Dynamic Bridge Compensation Mechanism

[uloxer]

Hi folks, i'd like to share an idea for discussion:

Dynamic Bridge Compensation Mechanism (DBC) for FDM 3D Printing

I'm not aware of this feature in slicers so please elaborate if you are aware of any that do or discuss specifics that support the idea or render it moot.

This proposal introduces a Dynamic Bridge Compensation Mechanism (BCM) to improve the accuracy and quality of bridges in FDM 3D printing. The mechanism dynamically adjusts the nozzle's Z-height layer-wise and span-wise, enabling bridges that are closer to the intended geometry, minimize sagging, and maintain tension or compression during filament deposition.

Key Features

Layer-Wise Z Compensation (Zb?):

Adjusts Z-height for the first few bridge layers to compensate for drooping or filament misalignment as layers are built.

The Z-height adjustment for each layer is defined as Zb?, where indicates the layer number.

Discussion assumes that the bridge height from the bed would be allowed for in actual values.

Example Adjustments (values shown are purely for representation and would need calibrated) :

Zb1: +0.1 mm (raised for the first bridge layer to reduce initial sag).
Zb2: +0.025 mm (lowered for the second layer to tension the filament and improve adhesion).
Zb3: +0.05 mm (gradual return to standard Z-height).
Zb4: 0.0 mm (returns to normal Z-height).

This example does not push a raised bridge back to nominal and assumes natural sag will be enough.
The first compensation value could be zero also.

2. Span-Wise Z Compensation Using a Function:

Accounts for sag along the bridge span by varying Z-height dynamically across the bridge width.

Compensation is maximum at the center of the span (where sag is greatest) and tapers to zero at the edges.

This could only be applied to the first layer to compensate for the sag and raise it or the subsequent layers to compensate the sag. Subsequent layers could also be used to push a raised bridge back to the neutral position.

The function could be linear or parabolic or use a catenary function, example below:

Catenary Equation:
Z(x) = a * cosh((x - L/2) / a) - C

Where:
Z(x) is the Z-height adjustment at position x.

a is the stiffness parameter based on material properties.
L is the total length of the bridge.
x is the position along the bridge.
C is a constant to ensure the edges have zero compensation (Z(0) = Z(L) = 0).

3. Combining Upward and Downward Adjustments:

Both positive (upward) and negative (downward) adjustments could be used to create bridges that match the native geometry and are horizontal along their span.

4. Material-Dependent Parameters:

The catenary stiffness parameter is based on material properties (e.g., PLA, PETG) and environmental factors (e.g., nozzle temperature, cooling).

Implementation
Layer-Wise Compensation Process:
Each bridge layer receives a unique Z-height adjustment:
The nozzle begins slightly higher for the first layer to reduce initial sag.
Successive layers are adjusted and then gradually return to the standard layer height.

2. Span-Wise Compensation Process:
   Within each bridge layer:
   The nozzle follows a catenary curve or some other function across the span.
   Z compensation is maximum at the center of the span and tapers off at the edges.

3. Integration into Slicer Software:
   Introduce Bridge Layer Compensation Settings for Zb? Values (customizable per layer).
   Add Span-Wise Compensation Profiles with selectable functions (catenary, parabolic, sinusoidal, hybrid).

4. Example G-code Implementation:
   (standard code redacted for clarity)

Layer-Wise Adjustments:
; First bridge layer (Zb1) G1 Z0.3 ; +0.1 mm ; Second bridge layer (Zb2) G1 Z0.55 ; +0.05 mm ; Third bridge layer (Zb3) G1 Z0.7 ; -0.5 mm ; Fourth bridge layer (Zb4) G1 Z0.8 ; -0.1 mm Return to standard Z-height

Advantages

1. Improved Bridge Geometry:
   Aligns bridges with the intended shape using precise Z-compensation.

2. Material Flexibility: Customizable settings for different filaments and environmental conditions.

3. Smooth Transitions: Both layer-wise and span-wise adjustments ensure continuous filament tension without abrupt movements.

4. Reduced Drooping: Dynamic Z-height adjustments counteract filament sagging effectively.

This is a potential solution to bridging sag in FDM 3D printing. By implementing these layer-wise and span-wise compensations, printers can achieve higher-quality, more accurate bridges across a variety of materials and geometries.

I can see this working in a variety of ways, and would need a fair bit of testing to get the compensation right based on the actual response of the material.

What do you think?