## Introduction

The aim of this project is to create a model of a Volvo EC160E excavator, able to predict forces exerted by the hydraulic cylinders and stress on the elements caused by the different working operations. The data to model the excavator is obtained directly from a brochure on the Volvo website[1]. The dimensional data present on the website are not complete, but only partial, so a series of test simulations will be run to validate the model from both a cinematic and dynamic point of view.

*Fig.1 Volvo EC160E Excavator
*

## Objectives

As said in the introduction, the dimensional data on the Volvo brochure are not complete, expecially for important parts such as the arm and boom. These have only the main size dimensions, while the positions of the joints between the elements and between elements and hydraulic cylinders are not quoted. The following simulations are defined to validate the model, evaluating the realism of the results and, when possible, comparing them directly with the values given by the producer:

**Range of motion**: After assembling the model, we evaluate shape and size of the range of motion in the saggittal plane, comparing them with values and images in the borchure.**Loads on the hydraulic cylinders**: We simulate two different lifts at a given range and height, with the maximum load for those spatial parameters. We the verify that the loads on the hydraulic cylinders are within the maximum limits, calculated from the pressure and bore read from the website.**Stress on the boom**: We make flexible the boom component and simulate a maximum capacity lift, evaluating the stress on it. Not knowing the maximum stress values, we only judge the realism of the results obtained.

To conclude we run a load-rotate-unload simulation, using another rigid body as a load instead of a concentrated force as before, and we evaluate the results of this final simulation.

## The Modeling

First of all CAD models of the components are created, which will then be exported as parasolid format in Adams to create our model. As anticipated, not all measurements are available to exactly recreate the parts, so starting from the size dimensions given (as shown in the picture) we try to mantain the same proportions as shown in the schemes.

*Fig.2 Dimensions of Boom and Arm
*

The single components are created on Solidworks, then assembled to do a preliminar test on the correct functionality of the model and to ease the exportation in ADAMS.

*Fig. 3 CAD model in solidworks
*

Satisfied with the result in solidworks, the model is saved as parasolid e and imported in ADAMS. The whole model is imported already assembled to ease the creation of joints between the bodies, as they already are in the correct relative positions.

*Fig.4 Model imported in ADAMS
*

Our mechanism is an open chain system, with 3 degrees of freedom for the arm, plus a fourth consisting in the rotation of the cabin (and the arm attached to it) around the vertical axis. The 3 degrees of freedom of the arm are the relative rotations in the saggital plane between bucket(1) and arm(2), arm and boom(3), and boom and body. These rotations are obtained by the action of hydraulic cylinders, attached to the two components between which they allow movement, except for the bucket, where they work between the arm and 4 supports which act as an auxiliary hinge.

*Fig. 5 Degrees of freedom of the arm and 3 main parts
*

The next step is to create joints between the parts, operation which must be done carefully to avoid redundancy of constraints. The arm of the excavator could be wrongfully modeled using only revolute joints, as it only rotates in one plane, but in the 3D space this would introduce a high amount of redundancies. Defined the 3 degrees of freedom of the arm, we proceed modeling the joints for 1 DoF at a time, keeping the other elements fixed, to gradually evaluate the absence of redundancies. Now we analyze in detail the joints used for the bucket-arm degree of freedom, shown in the picture:

*Fig.6 Detail of the bucket-arm degree of freedom
*

For this degree of freedom the following bodies need to have joints added between them: bucket, arm, 4 bucket supports (numbered in the picture), rod and cylinder of the hydraulic cylinder. The joints used are the following:

- Bucket-arm: Revolute
- Bucket-support 1: Spherical
- Bucket-support 2: Spherical
- Support1-support4: Spherical
- Support2-support3: Spherical
- Cylinder-arm:Spherical
- Support1-rod: Cylindrical
- Support2-rod: Cylindrical
- Support3-arm: Cylindrical
- Support4-arm: Cylindrical
- Rod-cylinder: Translational

Considering fixed the arm, the Grubler equation gives:

GdL=6×8-6-2×5-4×4-5×3=1

ADAMS conferms the absence of redundancies and only 1 degree of freedom. Then the fixed joints are removed from arm, rod and cylinder of the arm hydraulic cylinder, and the joints are applied in a similar fashion to avoid redundancies, and the same procedure is repeated for the rotation between boom and body. The whole set of joints is obtained (as shown in the picture) with only 3 degrees of freedom for the arm plus the body rotation, without any redundancy.

