceleration through a critical speed (A critical speed of a summed-and-differential harmonic oscillation)

Abstract: Nonstationary vibration of a flexible rotating shaft with nonlinear spring characteristics during acceleration through a critical speed of a summed-and-differential harmonic oscillation was investigated. In numerical simulations, we investigated the influence of the angular acceleration λ, the initial angular position of the unbalance ψn and the initial rotating speed ω on the maximum amplitude. We also performed experiments with various angular accelerations. The following results were obtained: (1) the maximum amplitude depends not only on λ but also on ψn and ω: (2) when the initial angular position ψn changes. the maximum amplitude varies between two values. The upper and lower bounds of the maximum amplitude do not change monotonously for the angular acceleration: (3) In order to always pass the critical speed with finite amplitude during acceleration. the value of λ must exceed a certain critical value.

Vibration and control of a flexible rotor supported by magnetic bearings : (control system analysis and experiments without gyroscopic effects)

Abstract: This paper is on the subject of active vibration control of flexible rotors supported by magnetic bearings. Using a finite element method for the mathematical model of flexible rotors, we have formulated the eigenvalue problem taking into account the interaction between the mechanical system of a flexible rotor and the electrical system of magnetic bearings and a controller. However, gyroscopic effects are disregarded in this paper for simplicity. We will be able to adapt this formulation to a general flexible rotor/magnetic bearing system. Controllability with and without collocation is discussed for the higher order flexible modes of the test rig. In conclusion, we have proposed that it is necessary to add new active control loops for the higher flexible modes even in the case of collocation. Then, it is possible to stabilize for the case of uncollocation by means of this method.

An Improved Method for Stability and Damped Critical Speeds of Rotor-Bearing Systems

Abstract: Many computer programs are available for stability and critical speed analysis of rotor-bearing systems. The iterative search-transfer matrix method is widely used for such programs. However, this method sometimes fails to converge or may miss some critical speeds. This paper describes an improved technique based on the transfer matrix-polynomial method, which reduces the computational time significantly and completely eliminates the possibility of missing some critical speeds

Internal rotor friction instability

Abstract: The analytical developments and experimental investigations performed in assessing the effect of internal friction on rotor systems dynamic performance are documented. Analytical component models for axial splines, Curvic splines, and interference fit joints commonly found in modern high speed turbomachinery were developed. Rotor systems operating above a bending critical speed were shown to exhibit unstable subsynchronous vibrations at the first natural frequency. The effect of speed, bearing stiffness, joint stiffness, external damping, torque, and coefficient of friction, was evaluated. Testing included material coefficient of friction evaluations, component joint quantity and form of damping determinations, and rotordynamic stability assessments. Under conditions similar to those in the SSME turbopumps, material interfaces experienced a coefficient of friction of approx. 0.2 for lubricated and 0.8 for unlubricated conditions. The damping observed in the component joints displayed nearly linear behavior with increasing amplitude. Thus, the measured damping, as a function of amplitude, is not represented by either linear or Coulomb friction damper models. Rotordynamic testing of an axial spline joint under 5000 in.-lb of static torque, demonstrated the presence of an extremely severe instability when the rotor was operated above its first flexible natural frequency. The presence of this instability was predicted by nonlinear rotordynamic time-transient analysis using the nonlinear component model developed under this program. Corresponding rotordynamic testing of a shaft with an interference fit joint demonstrated the presence of subsynchronous vibrations at the first natural frequency. While subsynchronous vibrations were observed, they were bounded and significantly lower in amplitude than the synchronous vibrations.

