Evaluating the efficiency of wheel loader bucket designs and bucket filling strategies with non-coupled DEM simulations and simple performance indicators

6. Fachtagung Baumaschinentechnik 2015
Maschinen, Prozesse, Vernetzung
Evaluating the efficiency of wheel loader bucket designs
and bucket filling strategies
with non-coupled DEM simulations
and simple performance indicators
Reno Filla
Dr. Reno Filla
Emerging Technologies, ATV
Volvo Construction Equipment
Bolindervägen 5
TCA 11, CE43110
SE-63185 Eskilstuna, Sweden

6. Fachtagung Baumaschinentechnik 2015 Technische Universität Dresden
Evaluating the efficiency of wheel loader bucket
designs and bucket filling strategies with non-
coupled DEM simulations and simple performance
indicators
In this paper we outline how optimising bucket design and bucket filling is connected to
improving the total energy efficiency of a wheel loader. Results from our work with particle
simulations are shown and it is discussed that, while ideally such simulations should be
coupled to models of the machine, operator and the work environment, it is nonetheless
possible to simulate stand-alone and utilise simple performance indicators to compare
different bucket designs and different bucket filling strategies in a reasonably fair manner.
Suitable and less suitable performance indicators are derived and discussed in detail.
1 Introduction
There is no doubt that construction machines need to be made significantly more energy
efficient. There is also no doubt that this is possible and that large improvements can be
achieved by approaching this task holistically. The journey that construction equipment
OEM’s will have to make towards significantly increased energy efficiency can be thought
of having four milestones:
- Understanding the machine as one system
- Understanding the interaction between machine, operator and working
environment
- Understanding the cooperation between several machines and their operators
- Understanding the regional, national and international transport and energy
systems and their role in human society
All milestones in this journey will be described briefly in the following, however the topic of
this paper is relates only to milestones 1 and 2.
1.1 Understanding the machine as one system
As an engineer it is easy to proudly focus on one’s domain and particular area of work, to
the point of neglecting that in a complex working machine everything is connected.
Depending on the perspective one’s system can be another engineer’s component or yet
another one’s mere boundary condition. Just like in a fractal, one can zoom in or zoom out
and will detect new details and connections almost ad infinitum.
For example, for an engine developer the internal combustion engine, ICE might be “the
heart of the machine” and thus most important, while for a powertrain engineer the ICE is
just one component of several within the system boundaries. An engineer concerned with
transmissions might consider the ICE as just a source of speed and torque, and the entire
hydraulic system as just a, seemingly random, torque deduction. In the other direction, the
system ICE can be zoomed into and new subsystems can be found, for example fuel
management. And further on, a fuel management component like a unit injector is a whole
multi-domain system in itself that needs to be studied in great detail in order to improve it.
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Reno Filla Evaluating the efficiency of wheel loader bucket designs (…)
All these different perspectives are understandable, but it is important to fully realise that
everything in the construction machine is connected: the machine is one system.
Auxiliaries
Bucket
Wheels
Lifting +
Breaking/Tilting
Travelling/
Penetration
Drive train
Hydraulics
Σ Engine
Linkage
External (+/-)
Gravel
pile
Figure 1: Simplified power transfer scheme of a wheel loader during bucket loading [1]
Fig. 1 above shows how in a wheel loader the primary power from the engine is split
between hydraulics and drive train in order to create lift and tilt movements of the bucket
and traction of the wheels, but is connected again when filling the bucket in, for example,
a gravel pile, which requires coordinated use of the machine’s main functions (dashed
boxes in Fig. 1). It is apparent that the tyres and the bucket as the final, ground-engaging
components of respective power transfer path, i.e. as the final links in each chain, are just
an important part of the total system as everything else and need therefore be considered
closely in the hunt for higher energy efficiency of the complete machine. Considering that
efficiency ratios are multiplied downstream from the power source, the case can be made
that it is even more important to save losses as close to the gravel pile as possible, since
each amount of power saved there leads to noticeably more savings for the engine – thus
saving energy.
1.2 Understanding the interaction between machine, operator and working
environment
Having mastered understanding of the machine as one system the next milestone to
achieve is to zoom out further and consider the meta-system in which the machine is used
as a tool by the human operator to achieve meaningful work in the working environment,
which significantly affects the machine’s energy efficiency in practice.
Auxiliaries
Bucket
Wheels
Lifting +
Breaking/Tilting
Travelling/
Penetration
Drive train
Hydraulics
Σ Engine
Linkage
External (+/-)
Gravel
pile
OperatorECU
ECU
ECU
ECU
Figure 2: Simplified power transfer and control scheme of a wheel loader during bucket loading [1]
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The inner loop in Fig. 2 shows how the human operator of a wheel loader interacts with
the machine. Three motions (and their corresponding driving forces) need to be controlled
simultaneously in order to fill the bucket: a forward motion (penetration trough rim pull), an
upward motion (lift) and a backward rotating motion of the bucket to collect material (tilt).
