where
k
u
u
V
k
n
N
n
N
n
N
−
−
=
, (14)
The parameter k allows us to find the "average" velocity with the working
medium of shank end during a period of time
.
On each temporary layer
1
+
n
t
, the equation system (12) - (14) is solved by the
sweep method. Let us consider the basic formulas of the sweep method for finding
boundary values. From the equation system
0
1
0
0
+
=u
u
,
,
we receive
1
0
=
,
0
0
=
.
We consider the equation system for calculation
1
+
n
N
u
(
)
ES
u
u
u
hR
ES
hC
u
u
n
N
n
N
n
N
n
N
n
N
1
0
1
1
1
,
1
−
+
+
−
−
+
+
=
,
1
1
1
1
1
−
+
−
+
−
+
=
N
n
N
N
n
N
u
u
.
From this system we find
(
)
1
1
0
1
1
1
1
,
−
−
−
−
+
−
+
−
−
=
N
n
N
n
N
n
N
N
n
N
ES
hC
ES
u
u
u
hR
u
.
The functional program scheme in the Mathcad system [5;14] is shown in Fig. 6
Figure6. The functional diagram of the program. The application of the main
function blocks: 1) DN (N, T, M, F, f) – control area; 2) trdag1 (a, b, c, f, N, Z0, Z1,
Z2) – realizes the sweep method; 3) R (U, V) is the power characteristic; 4) f (x) and
5) F (x) are the corresponding distributions of the initial displacement and the speed
of the shank sections; 6), 7), 8) – realize the Fourier method for the linear problem; 9)
the determination of the maximum deviation of the contact shank end in the first
iterative loop
k
t=
1
0
u
u=
- 1568 -