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Causes of Errors in Estimating the Characteristic Frequencies of Antiresonant Conveyors Cover

Causes of Errors in Estimating the Characteristic Frequencies of Antiresonant Conveyors

Acta Mechanica et Automatica
Volume 19 (2025): Issue 3 (September 2025)
By: Jerzy MICHALCZYK,  Marek GAJOWY and  Krzysztof MICHALCZYK  
Open Access
|Sep 2025

Figures & Tables

Fig. 1.

VIBRAflex II Sanitary Antiresonant Vibratory Conveyor – PFI, which dynamic and discret model is presented in Fig. 2
VIBRAflex II Sanitary Antiresonant Vibratory Conveyor – PFI, which dynamic and discret model is presented in Fig. 2

Fig. 2.

Diagram of the dynamic vibration eliminator: M – protected mass, me – eliminator mass, K, C – constants of elasticity and damping of support elements of protected mass, ke, ce – constants of elasticity and damping of elastic elements of the eliminator, Poeivt – harmonic excitation force
Diagram of the dynamic vibration eliminator: M – protected mass, me – eliminator mass, K, C – constants of elasticity and damping of support elements of protected mass, ke, ce – constants of elasticity and damping of elastic elements of the eliminator, Poeivt – harmonic excitation force

Fig. 3.

Plot of dimensionless amplitudes z1 for absolute displacements of the protected system A, the vibration eliminator B, and the system without the eliminator Ao, as a function of the ratio δ for the excitation frequency ν to the partial frequency of the eliminator ωn, equal to the antiresonant frequency (10) of the system, where z1 – the ratio of amplitudes to the value of static deflection of the protected mass
Plot of dimensionless amplitudes z1 for absolute displacements of the protected system A, the vibration eliminator B, and the system without the eliminator Ao, as a function of the ratio δ for the excitation frequency ν to the partial frequency of the eliminator ωn, equal to the antiresonant frequency (10) of the system, where z1 – the ratio of amplitudes to the value of static deflection of the protected mass

Fig. 4.

Graph showing the ratio of the resonance frequencies to the antiresonance frequency v/ωn of the analysed system, compared to the ratio of masses me/M = μ in the equality of partial frequencies of the protected and eliminator masses
Graph showing the ratio of the resonance frequencies to the antiresonance frequency v/ωn of the analysed system, compared to the ratio of masses me/M = μ in the equality of partial frequencies of the protected and eliminator masses

Fig. 5.

Graphs showing the ratio of the upper and lower resonance frequency to ωn as a function of the mass ratio μ, depending on the value of the parameter Δ. Note: upper frequency graphs for Δ>>1 values (Δ = 4 to 7) coincide approximately on the graph
Graphs showing the ratio of the upper and lower resonance frequency to ωn as a function of the mass ratio μ, depending on the value of the parameter Δ. Note: upper frequency graphs for Δ>>1 values (Δ = 4 to 7) coincide approximately on the graph

Fig. 6.

Plots of the ratios of the upper and lower frequency of the system to the antiresonance frequency ωn as a function of Δ
Plots of the ratios of the upper and lower frequency of the system to the antiresonance frequency ωn as a function of Δ

Fig. 7.

Discrete model of an antiresonant vibratory conveyor shown in Fig. 2
Discrete model of an antiresonant vibratory conveyor shown in Fig. 2

Fig. 8.

Continuous spring model (flat spring during deformation)
Continuous spring model (flat spring during deformation)

Fig. 9.

Scheme of the elastic support system, (a) A – flat spring, B – distancing mass, C – mounting washers in the vice jaws, D – pressure plates, E – screws M5x40, F – nuts, G – washers; (b) the system attached to the foundation with a vice
Scheme of the elastic support system, (a) A – flat spring, B – distancing mass, C – mounting washers in the vice jaws, D – pressure plates, E – screws M5x40, F – nuts, G – washers; (b) the system attached to the foundation with a vice

Fig. 10.

