機械設計外文翻譯-礦井提升機和數(shù)值的摩擦熱分析模擬墊片的溫度場【中文4130字】【PDF+中文WORD】
機械設計外文翻譯-礦井提升機和數(shù)值的摩擦熱分析模擬墊片的溫度場【中文4130字】【PDF+中文WORD】,中文4130字,PDF+中文WORD,機械設計,外文,翻譯,礦井,提升,數(shù)值,摩擦,分析,模擬,墊片,溫度場,中文,4130,PDF,WORD
Mining Science and Technology 19 (2009) 0040–0044
MINING SCIENCE AND TECHNOLOGY
www.elsevier.com/locate/jcumt
Frictional heat analysis of mine hoist and numerical simulation on temperature field of gasket
HAN Dong-tai, GE Shi-rong, DU Xue-ping
School of Mechanical and Electrical Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China
Abstract: The frictional performance of gaskets is greatly affected by frictional heat in operational mine hoists. Based on frictional mechanism and heat transfer theory, the mathematical model of the temperature field of the PVC gasket in an operational mine hoist was investigated, a numerical simulation using ANSYS is presented and the distribution of the temperature and heat flux were studied under basic assumptions. The results show that the temperature gradually decreases as the radius of the model increases and the isotherms are arcs of concentric semi-circle. The heat flux is of bilateral symmetry in the model and decreases radially. The theoretical values correspond with the measured values for a short time (τ 三 100 s) when the steel wire rope slides.
Keywords: mine hoist; frictional heat; gasket; numerical simulation; temperature field
1 Introduction
These days, gaskets of mine hoists are mainly made of PVC plastic and PU polyurethane which have polymer properties. The thermal conductivity of PVC plastic and PU polyurethane is relatively small, thus the rise of the temperature of the material, caused by frictional heat while sliding, will lead to a change in the phase state and in structure. Previous experiments proved that frictional heat is one of the most important factors affecting the frictional per- formance of the gasket. This is largely indicated by the friction coefficient, which decreases with an in-
crease in temperature of the polymer gasket[1]. Poly- mers are sensitive to heat, which can change the fric-
tional condition of its surface, aggravates abrasion and results in the demineralization or abscission of the surface layer[2]. Therefore, frictional heat and its
effects should be considered in investigating the fric- tional mechanism between the steel rope and the gasket. The primary step is to know about the distri- bution and variation of the temperature field of the gasket during the friction process, in order to obtain an insight of the various factors affecting frictional heat.
2 Mechanism of sliding frictional heat
2.1 Sliding modes
In general, both absolute and relative slides exist
for certain reasons while the mine hoist is in opera- tion[3].
The absolute slide (pure slide) takes place under two conditions: the first one is that the steel wire rope rests as the friction wheel is rotating, just at the point where it cannot lift the weight while hoisting; the other is that the steel wire rope slides on the frictional gasket, similar to that in the case of emergency brak- ing.
The relative slide is caused by the difference of the absolute velocities of the friction pairs while working and usually also takes place under two conditions: the first one is that the speed of the steel wire rope is lar- ger than that of the friction wheel, which is equivalent to the sliding as the hoist unloads its weight and slows down; the other condition is that the speed of the fiction wheel is larger than that of the steel wire rope, which is equivalent to sliding when the hoist operates under overload.
2.2 Mechanism of frictional heat generation be- tween steel wire rope and gasket
Frictional heat is the main effect of friction during sliding. The heat is generated from the frictional work which directly relates to the friction force and sliding
speed. The Euler formula for soft wire drive is the main driving principle of the friction hoist[4]. The limit ratio of the stretch forces of the steel wire rope
on the two sides of the friction wheel, as seen in Fig.
1. It can be written as:
Received 12 May 2008; accepted 15 August 2008
Projects 50225519 supported by the National Outstanding Youth Science Foundation of China and 0E4458 by the Youth Science Foundation of China Univer- sity of Mining and Technology
Corresponding author. Tel: +86-15852498680; E-mail address: handongtai@cumt.edu.cn
HAN Dong-tai et al
Frictional heat analysis of mine hoist and numerical simulation …
43
Fig. 1 Stretch forces of steel wire rope on both sides of the fiction wheel in its penultimate state
ally increases in the sliding direction, as shown in Fig.2(3) and the heat at the inlet q ￠ is always larger than the heat at the outlet q￠ [1–2]. In research, the
gasket is usually adopted as the target as a result of the complexity and heterogeneity of the structure of the steel wire rope. It is more convenient to consider the gasket as continuous homogeneous material[7].
