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Evaluating CNC plasma cutter support stiffness

This blog post will delve into another structural design problem that was solved with Scan&Solve.  A CNC plasma cutter was designed and a question arose regarding the end plates supporting the CNC gantry:  are the end plates stiff enough to resist the inertial forces from the cutter?  For CNC machinery, limiting deflection is critical as it ensures quick and accurate machining.

The CNC plasma cutter will accelerate along the gantry (horizontal axis in the image above) as it cuts the part.  The acceleration produces an inertial force, causing bending in the vertical end plate (shown in green) which supports the gantry.  Linear guides (blue) secure the end plate to a rail (yellow), giving the cutter its second axis of motion.

To efficiently analyze this system, it can be broken down into smaller sections near the area of interest.  In this case, the entire gantry did not need to be modeled to understand the bending of the end plate.  Only part of the gantry near the plate was modeled in Rhino. As long as the gantry does not significantly bend under the applied load, the length of the gantry to model does not need to be increased.

Now, we will specify the restraints for the Scan&Solve simulation.  The restraints at the bottom need to restrain the model in the Y and Z directions, but not over-restrain it and artificially limit the bending of the plate.  The vertical faces of the guides were restrained in the Z-direction and the horizontal faces were restrained in the Y-direction.  While these restraints may seem counter-intuitive, they produce realistic results that allow for limited bending in the guides.

However, there is an issue with modeling the rail as a zero-displacement restraint.  Since the rail and guides are both made of steel, the rail is equally stiff as the guides and will also deform under stress.  However, as long as the displacements of the guides remain small relative to the bending of the plate, the contributions of the rail deflection can be neglected.

The end face of the gantry beam was also restrained to limit its ability to bend in a direction that would not likely occur if the full gantry were modeled.  The loaded face was restrained so it would remain in its original orientation, but would be allowed to move in the Y-direction.  The end of the beam was similarly restrained in the X-direction to also keep the beam straight.  These restraints are shown below.

The following image shows the effect of not restraining the loaded end of the gantry.  The gantry has deformed in a way that would not be possible if the full model were considered, as the gantry would not deflect downwards so significantly under a horizontal force.

The applied load was considered to be a result of linear acceleration along the gantry.  The specified acceleration was 0.9m/s/s and the mass of the plasma cutter is 6kg, so from Newton’s second law and a modest factor of safety, a 10N force was applied to the end of the gantry.  This force was applied axially to the end of the gantry.  The model was simulated with Scan&Solve and the following shape of deflection was found.

Two designs were considered to reduce the bending of the end plate.  First, a square tube of identical dimensions as the gantry was joined to the back face of the end plate.  The second design extended the gantry through the plate and added two gusset plates connecting the extended portion of the gantry to the end plate.  These gussets extended to the bottom of the plate to maximize their contribution to the bending stiffness.

Both designs were quite successful in reducing the bending of the plate and deflection of the gantry.  The square tube and the gusset plate design both obtained quite similar maximum displacements, reducing the maximum displacement by over a factor of 10.

Design

Maximum deflection (cm)

No ribs

9.1e-4

Square tube support

7.3e-5

Gusset plates with extended tube

7.5e-5

The square tube deflection is shown on the left, and the gusset plate deflection is shown on the right.  The shape of deflection is quite similar for both designs.

At this level of displacement, the bending of the gantry beam is noticeable compared to the bending of the plate.  This is in contrast to the first bending illustration, where the plate was bending much more than the gantry.  In addition, the rail mounts have begun to twist, which is just noticeable in the image showing the deflection of the gusset plate design.

To proceed with trying to achieve further stiffness, the stiffness of the rail itself must be modeled as well as an extended length of the gantry.  However, it is likely that further stiffness would be difficult to achieve without changing the thickness of the plate, gantry, or the size of the rail and guides.

The meshless advantage of Scan&Solve was particularly useful in enabling rapid analysis of design changes.  Being able to change a model and immediately run an analysis to measure its effect is an immense timesaver.

Thanks for reading!  If you have any questions, feel free to ask in the comments.

Will

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