Showing papers on "Critical speed published in 1993"

Frictionally Excited Thermoelastic Instability in Automotive Drum Brakes

Abstract: Thermoelastic instability in automotive drum brake systems is investigated using a finite layer model with one-sided frictional heating. With realistic material properties of automotive brakes, the stability behavior of the one-sided heating mode is similar to that of the antisymmetric mode of two-sided heating but the critical speed of the former is higher than that of the latter. The effects of the friction coefficient and brake material properties on the critical speeds are examined and the most influential properties are found to be the coefficient of friction and the thermal expansion coefficient of drum materials. Vehicle tests were performed to observe the critical speeds of the drum brake systems with aluminum drum materials. Direct comparisons are made between the calculation and measurement for the critical speed and hot spot spacing. Good agreement is achieved when the critical speeds are calculated using the temperature-dependent friction material properties and the reduced coefficient of friction to account for the effect of intermittent contact.

Nonlinear oscillations in magnetic bearing systems

Abstract: Nonlinear oscillations in magnetic bearings caused by gyroscopic effects at high speeds are analyzed. First a nonlinear model for the magnetic bearing is set in state-variable form using airgap flux, gap displacement, and velocity as state variables. The system, which is unstable in nature, is stabilized locally around the equilibrium point of zero speed using an optimal robust servo controller. It is shown that as the speed changes the system undergoes Hopf bifurcation to periodic solutions around some critical speed. The periodic solutions are shown to be unstable, so the methods of nonlinear bifurcation control are used to stabilize them. An easily implemented nonlinear feedback control of quadratic order is derived to control the Hopf bifurcation occurring in the system. The transient response of the system with and without nonlinear feedback is obtained to show the effectiveness of nonlinear feedback. >

Whirling of Composite-Material Driveshafts including Bending-Twisting Coupling and Transverse Shear Deformation

Abstract: A simplified theory for predicting the first-order critical speed of a shear deformable, composite-material driveshaft is presented. The shaft is modeled as a Bresse-Timoshenko beam generalized to include bending-twisting coupling. Numerical results are compared with those for both thin and thick walled shell theories and generalized Bernoulli-Euler theory

Modeling Rotating Shafts Using Axisymmetric Solid Finite Elements with Matrix Reduction

Abstract: An axisymmetric harmonic finite element representation is used to calculate shaft lateral critical speeds and perform stability analysis Unlike a beam element model, an axisymmetric solid element representation allows the actual rotor geometry to be modeled A Fourier series representation allows the three-dimensional shaft geometry to be modeled in two dimensions by only considering the radial and axial coordinates Thus, the degrees of freedom of this element type are different from the usual two translations and two rotations at each node associated with bending of a three-dimensional beam element A required gyroscopic matrix is also presented for completeness in analysis of rotating shafts A matrix reduction technique is used to reduce the size of the shaft mass, gyroscopic, and stiffness matrices by condensing out slave degrees of freedom in terms of the retained master degrees of freedom The formulation is applied to various examples for verification and to investigate the effect of selection of different master degrees of freedom for this element type on the results

Automatic Balancer : Static Balancing and Transient Response of a Multiball Balancer

Abstract: This type of device is simple in construction and has a high capacity to compensate automatically for the unbalance of a rotor above the critical speed. Below the critical speed, however, the displacement of balls introduces an unbalance, and a violent self-excited vibration takes place in the neighbourhood of the critical speed. To cope with these problems, this paper deals with the theoretical and experimental investigations on the static balance and the transient response at a constant acceleration of an automatic balancer using three or more balls placed in the race which is partitioned into equal sectors. It is shown that partitioning the race is very effective against the unbalance and the self-excited vibration. It is found that, when the acceleration of the rotor surpasses a certain value, the effect of decreasing its maximum amplitude near the critical speed is reduced rapidly.