This task is non-trivial and highly affects the overall energy efficiency in a loading cycle
such as short loading (Fig. 3), which is described in more detail in [1] and [2].
Figure 3: Short loading cycle for wheel loaders [3]
While evaluating the efficiency of wheel loader bucket designs is of interest in the context
of milestone 1, evaluating the efficiency of bucket filling strategies is related to how the
operator uses the machine as a tool in the work place, therefore milestone 2.
1.3 Understanding the cooperation between several machines and their
operators
Zooming out even further, the third milestone requires realising that very seldom only one
single machine operates alone at a working site; rather there are several machines with
their respective operator who have to cooperate in order to achieve a common goal
together. There is thus a potential to optimise the fleet in terms of number and type of
machines employed and the work process itself, for example by increased connectivity.
This is studied in, among others, [4, 5] and there cited papers.
1.4 Understanding the regional, national and international transport and
energy systems and their role in human society
Extending the view to this last, in the present context meaningful zoom level might seem
philosophical at first, but simply considers the business environment the OEM and its
customers operate in. For example, publications [6] and [7] discuss alternative power
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systems on a machine and site level and focus on electric hybrid systems, rather than
hydraulic or mechanical hybrids, because this is most promising from a holistic and long-
term viewpoint: human society is already electrified with an established power distribution
system and there is a clear trend to electrify more parts of the transport system than just
trains. It is therefore logical to long-term consider electric hybrid solutions for construction
machines, even though highly efficient hydraulics and mechanical components, including
energy storage systems in these domains are of great interest, too, and will be used –
though perhaps in an otherwise electrified machine. Thus, the high-level understanding
gained at milestone 4 gives important input to engineering work done at milestones 1 to 3.
2 Background
Bucket design and how bucket filling is accomplished have a heavy influence on the
overall energy efficiency of a wheel loader in a working cycle, as established above.
Prior to this paper we have reported the study of possible bucket trajectories as part of a
bucket filling automation for assisting the operator [2]. In this work we have chosen to
isolate the bucket and employ stand-alone particle simulation using the Discrete Element
Method, DEM. However, according to the previous section and also the reasoning in [8],
published back in 2003, such a simulation should be extended with a complete machine
model operated by an adaptable operator model in a complete working cycle.
Kunze, Katterfeld et al. have taken one step towards this by coupling DEM simulation to
an MBS model of a wheel loader, as reported in [9]. Now, together with the results of
previous work on operator models [10, 11], (almost) all necessary pieces of the puzzle are
on the table, but the computational effort required is still overwhelming.
Therefore simplification is still needed. On a philosophical note it must be considered that
any simulation always is a simplification of reality – even comprehensive physical testing
is actually a simplification since real work is simulated in defined testing scenarios in a
defined testing environment, as for example in [12]. The paradox is that the more detailed
a simulation gets the more it also captures those sides of reality that engineers normally
want to suppress, such as too many degrees of freedom (i.e. too many parameters to
consider), complex interactions obscuring cause and effect (everything affects everything
else), result variations due to non-constant boundary conditions (i.e. reduced repeatability
due to environmental factors outside of the experimenter’s control) etc. The engineer’s
goal must be to find the right level of simplification that produces appropriately detailed
results. Like a scientific experiment any simulation (including physical testing) should be
designed to give answer to an a priori formulated question – or even better: a specific
hypothesis. The question or hypothesis controls the design of experiment, including which
simplifications are acceptable or even a necessity. The level of detail of simulation models
is therefore a direct consequence of the purpose of the simulation.
If the efficiency of wheel loader bucket designs and bucket filling strategies is the question
to be answered by simulation then, according to the previous reasoning at milestone 2,
the full scope would be a complete machine model with an operator model that uses the
machine in an adaptive way, according to a human-like mental model of the working cycle
and process, in a fully modelled working environment. The final efficiency value and
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therefore which bucket design and bucket filling strategy is optimal, is first decided after
the working cycle is completed (see Fig. 3 for a depiction of the short loading cycle, which
is highly representative for wheel loaders). However, the vast amount of details and
functions to model and the many parameters and degrees of freedom to consider make
this undertaking not feasible today – simplification is a necessity and only selected pieces
of the problem can be considered in detail.
Such a “divide and conquer” approach is common engineering practice. In earlier studies
[10, 11] we use only a simple model of a gravel pile based on Bekker’s formula and focus
on the operator model, while in [13] we consider the problem of optimising the shape of
the short loading cycle itself and simplify everything else heavily – but are still able to
arrive at interesting conclusions. Likewise in the study partly reported in [2] and continued
in this paper.
