COMSOL 6.4 - Optimization of a Crane Link Mechanism

In complex mechanical systems, it can be challenging to find an optimal (or even good enough) solution only through engineering insight or trial-and-error procedures. Using mathematical optimization methods can then be an efficient path to a better design.

In this example, a link mechanism in a crane modeled in the Multibody Dynamics Module is optimized using the Optimization Module. The target is to reduce the cylinder force needed to carry a certain payload in a worst case operating cycle.

This example is a continuation of the model Truck Mounted Crane.

This model requires the Multibody Dynamics Module and the Optimization Module.

Model Definition

The complete crane geometry is shown in Figure 1.

Figure 1: Crane geometry.

A close-up of the link mechanism used for controlling the inner boom is shown in Figure 2. For more details about the crane model, please refer to the description of the model Truck Mounted Crane.

Figure 2: Close-up of link mechanisms.

A key to the coloring of the parts constituting the link mechanism is given in Table 1.

Table 1: Identification of crane parts in Link mechanism
Part	Name in model	Color in figure
Base	Base	Blue
Inner boom	Boom1	Green
Boom lift cylinder	Cylinder1	Red
Boom lift piston	Piston1	Yellow
Link mechanism	Link1, Link2	Magenta, Black

Operating cycle

The operating cycle is selected so that the moment carried by the link mechanism is as large as possible.

•

The inner boom is raised from its lowest position, 45° downward slope, to its highest position (vertical) in steps of 15°.

•

The telescopic extensions are as far out as possible in all positions.

•

The angle of the outer boom is chosen so that the crane tip (and thus the payload) is as far out as possible.

Loads

•

Self-weight in the negative Z direction.

•

A payload of 1000 kg at the tip of the crane.

Optimization problem

The positions of three axles can be modified, as indicated in Figure 3:

•

The axle connecting the first link arm to the base.

•

The axle connecting the second link arm to the boom.

•

The axle connecting the two link arms and the piston of the hydraulic cylinder.

It is also necessary to ensure that the two latter axles do not move more than 10 mm closer to each other than they are in the original configuration to avoid mechanical interference.

Figure 3: The optimization variables (blue) and the constraint (red).

The limits of the shifts on the axle positions are given in Table 2.

Table 2: Allowed shifts in axle positions
Axle	Horizontal [mm]	Vertical [mm]
Base-Link1	dYL1 = [-100, +50]	dZL1 = [-150 - +30]
Boom1-Link1	dYL2 = [-50, +50]	dZL2= [-50, +100]
Link1-Link2-Piston1	dYPE = [-50, +120]	dZPE = [-100, +20]

Results and Discussion

The force in the cylinders controlling the boom are shown in Figure 4. With the new design, it is possible to decrease the force by 31%, from 597 kN to 413 kN. This is a substantial improvement, and depending on the actual purpose of the analysis it can be utilized in two ways:

•

The allowed payload can be increased. Since a significant fraction of the crane capacity is used for supporting its own weight, the increase in payload is more than 31%.

•

For a constant payload, the reduced forces in the link mechanics does make it easier to reach stress and fatigue criteria for the link mechanism.

Figure 4: Variation of the cylinder force during the load cycle.

As an example of the effect of the optimization on other parts, the forces on the axle forming the hinge between the base and the boom is shown in Figure 5.

Figure 5: The forces acting on the axle between the base and the boom.

The actual values of the control variables in the optimized state may not be the same when this model is solved on different computers. The reason is that the minimum for the cylinder force can be obtained in different ways. There are multiple solutions which (within a small tolerance) give the same optimal values.

Notes About the COMSOL Implementation

Since all crane parts are rigid bodies, it is not necessary to actually move or deform the links during the optimization. It is sufficient to change the centers of the joints which mathematically represent the axles. This, however, leads to a nonintuitive graphic representation, as the links no longer rotate around the axles in the geometry.

The cylinder and piston are rotated physically in the model, since the direction of the cylinder force must be correct. Visually, the piston may look as if it was pulled out of the cylinder. This is also a graphical artifact, since another cylinder would be chosen if the modified geometry were to be selected for the final design.

In the optimization, the BOBYQA method is used. A gradient free method is suitable, since it is not possible to compute derivatives of the maximum cylinder forces with respect to the optimization parameters.

Multibody_Dynamics_Module/Machinery_and_Robotics/crane_link_optimization

Modeling Instructions

Application Libraries

From the menu, choose .

In the window, select > > in the tree.

Click

Root

Add the parameters needed for parameterizing the link.

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file crane_link_optimization_parameters.txt.

Component 1 (comp1)

The cylinder and the piston must have the correct direction in order to get the correct cylinder force.

Geometry 1

Rotate 1 (rot1)

In the window, expand the node.

Right-click > and choose > .

Select the objects and only.

In the window for , locate the section.

In the text field, type YCE.

In the text field, type ZCE.

Locate the section. In the text field, type cylRot.

From the list, choose .

Multibody Dynamics (mbd)

In the window, expand the > node.

Hinge Joints

In the window, expand the > > node.

Hinge Base-Link1

Parameterize the joint centers for the adjustable joints.

In the window, expand the > > > node, then click .

In the window for , locate the section.

From the list, choose .

Specify the Xc vector as


XC	x
mYL1	y
mZL1	z

Hinge Boom1-Link2

In the window, click .

In the window for , locate the section.

From the list, choose .

Specify the Xc vector as


XC	x
mYL2	y
mZL2	z

Slot Link1-Link2

In the window, expand the > > node, then click .

In the window for , locate the section.

From the list, choose .

Specify the Xc vector as


XC	x
mYPE	y
mZPE	z

Slot Link1-Piston1

In the window, click .

In the window for , locate the section.

From the list, choose .

Specify the Xc vector as


XC	x
mYPE	y
mZPE	z

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
ExtLen	5.5[m]	5.5 m	Total extension length

Study 1

Change the load cycle to a worst case scenario and compute.

Step 1: Stationary

In the window, expand the node, then click .

In the window for , locate the section.

In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
Angle1 (Angle to horizontal, inner boom)	range(-45,15,90)	rad
RelAng (Angle between booms)	0 0 0 range(0,-15,-90)	rad