Simulative Calculation and Optimal Design of Scissor Lifting Mechanism Tao Liu1, Jian Sun2
1. School of Automobile Engineering, Harbin Institute of Technology, Weihai, 264209, China E-mail:
[email protected] 2. Department of technology, Weihai Chemical Machinery Co., Ltd., Weihai, 264203, China Abstract: A mathematical model has been established for the research on scissor elevator. The kinematical and kinetic simulation analysis was carried out with MATLAB/Simulink. The relative kinetic relation between hydraulic cylinder and other parts, as well as its rules of change has been found. A 3-D model of scissor lifting mechanism was established with Pro/E. The design of the mechanism was optimized in Pro/Mechanical based on the findings from simulation analysis, which may guide and improve the further design. The design was proved to be scientific and reasonable and could serve as the theoretical guidance and reference for the design of scissor lifting mechanism of other uses. Key Words: Mechanical engineering, Scissor lifting mechanism, Simulative calculation, Optimal design
1
INTRODUCTION
Scissor lifting mechanism is the first choice for automobiles at high altitude work. These automobiles must be highly secure and reliable for the sake of the personnel safety. In the past the design of scissor lifting mechanism at high altitude work has simplified the dynamic problem and treated it as static. The kinetic reaction has been considered with live load coefficient. The problem was simplified but the most serious defect was that the machines’ real working condition and kinetic features couldn’t be accurately reflected, which may lead to the unreasonable and inaccurate calculation for analysis and design. In order to solve the problem before-mentioned, a mathematical model of scissor lifting mechanism has been established and the kinematical and kinetic simulation analysis was carried out. The kinematical and kinetic parameters of the hydraulic cylinder and other parts have been obtained. The primary design has been improved by applying entity model and optimal design. It is significant for guaranteeing the security of automobiles at high altitude work and improves its working performances and efficiency[1~3].
2 2.1.
KINEMATICS and SIMULATION RESEARCH
KINETICS
Fig.1. Configuration of scissor lifting mechanism of automobile at high altitude work
2.2.
Kinematics simulation research
(1) Mathematical model The scissor lifting mechanism is illustrated as Figure 2. The length of 1 is r1, the length of 2 is r2, the length of 3 is r3, the length of 4 is r4, mg is the weight of hoisting terrace.
Configuration of scissor lifting mechanism
In Pro/E, the 3-D model of scissor lifting mechanism was established. The configuration of scissor lifting mechanism is shown in Figure 1. The scissor lifting mechanism is composed of outer hoisting frame, inner hosting frame, hydraulic cylinder and other parts. It is driven by hydraulic cylinder.
θ3
θ4
θ2
Fig.2. Sketch of the lifting mechanism 1 Assistant Frame 2 Inner Hoisting Frame 3 Outer Hoisting Frame 4 hydraulic cylinder 5 Hoisting Terrace
The mathematical model is established for the kinematical analysis of the scissor lifting mechanism with reference to the closed-ring vector equation. The choice of c 2009 IEEE 978-1-4244-2723-9/09/$25.00
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frame of axes is illustrated as Figure 2. Each connecting bar can be shown by a displacement vector. Thus the following formula can be got: R3 +R2 =R1 (1)
R4 +R2 (a+r2 )/r2 =R 1
(2)
The vector equation can be divided into two scalar quantity formulas: one is in the direction of x axis and the other is in the direction of y axis. The following group of formula can be got:
r3cosθ3 +r2 cosθ 2 =r1 r3sinθ3 +r 2 sinθ 2 =0 r4 cosθ 4 +(a+r2 )cosθ 2 =r1 r4sinθ 4 +(a+r2 )sinθ 2 =0 Where:
The data may make preparation for further kinetic simulation. 2.3.
Kinetics Simulation
(1) Mathematical model The analysis of the stress on outer hoisting frame is shown by Figure 4. m3g is the weight of outer hoisting frame.
(4) (5)
θ3
(6)
Fig.4. Stress on outer hoisting frame
(7)
θ 2 ǃ θ3 ǃ θ 4 is shown in figure 2.
(2) Kinematics Simulation research From the former group of formula the simulated model is established based on the kinematics relation of the mechanism, as is shown in Figure 3.
It can be got from Figure 4 that:
F13x + F23x = m3 ac3x
(8)
F13y + F23y − F53y − m3g = m3 ac3y
(9)
F13x L sin θ3 − F53y L cos θ3 − F13y L cos θ3 = I 3α 3
(10)
Where: I3 is the moment of inertia of the bar, others are shown in figure 4. The mathematical models of the stress on the inner hosting frame, the hydraulic cylinder and the upper terrace can be got in a similar way. (2) Kinetics Simulation research The simulated model of the kinetic mechanism is established based on the mathematical model got from former group of formula, as is shown in Figure 5.
Fig.3. Kinematics simulated model
The data of each bar’s position, palstance and angular acceleration can be got by running the simulated model.
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Fig.5. Kinetics simulated model
(3) Simulation result By running the simulated model the data of acting force with the change of time can be got (as shown in table 1) which may make preparation for further optimized design. Table1. Results of kinetics simulation
3
OPTIMAL DESIGN
Based on Pro/Mechanical, the 3-D model of the scissor lifting mechanism can be optimized to minimize the total quality of hoisting frames[4][5]. The constraint conditions are:
Force
Max /N
Time /s
Min /N
Time /s
F12y
14610
0.4
8547
0.2
F13x
59286
0
18950
6
F13y
34178
0.4
24587
0.2
4mm ≤ s2
of ≤ 20mm .
F14x
56284
0
17000
6
(3) The
thickness
F14y
110800
0.2
100000
0
4mm ≤ s3 ≤ 12mm .
F23x
24927
6
66285
0
F23y
88782
0
50350
6
F52y
34000
0
27653
0.2
F53y
34000
0
27653
0.2
P
114586
0
103874
6
(1) The
thickness
of
the
inner
flitch
s1:
4mm ≤ s1 ≤ 12mm . (2) The
thickness
of
the the
plate
s2:
bridge
s3:
reinforcing vertical
(4) The maximal stress σ : σ ≤ 345/1.5=230MPa The results of optimized design can be got by running the program, as is shown in Table 2.
Table2. Results of optimal design
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Parameters Thickness of the inner flitch(mm) Thickness of the reinforcing plate(mm) Thickness of the vertical bridge(mm)
Original Design
Optimized Design
Round
8
5.43
6
12
9.76
10
10
7.60
8
REFERENCES
The total quality of the scissor lifting mechanism is 1846.58kg with a 290.4kg reduction compared with 2136.98kg before optimized.
4
CONCLUSION
The kinematical and kinetic simulation analysis of scissor lifting mechanism for automobiles at high altitude work was carried out with MATLAB/Simulink. The curve of kinematical and kinetic parameters’ relations for the components has been obtained. A 3-D model of scissor lifting mechanism was established with Pro/E. By using Pro/Mechanical the design was optimized based on the simulation analysis results. The quality of scissor lifting
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mechanism is effectively reduced in the premise of ensuring the intensity. The proposal can be easily put into operation and provide reference for engineering application.
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