A Comparison of Several SDOF Models of Gear Dynamics

2016 ◽  
Author(s):  
Wennian Yu ◽  
Chris K. Mechefske ◽  
Markus Timusk
Keyword(s):  
Damping Ratio ◽  
Low Noise ◽  
Mesh Stiffness ◽  
Single Degree Of Freedom ◽  
Gear Dynamics ◽  
Advantages And Disadvantages ◽  
Gear Manufacturing ◽  
Steady State Responses ◽  
Clearance Nonlinearity ◽  
State Responses

It is commonly believed that a complete understanding of gear dynamics is essential for the design of gear transmission systems capable of running at low noise and vibration levels with prolonged service life. Several single degree of freedom (SDOF) models of gear dynamics with clearance nonlinearity are generalized based on previous research, while a constant damping ratio is assumed and the friction is neglected. These models include the effects of time-varying mesh stiffness, gear manufacturing errors, profile modifications and backlash. Comparisons of the steady responses predicted by these SDOF models are intensively studied and the relationships between these models are discussed. Even though, different types of mesh stiffness and different treatments of the gear error functions in the analysis are used in these models, the steady-state responses predicted by these models are generally consistent with each other and agree well with experimental results. However, some discrepancies and relationships do exist among these models. The advantages and disadvantages of each model are highlighted.

CAPABILITY TO CAPTURE DYNAMIC LOADING IN LINEAR DYNAMIC ANALYSIS OF SINGLE DEGREE OF FREEDOM SYSTEMS

2013 ◽  
Vol 13 (05) ◽  
pp. 1350012
Author(s):  
SHUENN-YIH CHANG
Keyword(s):  
Dynamic Loading ◽  
Integration Method ◽  
Discretization Error ◽  
Time Step ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Dynamic Loadings ◽  
Steady State Responses ◽  
State Responses ◽  
Transient And Steady State

In this work, the importance of the capability to capture dynamic loading for an integration method is emphasized. In a step-by-step integration procedure, amplitude distortions in the transient and steady-state responses depend on the step discretization error of dynamic loading for each time step. Correlations between amplitude distortion and step discretization error for dynamic loadings are analytically established for a specified integration method. These correlations may be considered as the basic numerical properties in evaluating a step-by-step integration method. As a result, the superiority of the previously published algorithm (PPA) [S. Y. Chang, Int. J. Numer. Meth. Eng.77(8) (2009) 1100–1120] over its modified form and the member of Newmark family method (MNM) with β = γ = 1/2 in capturing dynamic loading is analytically verified (even though the three algorithms have exactly the same characteristic equation).

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.

scholarly journals Estimation of Additional Equivalent Damping Ratio of the Damped Structure Based on Energy Dissipation

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Xiuyan Hu ◽  
Qingjun Chen ◽  
Dagen Weng ◽  
Ruifu Zhang ◽  
Xiaosong Ren
Keyword(s):  
Energy Dissipation ◽  
Damping Ratio ◽  
Theoretical Concept ◽  
Estimation Methods ◽  
External Excitation ◽  
Single Degree Of Freedom ◽  
Equivalent Damping ◽  
Seismic Motion ◽  
Practical Engineering ◽  
Energy Dissipation Capacity

In the design of damped structures, the additional equivalent damping ratio (EDR) is an important factor in the evaluation of the energy dissipation effect. However, previous additional EDR estimation methods are complicated and not easy to be applied in practical engineering. Therefore, in this study, a method based on energy dissipation is developed to simplify the estimation of the additional EDR. First, an energy governing equation is established to calculate the structural energy dissipation. By means of dynamic analysis, the ratio of the energy consumed by dampers to that consumed by structural inherent damping is obtained under external excitation. Because the energy dissipation capacity of the installed dampers is reflected by the additional EDR, the abovementioned ratio can be used to estimate the additional EDR of the damped structure. Energy dissipation varies with time, which indicates that the ratio is related to the duration of ground motion. Hence, the energy dissipation during the most intensive period in the entire seismic motion duration is used to calculate the additional EDR. Accordingly, the procedure of the proposed method is presented. The feasibility of this method is verified by using a single-degree-of-freedom system. Then, a benchmark structure with dampers is adopted to illustrate the usefulness of this method in practical engineering applications. In conclusion, the proposed method is not only explicit in the theoretical concept and convenient in application but also reflects the time-varying characteristic of additional EDR, which possesses the value in practical engineering.

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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