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This
paper is devoted to the consideration of the lifting
machine with pulley friction in terms of investigation
of dynamic loads encountered in her work.
One
of the varieties of multiple-rope hoist is an elevator, in which the
goods or people are transported from one level to
another in a closed cabin, moving in vertical guides,
set out in a closed mine at full height with lockable
doors for loading and unloading at client sites .
The
high degree of security multiple-rope hoist confirmed
the broadest practice operation of freight and passenger
elevators in tall buildings. Typically elevator
installation uses a 4 head rope. Also widely used
multiple-rope hoist can be found in the industry.
Calculation of head pipe installations such as the rule
is a static method, the rope is calculated on the
strength of a homogeneous rod is exposed only to its own
weight and the weight of the load. To take into account
other efforts, in addition to static, taking excessive
margins, which should cover all the efforts resulting in
the ropes when climbing / omitting the goods.
Problems of study of the elevator are in this area for
many years since the invention of EG Otis elevator in a
safe 1852g [9]. Currently, he founded the company serves
more than 1.9 million elevators around the world,
demonstrating the crucial role of the elevators in the
modern economy. Among the local professionals involved
in the study of the dynamics of the elevators, you can
list the following: Korneyev GK [4], Chutchikov PI [7],
short, MG [4]. The study of dynamics of hoisting
machines with friction pulley, which is very similar to
elevators in their construction, was professor, DPhil
Dvornikov VI [5].
Speaking of the Ukrainian industry are the work of the
plant Otis in Kiev, issued in 2005, 3000 and lift,
which demonstrates the high demand for elevator
equipment in the domestic market.
In
most cases, the calculation of edge lifting machine is a
static method, the rope is calculated on the strength of
a homogeneous rod is exposed only to its own weight and
the weight of the load. To take into account other
efforts, in addition to static, taking excessive margins,
which should cover all the efforts resulting in the
ropes when climbing / omitting the goods. This margin is
often substantially higher than the required strength of
the rope to ensure its normal operation, resulting in an
increase in diameter of rope, and, consequently, to
increase the remaining nodes lifting machine, for
example, rope-driving pulley. This raises the need
to use heavy-duty than is actually needed.
Faithful to the calculation of the lifting machine ropes,
covering the largest possible number of factors
affecting the effort in the branches of cables is
important, both to ensure the safety car, and in
optimizing the use of resources in its construction.
Construction of mathematical models of the multiple-rope
hoist with pulleys friction will
continue to study further the work of the individual
nodes to select their optimal performance. Which in turn
will improve the safety of the lift installation, and
this is particularly important when considering the
passenger elevators (the primary characteristic of a
passenger elevator), to optimize speed elevators, as
well as to examine the wear of equipment from the
dynamic effort to further eliminate the existing
problems.
From
this we can say that a detailed study of the dynamics of
the elevator will provide the necessary data to improve
performance throughout the installation.
Based
on the above described should be the topic of this work
is relevant.
The
aim of this work is to develop a mathematical model of
the dynamics of the elevator.
To
achieve this goal the following main tasks:
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To investigate the mutual movement of the
installation with the recovery of the goods.
-
To analyze the pattern of substitution with the
subsequent installation of finding the equations of
motion.
-
Develop a methodology for determining the numerical
values of natural frequencies of oscillations
-
Give the equation of displacement, velocity and mass
installation of the type of elementary formulas
-
Write an expression to determine the magnitude of
dynamic loads that arise in the elastic connections
- line.
-
Develop a program that simulates the dynamic
processes in the system of lift installations, on
the basis of the formulas in MS Excel environment to
the programming language VBA.
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2.
Development of
the mathematical model of the lifting machine |
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In
terms of mine lifting cargo at some height is often a
special plant, called a lifting machine with
rope-driving pulley friction, in which the
pulling force is created due to the forces of friction
between rope and pulley lining rope-driving (drum).
Scheme of multiple-rope hoist is
depicted in Figure 2.1 b.
One
feature of this installation is the special equipment
balance rope which is suspended from the bottom to lift
vessels with masses m1 and m2 to compensate for the
difference between the weights of the vertical
head-ropes [l1, l2] and [l3, l4].
A
similar kinematical pattern, but with no counterbalance
the rope has a passenger and freight elevators are
widely used in industrial and civil construction (Figure
2.1. A). In this case, performing the role of vascular
cage and contrast. |
