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Сборник докладов международной научно техической конференции 21

y
x



, we get 
 
 











,
0
sign
)
(
)
(
;
sin
sign
3
2
3
2
2
1
1
1
y
M
M
y
y
j
t
kU
x
M
x
x
j
m






(8) 
At separate time intervals of one oscillation period, the movement of the driving and 
driven shafts of an electromechanical drive is described by linear differential equations, 
which can be reduced to the standard form: 

















;
;
sin
;
sin
3
2
3
1
2
2
3
2
1
1
1
m
m
y
y
T
m
t
U
k
x
x
T
m
m
m
t
U
k
x
x
T
m
m





(9) 
where 
T
1
– time constant of the device when engaging the drive and driven shafts, 
T
2
– 
time constant of the drive shaft when there is no clutch with the driven shaft, 
T
3
– time 
constant of the driven shaft when there is no clutch with the drive shaft, 
k
1
– transmission 
ratio of the drive control voltage to the speed of rotation of the driven shaft when 
engaging it with the drive shaft, 
k
2
– transmission ratio of the drive control voltage to the 
rotation speed of the drive shaft in the absence of clutch with the driven shaft, 
m
1

m
2
 
and 
m
3
– constant values characterizing the influence of dry friction moments, respectively 
M
1

M
2
and 
M
3

The constant coefficients of equations (9) are related to the coefficients of 
equations (7) and (8) by the following relations: 
.
;
;
;
;
;
;
;
3
3
3
2
2
2
1
1
1
1
2
3
2
1
1
3
2
2
3
1
1
2
3
2
1
2
1
1













M
m
M
m
M
m
k
k
k
k
j
T
j
T
j
j
T
















МЕЖДУНАРОДНАЯ НАУЧНО-ТЕХНИЧЕСКАЯ КОНФЕРЕНЦИЯ 
АКТУАЛЬНЫЕ ПРОБЛЕМЫ ЦИФРОВИЗАЦИИ ЭЛЕКТРОМЕХАНИЧЕСКИХ И
ЭЛЕКТРОТЕХНОЛОГИЧЕСКИХ СИСТЕМ
153
In the most general case, for forced oscillations of the considered drive at one oscillation 
period, five phase angles are characteristic, which determine the limits of validity of 
individual linear equations (9): 
1
1
t



– corresponds to the moment of time 
t
1
of disengagement of the driven and 
driving shafts; 
2
2
t



– corresponds to the time 
t
2
when the speed of the drive shaft becomes zero; 
3
3
t



– corresponds to the moment in time 
t
3
, when the driving or driven shaft begins 
to move after stopping; 
4
4
t



– corresponds to 
t
4
– stop of the driven shaft; 
5
5
t



– corresponds to 
t
5
– backlash selection time. 
To implement each of the above nonlinear characteristics on a computer, it is necessary to 
have a number of software modules. 
With high demands on the quality indicators of modern controlled EMS, it is necessary to 
take into account the effects associated with such nonlinearities as backlash, friction, 
saturation and dead zone. Having analyzed many nonlinearities, we can conclude that 
some of them can be considered as special cases of others. This makes it possible to 
reproduce several nonlinearities with one software module. With this simplification, some 
parameters used to specify one nonlinearity may be zero for another. When creating a 
basic set of nonlinear blocks, it is necessary to proceed from both the requirements for 
universality and the feasibility of reducing the number of blocks, and the requirements for 
their speed. 
In the case of implementing complex nonlinear characteristics that are difficult to 
describe analytically, there is a need to develop a universal module where they would be 
specified in a table. The use of such a module can be effective in cases where nonlinear 
elements are specified using experimental data. However, this representation requires 
large amounts of RAM, which in some cases can lead to limitations in the implementation 
of models that include a large number of complex nonlinear dependencies. 
Thus, for the effective use of modeling software, it is necessary to create a set of 
software modules for typical nonlinearities that would provide the most complete 
coverage of all kinds of frequently encountered nonlinear characteristics for the class of 
controlled EMS. 

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