3 Simulation setup
We have developed four different principle trajectories along which the bucket is moved in
DEM simulations. Each trajectory type is the result of interviews with experienced wheel
loader operators and represents a different bucket filling strategy commonly employed.
3.1 Trajectory generation
In addition to the desired bucket fill factor most trajectories types offer at least one
parameter to vary the individual shape. The bucket trajectories are generated in MathCad
using a kinematic model of the wheel loader’s front body, complete with linkage, hydraulic
cylinders, bucket, and front axle. Controlling the bucket motion indirectly through cylinder
displacements and a longitudinal motion of the machine ensures that only valid bucket
positions are prescribed, corresponding to a valid state of the wheel loader’s linkage. The
major simplification with this approach is that only the nominal motion of the bucket is
prescribed, independent of any resistive forces that might interfere with the actual control
and without the adaptive behaviour of a human operator. This lack of force feedback is a
significant limitation, but the study gives meaningful answers, nonetheless.
3.1.1 Literature research
There are a great many publications, both academic papers and industrial patents (or
patent applications) on the topic of bucket automation and autonomous excavation.
In a publication from 1994 [14] Hemami studies bucket trajectories in order to minimise
energy consumption in the scooping and loading process. He concentrates on the motion
pattern itself and does not consider resistive forces in this paper. One of his conclusions is
that simply estimating the bucket load achieved as the area between the trajectory and
the uncut contour of the material will lead to deviations that need to be corrected by an
experimentally determined factor. We have used the same estimation in our study but
have a different method of compensation, using results from DEM simulations [2].
Further references, found to be relevant to our work with bucket filling strategies of wheel
loaders, especially with the focus on automating this task, are discussed in detail in [2].
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3.1.2 Type A: “Slicing cheese”
This type is a faithful implementation of a bucket filling strategy advocated by several
professional machine instructors who were interviewed prior to our study. Their advice
was to move the bucket such as if carving a slice of constant thickness off the material
pile.
In the diagram to the left in Fig. 4 we see the trace of the bucket tip moving at a constant
distance to the slope until a height of about 2.5m (corresponding to the hinge pin of the
bucket being at 2m), at which point the bucket is fully tilted back. The diagrams in the
middle and to the right in Fig. 4 show how this is accomplished: the bucket is constantly
lifted from ground position to exit height (set a priori), while at the same time being tilted
back proportionally from initial angle (zero) to maximum angle (which is the slope angle of
the material pile, because once the bucket is parallel with the slope, no further
advancement can be made without the bucket’s bottom pushing into the material, which
creates a large reaction force and is a waste of energy). After stopping at exit height the
bucket is just tilted back and retracted. The forward motion of the complete machine is
controlled so that the bucket tip is always at a constant distance to the pile’s slope.
Figure 4: Example trajectory acc. to type A, optimised for exit height at 2m and fill factor 1
In our algorithm the exit height can be chosen freely, while the slice thickness is a result of
the targeted fill factor and thus subject to parameter optimisation (i.e. an optimisation is
performed to find the value that fulfils the targeted fill factor).
3.1.3 Type B: “Just in & out”
This simple algorithm mimics the bucket filling style of operators who rely mostly on
momentum and rim pull (traction force) to fill the bucket: they just push the bucket into the
pile, then tilt back and leave. No further advancement is made after the initial penetration.
Figure 5: Example trajectory acc. to type B, optimised for fill factor 1
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In the diagram to the left in Fig. 5 we see the trace of the bucket tip accomplished purely
by the motions of the hydraulic cylinders without any further longitudinal motion after initial
penetration of the pile, as exhibited in the diagram to the right. The diagram in the middle
discloses that in order to accomplish the targeted fill factor, the bucket’s hinge pin height
also needed to be increased slightly (ca. 25mm) by using the lift function simultaneously
with the tilt function that controls bucket angle.
This trajectory type offers no additional parameter since the initial penetration is a result of
the targeted fill factor and thus subject to parameter optimisation.
3.1.4 Type C: “Parametric parabola”
This algorithm can be parameterised to generate trajectories of seemingly different
shapes. The control in this algorithm is similar to type A, but instead of following a line with
constant distance parallel to the slope, the bucket tip is controlled to follow a quadratic
curve, i.e. a 2nd
order polynomial. The parabola is controlled through a shape-influencing
parameter (which has been chosen to be the height of that point on the trajectory that
corresponds to the highest penetration depth counted from the slope surface).
In the diagram to the left in Fig. 6 we see the trace of the bucket tip moving on a quadratic
curve in relation to the slope until a height of about 1m (corresponding to hinge pin height
of 0.50m) at which point the bucket is fully tilted back. This is accomplished in a similar
fashion as for type A, as can be seen in the middle and right diagram in Fig. 6; however,
this time the forward motion is controlled so that the bucket tip is always at that distance to
the pile’s slope which is prescribed by the quadratic curve.