*Fig. 7 List of joints in the model
*

Defined the joints, now we need to give a mass to the various bodies of the excavator. Knowing the exact geometry of the components, we could simply add the material density and ADAMS would calculate mass, inertia and centre of mass. However the internal geometry of the parts is not known and they have been modeled as full. For this reason we define directly the masses, which are known thanks to the techincal sheets from the website, and as centres of mass the ones computed for the full bodies are used. This approximation is deemed acceptable as, trying to hollow in different ways the bodies on solidworks, the centre of mass moves only by around 10cm.

Now we can proceed with the planned simulations for our model.

## Simulations and result analysis

**Range of Motion**

As anticipated in the objective, the first simulation evaluates the range of motion of the arm in the sagittal plane, keeping the body fixed. The 3 components of the arm are flexed and extended at full range in sequence, and then a marker placed on the tip of the bucket is traced. The result is compared to the one shown in the brochure:

*Fig.8 Comparison between simulated and official ranges of motion
*

From a geometrical point of view the range of motion appears to be compatible enough to consider comparable the forces that will be be subsequently analized, although some differences can be spotted, which are caused by modeling approximations expecially in the positions of the joints, present because of the lack of information, Comparing the measurement values the following numbers are obtained:

**Max Height**F=8,26m in ADAMS, 8,56m from the sheet**Max Range**A=8,5m in ADAMS, 8,66m from the sheet**Max Depth**C=5,3m in ADAMS, 5,4m from the sheet

We have a maximum error of 3%, which can be considered acceptable given the levels of geometrical approximation used, and we can continue with the next simulations.

**Loads on Hydraulic Cylinders**

For the excavators reference tables are given showing the maximum loads than can be lifted when they are used as cranes, depending on distance from the cabin and height from the ground level. Loads are limited by two factors, the risk of overturing the machine and the maximum force that can be exerted by the cylinders, and these tables specify which one of these two factors is the limiting one in a certain configuration. To evaluate the maximum force of the cylinders, two configurations are chosen in which the load is limited by the maximum force of these.

The simulations consist in two lifts, one at 3m of range and one at 6m, both from 1,7m of depth to 3,2m of height. The maximum loads for these configurations are 4.100kg for 6m in range and 3m in height and 10.200kg for 3m in range and 1,5m in depth. In the second configuration there are no loads shown above 1,5m of depth, which means that the machine shouldn’t attempt lifts in that configuration. It will be interesting to see how the machine behaves in this situation. Loads are applied as forces acting on the middle point between the bucket supports, where usually buckets have a hook or the loads are fixed with cables:

*Fig.9 Load configuration for a lift
*

To evaluate the loads on the cylinders, first of all a vertical motion is imposed on the bucket, measuring the movements of the cylinders to obtain it, as shown. Thene these measures are converted into splines, and imposed as motions to the cylinders, and the force to obtain these motions is measured.

*Fig.10 Cylinder movements for the 6m lift
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Now the 6m lift is analyzed:

*Fig.11 Start and end of the 6m lift
*

The forces are the following, keeping in mind that the boom force is shared between two cylinders and the value must be halved, and that those cylinders only act with pushing forces, so they can exert higher forces:

*Fig.12 Force of cylinders over time for the 6m lift
*

Halving the blue curve, we have a maximum pushing force of 235kN by the boom cylinders at the start of the lift, and a pulling force of 120kN by the arm cylinder at the end. The bucket cylinder forces are very low, so not of interest for this simulation. The critical configuration is at the end of the lift, where the arm cylinder reaches it’s maximum force, so this should be the maximum load of that cylinder. From the data sheet the pressure in the cylinders is of 34MPa and the bore of the cylinder is 120mm. From the data obtained from a company producing cylinders, Liebherr [2], we can expect a maximum pulling force of about 200kN for this bore and pressure. The Volvo technical sheet states that the cylinders don’t go beyond 87% of their maximum capability, so 174kN, and considering that no friction is present in this simulation the result can be considered realistic.

