Easy Example: The Wrench
Torquing a Wrench
Working with hand tools gives you a practical introduction to basics of engineering. In all likelihood, you have tightened a bolt using a wrench at some point in your life. This exercise will take you through a model that will analyze this very basic task, going into deeper details including associated geometric tolerances, torque specs, and the intrinsic contact problem.
In principle, a bolt replaces the need for external fastening by providing an internal clamping force via pretension. The tensile stress in a bolt is produced when it is torqued into a matching threaded hole or nut. The magnitude of this stress depends on many factors such as material selection, assembly configuration, and lubrication.
Control of these parameters, in turn, becomes the focus of much engineering effort, especially in critical applications such as automotive engines, brakes, aircraft, and structural installations. The following model presents both a bolt and a wrench at the moment of installation.
Model Wizard
Go to the Model Wizard window and click Next.
In Add Physics tree, select Structural Mechanics>Solid
Mechanics (solid).
Click Next.
In the Studies, select Preset Studies>Stationary.
Click Finish.
Geometry 1
In the Model 1 branch, right-click Geometry 1 and left-click
Import to select it.
Locate the Geometry import: drop down list and select 3D CAD
file.
Click the Browse button and locate the file wrench.mphbin in
the Model Library folder COMSOL Multiphysics\Structural_Mechanics.
Click the Import button, which results in the display of the
geometry in the Graphics window.
Materials
The chosen bolt material and tool steel are important characteristics of this contact problem. Here is how to choose them in COMSOL.
In the Model 1 branch, right-click Materials and left-click
Open Material Browser.
Locate the Material Selection section, expand the Built-In
folder, find Structural Steel, and left-click Add Material to Model.
Observe how COMSOL categorizes available material information
with respect to what the currently active physics requires.
Domain Physics—Boundary Conditions
With the geometry and materials defined, you are now ready to revisit the governing physics introduced in the Model Wizard section.
In the Model Builder window, right-click Solid Mechanics
(solid) and left-click Fixed Constraint to select it.
Rotate the geometry by left-clicking and dragging into the
position shown. Then left-click the cut-face of the partially modeled
bolt (which turns the boundary red) and right-click to select it (which
turns the boundary blue).
Cross-check: Boundary 35.
Left-click the Go to Default 3D View button to restore the
earlier view.
Then use the Zoom Box button to prepare the view shown in 10.
In the Model Builder window, right-click Solid Mechanics
(solid) and left-click Boundary Load to select it.
Rotate the geometry by left-clicking and dragging into the
position shown. Then select the top socket face by left-clicking to
highlight the boundary and right-clicking it to add it to the list.
Cross-check: Boundary 111.
In the corresponding Settings window, choose the Load type:
Total force and specify -150 N. The negative sign indicates the negative
Z direction or simply downward.
Mesh
COMSOL uses finite elements to find the displacement and stress fields.
In the Model Builder window, right-click Mesh 1 and left-click
Free Tetrahedral to select it.
In the Settings window,
click the Build All button 
.
Study
Right-click the Study 1 branch and left-click Compute to
select it.
Display Results
COMSOL finishes after about one minute of computation time and displays the displacement field by default. To determine the location of greatest tension, plot the principal stress field s1.
Right-click the Results branch and left-click 3D Plot Group.
Right-click the 3D Plot Group 3 just added and left-click
Contour to select it.
In the corresponding Settings window, click the Replace
Expression button and select Principal stresses 10 (solid.sp1), which is
representative of the s1 field.
In the same Settings window, check Description, change it to Principal Stress Field
S1, set the Total levels to 12, and the Contour type to Filled.
Click the Plot button and rotate the geometry approximately to
the orientation shown.You can see that the tensile stress concentrates
at the handle's top toward the open end, which is consistent with the
downward force applied to the socket. Also note high stresses in the
head to shank transition of the bolt.