Figure 6: Example trajectory acc. to type C, optimised for exit height 0.50m,
maximum chip depth at 0.4m, and fill factor 1
The bucket exit height and the control point height where the maximum penetration depth
counted from the slope is achieved can be chosen freely, while maximum penetration
itself is a result of the targeted fill factor and thus subject to parameter optimisation.
3.1.5 Type D: “Stairway”
This trajectory is composed of an adjustable, pre-defined number of steps, like a stairway.
Within each step the wheel loader stands still and only the hydraulic functions lift and tilt
are executed. A new step is inserted by advancing machine and bucket forward using the
drive train.
In the diagram to the left in Fig. 7 we see an example stairway consisting of two stairs
after initial penetration. In between the steps the bucket is constantly lifted and tilted.
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During forward advancement the bucket height and angle also need to be controlled in
order to avoid pressing the bucket’s bottom against the cut surface of the gravel pile. At
the end of the sequence the bucket is tilted back fully and then retracted.
Figure 7: Example trajectory acc. to type D, optimised for two steps,
depreciation factor 0.5, and fill factor 1
In this algorithm the number of stairs can be chosen freely, together with a depreciation
factor that controls the subsequent advancements in relation to the initial penetration (a
depreciation of 0.5 means that the depth of each subsequent penetration is only half as
deep as the previous one). The initial penetration depth is a result of the targeted fill factor
and thus subject to parameter optimisation.
3.2 Particle simulation
The particle simulations utilise the DEM code Pasimodo. The model consists of ca. 16000
spherical and non-rotational particles of diameters ranging from 8 to 12cm. A 5m high pile
is modelled as a particle layer of 4m thickness over a solid inclined surface. More details
on this setup and lessons learned can be found in [2].
All trajectories have been simulated varying each adjustable parameter in three or four
steps, which results in the number of simulations as per Table 1.
Table 1: Trajectories simulated
Type Name Parameters Simulations
A
B
C
D
Slicing cheese
Just in & out
Parametric parabola
Stairway
2
1
3
2
9
3
27
12
The bucket fill factor achieved is determined as the ratio of the loaded mass to the rated
mass of the bucket, the former obtained through the vertical force that is required to
balance the bucket after complete retraction from the pile. Due to the complexity of the
granular flow the amount of material loaded into the bucket always shows deviations from
the target, which has been simply estimated a priori as the area between the trajectory of
the bucket tip and the uncut contour of the material pile. Our approach has therefore been
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to simulate each trajectory several times with various horizontal offsets and through
interpolation, using the simulated fill factors, to determine which profile offset was required
to reach the exact bucket fill factor that has been originally aimed for. New trajectories
have then been generated with the profile offset added to the initial penetration in the
beginning of the filling sequence and verified in a final simulation [2].
3.3 Postprocessing
MathCad has also been used for postprocessing, like converting the forces acting on the
bucket into cylinder forces and rim pull demand, determining the energy required for the
prescribed trajectory and generating the different performance indicators.
4 Analysis, observations and results
This section focuses on how to determine the most energy-efficient bucket filling strategy
and bucket design. Ways of comparing the results of such bucket filling simulations are
discussed and the rationale behind each performance indicator is described.
4.1 Comparing the efficiency of bucket filling strategies
The task is to decide which of the four simulated trajectory types is superior, based on the
simulations performed. It must be noted that no statement on general optimality can be
given since only four strictly defined trajectory types have been simulated and their
respective parameters have been varied in only a few steps. Some interesting results
have been obtained nonetheless, suggesting general conclusions about trajectory types A
and B. However, the main contribution of this paper lies in developing and discussing the
performance indicators.
4.1.1 Absolute and specific work invested
The natural choice as performance indicator of a trajectory is simply the amount of work
that has been invested during its execution. A fair comparison demands acknowledging
the different bucket loads achieved: as mentioned previously the obtained bucket load
always deviates from the target value – by how much is specific for the trajectory type and
the parameter settings.
The relationship between bucket load (in t) and invested work (in kJ) is linear only for the
lifting part of a trajectory, but non-linear for the filling sequence as a whole. This means
that while one way to compare trajectories of similar fill factors is to calculate the specific
work invested (in kJ/t), a fair comparison between trajectories of significantly different fill
factors is more difficult to achieve. It is therefore recommended to plot performance
indicators against respective bucket fill factor (i.e. the ratio of achieved bucket load and
the bucket rating according to ISO 7546), also when the performance indicator is already
normalised to bucket load, such as specific work invested.
