COMSOL 6.4 - Ladder Frame

The ladder frame, or ladder chassis, is a common structure used in some light truck and SUV designs. An advantage of this structure is its simplicity: two longitudinal members connected by multiple transverse members.

The purpose of the chassis is to connect the upper body, the engine, and the wheel system. The stiffness of the chassis is important for the stability of the vehicle under operating conditions.

In this model, an eigenfrequency analysis is first performed on the unconstrained chassis structure. This is followed by a static analysis including a simplified suspension system with loads corresponding to the engine, the upper body, and an estimated payload. For the static load case, a weld verification at a critical location is also performed.

Model Definition

The ladder frame consists of a steel structure that is 4.5 m long and 1 m wide at maximum, as shown in Figure 1. The longitudinal members have a rectangular section with a thickness of 8 mm. The transverse members have a C-shape section of 5 mm thickness. The geometry is imported from a STEP-file as a solid object.

Figure 1: Shell geometry.

The nine lowest eigenfrequencies (natural frequencies) are computed. The eigenfrequency analysis is performed on the structure absent any connections to other vehicle components, and absent external constraints. This means that the six lowest eigenfrequencies correspond to rigid body modes, and are numerically zero. Higher modes correspond to deformations of the ladder frame.

For the stationary analysis, a simplified suspension component system is used to prevent over-constraint conditions when directly applying external loads to the structure.

The front suspension system is modeled using a 106 N/m spring constant, and the rear suspension system is modeled using a spring constant of 3·106 N/m.

The applied loads consist of

•

the weight of the chassis

•

the weight of the engine, estimated at 400 kg

•

the weight of the upper body, combined with the payload, estimated at 2000 kg

Figure 2 shows the applied load on the chassis for the static analysis.

Figure 2: Load distribution.

Results and Discussion

Figure 3, Figure 4, and Figure 5 show the first, second, and third natural frequencies of the chassis, respectively (disregarding the six rigid body modes). The first frequency (27.5 Hz) corresponds to a torsion mode, the second one (30.4 Hz) to a bending mode in the vertical direction, and the third one (47.6 Hz) also to a bending mode, in the lateral direction.

Figure 3: First natural frequency (torsion).

Figure 4: Second natural frequency (bending).

[

Figure 5: Third natural frequency (bending).

Figure 6 shows the displacement of the chassis subjected to engine and upper body weight, as well as the payload.

Figure 6: Chassis displacement.

Figure 7 shows the von Mises stress distribution in the chassis. Note that there is a stress concentration where the spring suspension is connected to the bracket. To improve the visualization of the stress distribution in the chassis, the maximum range value is set to 180 MPa.

Figure 7: von Mises Stress distribution in the chassis.

Figure 8 shows that the weld failure index between the suspension bracket and the longitudinal beam is below 1, when the ladder frame is subjected to the external loading.

Figure 8: Weld verification.

Modeling in COMSOL Multiphysics

For geometries with a high aspect ratio in one direction, shell elements are preferred compared to solid elements. Using the Design Module, you can convert a solid geometry representation to a surface object by removing its thickness. In addition, the Design Module includes geometry defeaturing and measurement tools. For instance, you can delete fillets that are not relevant to the analysis to reduce the number of elements.

Using the Resultant load type, you can specify a given force at a specific application point; the corresponding load is then distributed at the geometry location.

To verify that the different parts in the Shell interface are well connected to each other, you can use the connected region indicator.

Figure 9 shows how the suspension bracket and the longitudinal members are connected to each other.

Figure 9: Connected region indicator.

Structural_Mechanics_Module/Beams_and_Shells/ladder_frame

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Click .

Click

In the tree, select > .

Click

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Select the checkbox.

The geometry sequence for the model is available in a file. If you want to create it from scratch yourself, you can follow the tutorial under applications/Design_Module/Tutorial_Examples. Otherwise, insert the geometry sequence as follows:

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file ladder_frame_geom_sequence.mph.

In the toolbar, click

Click the

button in the toolbar.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Right-click and choose .

In the toolbar, click

to close the window.

Shell (shell)

Thickness and Offset 1

In the window for , locate the section.

In the d0 text field, type th2.

