In a previous post on forces, we analyzed the loads acting on a 3D printer frame. In this article, we will examine the forces acting on a  cantilevered print bed  during 3D printing and how they affect the printed part.

Printed Part Mass

In most cases, the mass of the printed part itself is negligible. Approximately 95% of printed parts weigh less than 1 kg, so within the scope of this analysis, the influence of this load on bed deflection can be ignored.

Inertial Forces from Extruder Movement

The primary source of excitation for a cantilever bed is the inertial forces generated by the movement of the extruder. These forces cause the bed to oscillate relative to its mounting axis, especially at high acceleration values.

There are several ways to influence these oscillations:

    • A. Increase or decrease the mass of the bed or other moving elements;
    • B. Shift the center of mass of the bed by changing the force application lever arm;
    • C. Use stiffer materials;
    • D. Increase the structural stiffness through design.

Effect of Increasing Bed Mass

Let us consider what happens when the mass of the cantilever bed is increased:

    • Increasing the mass by  10–20%  has an almost imperceptible effect on the system dynamics.
    • Increasing the mass by  2–3 times, without increasing stiffness, makes the oscillations “slower,” but their  amplitude increases, especially during sharp acceleration changes.

Therefore, simply increasing mass is not an effective solution.

Shifting the Center of Mass

A more reasonable approach is to shift the center of mass closer to the linear rails. The farther the center of gravity is from the mounting point, the greater the bending moment, which leads to stronger oscillations caused by inertial forces.

This directly follows from the basic relationship:

M=F⋅L,

where L is the lever arm from the mounting point to the center of gravity.

By reducing this lever arm, the bending moment decreases, which in turn reduces torsional and bending vibrations. The same principle applies to the standard formula for maximum beam deflection.

Result: Even with constant stiffness, reducing the moment significantly improves real-world behavior.
However, in my case, the center of mass is located 133 mm from the rails, and building a crane-like structure to move it closer (to 70–80 mm) is not practically feasible.

Based on this, options C and D remain the most reasonable .

Comparison of Bed Design Options

Let us compare three design variants:

  1. Brackets 3D-printed from PETG;
  2. The same brackets manufactured from aluminum;
  3. A cantilever frame bent from sheet metal.

Initial Data for Calculations

    • Mass of moving elements: 1.2 kg
    • Actual accelerations: 7000 mm/s²
    • Other parameters: Taken from SolidWorks material libraries
    • Distance to edge 255 mm

Inertial Force Calculation

F = m ⋅ a = 1.2 ⋅ 7 = 8.4 N

Analysis Results

Plastic Brackets




As shown in the results, the edge of the bed deflects:

    • 0.108 mm when the print head moves from Ymax to Ymin
    • 0.040 mm when moving from Ymin to Ymax

The total edge displacement is approximately 0.12 mm.

If parts are placed closer to the rails, this deflection becomes comparable to the numerical accuracy of the simulation.

Note:  In practice, wet filament affects surface quality much more significantly than this level of bed movement.

Aluminum Brackets


Here, theory is fully confirmed: the plastic brackets are clearly the weakest link.

    • Deflection from Ymax to Ymin: 0.047 mm
    • Deflection from Ymin to Ymax: 0.017 mm

Total edge movement: 0.064 mm.

Sheet Metal Cantilever

The sheet metal design shows a dramatic improvement:

    • Deflection from Ymax to Ymin: 0.007 mm
    • Deflection from Ymin to Ymax: 0.003 mm

Total edge movement: approximately 0.01 mm.

This naturally raises the question: is there any reason to mill such parts if the same problem can be solved more efficiently with a sheet metal design?

Conclusion

  • If you print with parameters close to those used in this analysis, plastic brackets are a functional and affordable solution, provided that parts are positioned closer to the rails.
  • If sheet metal manufacturing is available, a bent sheet metal cantilever is a more practical and rational choice.
  • The milled aluminum bracket option is likely to be more expensive while offering comparable performance, making it the least attractive option overall.