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翻譯部分
英文原文
The Design of Four-bar Linkage of Large Inclined Angle Hydraulic Support
Abstract- Four-bar linkage is one of the most important
components of shield-type powered support or chock-shield-type
hydraulic support. Parameterized modeling, simulation and
optimization of four-bar linkage is firstly accomplished by use of
ADAMS software in designing a large inclined angle hydraulic
support. Then based on three-dimension model of the whole
hydraulic support, applying COSMOS/Works software, finite
element analysis is made under the front torsion load of roof beam.
The analysis result validates the feasibility of four-bar linkage
design and meets the design requirements very well. This method
can effectively shorten the design cycle and improve design
efficiency of hydraulic support.
Keyword-hydraulic support; four-bar linkage; optimization
design; ADAMS; finite element analysis
1. Introduction
Four-bar linkage is one of the most important
components of shield-type hydraulic support or
chock-shield-type hydraulic support. Its function has two
aspects: One, as the support legs rises or lowers, the leading
edge of roof beam moves up and down nearly vertically,
thus maintaining a nearly constant unsupported distance
between the coal wall and the leading edge of roof beam.
This is a feature that is widely considered most desirable for
good roof control. Second, it makes the support to be
capable of bearing larger horizontal load.
In designing a large inclined angle hydraulic support,
optimization of the four-link design is an important work.
The size of four-bar linkage directly influences the
performance and status of hydraulic support. In the
traditional four-bar linkage design, BASIC program is used
to compute [1], but the results often can not meet the design
requirements and can not obtain the optimal solution.
Currently, ADAMS software is more and more applied in
the mechanical dynamics field [2]. So, the paper makes use
of the ADAMS software to model and simulate the
four-bar linkage in order to achieve the optimal design
solution[3-4]. In order to validate the feasibility of four-bar
linkage design[5], applying COSMOS/Works software,
finite element analysis is made.
2. Dimension calculation of four-bar linkage
As shown in Fig. 1, is the calculation height in the
maximum position. Mathematically, the parameters of
four-bar linkage is supposed that:
Figure 1. Parameters of four-bar linkage
2.1 The calculation of rear bar and shield beam
As shown in Fig. 2, if H1 is determined, the length of
shield beam is:
（1）
(1)The length of rear bar??
A=I·G （2）
The distance between top link point of front bar and top link
point of rear bar is:
B=I1·G （3）
The distance between top link point of front bar and top link
point of shield beam is:
F=G-B （4）
The distance between bottom link point of rear bar
and origin of coordinates is , as shown in Fig. 2. 1 E
2.2 The Calculation of length and angle of front bar
1) Coordinate of 1 point b
When the support is in the highest position , the
coordinate of point is:
X1=F·COS（P1） （5）
y1=H1-F·SIN(P1) （6）
??Figure 2. Geometrical relationship of four-bar linkage
2) Coordinate of 2 point b
When the support is in the lowest position , the
coordinate of point is:
（7）
（8）
When the support is in the lowest position, ??25°~30°,
according to the geometric requirements.
Mathematically, it is supposed that .
（9）
3) Coordinate of 3 point b
When it is right-angle between shield beam and rear
bar, the coordinate of 3 point is: b
（10）
（11）
（12）
（13）
4) Coordinate of c point
is the length of front bar. So the
length of front bar can be calculated by use of the equation
of circle. The coordinate of c point is:
（14）
（15）
The length and angle of front bar can be calculated after
determining the coordinate of c point.
2.3 The calculation of the height D of the front bar
bottom link point, and the projective distance E on
the base between bottom link point of front bar and
bottom link point of rear bar
After calculating the coordinate of c point, the height D
and length E is:
（16）
（17）
As to the top coal caving hydraulic support that the
maximum supported height is 2600mm, the supported
height properly should be increased in order to meet the
design requirements of hydraulic support in deeply inclined
coal seam, the calculation height H1 is increased to 2118mm.
By use of the program that sloping line is thought as the
objective function, the below result can be obtained.
tan?? = 0.338, Q1= 75.10°, Q2= 29.98°,
P1= 59.96°, P2= 15.09°, A= 988.78mm,
B= 295.56mm, C= 995.82mm, D= 367.30mm,
E= 421.91mm, G= 1343.45mm.
3. Parameter optimization of four-bar linkage size
According to Fig. 1 and the physical dimension
calculated by program, the four-bar linkage is modeled by
means of ADAMS/View. Because the linkage size
parameter that calculated in computational program is not
the optimal result by analyzing the simulation result,
optimally designing the linkage of should be parameterized
modeling so as to obtain the optimal result that meet the
design requirement.
