Showing papers on "Critical speed published in 1980"

Sensitivity of the Critical Speeds of a Rotor to Changes in the Design

Abstract: When designing a rotor it is frequently required to shift one or several critical speeds by making proper changes in rotor dimensions. This paper presents a scheme for computing the percentage change in critical speed as caused by a percentage change in any element of the rotor model. In this way it becomes possible to determine which elements are the most critical, and by how much they should be changed to effect the desired shift in critical speed. Such data also make it possible to adjust a given rotor model to bring it into agreement with measurements. The method can readily be incorporated into the conventional critical speed calculation and the additional computing time is insignificant.

Experimental Study of Three Journal Bearings with a Flexible Rotor

Abstract: The unbalance response and stability of a simple flexible rotor was tested over a speed range with three different types of journal bearings: axial groove, pressure dam and tilting pad. Measurements were made of total rotor response, synchronous response and frequency spectrums at various running speeds and at selected locations along the shaft. Axial groove bearings were better for low-speed use and near the critical speed but oil whip occurred at approximately twice the first rotor critical speed. Two sets of pressure dam bearings with different geometries were tested and both controlled vibrations at the critical speed. Whip occurred at twice and thrice the critical speed for the two pressure dam bearings. Tilting-pad beatings exhibited large vibration amplitudes near the critical speed, but did not go into oil whip at speeds up to three times the first rotor critical speed. Presented at the 34th Annual Meeting in St. Louis, Missouri, April 30-May 3, 1979

Extension of the Transfer Matrix Method for Rotordynamic Analysis to Include a Direct Representation of Conical Sections and Trunnions

Abstract: The transfer matrix method for rotordynamic analysis (alternately hnown as the HlI1P or LMP method) has enjoyed wide popularity due to its flexibility and ease of application. A number of computer programs are generally available which use tfl,is method in various forms to perform undamped critical speed, unbalance response, damped critical speed and stability analyses. For all of these analyses, the assembly of the transfer matrices from the rotor model is essentially the same. In all cases, the rotor model must be composed entirely of cylindrical beam elements. There are two situations when this limitation is not desirable. The first situation is when the rotor being modelled has one or more sections whose cross sections vary continually i'IJ the axial direction. The most common of these sections is the conical section. Pres­ ently, a conical section must be modelled as a series of "steps" of cylindrical sections. This adversely affects both the simplicity and accuracy of the rotor model. The second situation when current transfer matrix techniques are not accurate is when the rotor being modelled has one or more sections that do not behave as beam elements. The most common example is a trunnion which behaves as a plate. This paper describes the analytical basis and the method of application for direct reprffSentation of conical sections and trunnions for a transfer matrix analysis. Analytical results are cur­ rently being generated to demonstrate the need for and advantages of these modelling procedures.

Experimental study of the critical speed response, of a jeffcott rotor with acceleration

Abstract: A small, lightly damped rotor (ζ=0.0088) was experimentally tested for a variety of acceleration and deceleration rates. In each case, the amplitude response was plotted as a function of operating speed, with the acceleration rate considered. In each case the results are compared with theoretical predictions. The results agree within 6% at the peak response. The results of the analysis indicate that for high acceleration rates the critical amplitude response may be reduced by a factor of four or more. The frequency of the effective critical speed may be shifted by up to 20%. Furthermore, a beating frequency was observed in the amplitude data after the rotor had passed through the critical speed. This phenomenon is shown to be the vector sum of a synchronous component of amplitude and a nonsynchronous transient component (at the critical speed). The transient nonsynchronous component is shown explicitly via electronic band-pass filtering, as is the forced response component. Finally, spectral analyses were performed over a range of operating speeds, yielding waterfall diagrams and further verification of the existence of the two components.

