Flexible impulse response of the multi-bar linkage with heavy load
It is based on the advantages of virtual prototyping technology, the dynamics mathematic model was established for the large mechanism by applying multi body dynamics theory. In order to adapt the users to special request of the strip width size, appeared the continuous casting and continuous rollin...
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| Цитувати: | Flexible impulse response of the multi-bar linkage with heavy load / Feng Xianzhang, Cheng Junwei, Cui Yanmei, Jiang Zhiqiang // Functional Materials. — 2016. — Т. 23, № 4. — С. 636-643. — Бібліогр.: 20 назв. — англ. |
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Feng Xianzhang Cheng Junwei Cui Yanmei Jiang Zhiqiang 2017-06-14T14:21:02Z 2017-06-14T14:21:02Z 2016 Flexible impulse response of the multi-bar linkage with heavy load / Feng Xianzhang, Cheng Junwei, Cui Yanmei, Jiang Zhiqiang // Functional Materials. — 2016. — Т. 23, № 4. — С. 636-643. — Бібліогр.: 20 назв. — англ. 1027-5495 DOI: doi.org/10.15407/fm23.04.636 https://nasplib.isofts.kiev.ua/handle/123456789/121500 It is based on the advantages of virtual prototyping technology, the dynamics mathematic model was established for the large mechanism by applying multi body dynamics theory. In order to adapt the users to special request of the strip width size, appeared the continuous casting and continuous rolling technology, and greatly reduce the width types of continuous casting. The components of the equipments are often considered the rigid body. The precision is not high premise in the process of work, usually the parts works as elastic under the high speed and the heavy load, neglects various components the elastic function will cause the result error, even will be wrong. Studied analysis dynamic characteristic of the adjustment width machine, and analyzed the component in detail for the rigid body or the elastic. The results provide the theoretically support to work out adjustment the width potentialities and strength analysis of the key parts. en НТК «Інститут монокристалів» НАН України Functional Materials Modeling and simulation Flexible impulse response of the multi-bar linkage with heavy load Article published earlier |
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Flexible impulse response of the multi-bar linkage with heavy load |
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Flexible impulse response of the multi-bar linkage with heavy load Feng Xianzhang Cheng Junwei Cui Yanmei Jiang Zhiqiang Modeling and simulation |
| title_short |
Flexible impulse response of the multi-bar linkage with heavy load |
| title_full |
Flexible impulse response of the multi-bar linkage with heavy load |
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Flexible impulse response of the multi-bar linkage with heavy load |
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Flexible impulse response of the multi-bar linkage with heavy load |
| title_sort |
flexible impulse response of the multi-bar linkage with heavy load |
| author |
Feng Xianzhang Cheng Junwei Cui Yanmei Jiang Zhiqiang |
| author_facet |
Feng Xianzhang Cheng Junwei Cui Yanmei Jiang Zhiqiang |
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Modeling and simulation |
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Modeling and simulation |
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2016 |
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English |
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Functional Materials |
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НТК «Інститут монокристалів» НАН України |
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Article |
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It is based on the advantages of virtual prototyping technology, the dynamics mathematic model was established for the large mechanism by applying multi body dynamics theory. In order to adapt the users to special request of the strip width size, appeared the continuous casting and continuous rolling technology, and greatly reduce the width types of continuous casting. The components of the equipments are often considered the rigid body. The precision is not high premise in the process of work, usually the parts works as elastic under the high speed and the heavy load, neglects various components the elastic function will cause the result error, even will be wrong. Studied analysis dynamic characteristic of the adjustment width machine, and analyzed the component in detail for the rigid body or the elastic. The results provide the theoretically support to work out adjustment the width potentialities and strength analysis of the key parts.