During parameterized modeling, every link point is set
to variable, and the design result of every variable is gotten
by analyzing the variables, as shown in Table 1.
Table 1. Design results of every variable
The scope and the influence on the design of design
variables can be observed. MSC.ADAMS/View provides
all kinds of drawing diagrams as the research report, which
include the sensitivity of design variables. As shown in
Table 1, the sensitivity of DV_1, DV_2, DV_4, DV_6 is
greater. This implies that these four variables influence the
optimization results more greatly.
Four greater sensitivity design points are set, the curve
of every design point is changed together by
ADAMS/PostProcesser, then are compared and optimized.
Through operating the optimization program, four design
points are optimized. At last the optimal physical dimension
of four-bar linkage is obtained by analyzing and calculating.
tan?? = 0.0035, Q1= 57.59°, Q2= 24.90°,P1= 46.40°,
A= 990mm, B= 260mm, C= 1125mm, D= 265mm,
E= 478mm, G= 1155mm.
By means of ADAMS software, modeling the four-bar
linkage according to the calculated size, then analyzing the
link point through the trajectory simulation, as shown in Fig.
3.
Figure 3. The optimized trajectory curve
The optimal result of the four-bar linkage size fully
meet the design requirements of hydraulic support by
analysis.
4. The finite element analysis of hydraulic support
According to the calculated dimension of four-bar
linkage, assembling with the other part of hydraulic support,
the three-dimensional model of hydraulic support is set up,
as shown in Fig. 4. Applying the software
COSMOS/Works, finite element analysis of the whole
hydraulic support is made under front torsion load.
Figure 4. The three-dimension model of hydraulic support
4.1 The finite element calculation
After finite element pre-processing, COSMOS/Works
automatically generates graphic solution. The graphic
solution can be defined according to the need. For example,
stress, strain and dynamic change animation of strain, and
formatting section graph can be obtained, as shown in Fig.
5.
(a) Front torsion load displacement
(b) Front torsion load stress
(c) Front torsion load strain
(d) Front torsion load local stress
Figure 5. The finite element analysis results of the whole hydraulic
support under front torsion load
According to the calculation result, maximum
deformation of hydraulic is 11.63mm, maximum equivalent
stress of roof beam is 562.7 a MP , and maximum
equivalent strain is 3.503E-03. All pin force state can be
seen in table 2.
Table 2. Force acted on the hinge-jointed pin
4.2 Data analysis
Maximum stress and strain mainly appear in the load
part and surrounding area of roof beam. Hydraulic legs are
unequally loaded. The stress of front and rear hydraulic leg
which are at the load side is also larger than the other side.
On the front part of roof beam, the effect is obvious under
the action of front part torsion load. The rear part is
uniformly acted by the load. If the load is too large, the
whole support has a torsion trend. Form table 2, it can be
found that the shearing resistance of left and right pin
joined roof beam with shield beam is different. The shear
resistance of pins jointed front bar with shield beam, rear
bar with shield beam, rear bar with substructure, front bar
with substructure are large.
The strength analysis shows that maximum stress
distribution is regional and partial. So, high strength steel
sheet is commonly used in the large stress area to improve
mechanical characteristic. The hydraulic support fully
reaches using standard in practice and satisfies the using
requirement of the large inclined angle mining.
5. Conclusion
Applying ADAMS software not only can carry out
parametric modeling, motion trajectory simulation,
optimization design of a large inclined angle hydraulic
support, but also can analyze motion state of related moving
elements with motion simulation. Through making finite
element analysis on whole hydraulic support, the feasibility
of four-bar design is verified, and the distribution regularity
of support stress is found out. The designed hydraulic
support fully reaches using standard in the coal mine, meets
the using requirements of the large inclined angle mining.
This method can effectively shorten the design cycle and
improve design efficiency of hydraulic support.