Solving Subsynchronous Whirl in the High-Pressure Hydrogen Turbomachinery of the SSME

Abstract: The high-pressure turbomachinery for the Space Shuttle Main Engine (SSME) has the highest power-to-weight ratio known. Subsynchronous shaft whirl of the high-pressure fuel turbopump (77,000 hp, 760 Ib) limited operation of the SSME for some months in early 1976. The means by which this problem was successfully attacked is presented herein. The principal forcing functions of the phenomena were adjudged to be turbine crosscoupling and interstage seal effects in combination with low-system stiffness and damping. The whirl inception speed and the first-shaft critical speed were increased by stiffening the shaft and bearing supports. System damping and stiffness were additionally augmented by utilizing the interstage seals as axial flow hydrodynamic bearings. The instability threshold speed is now greater than the operating speed at rated engine thrust.

Nonlinear stability and response of car-trailer combinations

Abstract: The technique of quasilinearization (describing function analysis) is used to study the effects of saturation of lateral tire force based on the traditional slip law concept. Deu to trailer swing velocity, the dynamic slip angle is shown to be greater than the trailer angle. Thus nonlinear results are important even for small displacements. Significant changes in frequency and damping ratio from linear values are shown for the transient response of a one degree of freedom model. The forced response is shown to be of the classical left-leaning softening type, with jump/drop phenomenon. A two degree of freedom model is shown to have a very small amplitude limit cycle for operation above the critical velocity. Conversely, a three degree of freedom model is shwon to have no stable limit cycle above the critical velocity.

Some Characteristics of the Disk-Scraper Oil-Feed Mechanism

Abstract: The disk-scraper mechanism is commonly used in self-contained journal bearings as a lubricator. Two types cf fixed clearance scrapers and a floating plow-type scraper were investigated experimentally. The effects of speed, viscosity, clearances and immersion on flow were found by systematic variation. For each type, the flow was found to increase, with speed, N, to a critical value, Nc, and then decrease, in some cases to zero at N ≃ 2.5 Nc. The dominant parameter affecting both critical speed and flow below critical speed was found to be the immersion. Viscosity and system clearances had comparatively mild effects. Of the scrapers tested, the floating-plow type was found to be superior in several respects. Presented at the 34th Annual Meeting in St. Louis, Missouri, April 30-May 3, 1979

Problem of Rotor Passing Through Critical Speed with Gyroscopic Effect : 3rd Report, Case of Rotating Shaft on Flexible Supports

Abstract: This paper studies the nonstationary vibration of a rotating shaft on flexible supports in passing through the critical speed. In particular the interaction or the coupling effect caused by near critical speeds in continuous passing through 1st and 2nd critical speeds has been studied. For the case of a rotor system on damped flexible supports, its approximate equation in transition through the critical speed has been derived by the asymptotic method as in the former report. Moreover, observing nonstationary maximum amplitudes, the analytical results have been considered. The experiments support the analysis.

Vibration of a Shaft Passing through a Critical Speed : 4th Report, Effect of Gyroscopic Moment

Abstract: Effects of the gyroscopic moment on the nonstationary vibration, which occurs when a rotor passes through its critical speed at a uniform acceleration rate, are analyzed. The numerical integration results show that the gyroscopic moment makes the maximum amplitude small and makes the rotational speed, where the maximum amplitude occurs, high comparing with the results of a single-degree-of-freedom system. These phenomena may be explained by assuming that the acceleration rate in the gyroscopic system becomes large in appearance. Formulas for the imaginary acceleration rate and the maximum amplitude are derived by considering both the nonstationary vibration of a single-degree-of-freedom system and the change of the natural frequency of the gyroscopic system. The estimated maximum amplitudes are compared with the numerical ones.

