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.
|| 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
||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
|| Sketch of typical working process
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)
|| Establishing key points in ADAMS
|| Eight-bar mechanism model in ADAMS
Which means the lifting cylinder extends 700 mm from the 2nd sec to the 6th
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 cylinders rod and body, as shown in Fig. 5, to keep the cylinder unmovable after the bucket rotates 45°.
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.
||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
Table 1 shows the initial values and the limit ranges of
all variables in the simulation optimization in ADAMS.
|| Design variables of optimization
|| 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 IDC
(Fig. 1) should be less than 170° and the constraint
functions built in ADAMS are:
||When the boom is lifted to the position of upper limit, angle
should be less than 170° and the constraint function built in ADAMS
where, Measure_angle_eba, Measure_angle_idc and Measure_angle_igk
are three functions created for measuring EBA,
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:
where, α is the bucket angle.
The objective function created in ADAMS is:
where, angle_bucket is the function for measuring the bucket angle in lifting as shown in Fig. 6. It can be created as:
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:
|| Measurement of bucket angle
|| The optimization of parallel lifting
|| 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:
where, H4 = 450.6 mm and R2 = 983 mm are constants.
MEA_PT2PT_R4and 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 CID,
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.
|| 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:
where, ω1 and ω2 are weighted factors.
The first sub objective function can be expressed in normalized form as:
Similarly, the second sub objective function can be expressed as:
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.
|| The optimization of μF
|| The optimization of parallel lifting
|| The comparison between initial value and optimized value
The final objective function created in ADAMS as:
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
||The comparison between the initial and the optimized models
||Results of simulation optimization aiming at different weighted
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.
Using the powerful analysis and calculation functions of ADAMS software, only
need to establish the correct optimization model and dont need to deduce
the complicated kinematic and dynamic equations and dont 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.
The author would like to acknowledge National Nature Science Foundation of China, under grant No. 50705011 for funding the research.