In Fig. 8 absolute and specific work invested during each filling sequence are plotted over
the achieved bucket fill factor. For improved visibility the trajectories of type A have been
grouped into point series of the same bucket exit height: “A1” contains all filling sequences
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where the bucket was retracted at the hinge pin height of 1m, “A2” for 2m, etc. The data
points in each A-series differ only in the target value of the bucket fill factor, which is
achieved by varying the “slice” thickness while keeping the bucket exit height constant. As
for all trajectories the target fill factor is varied in the interval of {0.85, 0.95, 1.05}.
Figure 8: Absolute and specific work invested, over bucket fill factor
The first observation that can be made is the expected clear trend to higher work invested
for higher bucket fill factors even when specific work is used for comparison (right diagram
in Fig. 8). As mentioned above, due to this non-linearity in the relationship of bucket load
and absolute work invested only trajectories resulting in reasonably close fill factors may
be compared fairly by using any work-based performance indicator.
Secondly, it appears from Fig. 8 that the A1-trajectories with a bucket exit height of 1m are
among the most efficient, while the A3-series with 3m exit height are the least efficient,
because a similar bucket fill factor requires 70-80% more work. However, it is only logical
that lifting the same bucket load higher requires more work. Also, there is a value in the
potential energy achieved, which is not credited by merely utilising the work invested for
comparison, no matter if specific or absolute. This issue will be addressed shortly.
Thirdly, the B-trajectories with the “just in & out” bucket filling strategy perform strikingly
poor. The argument is often made that such a trajectory must be surely efficient as very
little work is invested into lifting the load and the work required for penetration is free
because (at least initially) the momentum of the moving wheel loader is used. Of course,
this work is not really “for free” in most cases, because accelerating the machine to a
certain speed requires work, too. Also, for realistic speeds the loader’s momentum is not
sufficient to penetrate the gravel pile as deeply as needed; and furthermore a smooth
penetration requires constant or even increasing rim pull, not decreasing. Fig. 8 shows
that the type B strategy is not very efficient when fully accounting for the penetration work,
even without crediting the lifting work included in all other trajectory types.
4.1.2 Ratio of potential energy achieved to work invested
Absolute or specific work invested for comparison of the efficiency of a bucket filling
strategy does not take into account the amount of work invested in also lifting the load.
This is a clear shortcoming as a performance indicator, because after all, the end state of
a filling sequence is a bucket filled with a load, tilted back and raised to certain height.
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In a short loading cycle according to Fig. 3, however, bucket filling is only the first phase of
ten. After bucket filling the machine operator drives backwards towards the reversing point
(phase 4) and steers the wheel loader to accomplish the characteristic V-pattern, with the
lifting function being engaged the whole time and the machine’s hydraulics competing with
drive train for the limited engine torque [1]. The operator chooses the reversing point such
that having arrived at the load receiver and starting to empty the bucket (phase 6), the
lifting height will be sufficient to do so without delay. In case of a bad matching between
the machine’s travelling speed and the lifting speed of the bucket, the operator needs to
drive back the wheel loader even further than necessary for manoeuvring alone. Such
additional leg transforms the V-pattern into a Y-pattern [3].
The height at which the bucket is retracted from the gravel pile thus affects the total
energy efficiency of the loading cycle, because it dictates the amount of lifting work still to
be performed during driving towards the load receiver, which in turn may affect the driving
pattern itself (extension of V to Y). A fair performance indicator must therefore somehow
credit the lifting work performed during bucket filling.
One might assume the ratio of the potential energy achieved (affected by bucket load and
bucket height) to the work invested can be a suitable performance indicator (Fig.9).
Figure 9: Left: Ratio of potential energy achieved to work invested, over bucket fill factor
Right: Potential energy achieved over work invested, absolute
The left diagram in Fig. 9 shows that such a comparison makes the A-type trajectories
appear vastly superior to all else: they seem up to four times more “efficient” than B, which
appears the worst possible bucket filling strategy to employ. The right diagram in Fig. 9
reveals that this is because the trajectories of type A exit the gravel pile at a much greater
height, therefore having achieved more potential energy than those of any other type.
Comparing bucket filling strategies based on the potential energy achieved related to the
amount of work invested is a poor choice because it implies that the sole utility of a bucket
filling sequence is a load being lifted. It totally neglects the utility of the bucket actually
being filled, which will always require a certain amount of work.
Besides, while the load lifting included in a bucket filling sequence should be credited, it is
wrong to assume it to be essential. In a typical loading cycle there is ample opportunity for
lifting to be performed in the phases 2 to 5 (see Fig. 3). Ending bucket filling at too great a
height is actually impractical because the remaining lift work might be so little that even
the shortest driving phase to the load receiver will be too long. This might be a waste, also
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depending on the general question whether it is more efficient to drive and lift concurrently
or sequentially (which in turn must be answered for each machine type, i.e. there might be
differences for a conventional loader vs. a hybrid). Furthermore, for acceptable machine
stability it is not common to drive and steer with a bucket fully loaded and raised high.
