外文原文.pdf

Optimization Design of Four bar Linkage of Hydraulic Support Based on ADAMS Xin Zhang1 2 Jianwu Zhang1 Qingliang Zeng2 Hanzheng Dai2 1School of Mechanical Engineering Shanghai Jiaotong University Shanghai P R China zhangxinmt 2College of Mechanical and Electronic Engineering Shandong University of Science and Technology Qingdao P R China Abstract In designing a large inclined angle hydraulic support the structure characteristics of four bar linkage is presented and ADAMS software is applied to four bar linkage modeling and simulation In order to attain optimal results parameterized modeling and optimization is achieved and the design results meets the practical requirements very well By means of this virtual design method the errors can be reduced and design efficiency can be improved effectively Keyword hydraulic support four bar linkage optimization design ADAMS 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 of 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 could not obtain the optimal solution Currently ADAMS software is more and more widely 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 2 Dimension calculation of four bar linkage 2 1 Structure characteristics of four bar linkage 1 When the hydraulic support rises from the minimal to the maximal height as shown in Fig 1 the leading edge of roof beam the maximal horizontal movement distance of the leading edge of roof beam should be less than or equal to 70mm the best should be less than 30mm 2 As shown in Fig 1 P is the angle between roof beam and shield beam Q is the angle between back link and horizontal line P and Qshould meet the following requirements When the support is in the highest position P 52 62 Q 75 85 When the support is in the lowest position tan PW It is to make the rock fall down and prevent the rock stay in the shield beam according to frictional theory If friction coefficient W of the steel and the rock is 0 3 P 16 7 For sake of the safety P 25 is suitable when the support is in the lowest position It should have a distance between the bottom of back link and bottom plate Q 25 30 3 As shown in Fig 1 is the angle between horizontal line and the connection line from the link point 1 e to the instantaneous center O 1 e is the link point between shield beam and roof beam In the support design should meet the condition tan0 35 because angle directly influences the additional force of support e1 h P Q o e 30 Figure 1 Structure characteristic of four bar linkage 2 2 Calculating the dimension of four bar linkage 2009 Second International Conference on Information and Computing Science 978 0 7695 3634 7 09 25 00 2009 IEEE DOI 10 1109 ICIC 2009 396 338 As shown in Fig 2 1 H is the calculation height in the maximum position Mathematically the parameters of four bar linkage is supposed that o a 2 A ab B cb C cd D 2 o d E 1 ae G 1 eb F 1 Jo S 1 Je L A I G 1 I G B tan S L U Figure 2 Parameters of four bar linkage 1 The dimension calculation of rear bar and shield beam As shown in Fig 2 if H1 is determined the length of shield beam is 1 11 sinsin H G PIQ 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 IG 1 3 The distance between top link point of front bar and top link point of shield beam is F GB 4 The distance between bottom link point of rear bar and origin of coordinates is 1 E as shown in Fig 3 Figure 3 Geometrical relationship of four bar linkage 2 The dimension calculation of length and angle of front bar Coordinate of 1 b point When the support is in the highest position 1 H the coordinate of 1 b point is 11 cosxFP 5 111 sinyHFP 6 Coordinate of 2 b point When the support is in the lowest position 2 H the coordinate of 2 b point is 22 cosxFP 7 222 sinsinyBP A Q 8 When the support is in the lowest position 2 Q 25 30 according to the geometric requirements Mathematically it is supposed that 2 25Q 2 2 12 2 12 cos arctan cos GEAQ P EAQ 9 Coordinate of 3 b point When it is right angle between shield beam and rear bar the coordinate of 3 b point is 33 cosxFP 10 333 sinsinyBPAQ 11 1 3 222 1 arctanarctan 2 EA P G GAE 12 33 2 QP 13 Coordinate of c point 123 cbcbcb is the length of front bar So the length of front bar can be calculated by use of the equation of circle 22 11cc Cxxyy 14 The coordinate of c point is 22222222 313123232331 31233123 2 c x x y yy yx x y yy y x x x y yy y x x 15 2 32133213 32 2 1 2 3 2 1 2 313 2 3 2 2 2 3 2 2 xxyyyyxx xxyyxxxxyyxx yc 16 The length and angle of front bar can be calculated after determining the coordinate of c point 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 length D and E is c Dy 17 339 1c EEx 18 For large inclined angle hydraulic support when the angle increases the gravity line of hydraulic support or the roof pressure and gravity force will deviate from the support base The support will spin axially acted by the resultant torque so that the support overturns According to the geometric relationship and the torque balance conditions the conclusion is drawn that the non overturn condition is QrGs 5 So the inclined angle of coal seam is deduced that the support couldn t overturn hNHQ NQ arctan 19 Where Q is the pressure on the roof N is the width of the support base H is the usage height of the support h is the height of gravity center of the support In designing a large inclined angle hydraulic support the maximum support height is 2600mm The support height should be increased in order to meet the design requirements of hydraulic support in deeply inclined coal seam the calculation height H1 increases 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 3 1 Four bar linkage modeling and lemniscates trajectory simulation ADAMS Automatic Dynamic Analysis of Mechanical Systems is the virtual prototype analytical software developed by MDI According to Fig 2 and the physical dimension calculated by program the four bar linkage is modeled by means of ADAMS view The center O point is chosen as the basis 2 o d coincides with x axis is cd coincides with y axis as shown in Fig 4 Figure 4 Simplified model of the four bar linkage After modeling rotating pair Revolute is added in the link point by use constraints Joints toolbar and the rotating driver is added in the revolute pair of o a 2 and ground link point Finally setting the simulation conditions the track of e1 point is drawn by ADAMS PostProcesser It is similar to lemniscates trajectory as shown in Fig 5 Figure 5 lemniscates trajectory of e1 point From the above analysis this lemniscates trajectory can not meet the design requirement It should be considered that angle influences the additional force of roof beam and large inclined angle influences the hydraulic support To reduce the maximum height of support and choose the poison of small angle the curve is chosen that the scope of vertical height is 927mm 1673mm as motion trajectory of the leading edge of roof beam 3 2 Four bar linkage parameterized modeling and optimization Because the linkage size parameter that calculated in computational program is not the optimal result by simulation and analysis 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 Design Variable Design Point Coordinate Initial Value mm Sensitivity mm Optimized Significance mm DV 1 POINT 1Y 367 3 4 4 265 DV 2 POINT 2X 421 91 2 3 478 DV 3 POINT 3X 981 96 0 46 1006 5 DV 4 POINT 3Y 814 88 5 9 835 25 DV 5 POINT 4X 756 22 3 5 829 40 DV 6 POINT 4Y 1001 99 0 86 1024 DV 7 POINT 5X 52 36 0 652 12 10 DV 8 POINT 1X 0 0 44 10 2 DV 9 POINT 2Y 0 0 375 9 58 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 340 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 to obtain the optimal results 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 6 Figure 6 The optimized trajectory curve The optimal result of the four bar linkage size fully meet the design requirements of hydraulic support by analysis 4 Conclusion Using advanced ADAMS software not only achieved four bar linkage parameterized modeling motion trajectory simulation and optimization design of a large inclined angle hydraulic support but also analyzed the motion state of concerned components The optimized hydraulic support fully met practical requirements of the la