Pseudo-High-Speed Balancing

Abstract: In industries like the aircraft gas turbine, trans-critical or super-critical operating speeds are quite common, and rotating machinery must be mass produced with very demanding precision in balance effectiveness, generally without recourse to high-speed balance procedures. A procedure has been developed which permits high-speed multi-plane (i.e., three or more plane) balance correction to be made on rotors in simple conventional low-speed balance machines (Patent Applied For). The procedure accomplishes most of the benefits of actual high-speed or modal or true multi-plane balancing by utilizing other known or available data on the particular rotor’s generic dynamic behavior (i.e., its natural or critical mode shapes) and data on the particular rotor’s generic design and manufacture (i.e., its perceived generic patterns of unbalance distribution). For (N ) balance planes, the procedure involves the specification of a Balancing Rule wherein a sequence of (J ) low speed balance steps is specified (where J equals the integer part of [(N + 7)/2]). At each of these steps, some fraction (called a Balancing Factor) of the measured two plane unbalance vectors is applied to one or two of the other balance correction planes, before final correction is made on the last two correction planes themselves. A procedure is derived to predetermine those (I ) Balance Factors (where I equals [N -2]). The procedure involves an iterative sequence for computing the optimized Balance Factors, with convergence driven by the Newton Raphson procedure, and requires the specification of (I ) pairs of generic unbalance distributions and natural mode shapes. The analytically derived Balancing Factors are designed to null the vibration response of the rotor excited by each of the specified generic unbalance distributions at the critical speed associated with the specified mode shape with which the generic unbalance distribution is paired.

Methodology for estimating safe operating speeds for heavy trucks and combination vehicles on interchange ramps

Abstract: A number of research studies have shown the significance of considering truck and combination vehicle performance in the geometric design of interchange ramps. The greater potential these vehicles have for offtracking and loss of control as well as rollover plays an important role in determining the safe speed of a ramp. The analysis procedure described provides highway engineers with a method, first, to determine the critical speed of a ramp for such heavy vehicles. The PHASE-4 computer model is used to simulate the dynamic behavior of the vehicle for a specified ramp geometry. The complete procedure is computerized with a user friendly interface for specifying ramp parameters and built-in data sets of vehicle parameters. Then, a method to convert the critical speed to a safe operating speed for the ramp is presented. Input parameters and results for an example ramp consisting of one simple horizontal curve are included as a demonstration. The ramp is analyzed with two types of combination vehicles. The method for estimating the safe operating speed is then demonstrated by converting the critical speeds to safe operating speeds.

Feedforward control to unbalance force cancellation for flexible rotor systems.

Abstract: This paper describes the active vibration control in the case of steady-state unbalance responses in flexible rotor systems. The control system consists of state feedback to stabilize a system and feedforward control to completely cancel unbalance forces at the designed rotational speed. This is called an output regulation theory with internal stability. At first, unbalance forces are regarded as state variables. Next, a state observer is designed in order to estimate unbalance forces because they cannot be directly measured. Feedforward control forces are produced by an opposite sign of the estimated values based on an observer. This theory has been applied to two kinds of flexible rotor systems, a single degree and two degrees of freedom systems. The amplitudes with control have been experimentally reduced to three percent near the first critical speed and twenty percent near the second critical speed.

Vibration Analysis of Circular Cylindrical Shells Connected to Bellows

Abstract: For the purpose of decreasing the lower critical speed of circular cylindrical shells which are used in centrifugal separators for uranium enrichment, and rotating at higher speeds, we consider circular cylindrical shells connected to bellows. Vibration analysis of circular cylindrical shells connected to bellows is carried out by the substructure synthesis method for various numbers and dispositions of bellows, and the optimum ones are examined. Moreover, the transfer matrix method, by which the critical speeds are simply obtained, is described, and the results are examined by the substructure synthesis method.

弾性ロータ・磁気軸受系の可制御・可観測性

Abstract: This paper is concerned with controllability and observability for a flexible rotor system supported by active magnetic bearings. The criterion of two steps concerning controllablity and observability is proposed based on the concept that a control system of magnetic bearings consists of position feedback and velocity feedback in general. The first step of the criterion is for a position feedback and the second step is for velocity feedback. The first step is to check free-free modes for only flexible rotors. In the second step, flexible modes including position feedback loops have to be analyzed because free-free modes are varied by position feedback gains. We can explain and make clear the experimental vibration behaviors which are very stable until just before the fourth critical speed, become unstable in passing through the fourth critical speed and then become stable again.