Most operators raise the bucket to unloading height as late as possible in the cycle, i.e. as
close as possible to the load receiver. This also means that loader operators usually don’t
leave the pile at too great a bucket height (generally not above the position where the
lifting arms are parallel to the ground). In contrast to this, the ratio of potential energy
achieved and work invested puts a premium on as high a bucket exit height as possible,
which shows that it is not a suitable performance indicator.
4.1.3 Subtracting potential energy achieved or adding remaining increase
With the previously discussed measures being unsuitable performance indicators because
they either ignore the utility of load lifting included in a filling sequence or over-emphasise
it, a solution might be to isolate the actual bucket filling by subtracting the lifting included.
Since this is a continuous and compound process it is not easily possible to calculate the
actual amount of work spent for filling vs. lifting. A practical approximation is to subtract
the potential energy achieved at the end of a bucket filling sequence from the work
invested for executing the trajectory (left diagram in Fig. 10).
Another variant is to do exactly the opposite and acknowledge the lifting part, but put it
into the context of a full loading cycle. As reasoned previously the bucket filling should not
be considered in isolation but rather as one phase in a complete loading cycle (see Fig.
3). For unloading in phase 6 to happen the bucket needs to be lifted sufficiently in the
phases prior to this. Any lifting work that has not been included in bucket filling (phase 1)
needs to be performed during driving towards the load receiver (phases 2-5). In the
proposed performance indicator the potential energy increase remaining after bucket
filling is added to the work invested for executing the trajectory (right diagram in Fig. 10).
Figure 10: Left: work invested minus potential energy achieved, specific
Right: work invested plus potential energy increase remaining, specific
Both diagrams in Fig. 10 give essentially the same picture: the “slicing cheese” trajectory
type A is superior to any other bucket filling strategy, especially compared to the B-type’s
“just in & out” style, which appears to be the worst option of all. There is little difference
between A-trajectories with different bucket exit heights and the spread between different
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strategies is less extreme than in Fig. 9 where the ratio of potential energy achieved to
work invested has been used.
It can be argued which performance indicator captures the truth better: the one that
deducts included lifting from the bucket filling sequence by subtracting the amount of
potential energy achieved at the end of the trajectory or the one that acknowledges lifting
by adding the increase in potential energy still remaining to be achieved in the subsequent
phases of the loading cycle. In both indicators the lifting work invested to achieve an
increase in potential energy is assumed without losses, which is a notable simplification.
4.2 Comparing the efficiency of bucket designs
In a subsequent batch of DEM simulations, performed in a different tool, we have run a
selected number of type A and B trajectories with different bucket designs. The ambition
with this study has been to achieve something akin to [12] in a simulation, but the initial
results point to more research and development still being needed. In these simulations
significantly different bucket designs led to the expected differences in the value of the
performance indicators – but more subtle design changes, which still should impact the
results, could not been shown to have made a difference. This might be an issue with the
newly developed tool or simply due to too low resolution, i.e. choosing an insufficient
particle size.
There is of course the theoretical possibility that these subtle design changes actually do
not improve the energy efficiency of bucket filling at all, at least not in the trajectories
tested, but practical experience suggests otherwise. We will therefore not publish the
results in this paper, but include some brief reasoning on the setup and analysis of such
study instead.
4.2.1 Trajectories used for comparing the efficiency of bucket designs
One might argue that it ought to be sufficient to simulate the different buckets in a few pre-
selected trajectories, especially when buckets of the same nominal size, i.e. volume rating
according to ISO 7546 are to be compared. Such reasoning though neglects the strong
possibility that the optimal, i.e. most energy-efficient bucket filling trajectory for each
design is slightly different. Forcing two buckets of different design along the same path
might skew the result if one design is favoured by this particular trajectory, while the other
one is disfavoured.
Besides, it needs to be asked the position of which physical or virtual point at the buckets
the trajectories control: it might be the upper or lower hinge pin, the bucket load’s centre of
gravity, the bucket tip or any other point. If the designs differ in the location of this point
relative to the bucket’s inner geometry then the problem is that a trajectory suitable for
one design might not work (accomplish essentially the same motion) for another, because
this other bucket is wider, longer or higher – or at a different distance or angle to the
wheel loader’s linkage. This also reiterates the necessity to take the machine’s linkage
geometry into account, as briefly discussed previously and in [2].