Modal simulation of gearbox vibration with experimental correlation

Abstract: A newly developed global dynamic model was used to simulate the dynamics of a gear noise rig at NASA Lewis Research Center. Experimental results from the test rig were used to verify the analytical model. In this global dynamic model, the number of degrees of freedom of the system are reduced by transforming the system equations of motion into modal coordinates. The vibration of the individual gear-shaft system are coupled through the gear mesh forces. A three-dimensional, axial-lateral coupled, bearing model was used to couple the casing structural vibration to the gear-rotor dynamics. The coupled system of modal equations is solved to predict the resulting vibration at several locations on the test rig. Experimental vibration data was compared to the predicitions of the global dynamic model. There is excellent agreement between the vibration results from analysis and experiment.

Closed-Loop Vibration Control of Flexible Rotors—An Experimental Study

Abstract: An experimental study has been made for the synchronous vibration control of a rotor-bearing system using a magnetic actuator to supply the control forces. Both open- and closed-loop strategies were implemented using measured displacement signals from various transducer configurations.Model reduction based on dominant mode methods was used to aid the design of the closed-loop strategies. These were based on pole placement techniques. It was shown that state feedback, without co-location of sensors and actuator, can be used to suppress critical speed responses without encountering spillover problems. The robustness of the strategies was also assessed by deleting selected feedback paths.

Multi-objective Optimization of Rotor-Bearing System With Critical Speed Constraints

Abstract: An efficient optimal algorithm is developed to minimize, individually or simultaneously, the total weight of the shaft and the transmitted forces at the bearings. These factors play very important roles in designing a rotor-bearing system under the constraints of critical speeds. The cross-sectional area of the shaft, the bearing stiffness, and the positions of bearings and disks are chosen as the design variables. The dynamic characteristics are determined by applying the generalized polynomial expansion method and the sensitivity analysis is also investigated. For multi-objective optimization, the weighting method (WM), the goal programming method (GPM), and the fuzzy method (FM) are applied. The results show that the present multi-objective optimization algorithm can greatly reduce both the weight of the shaft and the forces at the bearings with critical speed constraints.

A rotary atomizer and a method of operating it

Abstract: In a rotary atomizer a disc- or wheel-shaped atomizing device (6) is secured to one end of a shaft (7) which is connected with the rotor (8) of a high frequency asynchronous electric motor (2). The motor (2) is operated at a rotational speed substantially higher than the first critical speed of the shaft (7) and atomizing device (6). The shaft (7) and the rotor (8) of the high frequency motor are designed as one integral unit radially supported only by bearings (9, 10) at either end of a part (7a) of the shaft (7) surrounded by the rotor (8).

The Effects of Friction in Axial Splines on Rotor System Stability

Abstract: An in-depth parametric evaluation of the effects of Coulomb friction in an axial spline joint on the stability of the rotor-bearing system was conducted through time transient integration of the equations of motion. The effects of spin speed, friction coefficient, spline torque, external damping, imbalance, and side load as well as asymmetric bearing stiffnesses were investigated. A subnsynchrounous instability is present at the bending critical speed when the spin speed is above this critical. The limit cycle orbit is circular, proportional to the product of the friction coefficient and spline torque ([mu]T), inversely proportional to the external damping, and independent of spin speed. When imbalance is applied to the rotor, beating between the subsynchronous natural frequency and the synchronous (spin speed) frequency occurs. The subsynchronous component of the orbit is proportional to [mu]T, while the synchronous component is proportional to the imbalance. When a static side load is applied, the unstable node at the center of the orbitally stable limit cycle grows into an elliptical orbitally unstable limit cycle, separating stable from unstable regions of the phase plane. Below a threshold value of side load, the transient motion approaches one to two asymptotic solutions depending on the initial conditions: themore » larger stable limit cycle or a point at the center of the smaller unstable limit cycle. Beyond the threshold value of side load, the rotor-bearing is the stable and all motions decay to a point. Asymmetry in the bearing stiffnesses reduces the size of the subsynchronous whirl orbit.« less

