Abstract: The objective of this study was to solve the positions of pin joints of an eight-bar mechanism of a wheel loader using simulation optimization. The parametric simulation model of the working mechanism of a wheel loader was established with Automatic Dynamic Analysis of Mechanical System (ADAMS) software. The optimization models, including design variables, objective functions and constraint functions, were presented according to the design requirements. Multi-objective functions were transferred into a single objective function in the Function Builder of ADAMS. Changing the values of weighted factors, different optimization results were obtained. Optimization results showed that the performances of parallel lifting and digging force were improved. The optimization method based on simulation presented in this study was visual and easily operable for completion of the design.
INTRODUCTION
The wheel loader is a highly efficient machine used in construction and mining (Wang and Yang, 1996). The working mechanism of a wheel loader is designed for shoveling and loading material. Common types of working mechanisms currently include six-bar and eight-bar mechanisms. With the development of a large-scale and multifunctional wheel loader, the eight-bar mechanism is acquiring wider application because of its advantages, including good performances of parallel lifting and unloading, as well as large unloading height and length. In this study, the eight-bar mechanism, as shown in Fig. 1 which consists of a bucket, a bar, a tilter, a boom, a turning cylinder and a lifting cylinder, will be considered.
The design of a working mechanism possesses an important part of the overall machine design. A key requirement in the design of a working mechanism is the optimum placement of the pin joints. Traditional graphical methods are time consuming for such a complex system. Multi-objective optimization is a hard-solving matter because of the interactions between objectives. But with the advancement of computer technology, design problems with multi-objective optimization can be undertaken. However, it is unlikely that all objectives reach their optimal results simultaneously. So numerous multi-objective optimizations can be combined into a single-objective optimization based on some conditions, through which the design can still adequately meet all performance requirements (Worley and Saponara, 2008; Zhang, 2008; Erkaya and Uzmay, 2009; Chen and Yang, 2005; Lan, 2009; Wang and Lan, 2008; Ghaderi et al., 2006; Chikhaoui et al., 2009).
ADAMS (Automatic Dynamic Analysis of Mechanical System) simulation software is widely used in the field of kinematics and dynamics analysis of mechanical systems. Moreover, a great deal of engineering problems can be solved with its built-in optimization module (Zhang et al., 2009; Yao et al., 2009; Niu et al., 2009; Guo, 2008; Briot and Arakelian, 2008; Zehsaz et al., 2009; Du and Yin, 2011) Model simulation is a simple and effective way to verify proposed method or system that many researchers used. Designers can use the analysis of eight-bar mechanism by ADAMS to decide as to which part they should give emphasis in the design of wheel loader (Fufa et al., 2010; Cong et al., 2011; Vakili-Tahami et al., 2009; Mohamed et al., 2008). In this study, two important indexes of an eight-bar mechanism, i.e., the parallel lifting and the transmission ratio of the turning cylinder will be optimized.
| Fig. 1: | Eight-bar mechanism of a wheel loader |
DESCRIPTION OF TYPICAL WORKING PROCESS OF THE MECHANISM
The typical process of the working mechanism of a wheel loader can be divided into the following four steps (Fig. 2):
| • | Digging: Turning cylinder retracts while the lifting cylinder is locked, causing the bucket to turn 45° counterclockwise to carry out the function of loading material (position 1→2) |
| • | Lifting: The lifting cylinder extends while the turning cylinder is locked, causing the bucket to be lifted to the maximum height (position 2→3) |
| • | Unloading: The turning cylinder extends while the lifting cylinder is locked, causing the bucket to rotate clockwise until the angle between the bucket and the horizontal plane is 45° to completely unload the material (position 3→4) |
| • | Lowering: The turning and lifting cylinders retract, causing the bucket to return to the starting position (position 4→1) |
DESIGN REQUESTS OF THE WORKING MECHANISM OF A WHEEL LOADER
From the process described in section 2, the following will be required (Wang and Yang, 1996):
| • | Parallel lifting: That is, during the process of lifting, changes of the angle between the bucket and the ground should be as low as possible. It is better to keep the bucket from undergoing large rotation during lifting to avoid the material falling from the bucket |
| • | Large digging force: That is, the digging force at the tip of bucket provided by the turning cylinder should be as large as possible at the beginning of digging process |
| • | Reasonable kinematic relation: All links of the working mechanism are required to meet basic linkage kinematic relation. Self-locking of the mechanism can not arise during the normal working process |
| Fig. 2: | Sketch of typical working process |
SIMULATION OPTIMIZATION
Building the initial model for simulation optimization Parametric modeling: Simulation software ADAMS provides the function of ‘Table of points’ (Fig. 3), in which coordinate values of all key points (such as pin joints) are input. With this function, a parametric model can be achieved. As shown in Fig. 4, the initial ADAMS 3D model of the mechanism of a wheel loader for simulation optimization can be built with ‘Table of points’. (Point ‘L’, as shown in Fig. 1, is the origin of coordinates of the ADAMS model.)