The best approach would certainly be to perform an optimisation of the bucket filling
trajectory’s shape, including a complete machine model, an adaptable operator model and
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a model of the process in the work environment, as already discussed. The different
bucket designs’ respective Pareto front consisting of the chosen performance indicator
over an interval of bucket fill factor values could then be used for a fair comparison – or
rather: should, because it is not reasonable to assume that the robustness of the chosen
performance indicator against variations in bucket fill factor is the same for different
bucket designs. Some design might show a pronounced peak in performance at a certain
fill factor while others are less influenced by this – and yet another design also shows a
peak but at a different fill factor value.
However, as will be discussed in a subsequent section, an optimisation at such a grand
scale is hardly possible with today’s computational hardware. The pragmatic approach to
work around this is to subject all bucket designs to a “fairly representative” collection of
trajectories that covers various types and parameter settings – including various targets
values for the bucket fill factor – just as described in this paper and [2]. In case the
designs differ only subtly and not in the principle bucket geometry (see discussion above)
one collection of trajectories that is common for all simulated buckets can be found.
As usual with optimisation some measure of robustness should be included in the analysis
in order to avoid designs that are intolerant of even the slightest deviation in settings, be it
of a trajectory parameter or the environmental conditions, such as the properties of the
material simulated. It has been noted already in early publications such as [12] from 1971
that different bucket designs are probably optimal for different materials. This needs also
to be taken into account when setting up such a study and analysing the results.
4.2.2 Performance indicators for comparing the efficiency of bucket designs
In any case, the performance indicator employed needs to be specific, i.e. normalised to
the bucket load because it can be expected that the different designs will lead to different
bucket fill factors for the same trajectory executed.
If a common set of trajectories has been used in simulation of each bucket design then
one might assume that a fair evaluation can be made by simply comparing the different
design’s specific work invested for the same trajectory. However, a probable outcome is
that one design will prove to be better using one particular bucket trajectory, while another
design is better using another trajectory. It is difficult to weigh such part results to arrive at
a final conclusion.
We therefore suggest using the performance indicators described previously in section 4.1
for evaluating the efficiency of bucket filling strategies. Also, as discussed in 4.2.1 a fair
comparison should involve the different bucket designs’ respective Pareto front (or an
approximation thereof) consisting of the chosen performance indicator over an interval of
bucket fill factor values, as well as a measure of robustness to other factors of influence.
4.3 Thought experiment
An interesting point has been raised in section 4.1.1 when discussing B-type trajectories:
some operators consider the “just in & out” bucket filling strategy to be quite energy-
efficient. According to their reasoning the work required for penetration is mostly for free
because (at least initially) the momentum of the moving wheel loader is used. This work is
15

not really “for free” in most cases, since accelerating the machine to a certain speed also
requires propulsion work to performed, meaning that the energy demand is just shifted in
time. However, there is at least one case where this is partly true: when the wheel loader
approaches in a downhill slope and the operator instead of using the service brakes slows
down by letting the bucket penetrating the gravel pile, thus using the gravel pile as an
“external brake”.
On the other hand, if the machine in question is a hybrid then it needs to be analysed in
detail whether recuperative/regenerative braking would have been the better choice from
an overall energy management perspective.
In a thought experiment we have investigated how the different bucket filling strategies
would compete if the work required for initial bucket penetration actually was for free. In
the diagrams shown in Fig. 11 the work invested in propulsion until the first movement of
either the lift or the tilt function has been subtracted from the total work invested in the
bucket filling sequence before calculating the different performance indicators.
Figure 11: Thought experiment of “free” initial penetration
In this thought experiment the B-type trajectories are heavily favoured as per definition all
penetration work is performed in one go in the beginning of this bucket filling strategy.
However, as already discussed in 4.1.1 for realistic travelling speeds the wheel loader’s
momentum is not sufficient to penetrate the gravel pile as deeply as needed. Also, a
smooth penetration requires a forward force that is constant or even increasing, not one
that decreases due to a braking effect produced by the increasing resistance the deeper
the bucket penetrates the gravel pile.
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5 Discussion
As noted in the beginning of this paper, in order to assure practicality several significant
simplifications have been required in the setup and analysis of this study. It is important to
recognise this and to discuss the implications.
A detailed discussion of the findings and lessons learned specific to the DEM simulations
performed in this study can be found in [2].
5.1 Method
It has already been mentioned that limiting the simulations to only the bucket-material
interaction, even though representing the loader’s linkage through the way the trajectories
have been generated and the simulation results have been analysed, falls short of the full
scope actually required: a complete machine model operated by an adaptable operator
model in a complete working cycle, executed in a comprehensive model of the work place
– and run in a global optimisation of the bucket trajectory. However, this is not feasible
today and must remain a vision for the moment being.
Varying the different trajectory types’ parameters in more than just three or four steps (see
Table 1 in 3.2) would have been an easy (though not inexpensive) way to approximate an
optimisation and raise the quality of the results.