Thickness and Offset 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the d0 text field, type th1.

From the list, choose .

Thickness and Offset 3

In the toolbar, click

and choose .

Select Boundaries 33, 34, 47, 48, 291, 292, 306, and 307 only.

In the window for , locate the section.

In the d0 text field, type th1.

Mesh 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Click

Study 1

Step 1: Eigenfrequency

As there are no constraints in the model, the eigenvalue solver will also compute the rigid body motion modes. The corresponding eigenfrequencies are very small. To exclude these modes, search for eigenfrequencies with a larger real part than the shift value (1 Hz).

In the window, under click .

In the window for , locate the section.

Select the checkbox.

From the list, choose .

In the toolbar, click

Results

Mode Shape (shell)

In the toolbar, click

In the window for , click

Click

Add the shell geometry plot as in Figure 1.

Result Templates

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Results

Shell Geometry (shell)

In the second part of the analysis, the suspensions are added to the model. Also, a weld verification analysis is performed for the connection between one of the suspension brackets and the longitudinal beam.

Geometry 1

Cross members (boxsel1)

In the window, under > click .

In the window for , click

Suspension Bracket

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

In the text field, type Suspension Bracket.

In the window, select the boundaries as in the figure below:

In the table below you can find the corresponding selected entities:


Entities to select
uni1: 75, 78, 86-90, 121-125, 130

Extract 2 (extract2)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Suspension Bracket (Edge)

In the toolbar, click

and choose .

In the window for , type Suspension Bracket (Edge) in the text field.

Locate the section. From the list, choose .

Select the checkbox.

In the window, select the edges that are adjacent to the suspension bracket and connect to the longitudinal member.

In the table below you can find the corresponding selected entities:


Entities to select
extract2(1): 22-27, 40-44

Long Beam (Edge)

In the toolbar, click

and choose .

In the window for , type Long Beam (Edge) in the text field.

Locate the section. From the list, choose .

Select the checkbox.

In the window, select the edges that are adjacent to the longitudinal member and connect to the suspension bracket .

In the table below you can find the corresponding selected entities:


Entities to select
extract2(2): 275, 277, 278, 280, 312, 314, 341, 342, 362, 364, 384

Global Definitions

Suspension Coordinates

In the window, under click .

In the window for , type Suspension Coordinates in the text field.

Locate the section. Click

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

Geometry 1

Centroid Measurement 1 (cm1)

In the toolbar, click

and choose .

On the object , select Points 543–546 only.

Centroid Measurement 2-5

Proceed to create four additional centroid measurements with the following settings:


Name	Vertex Selection
Centroid Measurement 2 (cm2)	extract2(2): 547, 548, 549, 550
Centroid Measurement 3 (cm3)	extract2(2): 606, 644
Centroid Measurement 4 (cm4)	extract2(2): 699, 705, 734, 740
Centroid Measurement 5 (cm5)	extract2(2): 700, 706, 735, 741

Line Segment 1 (ls1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

In the text field, type geom1.cm1.x.

In the text field, type geom1.cm1.y.

In the text field, type geom1.cm1.z.

Locate the section. From the list, choose .

In the text field, type x_fwl.

In the text field, type y_fwl.

In the text field, type z_fwl.

Line Segment 2-5

Proceed to create four additional line segments with the following settings:


Name	Starting point coordinates	End point coordinates
Line Segment 2 (ls2)	geom1.cm2.x, geom1.cm2.y, geom1.cm2.z	x_fwl, y_fwl,z_fwl
Line Segment 3 (ls3)	geom1.cm3.x, geom1.cm3.y, geom1.cm3.z	x_fwl, y_fwl, z_fwl
Line Segment 4 (ls4)	geom1.cm4.x, geom1.cm4.y, geom1.cm4.z	x_rwl, y_rwl, z_rwl
Line Segment 5 (ls5)	geom1.cm5.x, geom1.cm5.y, geom1.cm5.z	x_rwl, y_rwl, z_rwl

Union 2 (uni2)

In the toolbar, click

and choose .

Select the objects , , , , and only.

In the window for , locate the section.

Find the subsection. Click .

In the dialog, type Truss in the text field.

Click .

Mirror 1 (mir1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

Select the checkbox.