翻譯中文
大傾角工作面液壓支架的四桿機(jī)構(gòu)的設(shè)計
摘要-四桿機(jī)構(gòu)是支撐式和支撐掩護(hù)式一個重要的組成部分。大傾角液壓支架四桿機(jī)構(gòu)的參數(shù)化建模、仿真和優(yōu)化首先在設(shè)計中使用ADAMS軟件。然后,基于三維模型的整體液壓支架,,建立了支架的有限元分析模型并對其進(jìn)行整架強(qiáng)度有限元分析，分析結(jié)果驗證了四桿機(jī)構(gòu)的可行性設(shè)計,很好的滿足了設(shè)計要求。該方法能有效縮短設(shè)計周期,提高液壓支架的設(shè)計效率。
關(guān)鍵字：液壓支架：四連桿機(jī)構(gòu)：最優(yōu)化設(shè)計：ADAMS：有限元分析
1. 介紹
四桿機(jī)構(gòu)是支撐式和支撐掩護(hù)式一個重要的組成部分。它的功能有兩個
方面:首先，作為支撐腿升高或者降低,帶動頂梁做近乎垂直的上下移動，從而維持頂梁前沿與煤壁的距離不變，這被認(rèn)為是最理想的頂板控制。其次，這樣做會讓液壓支架
有較大的水平荷載的能力。
在設(shè)計大傾角工作面液壓支架,四連桿機(jī)構(gòu)優(yōu)化的設(shè)計是一項重要的工作。四桿機(jī)構(gòu)的大小直接影響著對液壓支架的性能和狀態(tài)。在傳統(tǒng)的四桿機(jī)構(gòu)設(shè)計、基本程序使用計算[1],但結(jié)果往往不能滿足設(shè)計要求要求并不能獲得最優(yōu)的解決方案。目前,利用ADAMS軟件被越來越多的應(yīng)用
機(jī)械動力學(xué)領(lǐng)域的[2]。所以,本文使用ADAMS軟件的模型和模擬四桿機(jī)構(gòu)以實現(xiàn)最優(yōu)的設(shè)計解決[3]。為了驗證該四的可行性連桿設(shè)計[5],運(yùn)用 COSMOS/Works 軟件進(jìn)行有限元分析。
2. 四連桿機(jī)構(gòu)的尺寸計算
在圖1所示,是假設(shè)四連桿機(jī)構(gòu)在最高位置時的計算方法
2.1后連桿與掩護(hù)梁計算
如圖2所示，如果H1是確定的，掩護(hù)梁的長度是：
（1）
后連桿的長度：
A=I·G （2）
前連桿上鉸接點與后連桿上鉸接點的距離是：
B=I1·G （3）
前連桿上鉸接點與掩護(hù)梁上鉸接點的距離是：
F=G-B （4）
后連桿下鉸接點與坐標(biāo)原點的距離是E1 如圖2所示
2.2 前連桿長度和角度的計算
1）點b1的坐標(biāo)
當(dāng)支架在最高位置H1時，b1點的坐標(biāo)是：
X1=F·COS（P1） （5）
y1=H1-F·SIN(P1) （6）
圖2 四連桿機(jī)構(gòu)的幾何關(guān)系
2） b2點坐標(biāo)
當(dāng)支架在最低位置H2時，b2點的坐標(biāo)是：
（7）
（8）
當(dāng)支架在最低位置，Q2≥25°~30°。 根據(jù)幾何要求，假定Q2=25°
（9）
3) b3點坐標(biāo)
當(dāng)掩護(hù)梁與后連桿呈直角時，b3點坐標(biāo)：
（10）
（11）
（12）
（13）
4) c點坐標(biāo)
所以前連桿的長度可以用方程圓計算出，c點的坐標(biāo)是：
（14）
（15）
確定c點的坐標(biāo)就能知道前連桿的長度和角度
2.3 通過計算得到后連桿下鉸點的高度D，并且可以得到后連桿與前連桿投影到底面的距離E當(dāng)計算出c點的坐標(biāo)，D點的高度、E點的長度是：
（16）
（17）
作為對放頂煤液壓支架最大限度的支持是2600mm高度的支持，應(yīng)在增加高度以滿足對液壓支架設(shè)計的要求,在大傾角煤層，H1高度增加到2118mm，利用該程序傾斜線為目標(biāo)函數(shù)的思想,可以得到以下的結(jié)果：
tan?? = 0.338, Q1= 75.10°, Q2= 29.98°,
P1= 59.96°, P2= 15.09°, A= 988.78mm,
B= 295.56mm, C= 995.82mm, D= 367.30mm,
E= 421.91mm, G= 1343.45mm.