The most immediate improvement in our study would have been achieved by connecting
an adaptable operator model to the particle simulations, which strives to actuate the
bucket according to a general strategy but also allows for local adaptations whenever
necessary, for example to counter high resistive forces, to avoid material spill etc. The
latter has been a minor, though existing issue caused by non-smooth transitions between
speed profiles for the hydraulic cylinders and the machine’s longitudinal motion. It can be
expected that the energy efficiency values of all trajectories are equally much affected to a
minor degree.
Figure 12: Material loss during bucket retraction
High resistive forces, in real work leading to bucket stall, have been tried to cope with a
priori by designing the trajectories such that overly high cylinder pressures and rim pull
requirements are unlikely to occur. However, this also means that there is an unused
performance margin: all trajectories might have been possible to execute more aggressive
in order to fully utilise the wheel loader’s performance, just as a human operator would do
in real work.
17

The calculations performed in postprocessing are based on the work performed by the
actuators lift cylinder, tilt cylinder and wheels. However, different machine architectures
will have different efficiencies for generating the actuator movements, for example a
series electric hybrid will likely be more efficient in generating an intermittent movement
than a conventional wheel loader is. Comparing these machines with the assumption of
lossless generation in both cases skews the picture: the same bucket moved along the
same trajectory might actually perform different with respect to overall energy efficiency of
the complete system. As an extreme consequence different bucket designs and different
bucket filling strategies might be optimal for two machines that only differ in that one, for
example is a series electric wheel loader and the other a conventional machine. This
issue can only be addressed when a model of the complete machine is included in the
bucket filling simulation and optimal control is performed over a complete loading cycle
(see previous discussions). While part solutions have been successfully demonstrated
[15, 16, 17] the full scope is still out of reach.
5.2 Results
It is no great surprise, though a welcome confirmation, to find the “slicing cheese” bucket
filling strategy of the type A trajectories the most energy-efficient. After all, professional
machine instructors have been advocating this bucket filling strategy for many years.
The true efficiency of type B’s “just in & out” strategy depends on how much additional
propulsion work needs to be invested for building up machine speed prior to ramming the
pile. A detailed assessment in simulation will require the full scope, as discussed above.
In most cases this filling strategy should be avoided, though the general idea of utilising
the machine’s momentum for initial penetration has merit, if applied correctly.
The results of the “parametric parabola” of type C have not been discussed much in this
paper. The efficiency lies in between A and B, because type C trajectories can approach
both depending on the parameter setting.
Type D’s “stairway” trajectories suffer the most from the lack of an operator model. In real
work, steps in the bucket trajectory are the operator’s reaction to bucket stall. Without an
operator model included in our simulations we had to introduce steps a priori. There is
thus a probable performance margin to stall, utilising which would surely have improved
the energy efficiency of type D.
6 Summary and conclusions
In this paper we started by explaining how studying the efficiency of bucket designs and
bucket filling strategies is part of the overall task of making construction machinery more
energy-efficient. With the details of the simulations performed already described in [2] the
main contribution of this publication lies in the easy to calculate performance indicators for
a fair comparison of different bucket designs and bucket filling strategies. The following
performance indicators are recommended to use:
- subtracting the potential energy achieved from the work invested
- adding the remaining increase in potential energy to the work invested
18

Applied to the trajectories studied in, admittedly only a limited set of simulations, these
performance indicators suggest that the “slicing cheese” bucket filling strategy, which has
been advocated by professional machine instructors for many years, is most efficient. The
“just in & out” strategy has been shown to be least efficient – unless the propulsion work
required for penetration is for free and could not have been recuperated or regenerated,
but needed otherwise be wasted in the machine’s service brakes.
The vision of performing optimisation of bucket filling trajectories in an outer loop of full-
scope simulations featuring detailed models of the working machine, operator, process
and environment, with inner loops for optimal control, remains a vision for the time being
because the computational requirements are unfeasibly high. Meanwhile, being able to
solve parts of the total problem in a simplified way, as presented in this paper and given
references, is of value to the engineering community and OEM’s.
Acknowledgements:
The DEM simulations have been set up and conducted by Martin Obermayr and Jan
Kleinert from the Fraunhofer ITWM institute in Kaiserslautern, Germany. Many thanks to
K.-E. Knappson for discussing strategy and helping in development of the code framework
for postprocessing.
References:
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University, Linköping, Sweden, 2011.
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[6] Filla, R.: Alternative system solutions for wheel loaders and other construction
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[7] Uhlin, E., Unnebäck, J.: On electrification of mass excavation. Proceedings from
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[16] Nezhadali, V., Eriksson, L.: Optimal Lifting and Path Profiles for a Wheel Loader
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[17] Nilsson, T.: Optimal Predictive Control of Wheel Loader Transmissions. Doctoral
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