High Order Subharmonic Response of High Speed Rotors in Bearing Clearance

1988 ◽  
Vol 110 (1) ◽  
pp. 9-16 ◽  
Author(s):  
F. F. Ehrich
Keyword(s):  
Natural Frequency ◽  
High Speed ◽  
Response Curves ◽  
Whole Number ◽  
Wave Forms ◽  
Vibration Responses ◽  
Subharmonic Response ◽  
Subharmonic Vibration ◽  
Exact Computer ◽  
Very High

Subharmonic vibration refers to the response of a dynamic system to excitation at a whole-number multiple (n) of its natural frequency by vibrating asynchronously at its natural frequency, that is, at (1/n) of the excitation. The phenomenon is generally associated with asymmetry in the stiffness vs. deflection characteristic of the system. It may be characterized as the “bouncing” of the rotor on the surface of the stiff support, energized by every nth unbalance impulse prior to contact. Second, third and fourth order subharmonic vibration responses have previously been observed in high speed rotating machinery with such an asymmetry in the bearing supports. An incident is reported where 8th and 9th order subharmonic vibration responses have been observed in a high speed rotor. A simple but exact computer model of the phenomenon has been evolved based on the numerical integration of a finite difference formulation. Response curves and wave forms of rotor deflection at individual speeds are computed. It is shown that the response is a series of pseudo-critical peaks at whole-number multiples of the rotational speed. Very high orders of subharmonic vibration are found to be possible for systems with low damping and extreme nonlinearity.

Spontaneous Sidebanding at Subharmonic Peaks of Rotordynamic Nonlinear Response

1997 ◽  
Author(s):  
Fredric Ehrich ◽  
Marc Berthillier
Keyword(s):  
Natural Frequency ◽  
Rotational Speed ◽  
High Speed ◽  
Nonlinear Response ◽  
Dominant Frequency ◽  
Critical Set ◽  
Whole Number ◽  
Subharmonic Response ◽  
Intermittent Contact ◽  
Response Peak

Abstract One of the authors has shown in previous papers (Enrich, 1995; Ehrich, 1996) that, when high speed rotors are operated in the transcritical range with the rotor located eccentrically in its rotor/stator clearance with the rotor in intermittent contact with the stator, a nonlinear response, at speeds both slightly above and slightly below the critical speed, is induced. The response at a particular speed will include significant components at an asynchronous frequency which is approximately equal to the natural frequency of the system. In particular, when the speed (normalized by the natural frequency) S is approximately (J+1)/J, the dominant frequency (normalized by the natural frequency) F is precisely J/(J+1) times S or approximately 1 (where values of the whole number J < 1 give the subcritical set of speeds and values J > 1 give the supercritical set of speeds). The phenomenon has been termed spontaneous sidebanding. Observations of similar asynchronous responses noted in a Campbell diagram of the rotordynamic response of an actual high speed rotor clustered around a subharmonic response peak at a rotational speed twice the natural frequency suggest that the phenomenon is also possible at any subharmonic pseudo-critical response peak. In this more general case, we would expect that at rotational speeds in the vicinity of the M th subharmonic pseudo-critical normalized speed where S is approximately (MJ+1)/J and the dominant normalized frequency F is precisely J/(MJ+1) times S or approximately 1 [where values of the whole number J < 1 give the sub(pseudo)critical set of speeds and values J > 1 give the super(pseudo)critical set of speeds]. A simple numerical model of the nonlinear system verifies that these asynchronous responses are indeed possible. Operation of the model at a rotational speed approximately double the natural frequency yields data which closely reproduce the asynchronous response seen in the actual machine.

On the Nonlinear Response of a Relief Valve

1978 ◽  
Vol 100 (4) ◽  
pp. 675-680 ◽  
Author(s):  
M. A. Dokainish ◽  
M. M. Elmadany
Keyword(s):  
Nonlinear Response ◽  
Forced Response ◽  
Distributed Parameter ◽  
Response Curves ◽  
Relief Valve ◽  
Single Degree Of Freedom ◽  
Third Harmonic ◽  
Valve System ◽  
Subharmonic Response ◽  
Subharmonic Vibration

The free and forced response of a relief valve system has been analyzed. The valve system consists of a valve having a mass, resting on a seat having nonlinear spring characteristics, and retained by a helical spring which is considered to be a distributed parameter element. The response curves of the first and third harmonic and one-third subharmonic, the amplitudes of which vary with the frequency of the external force, are investigated and presented graphically. It is found that harmonic, higher-harmonic, and subharmonic response of the system may become unstable within certain frequency ranges. Jump and hysteresis phenomena analogous to that of nonlinear single-degree-of-freedom systems are observed. It is also observed that subharmonic vibration may exist in a number of specified frequency ranges.