T1 / T2 = e
ma0
(1)
where e is the natural logarithm to the base 2.71828,
a0 the enclosed angle of the steel wire rope with
respect to the friction wheel, m the frictional coeffi- cient between steel wire rope and gasket and T1 and
T2 are the stretch forces on the weight and light side,
respectively. The relationship between the stretch force and normal pressure is
Fig. 2 Frictional heat conditions of steel wire rope and gasket during sliding
3 Temperature distribution model of gas-
Ni = Tdq
(2)
ket
where
Ni is normal pressure, T the stretch force and
dq the micro-angle corresponding to a unit of con-
tact radian.
During the sliding, the total frictional force is (T1–T2) and if the slide speed is u , the total fric-
tional work (Wf ) is the sum of many mini-curve fric-
3.1 Basic assumptions
Considering that the heat is unchangeable on a certain contact area of the steel wire rope and gasket and that it only changes with the enclosed angle a0
tional works (Wi) per unit of time[5]:
as the sliding condition is unchanged, the following
assumptions are made:
Wf = 工Wi = (T1 - T2 ) ×u
(3)
1) We ignore the abrasion of the gasket in the slid- ing process; the contact form of the steel wire rope is
The contact surface of the gasket is always heated
by frictional heat during the absolute slide. Generally,
unchangeable under certain working conditions. The entire form is a large arc with radius R and the local
if the two objects are similar to each other in texture
and geometry, the frictional heat is usually well-dis-
contact area is an arc with radius steel wire rope);
r0 (the radius of the
tributed[6]; otherwise, more heat will conducted to the
object with good conductivity. During the sliding between the steel wire rope and gasket, the steel wire rope will gain more heat, but the gasket gains only 5%. The frictional heat is generated largely on the segregated surface which is easily abraded, so it badly affects the gasket. In order to understand fully the frictional heat effect, the generation of frictional
2) The gasket is a homogeneous, continuously iso- tropic polymer with a constant heat conductivity, thermal diffusivity, heat capacity and density;
3) The non-contact surface, which is exposed in air, is heat insulation, i.e., it will not transfer heat to the air;
4) The heatqat any cross-section of the contact arc is constant and well-distributed on the small contact
heat should be considered on the entire contact area.
arc with radius
r0 ;
The conduction between the steel wire rope and the
gasket is unstable. The frictional heat conditions of the steel wire rope during sliding are shown in Fig. 2(1). It is rather complex because the semi-circle is heated and the other parts release heat. The heat transfer condition at a cross section of the contact area between the steel wire rope and gasket is shown in Fig. 2(2), which shows that the heat q is well-dis-
5) The heat transfer is conducted in the direction of radius r and the isotherms are pieces of the concentric semi-circle whose centre is the axes of the steel wire rope.
3.2 Governing equation
Based on the assumptions above, we obtained the physical model as shown as Fig. 3. The model has
tributed on the contact arc with radius
r0 . The sur-
three surfaces in contact with the surroundings: I is
face heat source will be created on the contact area
during the sliding of the entire friction wheel to heat the steel wire rope and gasket. The heating surface is the contact area. According to the variation of the friction angle, the intensity of the heat source gradu-
the contact surface of the steel wire rope and gasket which is heated directly by friction, where the heat q
is well-distributed; II is the contact surface of the gasket and its surrounding air, on which the heat has
effect on an extremely thin layer, thus the tempera-
ture changes little and the heat convection with the air
certain distance between them. Therefore,
q (j )
can
can be ignored[1]; I
is the contact surface of the
be considered as a constant and the heat conduction
gasket and the deposit of the contact area. For the
same reasons, the heat transfer can be ignored. The coordinate system of the three-dimensional model is established with the coordinates r , q and j . r
is the distance between a certain point in the cross-section of the gasket and the rope core, q is the angle from the point to the symmetric plane and
j is the counter-clockwise angle between the
cross-section of the gasket and its horizontal position.
can be transformed to an unstable heat conduction of a one dimensional hollow cylinder with equal heat flux on the inner wall. The simplified physical model is shown as Fig. 4 and the mathematical model at any
angle j is obtained as follows:
q(j )
is the heat at angle j .