3 四桿機(jī)構(gòu)參數(shù)優(yōu)化
根據(jù)圖1和實際尺寸用程序來計算模擬四桿機(jī)構(gòu)指的是用ADAMS/View。因為連桿大小在計算程序的參數(shù)計算是不真實的，通過分析最優(yōu)結(jié)果的仿真結(jié)果,優(yōu)化設(shè)計聯(lián)動應(yīng)該參數(shù)化模型以獲得最優(yōu)結(jié)果，滿足了設(shè)計要求。
在參數(shù)化建模方法,每一個環(huán)節(jié)都是可變的，每個變量的設(shè)計結(jié)果通過分析，顯示在表1。
變量范圍和影響設(shè)計的變量可以觀察到。MSC.ADAMS/View提供各種各樣的繪圖，以便研究報告，包括設(shè)計變量的靈敏度。如圖所示，表1的靈敏度,DV_2 DV_4 DV_1,DV_6, 較大。這意味著這些四個變量對優(yōu)化結(jié)果更有很大的影響。
選擇四個較為敏感的設(shè)計點，讓每個設(shè)計點在ADAMS/PostProcesser下彎曲，然后進(jìn)行比較和優(yōu)化。通過操作優(yōu)化程序，對四個設(shè)計點進(jìn)行優(yōu)化。最后最優(yōu)物理維度到的四桿機(jī)構(gòu)分析和計算。
tan=0.0035, Q1=57.59°, Q2=24.90°,P1=46.40°,
A=990mm, B=260mm, C=1125mm, D=265mm,
E=478mm, G=1155mm.
利用ADAMS軟件，通過計算結(jié)果對四連桿機(jī)構(gòu)建模。并分析了連桿點通過軌道仿真,顯示在圖。
3.
圖3,優(yōu)化軌跡曲線
該研究結(jié)果的四桿機(jī)構(gòu)尺寸完全相同滿足設(shè)計要求的液壓支架分析。
4. 液壓支架的有限元分析
根據(jù)計算四維度聯(lián)動、裝配時的另一部分液壓支架, 對液壓支架進(jìn)行三維模型的建立, 如圖4所示，應(yīng)用軟件COSMOS/Works，有限元分析的整體液壓支架是由前負(fù)荷下扭轉(zhuǎn)。
圖4，液壓支架的有限元分析
4.1 有限元計算
有限元預(yù)處理、COSMOS/Works、動生成圖形的解決方案。根據(jù)圖形需要可以制定解決方案。例如：應(yīng)力、應(yīng)變及動態(tài)變化的應(yīng)變，可以得截面到格式圖,如圖5。
(a)前扭轉(zhuǎn)載荷位移
(b)前扭轉(zhuǎn)荷載應(yīng)力
(c)前扭轉(zhuǎn)荷載張力
(d)前扭轉(zhuǎn)負(fù)荷局部應(yīng)力
圖5，前扭轉(zhuǎn)荷載有限元分析結(jié)果
根據(jù)計算結(jié)果,最大值11.63mm，頂梁最大壓力為562.7MP，最大張力為3.503E-03。所有應(yīng)力見表2
表2 鉸接軸應(yīng)力
4.2 數(shù)據(jù)分析
最大應(yīng)力和應(yīng)變主要出現(xiàn)在負(fù)荷分和頂梁周邊。液壓支架受的是不平等載荷。液壓支架的前后連桿部分也比其他地方負(fù)荷大。頂梁的前半部載荷明顯下降。而后面不封則一直負(fù)載。從表2可以看出，左翼和加有側(cè)護(hù)板的右翼抗剪承載力是不同的。掩護(hù)梁與底座的前后鉸接點的剪切應(yīng)力也非常大。
分析表明,強(qiáng)度最大應(yīng)力只分布在局部區(qū)域。所以，高強(qiáng)度鋼常用在大應(yīng)力區(qū)來改善 機(jī)械的特性。使液壓支架在實踐中達(dá)到使用標(biāo)準(zhǔn)并滿足大傾角采礦的使用要求。
5. 結(jié)論
應(yīng)用ADAMS軟件不但能執(zhí)行參數(shù)化建模、運(yùn)動軌跡仿真，對大傾角液壓支架進(jìn)行優(yōu)化設(shè)計，而且也可以分析運(yùn)動狀態(tài)相關(guān)的移動，元素與運(yùn)動仿真。通過制作有限元分析整體液壓支架四連桿機(jī)構(gòu)的可行性已經(jīng)被證實，支架應(yīng)力的分布規(guī)律被發(fā)現(xiàn)。全達(dá)到煤礦的使用標(biāo)準(zhǔn)，滿足大傾角采礦的使用要求。該方法可以有效地縮短設(shè)計周期和提高設(shè)計效率的液壓支架。