Optimization of vibratory conveying upward by inclined track with polyharmonic normal vibrations

The paper is devoted to the research of vibratory conveying of piece goods along an inclined track, performing harmonic longitudinal and polyharmonic normal vibrations. It is considered the conditions of reaching maximum conveying velocity at specified values of frequency and amplitude of longitudinal vibrations – the conditions of maximum dimensionless conveying velocity, depending on several dimensionless parameters in the moving modes without hopping. These dimensionless parameters are the inclination angle parameter – a ratio of an inclination angle tangent to a frictional coefficient, the intensive vibration coefficient – a ratio of the longitudinal amplitude of vibration to the amplitude of the first harmonic of normal vibration and frictional coefficient. Maximal conveying velocity is achieved at the certain values of normal vibration amplitudes and values of phase difference angles between longitudinal and normal vibrations, which are called optimal, and their values are dependent on these two dimensionless parameters, while maximum normal vibration acceleration should be equal to the gravitational acceleration. The research was made by approximate harmonic balance method and by numerical step-by-step integration method, which allows performing calculations with any given accuracy. The results obtained by the two methods are compared. To determine the maximal and optimal values of elevation angles, there are calculated the maximal value of the inclination angle parameter at which the value of dimensionless velocity is equal to zero, and the value of the inclination angle parameter at which a particle moves to a specified height in the minimum time. The optimal values of amplitudes of harmonics of polyharmonic normal vibration are determined in dependence on the inclination angle parameter with the number of harmonics from four to seven. The graphs of these dependencies are presented and the most important values of dimensionless parameters are presented in the table.

Download Full-text

Vibratory Conveying by Harmonic Longitudinal and Polyharmonic Normal Vibrations of Inclined Conveying Track

Journal of Vibration and Acoustics ◽

10.1115/1.4051228 ◽

2021 ◽

pp. 1-14

Author(s):

Ihor Vrublevskyi

Keyword(s):

Inclination Angle ◽

Normal Vibration ◽

Longitudinal Vibration ◽

Frictional Coefficient ◽

Material Point ◽

Normal Vibrations ◽

Dimensionless Parameters ◽

Optimal Values ◽

Vibration Parameters ◽

Angle Parameter

Abstract Vibratory conveying of a material point by harmonic longitudinal and polyharmonic normal vibrations of an inclined conveying surface is considered. The dependence of dimensionless conveying velocity – a ratio of velocity to the product of frequency and amplitude of longitudinal vibration – on several dimensionless parameters is investigated in the moving modes without hopping. Maximal conveying velocity is achieved at the certain values of normal vibration amplitudes and phase difference angle between the longitudinal and normal vibrations, which are called optimal. Their values are dependent on two dimensionless parameters: the inclination angle parameter – a ratio of an inclination angle tangent to a frictional coefficient, the intensive vibration coefficient – a ratio of the longitudinal amplitude of vibration to the amplitude of the first harmonic of normal vibration and frictional coefficient. In a condition of the intensive longitudinal vibration, when its amplitude significantly greater than amplitudes of normal vibration, dimensionless velocity is almost independent of the intensive vibration parameter and it depends only on inclination angle parameter, i.e. on inclination angle and frictional coefficient. The optimal values of harmonics' amplitudes of polyharmonic normal vibration are determined in dependence of inclination angle parameter with the number of harmonics from 2 to 7. The graphs of considered dependencies are presented and the most important values of parameters are presented in the table. Conclusions are made to determine the optimal vibration parameters and the problems of further research are indicated. The considered vibrations can be used in different vibratory conveying devices with electromagnetic drives.

Download Full-text

Convergence rates of Harmonic Balance Method for periodic solution of smooth and non-smooth systems

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2021.105826 ◽

2021 ◽

pp. 105826

Author(s):

Li Wang ◽

Zhong-Rong Lu ◽

Jike Liu

Keyword(s):

Periodic Solution ◽

Harmonic Balance ◽

Convergence Rates ◽

Harmonic Balance Method ◽

Balance Method

Download Full-text

Identification of a Nonlinear Dielectric Elastomer Actuator Based on the Harmonic Balance Method

IEEE/ASME Transactions on Mechatronics ◽

10.1109/tmech.2020.3044492 ◽

2020 ◽

pp. 1-1

Author(s):

Jakub Bernat ◽

Jakub Koota ◽

Samuel Rosset

Keyword(s):

Harmonic Balance ◽

Harmonic Balance Method ◽

Dielectric Elastomer ◽

Balance Method ◽

Dielectric Elastomer Actuator ◽

Nonlinear Dielectric

Download Full-text

Analysis of Harmonically Forced Duffing Oscillator with Time Delay State Feedback by Incremental Harmonic Balance Method

Journal of Vibration Engineering & Technologies ◽

10.1007/s42417-021-00293-y ◽

2021 ◽

Author(s):

Han Wu ◽

Xiaohui Zeng ◽

Yubiao Liu ◽

Jiang Lai

Keyword(s):

Time Delay ◽

Harmonic Balance ◽

State Feedback ◽

Duffing Oscillator ◽

Harmonic Balance Method ◽

Balance Method ◽

Incremental Harmonic Balance Method ◽

Incremental Harmonic Balance ◽

Harmonically Forced Duffing Oscillator

Download Full-text

Prediction of Transient Pressure Fluctuations within a Low-Pressure Turbine Cascade Using a Lanczos-Filtered Harmonic Balance Method

International Journal of Turbomachinery Propulsion and Power ◽

10.3390/ijtpp6030025 ◽

2021 ◽

Vol 6 (3) ◽

pp. 25

Author(s):

Jan Philipp Heners ◽

Stephan Stotz ◽

Annette Krosse ◽

Detlef Korte ◽

Maximilian Beck ◽

...

Keyword(s):

Turbulence Model ◽

Harmonic Balance ◽

Separation Bubble ◽

Pressure Fluctuations ◽

Harmonic Balance Method ◽

Low Pressure ◽

Filter Method ◽

Turbine Cascade ◽

Transient Pressure ◽

Low Pressure Turbine

Unsteady pressure fluctuations measured by fast-response pressure transducers mounted in a low-pressure turbine cascade are compared to unsteady simulation results. Three differing simulation approaches are considered, one time-integration method and two harmonic balance methods either resolving or averaging the time-dependent components within the turbulence model. The observations are used to evaluate the capability of the harmonic balance solver to predict the transient pressure fluctuations acting on the investigated stator surface. Wakes of an upstream rotor are generated by moving cylindrical bars at a prescribed rotational speed that refers to a frequency of f∼500 Hz. The excitation at the rear part of the suction side is essentially driven by the presence of a separation bubble and is therefore highly dependent on the unsteady behavior of turbulence. In order to increase the stability of the investigated harmonic balance solver, a developed Lanczos-type filter method is applied if the turbulence model is considered in an unsteady fashion.

Download Full-text