Considering now the next lift, at 3m in range:

*Fig.13 Start and end of the 3m lift
*

These are the forces obtained, still with the boom one to be halved:

*Fig.14 Force of cylinders over time for the 3m lift
*

The trend of the forces in this case is more peculiar, as we can see for example that the arm cylinder goes to zero at a certain point to then grow again. This is beacuse the force allignes with the joint between arm and boom, so the whole load is directly transfered to the boom. At 1,5m of depth, the boom cylinders push for 350kN. In this case the cylinders have a bore of 115mm and the same pressure of 34MPa, but work only pushing so the maximum force obtained from the previous source as before is of 365kN. As before the limit is 87% of the maximum force, so 320kN. This time the measured force exceeeds the theorical by about 9%, maybe because incorrect dimensions cause the forces to act with different lever arms around the joints of the mechanical system.

Considering the area out of the lifting limit, up to 2.5m of height force stay within the previously calculated limits, so perhaps the cause of impossiblity of lifting in this configuration is not a load limit on the cylinders but the risk of overturing, excessive stress on the componens, or other safety limits.

So summarizing, the difference bewteeen measured and expected forces in the two cases is:

**6m Lift**: Expected 174kN, Measured (no friction) 120kN, 30% less**3m Lift**: Expected 320kN, Measured (no friction) 350kN, 9% more

Both forces are close to the expected values, with a predictable error margin because of dimensional approximations and the absence of friction. Increasing the forces because of friction, we can estimate an error margin of around 20%, which gives an idea of the forces needed for an operation, but not an exact value.

Considering the interactions between cylinders and components as levers, we can state that probably the lever arm for the arm cylinder is too big, while the boom cylinder lever arm is too small. This is why the measured forces are respectively lower for the arm and higher for the boom than expected. The maximum values though are still in the expected configurations, validating the model. We can now proceed with the stress analysis on the boom.

**Stress on the Boom**

We choose to analyze the stress on the boom component because it has to lift the most weight, having to bear also the bucket and arm, and it’s geometry is simple enought to not cause stress concentration problems in case of approximated modelling.

The pieces were created as full and the mass was imposed as written in the technical sheets, but making flexible the full pieces wouldn’t give obviously any meaningful result. The boom is therefore hollowed, reducing the wall thickness until, using the density of steel (7800kg/m^3), the weight of the piece is the same as in the sheets. The resulting wall thickness is 15mm, and the weight actually used is about 15% more than the one in the sheets. We choose to do this because we don’t use an accurate desing for example thickening the more stressed parts, but have a constant thickness all around the component. It is believed that having it a little thicker everywhere should give more realistic results.

*Fig.15 Full and hollow pieces in solidworks
*

The hollowed boom is imported as parasolid and substituted to the full one in the model, and then meshed with the ADAMS integrated mesher. Revolute joints are used since it is a flexible piece and rather than redudndancies we risk unwanted motions, and between boom and arm and boom and body two revolutes are used, one per side, to better distribute the load.

*Fig.16 Model with the fexible boom meshed in ADAMS*

A similar lift to the previous ones is executed, at 4,5m in range and 3,5m in height with 6.500kg of load, the maximum value obtained from the same tables. The resulting equivalent stress is shown in the picture:

*Fig.17 Stress map acting on the boom at the end of the lift
*

The maximum is 70MPa, a bit low even considering fatigue limits and safety factors. This value though is next to the revolute joint between cylinder rod and boom, where the flexible boom is connected with a spider, a finite number of beam elements. This will cause a high stress concentration, so the values obtained could be not too reliable. In fact, the first 23 nodes ordered by stress are all concentrated in this spot.