Time course of vibration velocity (a), FFT analysis results (b)
Time course of vibration velocity (a), FFT analysis results (b)

Fig. 11.

An experimental determination of the transverse stiffness of flat springs: (a) view of the station, (b) force-displacement diagram for one of the spring
An experimental determination of the transverse stiffness of flat springs: (a) view of the station, (b) force-displacement diagram for one of the spring

Fig. 12.

Experimental determination of the stiffness of the entire system (a) before and after the load, (b) the relationship between the transverse force and the stiffness kf of the system
Experimental determination of the stiffness of the entire system (a) before and after the load, (b) the relationship between the transverse force and the stiffness kf of the system

Fig. 13.

Continuous model of the tested system showing the first natural frequency (a), discrete equivalent model of the tested system for the first natural frequency (b)
Continuous model of the tested system showing the first natural frequency (a), discrete equivalent model of the tested system for the first natural frequency (b)

Fig. 14.

The results of the modal analysis performed in the ANSYS environment - the first form of vibration from Fig. 8 and 9 - the simulation result is 97,74 Hz (Tab.4) for three finite element layers on flat springs
The results of the modal analysis performed in the ANSYS environment - the first form of vibration from Fig. 8 and 9 - the simulation result is 97,74 Hz (Tab.4) for three finite element layers on flat springs

Parameters of the dynamic model from Fig_ 2

ParameterValueUnit
M600kg
me450kg
K719.387N/m
ke4.963.770N/m
C142Ns/m
ce298Ns/m
P14.450N

Geometric and physical parameters of flat springs and other components of the test system (Fig_ 9) - mass values are given with an accuracy of 0_01 g

ParameterValueUnitMeaning
lc =0.1mtotal length of the spring
l =0.06mactive length of the spring
b =0.02mspring width
h =0.001mspring thickness
mr =0.00948kgmass of the active part of a single spring
mzr =0.00352kgreduced mass of a single spring (45)
md =0.09609kgvibrating mass B + D + E
mz =0.10314kgtotal weight reduced
EJs1 =348058Nmm2spring stiffness no. 1
EJs2 =346149Nmm2spring stiffness no. 2

Comparison of the frequency results of the first form of bending vibrations

A type of modal analysisf [Hz]ε[%] *
theoretical without taking into account the mass of flat springs100.8318.21
theoretical taking into account the mass of flat springs97.3314.10
numerical97.7414.58
experimental85.300

Parameters of the dynamic model from Fig_ 7

ParameterValueUnit
Mr1000kg
Mk2500kg
Jk12200kgm2
Jr5000kgm2
ky2328000N/m
kx1164000N/m
kf10962000N/m
by0 *Ns/m
bx0 *Ns/m
bf0 *Ns/m
L2m
Lr1.92m
H0.48m
hr1.1m
β30deg

The form of the vibration

f2 = 3.47 Hzf3 = 4.41 Hzf4 = 19.84 Hz
[ ABCD ]= [ 18.2212.518.801 ] · D [ −10.7545.26−11.101 ] · D [ −0.25−0.15−0.000141 ] · D

Parameters of modal analysis

Number of layers in thickness h123
Total number of nodes / number of nodes of one spring379514/15629397475/24586415436/33543
Average Skewness parameter0.247760.239400.23175
Average Orthogonal Quality0.870480.875670.88043
The 1st natural frequency98.01 Hz97.80 Hz97.74 Hz
DOI: https://doi.org/10.2478/ama-2025-0054 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
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Language: English
Page range: 460 - 470
Submitted on: Sep 7, 2024
Accepted on: Aug 13, 2025
Published on: Sep 30, 2025
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
dynamic damper,
characteristic frequencies,
self-synchronisation,
reduced mass,
flat spring
Related subjects:
Engineering,
Electrical engineering,
Electronics,
Mechanical engineering,
Mechanics,
Bioengineering and biomedical engineering,
Biomechanics,
Civil engineering,
Environmental engineering

© 2025 Jerzy MICHALCZYK, Marek GAJOWY, Krzysztof MICHALCZYK, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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