Adding motion driver: After the parametric model is built, it is necessary to add the kinematic condition on the model to simulate the actual motion. In order to simulate mechanism motion, it is necessary to add a motion driver.
Add a translation motion on the lifting cylinder and the motion function is:
| • | STEP (time, 2, 0, 6, 700) |
| Fig. 3: | Establishing key points in ADAMS |
| Fig. 4: | Eight-bar mechanism model in ADAMS |
Which means the lifting cylinder extends 700 mm from the 2nd sec to the 6th sec.
Add a ‘Rotational Joint Motion’ as shown in Fig. 5 on the joint between the boom and the bucket. The kinematic function created on the motion is as follows:
| • | STEP (time, 0, 0, 2,45D) |
Which means the bucket will rotate anticlockwise 45° in 2 sec.
Create a ‘Fixed Joint’ on a marker between the turning cylinder’s rod and body, as shown in Fig. 5, to keep the cylinder unmovable after the bucket rotates 45°.
Optimization model
Initial condition of optimization design: In order to enhance the interchange
ability of some parts for cost reduction, three parts, the front frame, the
bucket and the boom, have fixed dimensions. Optimization tasks take place only
for the other parts to improve the working performance, that is (Fig.
1):
| • | The placements of three link points (‘L’, ‘K’, ‘J’) on the front frame are fixed |
| • | The placements of two link points (‘A’, ‘B’) on the bucket are fixed |
| • | The placements of all link points (‘A’, ‘C’, ‘H’ ‘L’, ‘F’) on the boom are fixed |
| • | The structural dimensions of the lifting cylinder are fixed |
Therefore, the variable parts include the tilter, the turning cylinder, the bar_1, the bar_2 and the bar_3. Namely, the corresponding variable link points are ‘I’, ‘G’, ‘E’ and ‘D’.
Design variables: From the initial condition of an optimization design, take two dimensional coordinates (x, y) of the four link points (‘I’, ‘G’, ‘E’, ‘D’) as the design variables of the simulation optimization. So, eight design variables can be got which can be expressed as:
| (1) |
Table 1 shows the initial values and the limit ranges of all variables in the simulation optimization in ADAMS.
| Table 1: | Design variables of optimization |
| Fig. 5: | Model for scripted simulation |
Constraint functions: The constraint functions ensure the geometry of the links is reasonable for normal operation and ensure that self-locking is avoided. That is:
| • | When the bucket angle reaches 45°, angle |
| (2) |
| (3) |
| • | When the boom is lifted to the position of upper limit, angle
|
| (4) |
where, ‘Measure_angle_eba’, ‘Measure_angle_idc’ and ‘Measure_angle_igk’
are three functions created for measuring
Three types of simulation optimizations: In this study, the purpose of simulation optimization using ADAMS software is to improve the performance of the eight-bar mechanism through the layout optimization of key pin joints. Two single-objective optimizations and one multi-objective optimization are considered.
The simulation optimization based on optimal performance of parallel lifting: During the process of lifting, take the minimum change of bucket angle as optimization objective. This can be expressed as:
| (5) |
where, α is the bucket angle.
The objective function created in ADAMS is:
| (6) |
where, ‘angle_bucket’ is the function for measuring the bucket angle in lifting as shown in Fig. 6. It can be created as:
| (7) |
Figure 7 shows curves of the change of bucket angle at different stages of the optimization iterations. The initial curve shows the change of bucket angle is approximately 25°. After optimization, the change of bucket angle is less than 1°.
The simulation optimization based on optimal performance of digging force: If μF is a transmission ratio, i.e., as the bucket is placed in plane state (bucket angle is 0°), one unit turning cylinder force can obtain the force on the tip of bucket, shown in Fig. 8 and it can be calculated as:
| (8) |
| Fig. 6: | Measurement of bucket angle |
| Fig. 7: | The optimization of parallel lifting |
| Fig. 8: | Sketch of calculation for μF |
Increasing the transmission ratio can improve digging force of the bucket for the same turning cylinder.
