the oscillation equation of a uniform cross section rod is investigated by the finite-
difference method. The solution of the linear initial-boundary value problem by the
Fourier method is used for the choice of rational parameters of the three-layer
difference scheme. High-frequency small-amplitude oscillations of the contact shank
end cause the changing of the design speed, which leads to a large error in determining
the resistance force. The average velocity is used to determine the motion direction of
the contact shank end.
Discrete model. The computational scheme of a dynamical system as a single-
mass model with mass m, dissipation coefficient B, elastic stiffness
3
c
and stiffness
іg
c
realized by engineering hysteresis, and its asymmetric power characteristic are shown
in Fig. 1.
Figure 1. а) The computational scheme of a dynamic system:
65
=
m
kg,
396
,
4
0
=
V
m/s; b) asymmetric power characteristic with sections on condition: 1 –
V>0; 2 – V <0; 3 – x <0,
789900
1
=
c
N/m,
87000
2
=
c
N/m,
60000
3
=
c
N/m
The initial-value problem was considered as:
0
,
2
2
=
+
dt
dx
x
R
dt
x
d
m
,
()
0
0=
x
,
()
0
0
V
dt
dx
=
. (1)
The power characteristic, which takes into account the stiffness c
3
:
3
'
1
1
c
c
c
+
=
,
3
'
2
2
c
c
c
+
=
, where
'
1
c
and
'
2
c
– stiffness of the element
іг
с
(fig.1а).
The power characteristic is given by formula
=
.
0
,
,
0
,
0
,
,
0
,
0
,
,
3
2
1
x
if
x
c
dt
dx
L
x
if
x
c
dt
dx
L
x
if
x
c
dt
dx
x
R
(2)
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