Breaking Ice with Gravity Waves

Abstract: The plane-wave impulse response of a laterally compressed floating elastic plate, derived in earlier work, provides a simple means of describing the response of a floating ice sheet to gravity waves induced by a moving vehicle. Vehicle speeds above the cut-off phase velocity produce gravity waves that grow in amplitude with time. These waves grow in amplitude most rapidly when the vehicle speed equals the critical gravity-wave phase velocity. For vehicle speeds above the critical phase velocity, the critical wave is excited at an angle to the vehicle motion; hence, the amplitude grows at a high but decreasing rate as the vehicle speed increases from the critical speed. The critical speed is the optimum speed for breaking an ice sheet by moving vehicle. Vehicles travelling at speeds below the cut-off phase velocity do not excite growing waves that increase the deflection of the ice sheet; thus, vehicular travel below the cut-off speed is recommended. Easily derived plots of the cut-off and critical phase velocities and wave lengths are presented as functions of ice thickness and water depth.

Impact of the Nonlinear Connection Torque Between Truck and Car-Body on the Transversal Stability of a Railway-Car

Abstract: Matrix (A) shows the dynamic behavior of a high speed free truck running on an aligned track under optimal geometric conditions. The maximum running speed will be lower than the critical speed inherent to the system which is determined by the first eigenvalue of the matrix for which the real part is small and positive. The increase of this critical speed has been observed by an increase of the connection stiffness between car-body and truck. In fact, the car-body truck connection includes more than the classical connection. It includes hydraulic damping devices whose force-displacement diagram is similar to that of a friction damping device. After considering the elastic deformation of the connecting system ensured by the damping devices between truck and car-body, and the connecting springs between truck and car-body mounted is parallel, we observe a drawback torque relative to the truck. This characteristic can be compared to an hysteresis cycle.

Balancing of a Power-Transmission Shaft With the Application of Axial Torque

Abstract: Evaluation of power transmission shafting for high-speed balancing has shown that when axial torque is applied, the imbalance response is altered. An increase in synchronous excitation always occurs if the axial torque level is altered from the value used during balancing; this was the case even when the shaft was balanced with torque applied. The twisting of the long slender shaft produces a change in the imbalance distribution sufficient to disrupt the balanced state. This paper presents a review of the analytic development of a weighted least squares approach to influence coefficient balancing and a review of experimental results. The analytic approach takes advantage of the fact that the past testing has shown that the influence coefficients are not significantly affected by the application of axial torque. The 3.60-m (12-ft) long aluminum shaft, 7.62 cm (3 in.) in diameter was run through the first flexural critical speed at torque levels ranging from zero-torque to 903.8 N-M (8000 lb-in.) in 112.9 N-M (1000 lb-in.) increments. Good comparison was achieved between predicted and experimental results.

Experimental results concerning centrifugal impeller excitations

Abstract: The effect of working fluid on the dynamics of an impeller with radial vanes was investigated. The impeller was supported vertically from a very flexible quill shaft in order to produce a low critical speed, and to allow the fluid dynamic effects on the impeller to predominate. The shaft was supported from ball bearings, so that there was no possibility of oil whip from fluid film bearings as a destabilizing influence. The impeller was run both in the atmosphere, and submerged in working fluids contained in a cylindrical housing, open at the top. Variable speed was obtained with a dc gearmotor drive unit. The speed was measured with a proximity probe pulse tachometer and electronic digital counter.

Critical Speeds and Vibrations

Abstract: This chapter discusses the effect of the radial loadings, hydraulic, and electrical, on the critical speed of a combined motor pump. The armature of the electrical motor rotates in a magnetic field. The effect of tolerances in measurement of bearing settings and of static deflection of the rotor, involves operation some distance away from the theoretical magnetic center This gives rise to an unbalanced magnetic pull, referred to as UMP, at the rotor, tending to deflect the shaft in a radial direction. The deflection of the shaft at the impeller under radial loading will have no effect on the critical speed of the pump portion of the shaft, which is determined in the usual manner. In the motor armature, however, considerably different conditions prevail, in that the UMP is proportional to the deflection from the magnetic centre. Because centrifugal force is also proportional to the deflection from the center, both these loadings must be added together in the determination of critical speed. The loadings, however, must be added under equal deflection conditions. They can be conveniently added, for example, at unit deflection or, more conveniently in this case, at the static deflection of the rotor under gravity, which is used in the determination of critical speed.