Improved method for the lateral vibration analysis of a rotor system

Abstract: A component modal synthesis technique for calculating the system dynamics of a rotor system is presented. In this method, the rotor system is divided into bladed disks, rotor shafts, and the nonrotating subsystems. The subsystem frequency transfer function matrices, geometric compatibility, and force equilibrium equations are combined to solve the critical speeds of the rotor system. The degrees of freedom in the final critical speed equation are reduced to the number of physical connections between subsystems. It is much smaller than the total number of substructure modes used in the synthesis. The proposed technique is capable of handling the rotor system with frequency-dependent properties, such as bearing stiffness. The method applies equally well for the synchronous and nonsynchronous rotor whirl. Numerical results indicate that the proposed method can efficiently and accurately determine the dynamic characteristics of a rotor system.

Critical Speeds of Continuous Shaft-Disc Systems

Abstract: This study is concerned with the combination of a linearly tapered stepped and uniform cross-sectioned continuous shaft-disc system on rigit supports.

Controlling method for spindle using static pressure gas bearing

Abstract: PURPOSE:To restrain the increase of vibration of a spindle when it passes at critical speed so as to make balancing work unnecessary by supplying air to a bearing at less than predetermined pressure before the rotating speed of the spindle exceeds the resonant point, and reducing the air supply pressure to below predetermined pressure after the speed exceeds the resonant point. CONSTITUTION:When a spindle 2 is rotated, a rotating speed detector 4 measures the rotating speed and outputs it to a pressure control valve controller 7. The controller 7 receives the output signal and next actuates a pressure control valve 6 so as to vary air supply pressure to a bearing 3, 3: i.e. when the rotating speed of the spindle is in the range of 0 to (b) point, a great amplitude is shown by the resonant point if the air supply pressure is P2, while if the air supply pressure is P1 a stable, low amplitude is shown. When the rotating speed is (b) to (a) point, a great amplitude is shown by the resonant point if the air supply pressure is P1, while if the air supply pressure is P2 a low, stable amplitude is shown. Thus, when the rotating speed is 0 to (b), the pressure is P1, while when the speed is more than (a) point the pressure is changed to P2 again, whereby it is made possible to rotate the spindle off each resonant point.

Critical speed avoidance logic for a variable speed wind turbine

Abstract: A variable speed wind turbine is controlled in a way which avoids the turbine lingering at a critical speed which would otherwise tend to cause excessive vibration. The disclosed method and apparatus increases speed at a selected rate with respect to generator output power except in the vicinity of the critical speed. The selected rate is changed in the vicinity of the critical speed to a different rate which is selected slower in the selected embodiment, to avoid commanding the critical speed. After the output power increases or decreases beyond the critical point, a deliberate discontinuity in the speed command signal is induced. A rapid speed change through the critical speed is accompanied by a corresponding power output change. If the speed is increasing at a selected slower rate below the critical speed, and the speed command signal is stepped to a higher level just before reaching the critical speed, the speed will rapidly increase and quickly pass through the critical speed while the power output decreases. Similarly, if the speed is decreasing at a selected slower rate above the critical speed, and the speed command signal is stepped to a lower level just before reaching the critical speed, the speed will rapidly decrease and quickly pass through the critical speed while the power output increases.

Stability of Flexible Rotor Supported on Journal Bearings

Abstract: This paper discusses stability conditions of a multy-degree of freedom rotorbearing system, incorporatign external damping elements such as, squeezefilm dampers. In general, from the previous work it is well known that rotors supported by journal-bearings can become unstable at speed higher than the first critical speed of the system. In this study the flexible rotor supported on journal-bearings was modelled as a multi degree of freedom system. The stifness and damping coefficient of end bearings as well as externally applied damper were included within the systems dynamics. The effect of journal-bearing parameters, such as oil viscosity, bearing clearance and excentricity ratio, on the stability conditions of the system were investigated. Also the effect of external squeeze-film damper, applied at intermediate shaft position, on the instability threshold speed were studied. For both cases, the results predicted from the theoretical model agreed well with those of obtained from the experimental investigations.

A Method for Dynamics Calculations of Rotor-Bearing-Foundation Systems

Abstract: The rotor is represented by a lumped parameter system. The equations of motion are derived and they can be solved either in matrix form or by a transfer matrix procedure (the Riccati method). A formulation in terms of a truncated modal expansion is developed, and the coupling to the foundation through the bearings is implemented. The method is applicable to critical speed calculations, response calculations, and stability investigations.