|
| issn |
1027-5495 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/121500 |
| citation_txt |
Flexible impulse response of the multi-bar linkage with heavy load / Feng Xianzhang, Cheng Junwei, Cui Yanmei, Jiang Zhiqiang // Functional Materials. — 2016. — Т. 23, № 4. — С. 636-643. — Бібліогр.: 20 назв. — англ. |
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AT fengxianzhang flexibleimpulseresponseofthemultibarlinkagewithheavyload AT chengjunwei flexibleimpulseresponseofthemultibarlinkagewithheavyload AT cuiyanmei flexibleimpulseresponseofthemultibarlinkagewithheavyload AT jiangzhiqiang flexibleimpulseresponseofthemultibarlinkagewithheavyload |
| first_indexed |
2025-11-26T01:39:31Z |
| last_indexed |
2025-11-26T01:39:31Z |
| _version_ |
1850603186154373120 |
| fulltext |
636 Functional materials, 23, 4, 2016
ISSN 1027-5495. Functional Materials, 23, No.4 (2016), p. 636-643
doi:https://doi.org/10.15407/fm23.04.636 © 2016 — STC “Institute for Single Crystals”
Flexible impulse response of the multi-bar
linkage with heavy load
Feng Xianzhang, Cheng Junwei, Cui Yanmei, Jiang Zhiqiang
School of Mechanical Engineering, Zhengzhou Institute of Aeronautical
Industry Management, Zhengzhou, Henan, 450015, P.R. China
Received Jily 15, 2014
It is based on the advantages of virtual prototyping technology, the dynamics mathematic
model was established for the large mechanism by applying multi body dynamics theory. In or-
der to adapt the users to special request of the strip width size, appeared the continuous casting
and continuous rolling technology, and greatly reduce the width types of continuous casting. The
components of the equipments are often considered the rigid body. The precision is not high prem-
ise in the process of work, usually the parts works as elastic under the high speed and the heavy
load, neglects various components the elastic function will cause the result error, even will be
wrong. Studied analysis dynamic characteristic of the adjustment width machine, and analyzed
the component in detail for the rigid body or the elastic. The results provide the theoretically
support to work out adjustment the width potentialities and strength analysis of the key parts.
Keywords: Rigid-elastic, dynamic system, key parts, large mechanism, heavy load.
Разработана динамическая математическая модель для больших механизмов, базируясь на
технологии виртуального макетирования, путем применения многочастичной динамической
теории. Для адаптации к специальным требованиям по ширине полос выработаны технологии
непрерывного литья и непрерывной прокатки, существенно ограничивая требования по
ширине процесса литья. Компоненты оборудования часто рассматриваются как твердые тела.
Точность невелика, т.к. в процессе работы детали часто проявляют эластичность при высокой
скорости или большой нагрузке, и пренебрежение этим фактором приведет к ошибочным или
даже полностью неправильным результатам. Исследованы динамические характеристики
согласования с деталями механизма и проведен анализ компонентов на предмет их твердости
или эластичности. Результаты дают теоретическое обоснование для возможности регулировки
по ширине и анализа механической прочности основных деталей.
Гнучкий імпульсний відгук многостержневих з’єднань при великих
навантаженнях. Фен Сяньчжан, Цуй Яньмей, Чен Цзюньвей, Цзян Чжицзян.
Розроблено динамічну математична модель для великих механізмів, базуючись на
технології віртуального макетування, шляхом застосування Багаточасткові динамічної
теорії. Для адаптації до спеціальним вимогам по ширині смуг вироблені технології
безперервного лиття і безперервної прокатки, істотно обмежуючи вимоги по ширині процесу
лиття. Компоненти обладнання часто розглядаються як тверді тіла. Точність невелика,
тому що в процесі роботи деталі часто виявляють еластичність при високій швидкості або
великому навантаженні, і нехтування цим фактором призведе до помилкових або навіть
повністю неправильних результатів. Досліджено динамічні характеристики узгодження з
деталями механізму і проведено аналіз компонентів на предмет їх твердості або еластичності.
Результати дають теоретичне обгрунтування для можливості регулювання по ширині і
аналізу механічної міцності основних деталей.
Functional materials, 23, 4, 2016 637
Feng Xianzhang et al. / Flexible impulse response of the multi-bar ...
1. Introduction
Steel industry is closely related to the na-
tional economy, the quality of steel products
has direct influence on household appliances,
automobiles, electronics, construction, and
shipbuilding, aerospace and so on. Today, qual-
ity steel sheet and strip become an important
symbol to measure the level of Iron and steel
industry for a country. [1-5]
In recent years, in order to adapt the fierce
competition, reducing energy consumption, im-
proving product quality and productivity, and
user's specific requirements of width of the
strip, the producers need more different kinds
of slab. To realize the convergence between
continuous casting and continuous rolling, the
technology of slab side pressing is an online
regulation width can meet these requirements,
and can effectively reduce the specification and
specs of continuous casting slab. Moreover,
make further improvement the level of integra-
tion for in casting and rolling. [6-10]
It is closely related between the slab casting
and rolling process and width adjustment. The
ability of vertical rollers is limited, in which lie
in front of the vertical roller mill decaling ma-
chine and Roughing mill, cannot undertake the
task of large lateral pressure-width-modulated.
