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Contact Impact Forces at Discontinuous 2-DOF Vibroimpact

V.A. Bazhenov
V.A. Bazhenov
, 
O.S. Pogorelova
O.S. Pogorelova
 und 
T.G. Postnikova
T.G. Postnikova
   | 14. März 2016
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Online veröffentlicht: 14. März 2016
Seitenbereich: 183 - 196
Eingereicht: 03. Dez. 2015
Akzeptiert: 10. März 2016
DOI: https://doi.org/10.21042/AMNS.2016.1.00014
Schlüsselwörter
© 2016 V.A. Bazhenov, O.S. Pogorelova, T.G. Postnikova, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Vibroimpact system model
Vibroimpact system model

Fig. 2

Global and partial views of contact force depending on exitation amplitude (ω=7.23 rad·s-1 )
Global and partial views of contact force depending on exitation amplitude (ω=7.23 rad·s-1 )

Fig. 3

Contact forces, external load, and phase portraits for: (a) (5,2)-regime; (b) quasiperiodic; (c) (1,1)-regime; (d) (2,3)-regime (ω=7.23 rad·s-1 )
Contact forces, external load, and phase portraits for: (a) (5,2)-regime; (b) quasiperiodic; (c) (1,1)-regime; (d) (2,3)-regime (ω=7.23 rad·s-1 )

Fig. 4

Contact forces during impact for quasiperiodic regime (ω=7.23 rad·s-1 )
Contact forces during impact for quasiperiodic regime (ω=7.23 rad·s-1 )

Fig. 5

Floquet multipliers jump (ω=7.23 rad·s-1 )
Floquet multipliers jump (ω=7.23 rad·s-1 )

Fig. 6

Global view of contact force depending on exitation frequency (P=500 N)
Global view of contact force depending on exitation frequency (P=500 N)

Fig. 7

Contact forces during impact at (1,1)-regime for different stiffness k2 (P=500 N, ω=7.23 rad·s-1 )
Contact forces during impact at (1,1)-regime for different stiffness k2 (P=500 N, ω=7.23 rad·s-1 )

Fig. 8

Contact forces and phase portrait for chatter (P=500 N, ω=7.23 rad·s-1 )
Contact forces and phase portrait for chatter (P=500 N, ω=7.23 rad·s-1 )

Fig. 9

"Stick" & "bell" for rigid and soft impacts (P=500 N, ω=7.0 rad·s-1 )
"Stick" & "bell" for rigid and soft impacts (P=500 N, ω=7.0 rad·s-1 )

Fig. 10

Global and partial views of contact force depending on exitation amplitude for soft impact (ω=7.23 rad·s-1 )
Global and partial views of contact force depending on exitation amplitude for soft impact (ω=7.23 rad·s-1 )

Fig. 11

Global and partial views of contact force depending on exitation frequency for soft impact (P=500 N)
Global and partial views of contact force depending on exitation frequency for soft impact (P=500 N)

j.AMNS.2016.1.00014.tab.001.w2aab3b7e1030b1b6b1ab1b2b4b9aAa

PRe(μ1)Im(μ1)|μ1|Re(μ2)Im(μ2)|μ1|
98.48-0.250.830.87-0.250.830.87
98.98-0.250.830.87-0.250.830.87
99.483.5703.571.1201.12

j.AMNS.2016.1.00014.tab.005.w2aab3b7e1030b1b6b1ab1b2b6c10aAa

R1=R2, mA=B, m-1Fcon,N·105
111.49
20.51.71
50.22.05
100.12.36

Parameters of vibroimpact system

Bodies’ characteristicRigid impactSoft impact
Main bodyAttached bodyMain bodyAttached body
Mass mi, kg10001001000310
Partial vibration frequency ωi,rad·s-16.2835.6466.2833.606
Young’s modulus Ei, N·m-22.1 · 10112.1 · 10112.44 · 1052.1 · 1011
Contact surface radius Ri, m2210.5
Coefficients A,B, m-1A = 0.5 B = 0.5A = 1.5 B = 1.5
Poisson’s ratio vi0.30.30.30.3
Damper coefficient ξi0.0360.0360.0360.036
Initial distance between bodies D, m0.050.05
Impact duration Tcon, s7.82 · 10-40.19
Coefficient of impact duration kcon, %0.0920.9

j.AMNS.2016.1.00014.tab.003.w2aab3b7e1030b1b6b1ab1b2b5b5aAa

ωi, rads.s-18.038.048.058.068.078.108.16
Re(μ1)-0.595-0.593151.490.165.937.419.7
IM(μ1)0.6540.65200000
|μ1|0.88280.8829151.490.165.937.419.7

j.AMNS.2016.1.00014.tab.002.w2aab3b7e1030b1b6b1ab1b2b4c12aAa

PRe(μ1)Im(μ1)|μ1|Re(μ2)Im(μ2)|μ1|
392.50.1970.9770.9970.197-0.9770.997
392.00.1970.9811.0010.197-0.9811.001
391.00.1970.9831.0030.197-0.9831.003

j.AMNS.2016.1.00014.tab.004.w2aab3b7e1030b1b6b1ab1b2b6b7aAa

MaterialSteelCopperAluminiumRubber
Young’s modulus, N m-22.101.110.690.00008
Maximum Fcon,N·1051.711.331.100.0309
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