Excluding these values, the maximum is of about 50MPa, which is even lower. Considering that loads of 10.000kg can be lifted, even if not in this configuration, the load is increased to evaluate the structural response of the piece. The stress distribution is similar to the previous one if 10.000kg is used as a load, but a maximum of 100MPa in measured next to the joint, and 70MPa is measuerd at the 24th highest node, so the first out of the joint area, as seen in the table below:

*Fig.18 Stress table for nodes out of the joint concentration area for the 10.000kg lift
*

The results are realistic, maybe a bit too low for a material like steel and such extraordinary load configurations. Defeinitive concIusions can’t be drawn since we have no reference value, but we can suppose that the apporximation used during the hollowing of the component was excessive and it could have been made lighter. However, not knowing the correct values that we are looking for it would be pointless to reiterate with a lighter piece, so we are satisfied with these results and procede with the last simulation.

**Load-rotation-unload with a body as a load**

Considering the model validated by the previous simulations, we now study the cylinder forces acting for a load-rotation-unload simulation using this time a rigid body to represent the load, and not a simple force as before. We add to the model the ground, a 550kg sphere representing a load of mud, and a container to dump the load into:

*Fig.19 Model for the load-rotation-unload simulation
*

All contacts are modeled as impact based, between load and ground, load and bucket, and load and container. The contact bewteen load and ground is not modified, as the sphere only rests stationary on it before being lifted by the bucket.

For the contact between bucket and sphere, the movements of the load inside of the buckets need to be reduced as much as possible after the lift, as every bounce of the sphere will generate forces which are not realistic for a bucket full of mud. For this reason, the stiffness of the function is reduced drastically to 0.1N/mm. Also the stiffness of the contact between sphere and container is reduced, to the value of 1000N/mm to avoid excessive bounces after the sphere is dropped in it. This doesn’t really influence the simulation, as these contact forces aren’t measured and it’s more for graphical reasons. We now procede to simulate imposing directly the motions on the cylinder with STEP functions to avoind discontinuities, for a total duration of the operation of 20s (shown sped up in the video). The forces measured of the cylinders are shown in the picture:

*Video of the 20s simulation*

*Fig.20 Forces in the 20s simulation
*

The highest forces are the ones on the boom cylinders, which, after halving as before, are around 50kN, while the other two cylinders stay at around 25kN. We can also see a sort of ‘butterfly’ in the forces exerted by the boom and arm cylinders, which corresponds to the beginning and end of the lifting phase of the simulation. This is probably caused by inertial effects of the load, caused by the speed of the operation, which also leads to the following oscillations. This is confirmed by slowing the lift operation by 10s, and studying again the forces:

*Fig.21 Forces in the 30s simulation
*

The magnitude of the forces doesn’t change, but the peaks and oscillations disappear. It is confirmed that, when modelling using bodies and not forces as loads, the speed of the operation greatly impacts the forces that are measured. While this holds true, we can state that our previous lift simulations are still realistic because given the extremely high loads, we can expect very low speeds of movement, so an almost static configuration, where inertial effects can be ignored. This means that the use of forces is an acceptable approximation in those cases.

## Conclusions

During this project a Volvo EC160E excavator was modeled, starting from a limited set of data obtained from the company website. Three different simulations were run to try and confirm the validity of the implemented model. From a cinematic point of view, we have very low errors compared to the original data, however introducing forces the error, while still staying realistic, increses to about 20%. The absence of stress data doesn’t allow a quantitative evaluation of the quality of the model in this aspect, but the results are still realistic.

The model can be improved, but it can be considered acceptable even at this stage to obtain reference values for the stress and forces on the machine during given operations. Starting from exact CAD files, we could probably make flexible all the components we wanted to using the modeling approaches shown, to obtain then reliable data on the forces exerted by the cylinders and the stress on the components in any working situation.

Finally the last simulation showed the importance of considering the movement speed of the machine to evaluate correctly the forces on the cylinders, and that using only forces instead of bodies as loads can ignore inertial effects which can cause significant force increases.

## References

[1] *Brochure Volvo EC160E* downloaded from https://www.volvoce.com/italia/it-it/products/excavators/crawler/ec160e/

[2]* Liebherr cylinder catalog* https://www.liebherr.com/shared/media/components/documents/hydraulics/hydraulic-cylinders/liebherr-hydraulic-cylinders-series-prduction-range.pdf