Shifting critical speeds out of the operating range by changing from tilting pad to sleeve bearings

Abstract: One property of heavily to moderately loaded sleeve bearings is the resulting asymmetric stiffness and damping coefficients. These asymmetric properties often result in split first critical speeds. Since the horizontal stiffness is much softer than the vertical, a horizontal first critical speed may appear from several hundred to several thousand revolutions per minute lower than the vertical first critical. Tilting pad bearings produce more symmetric bearing properties. This symmetry usually results in a single unsplit first critical speed that is located approximately midway between the sleeve bearing split peaks. Two different case histories are examined. An induction motor and a steam turbine were both initially designed with tilting pad bearings. Both rotor bearing systems resulted in first critical speeds in the operating speed range. Numerous attempts to shift the critical out of the operating range were explored without success. As a last attempt short of a complete rotor redesign, switching to sleeve bearings was successful. Analytical results that support the decision to switch to sleeve bearings are shown along with actual test stand response plots. Additionally, for the steam turbine, results from a high speed balance are presented along with actual field speed-amplitude plots. While a tilting pad to sleeve bearing change is not recommended for all classes of turbomachinery to shift critical speeds, it is a powerful design tool as it may produce critical speed changes of up to 1000 rpm.

A Study of the Influence of Rubbing on the Dynamics of a Flexible Disk Rotor System

Abstract: This study is concerned with investigating the influence of lateral disk flexibility on the dynamics of a rotor system experiencing rub. A rotating, flexible continuous disk/shaft model was developed and the dynamical behavior of this system with and without rubbing was studied. The model developed in this study is similar to the Jeffcott rotor model except that the disk is treated as a laterally flexible continuous circular plate. The motion of the disk was transformed from physical coordinates to a set of generalized coordinates under which the generalized motion was uncoupled and the responses were calculated. Then the inertial moment acting on the shaft was computed and introduced into the governing equations of the shaft motion.Direct integration and the harmonic balance method were used to study the steady state motion of the system. A number of parameter variation studies were performed for varied rub clearances and disk mass influence ratios. The system responses to the rub, its occurrence and development, and the global stability of the observed responses were studied.The results show that rub can be classified into two types: light rub and heavy rub, and the light rub has the forms of forward, backward, or mixed whirling motion. The results also show that the disk flexibility may alter the critical speed to some degree and may also significantly affect the amplitude and stability of the rotor vibration.Copyright © 1993 by ASME

Rotor for high speed rotation

Abstract: PURPOSE:To rise the critical speed of an overhang part, simplify the vibration property of a rotor at a rated speed and facilitate its balancing. CONSTITUTION:The overhang part 9 of a rotor 1 is ended by a thrust bearing collar 10 and a shaft part does not exist in the outside of this collar 10. The weight of this part is lightened by this structure. A center hole 13 is arranged on the shaft part of the overhang part 9 so as to be hollow and then the weight/ the section bend rigidity ratio of this part can be reduced.

Basic Study of Tensioning Effect on Thermally Stressed Disk Vibration.

Abstract: In cutting with a tipped saw, the dynamic stability is affected by cutting thermal stress. In this study, the relationship between thermal stress and dynamic stability, and the tensioning effect were investigated analytically and experimentally using normal and tensioning disks. The following conclusions were reached. (1) Natural frequencies of more than second vibration modes decrease with the temperature difference between flange and peripheral. (2) Critical speed and buckling temperature are increased by tensioning. (3) With the temperature difference until buckling, transfer function of more than second vibration modes increases, and the dynamic stability decreases. This tendency is improved by tensioning. (4) In the region of postbuckling, natural frequencies of each vibration mode were examined.