Parametric Vibration Responses of Electromechanical Integrated Toroidal Drive

2012 ◽  
Vol 271-272 ◽  
pp. 1383-1387
Author(s):  
Xiu Hong Hao ◽  
Xue Jun Zhu
Keyword(s):  
Natural Frequency ◽  
Parametric Vibration ◽  
Time Varying ◽  
Vibration System ◽  
Response Curves ◽  
Design And Optimization ◽  
Meshing Stiffness ◽  
Electromechanical Integrated ◽  
Vibration Responses ◽  
Time Domain Response

There are periodic changes of meshing teeth in electromechanical integrated toroidal drive, that lead to time-varying meshing stiffness. By converting time-varying stiffness into the form of Fourier series, dynamics model and the corresponding differential equation of parametric vibration system are established. Then approximate analytical solution of the system is obtained by multi-scale method, and time domain response curves of damping vibration system are given. The analysis results show that free vibration of the system not only include natural frequency, but also contains combination frequencies between natural frequency and meshing frequency. So there are multi-resonance frequency sections. Those will provide more theoretical supports for system dynamic design and optimization.

Vibration of a Rotor With Extremely Nonlinear Stiffness Passing Through Critical Speeds

1993 ◽  
Author(s):  
Baojiang Liu ◽  
Litang Yan ◽  
Qihan Li ◽  
Zigen Zhu
Keyword(s):  
Transient Response ◽  
Damping Ratio ◽  
Maximum Amplitude ◽  
General Nature ◽  
Response Curves ◽  
Nonlinear Spring ◽  
Critical Speeds ◽  
Offset Distance ◽  
Wave Forms ◽  
Subharmonic Vibration

Soft spring nonlinearity refers to supporting stiffness becomes smaller with increase of vibratory displacements. In this paper, transient response and subharmonic vibration of a rotor with extremely soft nonlinear spring characteristics are investigated. A simple but exact computer model of the phenomena has been evolved based on the numerical integration of a finite difference formulation. Response curves and wave forms of the rotor vibration passing through critical speeds are computed. The subharmonic vibration of the rotor with soft nonlinear spring characteristics has been observed by spectral analysis of vibratory response. It is shown that the rotor will tend to bounce when its vibratory displacements exceed the offset distance of the system with stiffness K1 when it is accelerated for passing through critical speeds and the vibratory motion after bouncing is predominantly at the forcing frequency. Maximum amplitude of transient response is affected mainly by damping ratio ξ, the degree of nonlinearity β and the offset distance h. A series of subharmonic pseudo critical peaks will appear in the acceleration of a rotor with soft nonlinear spring characteristics. But the general nature of the subharmonic vibration is much different from that with hard ones. Finally some computational results are demonstrated by an experiment.

Structural changes in silicon-on-insulator material during post-implantation annealing

1986 ◽  
Vol 44 ◽  
pp. 736-737
Author(s):  
C. O. Jung ◽  
S. J. Krause ◽  
S.R. Wilson
Keyword(s):  
Integrated Circuits ◽  
Oxide Layer ◽  
High Speed ◽  
Structural Changes ◽  
Device Fabrication ◽  
Silicon On Insulator ◽  
High Quality ◽  
Radiation Hardened ◽  
Post Implantation ◽  
Very High

Silicon-on-insulator (SOI) structures have excellent potential for future use in radiation hardened and high speed integrated circuits. For device fabrication in SOI material a high quality superficial Si layer above a buried oxide layer is required. Recently, Celler et al. reported that post-implantation annealing of oxygen implanted SOI at very high temperatures would eliminate virtually all defects and precipiates in the superficial Si layer. In this work we are reporting on the effect of three different post implantation annealing cycles on the structure of oxygen implanted SOI samples which were implanted under the same conditions.

YSS HAP72

Alloy Digest ◽  
2019 ◽  
Vol 68 (10) ◽  
Keyword(s):  
Wear Resistance ◽  
High Temperature ◽  
Powder Metallurgy ◽  
Tool Steel ◽  
High Speed ◽  
High Wear Resistance ◽  
Bend Strength ◽  
Temperature Performance ◽  
Very High

Abstract YSS HAP72 is a powder metallurgy high-speed tool steel with a very high wear resistance. This datasheet provides information on composition, hardness, and bend strength. It also includes information on high temperature performance. Filing Code: TS-779. Producer or source: Hitachi Metals America Ltd.

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