Locate the section. In the text field, type 1.

In the text field, type 0.

Locate the section. Find the subsection. From the list, choose .

Click

Form Union (fin)

In the window, under > click .

In the window for , locate the section.

From the list, choose .

Upper Body Bracket

In the toolbar, click

and choose .

In the window for , type Upper Body Bracket in the text field.

Locate the section. From the list, choose .

Select the checkbox.

In the window, select the edges around the hole for all brackets which are located at the exterior of the frame. This is shown in the figure below. Note that only the four brackets at the front of the frame are shown. The full selection includes twelve brackets.

In the table below you can find the corresponding selected entities:


Entities to select
extract2(2): 21, 22, 25, 26, 64, 65, 211, 212, 239, 240, 256, 257, 856, 857, 864, 865, 898, 899, 1004, 1005, 1076, 1077, 1082, 1083

Engine Bracket

In the toolbar, click

and choose .

In the window for , type Engine Bracket in the text field.

Locate the section. From the list, choose .

Select the checkbox.

In the window, select the edges around the holes for all brackets located at the interior of the frame, as in the figure below:

In the table below you can find the corresponding selected entities:


Entities to select
extract2(2): 457, 458, 463, 464, 621, 622, 639, 640

Shell (shell)

The geometry is formed as an assembly which means that the suspension bracket and the beam are no longer connected.

Edge to Edge 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Select the checkbox.

Click to expand the section. Locate the section. In the a text field, type 3[mm].

In the σeqmax text field, type 500[MPa].

In the σ⊥max text field, type 500[MPa].

Add the upper body weight and the payload, distributed over the supporting brackets. The load is defined using the resultant and the center of gravity.

Upper Body and Payload

In the toolbar, click

and choose .

In the window for , type Upper Body and Payload in the text field.

Locate the section. From the list, choose .

Specify the F vector as


-2000[kg]*g_const	z

From the list, choose .

Specify the xa vector as


3[m]	Y
1[m]	Z

Add the load corresponding to the engine weight.

Engine

In the toolbar, click

and choose .

In the window for , type Engine in the text field.

Locate the section. From the list, choose .

Specify the F vector as


-400[kg]*g_const	z

From the list, choose .

Specify the xa vector as


0.4[m]	Y
0.1[m]	Z

Gravity 1

In the toolbar, click

and choose .

Attachment 1

In the toolbar, click

and choose .

Select Edges 606–609 only.

Attachment 2

Right-click and choose .

Attachment 2-10

Proceed to create nine additional attachments with the following settings:


Name	Edges
Attachment 2 (att2)	610-613
Attachment 3 (att3)	697, 698
Attachment 4 (att4)	303-306
Attachment 5 (att5)	307-310
Attachment 6 (att6)	910, 911
Attachment 7 (att7)	795, 796, 836, 837
Attachment 8 (att8)	797, 798, 838, 839
Attachment 9 (att9)	87, 88, 124, 125
Attachment 10 (att10)	89, 90, 126, 127

Add Physics

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Truss (truss)

In the window for , locate the section.

From the list, choose .

Linear Elastic Material 1

In the window, under > click .

In the window for , locate the section.

From the E list, choose . In the associated text field, type 1e15.

From the ν list, choose . From the ρ list, choose .

Prescribed Displacement 1

In the toolbar, click

and choose .

Select Point 647 only.

In the window for , locate the section.

From the list, choose .

In the u 0 x text field, type shell.att1.u.

From the list, choose .

In the u 0 y text field, type shell.att1.v.

From the list, choose .

In the u 0 z text field, type shell.att1.w.

Prescribed Displacement 2

Right-click and choose .

Prescribed Displacement 2-10

Proceed to create nine additional prescribed displacements with the following settings:


Name	Edges
Prescribed Displacement 2 (disp2)	648
Prescribed Displacement 3 (disp3)	649
Prescribed Displacement 4 (att4)	623
Prescribed Displacement 5 (disp5)	624
Prescribed Displacement 6 (disp6)	622
Prescribed Displacement 7 (disp7)	651
Prescribed Displacement 8 (disp8)	652
Prescribed Displacement 9 (disp9)	619
Prescribed Displacement 10 (disp10)	620