Effect of Lateral Disk Flexibility on the Dynamics of Squeeze Film Damper Supported Rotors

Abstract: This paper investigates the influence of disk flexibility on the dynamical behavior of a flexible disk/shaft rotor system supported with squeeze film dampers. A simplified nonlinear rotor model incorporating disk/shaft coupling dynamics is developed for lateral vibration of a rotor system. The steady state performance of the system is explored over a wide range of operating conditions using numerical integration and harmonic balance analysis. It is shown that disk flexibility may significantly affect the dynamical behavior of the system at high operating speed by creating an additional critical speed. It is observed that both the SFD journal motion and the disk motion associated with the additional critical speed are aperiodic and of large amplitudes. It is demonstrated that the influence of disk flexibility can be shifted out of the operating speed range by increasing the retainer spring stiffness.Copyright © 1993 by ASME

Distributed Parameter Rotor-Bearing Systems

Abstract: The transverse vibration of rotor systems with distributed mass becomes an important issue when one needs to gain deep insight into the dynamic behavior of rotor systems. As far as the equations of motion are concerned, the complexity of the analysis increases as the rotary inertia [1,2], gyroscopic moments [3], shear deformation [4,5] and their combined effects [6,7] are taken into account. Regardless of the complexity introduced in rotor models, the resonant frequency, critical speed calculations and stability analysis are relatively straightforward. However, the mode shapes associated with the natural frequencies and thus the forced response analysis(modal analysis) of distributed mass rotor systems with the added complexity are not readily available except in the extremely simple case of an Euler-Bernoulli rotor model(without the gyroscopic terms) [1,8]. It has already been pointed out in the previous chapters that the Euler-Bernoulli rotor model is not a suitable model for investigating those aspects of rotor systems which distinguish them from ordinary structures. The difficulties in modal analysis of rotor systems arise from the fact that their eigenvalue problems are characterized by the presence of skew symmetric matrices with differential operators as elements due to rotation and/or damping, leading to non-self-adjoint eigenvalue problems [9].

Compound type superconducting bearing device

Abstract: PURPOSE:To raise the rotating speed of a rotary shaft supported by a superconducting bearing beyond the critical speed. CONSTITUTION:Until a speed exceeds its critical lead a lower bearing 18b is raised so as to support a rotary shaft 10 with the lower bearing 18b and an upper bearing 18a. Hereby, rigidity and load capacity in the radial direction is enlarged, large whirling of the rotary shaft 10 can be prevented at the time of passing the critical speed, and when the speed exceeds its critical level, the lower bearing 18b is brought down so as to support the rotary shaft 10 with superconducting bearings.

Harmonic Response of Rotor-Bearing Systems

Abstract: Vibration analysis is a prerequisite for design and diagnosis of rotating machinery. Most vibrations in rotating machinery are induced by rotation-related sources: rotating unbalance is the major source of vibration synchronous to the rotational speed (Ω); misalignment and cracks in shafts cause the vibration of frequency iΩ (i is an integer); ball bearing defects cause vibration with frequency nΩ (n is a real number), and so forth [1–6]. Thus, forced vibration analysis of rotating equipment subject to asynchronous harmonic excitation is essential for identifying the vibration sources or ensuring proper design of the equipment.

Fluid Film Bearings

Abstract: Fluid film bearings are commonly used in heavy rotating machines because they possess not only high load carrying capacity but also inherent damping properties. Unlike rolling element bearings, fluid film bearings are an important machine element which offers, in addition to support stiffness, substantial damping to insure rotordynamic stability. This feature is also retained in the squeeze film damper. The stiffness and damping properties of the fluid film significantly alter the critical speeds and unbalance response of a rotor, lowering its critical speed by up to 25 % in practice. It was shown in the previous chapters that internal damping in the rotor without support(external) damping easily causes rotordynamic instability. However, some types of fluid film bearings, as well as seals, are characterized by cross-coupled, as well as direct, stiffness and damping, leading to complicated system behavior and, sometimes, system instability. This type of rotor instability due to a bearing fluid film effect is known as a self-excited vibration.