Fig. 4 Simplified physical model of gasket
Fig. 3 Physical model of gasket
?t
?t
?2t
= a 2
飛 ?r
1 ?t
+ r ?r or
?t = a
?t
1 ?
飛
r ?r r
?t
?r
The diffusion of the frictional heat is unstable, thus we have the mathematical heat transfer model[5] as
｛t = 0，t一t0
?t
0
l
r=r - πl(wèi)r = q (j )
(6)
follows:
l ?r
1 ?t
?2t
( R - 2r cosq ) ?t
1 ?2t
where t is the temperature at radius r at any time in
= + +
the gasket;
ql (j )
is the heat flow rate of unit arc
a ?t
?r 2
r ( R - r cosq ) ?r r 2 ?q 2
+ sinq ?t + 1
?2t
(4)
length on the contact surface.
r ( R - r cosq ) ?q
( R - r cosq )2 ?j 2
4 Numerical simulation of the tempera-
where l is the heat conductivity, t temperature,
t time, R the distance between the capstan axes and the steel wire rope core, which is constant;
ture field
4.1 Finite element analysis
The heat transfer analysis of the gasket is investi-
a = l / ( rcp )
, denoting thermal diffusion. The
gated by the FEM software ANSYS, which is advan-
boundary conditions and initial conditions are
tageous in temperature simulation for its special
multi-field coupling function.
π
q = 0, q = ±
?t = 0
The heat transfer analysis process using ANSYS is
2 ?q
as follows: first, divide the object to finite units (in-
[8]
j = p
?t = 0
cluding some nodal points)
; second, solve the heat
2
｛
?j
(5)
balance equation of each nodal point under the given
boundary and initial conditions, according to the en-
?t
ergy conservation principle; third, work out the tem-
r = r0
- πl(wèi)r
?r
= ql (j )
t = 0
perature at each point and finally, solve for the other
[9]
lt = 0
t ( r,q ,j ) = t0
relative variables
. The simplified model is an un-
Eq.(4) is a partial equation, since the heat transfer in the gasket is considered as a whole. The solution of Eq.(4) is very complex by analytical or numerical technique and has to be simplified in practice. The surface layer affected by the frictional heat is very thin, thus the heat effect is small; and further, the dif-
stable heat conduction problem of a 3D hollow cyl-
inder with equal heat flux on the inner wall; therefore just one cross-section needs to be analyzed. At this cross-section, the inner radius is equal to the steel wire rope radius, that is, r0=1.9 mm, its thickness 2.1 mm and the cross-section is a half annulus whose cross-section area and grid distribution are shown in
ference between
q (j )
and
q (j + Δj )
is small
Fig. 5. There are 20 equal divisions in the radius and
when Δj
is very small, and the effect between
80 equal divisions in the periphery. The grid distribu-
tions are given by the ANSYS menu: Mesh->Areas.
q (j )
and
q (j + Δj )
is small as long as there is a
coefficient of steel wire rope relative to the gasket μ as 0.35, on the assumption that 5% of the frictional heat is conducted to the gasket and the heat flux on the gasket is the frictional heat per unit circle length. The calculation formula can be deduced from Eqs.(1) and (3)
q0 = 0.05(T2 e
ma0
- T ) u / πr0
(6)
Fig. 5 Physical model size and grid distribution
Because the heat flux of the three thermally insu-
4.2 Gasket properties and initial boundary con-
lated sides is zero, the calculated value q0
can be
ditions
1) Material properties: PVC plastic with den-
directly added to each nodal point in the cross sec- tion[10].
sity (r )
1390 kg/m3, specific heat (c )
1842.2
4.3 Results and analysis
p
J/(kg·°C) and heat conductivity(l )
0.145 (W/(m·°C);
The results such as the temperature field, heat flux field, heat gradient field can be shown in a drawing
2) Size and dynamic parameters: inner radius is 1.9
mm, external radius is 4 mm, T2=217.56 N and
u =69.33 mm/s;
3) Boundary conditions: the ab, bc and cd sides are thermally insulated, the ad side is of equal heat flux; initial conditions: τ=0, t0=20 °C; r=4 mm, q=0; r=1.9 mm, q = q0 .
