Reduced-Order Modeling of Bladed Disks With Friction Ring Dampers

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Seunghun Baek ◽  
Bogdan Epureanu
Keyword(s):  
Steady State ◽  
Dry Friction ◽  
Friction Model ◽  
Contact Friction ◽  
Bladed Disks ◽  
Transient Dynamic Analysis ◽  
Reduced Order ◽  
Bladed Disk ◽  
Steady State Responses ◽  
State Responses

An efficient methodology to predict the nonlinear response of bladed disks with a dry friction ring damper is proposed. Designing frictional interfaces for bladed-disk systems is an important approach to dissipate vibration energy. One emerging technology uses ring dampers, which are ringlike substructures constrained to move inside a groove at the root of the blades. Such rings are in contact with the bladed disk due to centrifugal forces, and they create nonlinear dissipation by relative motion between the ring and the disk. The analysis of the dynamic response of nonlinear structures is commonly done by numerical integration of the equations of motion, which is computationally inefficient, especially for steady-state responses. To address this issue, reduced-order models (ROMs) are developed to capture the nonlinear behavior due to contact friction. The approach is based on expressing the nonlinear forces as equivalent nonlinear damping and stiffness parameters. The method requires only sector-level calculations and allows precalculation of the response-dependent equivalent terms. These factors contribute to the increase of the computational speed of the iterative solution methods. A model of a bladed disk and damper is used to demonstrate the method. Macro- and micro-slip are used in the friction model to account for realistic behavior of dry friction damping. For validation, responses due to steady-state traveling wave excitations are examined. Results computed by ROMs are compared with results from transient dynamic analysis (TDA) in ansys with the full-order model. It is found that the steady-state responses predicted from the ROMs and the results from ansys are in good agreement, and that the ROMs reduce computation time significantly.

Reduced Order Modeling of Bladed Disks With Friction Ring Dampers

2016 ◽  
Author(s):  
Seunghun Baek ◽  
Bogdan Epureanu
Keyword(s):  
Steady State ◽  
Dry Friction ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Friction Model ◽  
Contact Friction ◽  
Bladed Disks ◽  
Transient Dynamic Analysis ◽  
Reduced Order ◽  
Bladed Disk

An efficient methodology to predict the nonlinear response of bladed disks with a dry friction ring damper is proposed. Designing frictional interfaces for bladed disk systems is an important approach to dissipate vibration energy. One emerging technology uses ring dampers, which are ring-like substructures constrained to move inside a groove at the root of the blades. Such rings are in contact with the bladed disk due to centrifugal forces, and they create nonlinear dissipation by relative motion between the ring and the disk. The analysis of the dynamic response of nonlinear structures is commonly done by numerical integration of the equations of motion, which is computationally inefficient, especially for steady-state responses. To address this issue, reduced order models (ROMs) are developed to capture the nonlinear behavior due to contact friction. The approach is based on expressing the nonlinear forces as equivalent nonlinear damping and stiffness parameters. The method requires only sector level calculation, and allows pre-calculation of the response-dependent equivalent terms. These factors contribute to the increase of the computational speed of the iterative solution method. A model of a bladed disk and damper, is used to demonstrate the method. Macro- and micro-slip are used in the friction model to account for realistic behavior of dry friction damping. For validation, responses due to steady-state traveling wave excitations are examined. Results computed by ROMs are compared with results from transient dynamic analysis in ANSYS with the full order model.

The “α-Invariant”: An Energy-Based Nonlinear Minimal Damping Model for Robotic Joints With Friction

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Bart Milne ◽  
Chris Hann ◽  
XiaoQi Chen
Keyword(s):  
Steady State ◽  
Linear Model ◽  
Low Frequency ◽  
Friction Model ◽  
Friction Behavior ◽  
Low Frequencies ◽  
Local Linear ◽  
Steady State Responses ◽  
Energy Dissipated ◽  
State Responses

System identification of the sinusoidal steady-state response of the Phantom Omni using a local linear model revealed that friction has a non-negligible effect on the accuracy of a global linear model, particularly at low frequencies. Some of the obvious errors observed with the global linear model at low frequencies were (i) the response amplitude was lower; (ii) local linear model coefficients became physically impossible (e.g., negative) at low frequencies; and (iii) low frequency inputs resulted in a greater nonlinearity in the response compared to higher frequency inputs. While standard friction models such as Coulomb friction could be used to model the nonlinearity, there is a desire to create a friction model that is not only accurate for sinusoidal steady-state responses, but can also be generalized to any input response. One measure that is universally present in dynamical systems is energy, and in this paper the relationship between a generalized measure of energy and damping for modeling the effect of friction is developed. This paper introduces the “α-invariant” as a means of generalizing the friction behavior observed with sinusoidal steady-state responses to other waveforms. For periodic waveforms, the α-invariant is shown to be equivalent to the energy dissipated in each cycle, which demonstrates the physical significance of this quantity. The α-invariant nonlinear model formulation significantly outperforms the linear model for both sinusoidal steady state and step responses, demonstrating that this method accurately represents the physical mechanisms in the Phantom Omni. Overall, the α-invariant provides an efficient way of capturing nonlinear dynamics with a small number of parameters and experiments.

Estimating the Audiogram Using Multiple Auditory Steady-State Responses

2002 ◽  
Vol 13 (04) ◽  
pp. 205-224 ◽  
Author(s):  
Andrew Dimitrijevic ◽  
Sasha M. John ◽  
Patricia Van Roon ◽  
David W. Purcell ◽  
Julija Adamonis ◽  
...  
Keyword(s):  
Steady State ◽  
Correlation Coefficients ◽  
Behavioral Threshold ◽  
Behavioral Thresholds ◽  
Sensorineural Hearing Impairment ◽  
Steady State Responses ◽  
Auditory Steady State Responses ◽  
Tonal Stimuli ◽  
Conductive Hearing ◽  
State Responses

Multiple auditory steady-state responses were evoked by eight tonal stimuli (four per ear), with each stimulus simultaneously modulated in both amplitude and frequency. The modulation frequencies varied from 80 to 95 Hz and the carrier frequencies were 500, 1000, 2000, and 4000 Hz. For air conduction, the differences between physiologic thresholds for these mixed-modulation (MM) stimuli and behavioral thresholds for pure tones in 31 adult subjects with a sensorineural hearing impairment and 14 adult subjects with normal hearing were 14 ± 11, 5 ± 9, 5 ± 9, and 9 ± 10 dB (correlation coefficients .85, .94, .95, and .95) for the 500-, 1000-, 2000-, and 4000-Hz carrier frequencies, respectively. Similar results were obtained in subjects with simulated conductive hearing losses. Responses to stimuli presented through a forehead bone conductor showed physiologic-behavioral threshold differences of 22 ± 8, 14 ± 5, 5 ± 8, and 5 ± 10 dB for the 500-, 1000-, 2000-, and 4000-Hz carrier frequencies, respectively. These responses were attenuated by white noise presented concurrently through the bone conductor.

Weighted averaging of steady-state responses

2001 ◽  
Vol 112 (3) ◽  
pp. 555-562 ◽  
Author(s):  
M.Sasha John ◽  
Andrew Dimitrijevic ◽  
Terence W Picton
Keyword(s):  
Steady State ◽  
Weighted Averaging ◽  
Steady State Responses ◽  
State Responses
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