It is an important skill to apply the synchronous
production control system between the continu-
ous casting and continuous rolling. [11, 12]
There are two types forms in the world: star-
ing and stopping, flying. For the type of staring
and stooping, the principle of lateral pressure
is shown in Figure 1.
2. Dynamics analysiss
2.1 Many-body dynamics analysis
There is physical contact between die and
workpiece during the working of width mechan-
ical press. Lateral linkage and the main eccen-
tric rod work under the majority load, in which
is from rolling force by the transmission line
from die to main eccentric axis of side pressing
machinery. It’s paramount importance to ana-
lyze stress and strain of major components.
At the same time, it’s significant to study
more accurate equations of die, normal opera-
tion and function of equipment.
Multi body system is consists of some flex-
ible bodies and rigid bodies, and interconnected
among these. Rigid multi-body system dynam-
ics is the study of is a discipline about the move-
ment of multiple body systems, and developed
on the basis of classical mechanics, involving
kinematics and biomechanics, space control,
robot dynamics, vehicle design, mechanical dy-
namics, etc.
2.2 Problems analysis
It can be divided into two different kinds of
problems by the task of research dynamics:
Inverse dynamics analysis:
Known the movement status and working
resistance, and to solve the variation ruler of
reaction force and the input torque in these ki-
nematic pairs.
The normal dynamics analysis:
Known the variation ruler of reaction force
and the input torque in these kinematic pairs,
and to solve the really the movement of the mo-
tion mechanism.
Also there are many types of body dynamics
analysis, such as static analysis, dynamic stat-
ic analysis, dynamic analysis, elastic dynamic
analysis, etc.
Static analysis:
Without consideration of influence of iner-
tial force for the mechanical device with slow
motion. By static method, it can obtain the load
balancing, where located at different position of
mechanical movement, then applied to the in-
put force or torque for drive component, as well
as reaction force in the motion pairs. This is the
method of force analysis in earliest history.
Kinetics static analysis:
Consideration of influence of inertial force
for the mechanical device with raise of speed.
It can obtain the balancing static load and dy-
namic load, where located at different position
of mechanical movement. Using Alembert prin-
ciple, the balance equation included static iner-
tia forces, and then applied to the input force or
torque for drive component, as well as reaction
force in the motion pairs. This is the method of
f kinetics static analysis in history.
Dynamic analysis
Fig. 1. Schematic go and stop
638 Functional materials, 23, 4, 2016
Feng Xianzhang et al. / Flexible impulse response of the multi-bar ...
For the idealized assumptions, although
this assumption is allowed in many cases, but
the machinery equipment can not maintain
constant speed of the drive components under
the load.
However, many engineering problems are
also often required to know the real movement
of the mechanical system in practical.
Consideration of influence of mechanical ex-
ternal force, solving real motion by the method
of the so-called dynamic analysis.
Abandoned ideal assumptions of the ruler of
movement of drive components, the mechanical
systems should be included Part of the original
motivation
Therefore, the entire object for dynamic
analysis is the whole mechanical systems. The
mathematical model solve linear algebraic
equations for the static analysis and kinetic
static analysis, however, the mathematical
model solve Differential equations for the dy-
namic analysis.
Kinetic elastic dynamics:
The components are assumed to be rigid for
the above three methods. But the real mechani-
cal components is a flexible body in the many
case,
The size of the elastic deformation is respon-
sible for its force, shape, stiffness and so on.
The natural frequency increases with increase
the flexibility of mechanical systems.
When the excitation frequency is close to the
natural frequency, it can occur a strong vibra-
tion to damage the movement accuracy of me-
chanical, also affect the fatigue strength, and
increase the friction in the motion pairs.
In the case, as a rigid body the analysis of
the component can not meet the requirements.
Therefore, there is an analytical method of ki-
netic elastic dynamics, considered the driving
force for the elastic component [17-20].
3. Motion analysis
The research of the transmission system is
shown in Figure 2.
The Figure 2 shows that have a main motor
for the main transmission system make the di-
rection of transmitted to change 0 5. π , after
two conical helical gear systems. By decelerate
device of cylindrical helical gear, pass move-
ment of the main motor drive system to verti-
cal shaft of side pressing mechanism, at last,
the dies can move along lateral direction, in
which lie in the front of lateral framework.
In order to analyze to sectional character-
istic and the quality of all the components for
entity model of the adjust machine, and acquire
the quality and its mechanics characteristic for
the synchronous mechanism and side pressing
mechanism, it can supply the useful informa-
tion to dynamics analytical.
For the stress of joints in the pressing mech-
anism, consider the symmetry of the mecha-
nism, taking one part of the mechanism as the
research object. In the process of adjust width,
the movement diagram of mechanism is shown
in Figure 2.