The objective function created in ADAMS is:
| (9) |
where, H4 = 450.6 mm and R2 = 983 mm are constants.
‘MEA_PT2PT_R4’and ‘MEA_PT2PT_R5’ are two functions for
measuring R4 and R5. Similarly, ‘MEA_ANGLE_cid’,
‘MEA_ANGLE_eba’ and ‘MEA_ANGLE_ceb’ are three functions
created for respectively measuring
The result of the simulation optimization is shown in Fig. 9. When the bucket angle is 0°, the initial transmission ratio is 0.43 and after optimization, the value is 0.6.
| Fig. 9: | The optimization of μF |
The multi-objective simulation optimization: The above two simulation optimizations were solved separately. However, it is preferred that both objectives are considered simultaneously. That is, the optimizations wish to make the transmission ratio as high as possible and for the same design, the change of bucket angle as low as possible.
A great deal of simulations show both keeping parallel lifting and enhancing the transmission ratio is contradictory. That is, enhancing transmission ratio is at the cost of reducing the parallel lifting.
A normalization process to the above-mentioned two objective functions can be made. That is, transfer the sub-objective functions into [0, 1] normalization objectives. Then, the objectives functions are combined as:
| (10) |
where, ω1 and ω2 are weighted factors.
The first sub objective function can be expressed in normalized form as:
| (11) |
Similarly, the second sub objective function can be expressed as:
| (12) |
By changing the values of the weighted factors, the relative importance of the sub-objectives can be varied. If ω1 = -ω2 = 1, then the two sub-objectives are equally important.
| Fig. 10: | The optimization of μF |
| Fig. 11: | The optimization of parallel lifting |
| Table 2: | The comparison between initial value and optimized value |
The final objective function created in ADAMS as:
| (13) |
In this function, the design need the change of bucket angle to be less than 10° and suppose the maximum transmission ratio is 0.6. That is, f1max (X) = 10, f2 max (X) = 0.6. ‘FUNCTION_MEA_1’ is a function for measuring F2 (X) in ADAMS.
The multi-objective optimization includes two working states of the eight-bar mechanism, digging and then lifting. So, it needs a scripted simulation based on the following ADAMS/Solver commands:
! Insert ACF commands here:
| • | DEACTIVATE/JOINT, ID = 50 |
| • | SIMULATE/kinematic, END = 2.0, STEPS = 50 |
| • | DEACTIVATE/SENSOR, ID = 1 |
| • | DEACTIVATE/MOTION, ID = 40 |
| • | ACTIVATE/JOINT, ID = 50 |
| • | SIMULATE/kinematic, END = 6.0, STEPS = 100 |
| • | Stop |
| Fig. 12: | The comparison between the initial and the optimized models |
| Table 3: | Results of simulation optimization aiming at different weighted factor |
The results of optimization are shown in Fig. 10 and 11. After ten optimization iterations, transmission ratio reached a maximum of 0.45 and the minimum change of bucket angle is less than 5°.
Table 2 gives the comparison of eight coordinate values of link points from initial value to the optimized values. The comparison between the initial and the optimized models is shown in Fig. 12.
The above optimization is based on the same weighted factor of the sub-objective functions, i.e.,ω1 = -ω2 = 1. If change the two weighted factors’ values, different optimization results will be obtained as given in Table 3. It can be found that enlarging -ω2 can improve the transmission ratio but decrease the performance of parallel lifting. On the contrary, enlarging the ω1 can effectively improve the performance of parallel lifting but decrease the transmission ratio. In actual engineering design, different results can be obtained by selecting different weighted factors.
CONCLUSIONS
Using the powerful analysis and calculation functions of ADAMS software, only need to establish the correct optimization model and don’t need to deduce the complicated kinematic and dynamic equations and don’t need to program a large number of codes to solve the optimal questions. So, the simulation optimization method supported by ADAMS can save much design time and greatly increase the optimization efficiency. Using the built-in Function Builder in ADAMS, the real-time measure of the performance parameters which are difficult to measure in reality, can be obtained. Function measures in optimization are easily acquired. Therefore, the parametric optimization based on simulation is suitable to solve the optimization design of mechanical systems like the eight-bar mechanism of a wheel loader. The parametric optimization based on simulation is easy to operate and has other merits such as visual 3D model, convenient post-processing, accurate optimization results and so on. In present study, optimization results showed the performance of parallel lifting and digging force are evidently improved.
ACKNOWLEDGMENTS
The author would like to acknowledge National Nature Science Foundation of China, under grant No. 50705011 for funding the research.