We have taken the enclosure angle of the steel wire rope and the friction wheel as π, and the frictional
which can make the change of each physical quantity with time or space more intuitive[11].
The distributions of temperature and heat flux at a certain time are clearly shown in Fig. 6. It shows that the temperature gradually decreases as the radius in- creases, the isotherms are arcs of concentric semi- circles, and the heat flux has a symmetric distribution and decreases radially.
(a) Isotherms (b) In X direction (c) In Y direction
Fig. 6 Distributions of temperature and heat flux at a certain time
Temperature （℃）
TF Sum （W/m2）
The changing process of temperature and heat flow at a certain point in time is shown in Fig. 7. Four points were chosen along the radius from near to far at different distances. The slopes of the curves at the small radial points are large at the preceding 40 sec- onds, which indicates that the temperature rise and
heat flux gradient are large, so the heat conduction is at an abnormal stage. After a while, the slopes of the curves approach a fixed value which means the heat flux at these points is constant, the rise in temperature and the heat flux gradient of each point become con- stant, so that the heat conduction is at a steady stage.
(a) Temperature
(b) Heat flow
Fig. 7 Changing process of temperature and heat flow at a certain point in time
It can be seen from Fig. 7b that the heat flow de- creases gradually with the increasing radius, which is the result of energy conservation. As the heat flow on the boundary is conducted inside the model, one part of the heat transferred into the unit is used for energy change of the unit; in other words, it provides the energy for the increase in temperature; the other part is exported to other units. These results indicate that the transient temperature field of the gasket can be accurately simulated by computer and the numerical simulation can reflect the changing trend of the tem- perature field of the part that cannot be measured eas- ily in practice (such as the inside of the gasket).
5 Tests
The experiment was carried out to verify the result of simulation. The experimental set-up is designed the same way as the real hoisting condition. The steel wire rope slides on the experimental wheel which is rotated by a reel driven by a DC motor. The sliding speed is controlled by the voltage of the DC motor, adjusted by a transformer and the stress on the gasket is adjusted by different balance weights. The condi- tion of absolute sliding can be achieved while the experimental capstan is fixed and the condition of relative sliding can be achieved while the speeds of the spool and capstan driven by two DC motors are different. The speed of absolute sliding or relative sliding can be measured by a tachogenerator and photoelectric sensor; the tensile forces at the inlet and outlet of the test part can be measured by a tensile force sensor and the temperature can be measured by the submerged thermocouple thermometer.
It has been proved that the theoretical value and the measured value are basically matched over a short time (τ 三 100 s) as the steel wire rope slides (shown in Fig. 7a as lines 1, 2, 3, 4 representing theoretical
values, while lines 1’, 2’, 3’, 4’ represent the test tem- peratures). Therefore, the heat transferred from the contact area to the gasket and the distribution of tem- perature in the gasket can be calculated by numerical simulation at the beginning of sliding. The error in the late period of sliding can be understood as the accumulation of heat on the surface that has affected
the gasket and resulted in the enlargement of its heat conductivity[12]. This indicates the lack of conformity between the measured temperature and the theoretical value in the late period.
6 Conclusions
The model of heat transfer between steel wire rope and gasket is established, which can be used to simu-
late the temperature field of gasket under different weights and speeds. The temperature gradually de- creases as the radius of the model increases and the isotherms are arcs of concentric semi-circles; the heat flux has a symmetrical distribution in the model and decreases radially; the theoretical values agree quite well with the measured values over a short time (τ 三100 s) as the steel wire rope slides.
Acknowledgements
Financial support for this work, provided by the National Outstanding Youth Science Foundation of China (No.50225519) and the Youth Science Founda- tion of China University of Mining and Technology (No.0E4458), is gratefully acknowledged.
References
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[3] Liu D P. Some problems of frictional heat effects. Lubrication Engineering, 1994, 15(6): 6–14. (In Chinese)
[4] Yang Z J. Studies on Tribology Characteristics of Gasket Material of Multiple-cable Friction Hoist [Master dis- sertation]. Xuzhou: China University of Mining and Technology, 1987. (In Chinese)
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