The Figure 3 shows that the mechanism in-
cludes lateral machine, synchronous machine
and width machine. Lateral machine is com-
pose by two pieces with crank slide block. Com-
pleting the side pressing is important function
for the slab.
synchronous machine is constitute by syn-
chronous electric motor, increase machine, two
eccentricity shifts and synchronous frame, it
supply the movement weight of the die to en-
sure the slab velocity to close the dies along
the direction of rolling line.
The width machine can adjust the distance
of the both dies, by screw turns to push side
presses a frame go forward or retreat, base on
the two sets adjust the breadth electrical engi-
neering, the umbrella wheel gear box, machine
device of worm pole and worm wheel with nut.
Fig. 2.Transmission system
Fig. 3.Force model of liner
Functional materials, 23, 4, 2016 639
Feng Xianzhang et al. / Flexible impulse response of the multi-bar ...
4. System equation
4.1 Kinematics analysis
Basis the related knowledge of the theories
and kinetics of element finite and kinematics,
a point in the elastic body, the elastic displace-
ment and rigid displacement can describe as
following:
δ δ
δ δ
{ } = éë ùû { }
{ } = éë ùû { }
ì
í
ïïï
î
ïïï
N
N
e
r r r
e
(1)
Where δ{ } , δr{ } are the elastic displacement
and rigid displacement for a point in the elastic
body. Néë ùû , Nr
éë ùû are the shape function matrix
elastic body and rigid body, no relation with
time. δ e{ } , δr
e{ } are the elastic displacement
and rigid displacement for a node in the ele-
ment.
Base on the formula (1), a point in the ele-
ment body, the deform velocity δ{ } and accel-
eration δ{ } can express as:
δ δ
δ δ
{ } = éë ùû { }
{ } = éë ùû { }
ì
í
ïïï
î
ïïï
N
N
e
e
(2)
Where δ{ } , δ{ } are the velocity and accel-
eration of a point in the element body. δ e{ } ,
δ e{ } are the velocity and acceleration of a node
in the element body.
Base on the formula (1), a point in the rigid
body, the deform velocity δr{ } and accelera-
tion δr{ } can express as:
δ δ
δ δ
r r r
e
r r r
e
N
N
{ } = éë ùû { }
{ } = éë ùû { }
ì
í
ïïï
î
ïïï
(3)
Where δr{ } , δr{ } are the velocity and accelera-
tion of a point in the rigid body. δr
e{ } , δr
e{ }
are the velocity and acceleration of a node in
the rigid body.
In the analysis for flexible body dynamic,
displacement, velocity and acceleration of a
point in element can express as:
δ δ δ
δ δ δ
δ δ δ
a r
a r
a r
{ } = { }+ { }
{ } = { }+{ }
{ } = { }+{ }
ì
í
ïïïïïï
î
ï
ïïïïïï
(4)
Where δa{ } , δa{ } is absolute velocity and abso-
lute acceleration of a point in element.
It can solve the kinematics questions under
appropriate displacement functions of rigid and
elastic bodies for the elastic kinematics analy-
sis.
2.2 Flexible dynamics equations
In order to build the equations of flexible
dynamics, at first, it should obtain the quality
matrix, the damping matrix and the stiffness
matrix of the element.
Quality matrix of the element:
Taking a decline cell from the element j,
and then quality matrix of the element j can
express as:
M N N dv
e Téë ùû = éë ùû éë ùûòòòρ (5)
Damping matrix of the element:
Taking a decline cell from the movement el-
ement in component, and then damping matrix
of the element Céë ùû
e can express as:
C C C M K
e
m k
e eéë ùû = éë ùû + éë ùû = éë ùû + éë ùûα β (6)
Stiffness matrix of the element:
Based on the theory of finite element, and
then arbitrariness stiffness matrix of the ele-
ment K
eéë ùû can express as:
K B D BdV
e Téë ùû = éë ùû éë ùû éë ùûòòò (7)
Where K
eéë ùû is stiffness matrix of the element,
Béë ùû is geometry matrix.
The finished flexible dynamics equations:
It can express as:
M U C U K U
F t M Ur
éë ùû { }+ éë ùû { }+ éë ùû { } =
= ( ){ }- éë ùû { }
(8)
Where Méë ùû is total quality matrix, it can de-
scribe as following:
M Me
éë ùû = éë ùûå
640 Functional materials, 23, 4, 2016
Feng Xianzhang et al. / Flexible impulse response of the multi-bar ...
Céë ùû is total quality matrix, it can describe as
following:
C Ce
éë ùû = éë ùûå
Kéë ùû is total Stiffness matrix, it can describe as
following:
K Ke
éë ùû = éë ùûå
It can obtain the result of and the equa-
tion to analyze the formula (8), the formula is
non-linearity differential equation of two steps,
there are many methods to solve the type equa-
tion groups, including numerical method,
such as direct integral calculus method, ad-
dition vibration type, Fourier series method,
and status space, the method of direct integral
calculus mainly based on the point of view of
mathematics, using the approach approximate
method of stepwise integral for the non-linear-
ity differential equation of two steps. It com-
mon uses the A Runge-Kutta method, Wilson
method, Newmark method, etc. There have al-
ready develop more mature, and already had
the business standard procedure can directly
transfer to use.
Fig. 4.Force of joint A
Fig. 5. Force of joint B
Fig. 6.Force of joint C
Functional materials, 23, 4, 2016 641
Feng Xianzhang et al. / Flexible impulse response of the multi-bar ...
5. Conclusions
5.1 Synchronous mechanism
In process of working for the side pressing
machine, the stress of joint A is shown in Fig-
ure 4.
From Figure 4, the x direction is the direc-
tion of the rolling line, the x direction is the di-
rection of gravity. The force is greater than the
other direction in the direction of the rolling
line, with the existence of differences between
the synchronization mechanism and lateral
mechanism.
In process of working for the side press-
ing machine, the stress of joint B is shown in
Figure 5.
From Figure 5, the motion pair B is similar
situation with the motion pair A, they should
meet the same law.
In process of working for the side press-
ing machine, the stress of joint C is shown in
Figure 6.
From Figure 6, the motion pair C is similar
situation with the motion pair A and B, they
should meet the same law.
In process of working for the side press-
ing machine, the stress of joint D is shown in
Figure 7.
From Figure 7, the motion pair D is similar
situation with the motion pair A, B and C, they
should meet the same law.
From Figure 4 to Figure 7, in process of side
pressing for the slab, considering the effective of
elastic of the lateral connecting rod, it’s value is
smaller than the simulation result of dynamics
model with clearance, because of flexible factor
of connecting rod, the clearance in the joints to
occur impact, the connecting rod as the elastic
body can absorb one part of energy, prolong the
contact time into all the joints, ultimate mak-
ing the trend to weaken for the stress in all the
joints.
Connecting rod as rigid body, it can be-
come greater or larger to the stress of in all the
joints, because of existent clearance in joints,
in which lead to immensity instant impact, for
the reasons that the connect rod can't absorb
immensity instant impact energy as the rigid
body during occurring the impact in the clear-
ance in the joints. Thereby, it can make the
stress enlarge in each joint.
5.2 Lateral machine mechanism
In process of working for the lateral machine,
the stress of joint M is shown in Figure 8.
From Figure 8, the x direction is the direc-
tion of the rolling line, the Y direction is the di-
rection of rolling force. The lateral mechanism
Fig. 7.Force of joint D
Fig. 8.Force of joint M
642 Functional materials, 23, 4, 2016
Feng Xianzhang et al. / Flexible impulse response of the multi-bar ...
is mainly responsible for the rolling force dur-
ing side pressing.
From Figure 9, the motion pair M is similar
situation with the motion pair N, they should
meet the same law.
In process of working for the lateral ma-
chine, the stress of joint P is shown in Figure
10.
From Figure 10, the motion pair P is similar
situation with the motion pair N and M, they
should meet the same law.
From Figure 8 to Figure 10, in turn angle
range of main crank from 300° to 360°, the con-
necting rod as rigid body, the stress of joint M,
N and P for rigid component is larger than the
result for the elastic body. When the angle of
main crank reach the 300°, whether the side
connecting rod is rigid or not, the stress fluctu-
ate increase in the join. It is the reason of the
beginning of the side pressing stage, the impact
effect of the rolling force and short action time
for dies, it is non-steady-state process, and the
elastic deformation had fluctuated in joint of
contact area. With the further side pressing of
continuous casting slab, according to the given
path on the slab for width adjustment, the elas-
tic deformation change smoothly had fluctuated
in joint of contact area.
Acknowledgements
This work is supported by the Plan For Sci-
entific Innovation Talent of Henan Province
(2017JQ0006), Science and Technique Founda-
tion of Office of Education of Henan Province
(14A460014),“HASTIT” (2012HASTIT023) and
“IRTSTH”(14IRTSTHN003).
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