# How This 3D Printer Ringing Calculator Estimates Acceleration
Ringing and ghosting on a 3D print are visible echoes of mechanical vibration. They usually appear as repeated ripples after a sharp corner, embossed letter, hole, or sudden infill direction change. The printer reaches a corner, the motion system changes direction, and stored energy in belts, rails, frame members, motor mounts, toolhead plates, and bed supports keeps oscillating after the command has already moved on. This calculator turns the most important first-order variable, moving mass, into a conservative acceleration recommendation.The starting point is Newtonian mechanics: a = F / m. A stepper motor and belt system can only create a limited horizontal force before torque drops, belts stretch, pulleys slip, or steps are missed. The calculator uses a conservative NEMA 17 class force assumption, converts the selected moving mass into kilograms, computes a theoretical acceleration ceiling, then applies a structural safety coefficient. That coefficient intentionally removes 20 to 30 percent of the theoretical limit because real printers are not rigid laboratory axes. 20-30% safety reduction from the theoretical force limit
a = F / m core mass and acceleration relationship
3-24 mm/s bounded jerk or square corner velocity output range
This is a conservative starting point, not an input shaper replacement
Klipper input shaping, accelerometer measurements, and print-based ringing towers can permit higher acceleration than a mass-only estimate. Use this calculator to avoid unreasonable starting values, then validate with real motion tests.
# Which Mass Matters on Cartesian, CoreXY, and Delta Printers
A printer does not always accelerate the same parts on every axis. On a Cartesian bedslinger, the X axis usually moves the toolhead while the Y axis moves the bed, the heater, the magnetic sheet or glass plate, clips, printed parts, and sometimes the cable chain. Because Y-axis bed mass can dominate ringing, this calculator compares the toolhead against a bed-load factor and uses the heavier effective group as the limiting motion mass.On a CoreXY printer, the bed normally moves only in Z, so X/Y ringing is mainly driven by the toolhead, gantry carriage, belt path, and the shared belt forces from the two motors. The calculator increases toolhead mass slightly for CoreXY because the belt path and carriage structure make the motor force less direct than a single straight X belt. On a delta printer, the moving effector is light, but three towers share direction changes, so the calculator treats the effector as the primary inertial load and keeps the result conservative.| Kinematic type | Mass emphasized by the calculator | Why it matters |
|---|---|---|
| Cartesian bedslinger | Toolhead or a reduced bed mass, whichever is larger | The Y bed can be much heavier than the hotend and can excite frame sway. |
| CoreXY | Toolhead mass with a belt-sharing factor | X/Y moves are produced by two motors and a long belt path through the gantry. |
| Delta | Effector mass with a delta factor | The effector is light, but direction changes are coupled through three towers. |
Measure the loaded bed for bedslingers
For a Cartesian Y bed, include the build plate, heater, magnetic sheet, clips, PEI plate, glass if used, and a representative print if you normally run large parts at high speed. The real ringing load is the mass that reverses direction.# Acceleration, Jerk, and Square Corner Velocity Are Related but Not Identical
Acceleration limits how quickly velocity changes over time. In slicer and firmware tuning, higher acceleration shortens slowdowns around corners and makes infill, travel moves, and short segments print faster. It also increases the force demanded from motors and belts. When acceleration is too high for the moving mass and frame stiffness, the printer may skip steps, make harsher motor noise, or show ringing after features.Classic Marlin jerk is a direction-change threshold expressed in millimeters per second. It controls how much instantaneous velocity change the planner allows before applying acceleration limiting. Klipper usessquare_corner_velocity, often shortened to SCV, for a similar corner-speed concept. The units are also millimeters per second, but the planning model differs. That is why this tool changes the output label when Klipper is selected instead of calling the value jerk.Acceleration
Main speed-force limit. It determines how hard the printer pushes the mass during velocity changes.
- mm/s2
- Raises motor force demand
- Strong effect on ringing
Marlin jerk
Corner transition threshold used by Marlin-style planners to avoid slowing for very small velocity changes.
- mm/s
- Firmware-specific behavior
- Too high can make corners harsh
Klipper SCV
Square corner velocity used by Klipper to model cornering speed through direction changes.
- mm/s
- Shown as SCV in this tool
- Usually tuned with input shaping
Firmware terminology matters
If you copy the result into Klipper, use
square_corner_velocity. If you copy it into Marlin settings, use jerk-related fields such as X jerk and Y jerk. The calculator keeps the numeric result conservative but labels it according to the selected firmware.# How Structural Rigidity Changes the Safety Coefficient
Two printers with the same toolhead mass can require different acceleration because the frame and motion system store different amounts of energy. A light cantilever bed, loose V-slot wheels, long unsupported rods, thin printed motor mounts, and flexible toolhead plates all lower usable acceleration. A braced aluminum frame with linear rails, short belt spans, rigid idler stacks, and a compact toolhead can tolerate more acceleration before the same mass produces visible ringing.The rigidity selector is therefore not cosmetic. Low rigidity applies the strongest reduction, medium rigidity represents a typical well-maintained desktop printer, and high rigidity leaves more of the theoretical force limit available. Even the high setting still keeps a reduction because belt stretch, motor torque falloff at speed, current limits, microstepping, and pulley grip prevent real machines from using the full idealF / m number reliably.| Rigidity setting | Typical machine condition | Calculator behavior |
|---|---|---|
| Low | Loose wheels, tall frame, flexible bed support, heavy direct-drive conversion | Most conservative acceleration and lower transition speed. |
| Medium | Stock or tuned desktop printer with reasonably tight motion components | Balanced reduction for everyday tuning. |
| High | Rigid CoreXY, braced frame, linear rails, compact toolhead, verified belts | Higher acceleration while retaining a step-loss margin. |
Raising acceleration after the calculator result
Advantages
- Higher acceleration can reduce print time on small parts with many short moves.
- A rigid frame and input shaping can support higher limits than a simple mass estimate.
- Testing in controlled increments shows where quality starts to degrade.
Disadvantages
- The same increase can make ringing more visible around letters, holes, and corners.
- Loose pulleys, belts, or bed mounts can make even modest acceleration look bad.
- Jumping directly to very high numbers can cause skipped steps and confusing artifacts.
# Reading the Result Table
The recommended acceleration is the main value to copy into firmware or slicer profiles. It is expressed in millimeters per second squared. The theoretical ceiling is shown separately so you can see how much margin was removed by the safety coefficient and target-speed penalty. A big gap between theoretical and recommended is normal because the calculator is designed for print-quality tuning, not for finding the absolute step-loss cliff.The effective moving mass is the mass the calculator considered most important for X/Y ringing. On a bedslinger, this may be influenced by the bed rather than the hotend. On a CoreXY or delta, it will usually be closer to the toolhead or effector value. The limiting motion group tells you which part of the kinematics is driving the estimate, which is useful when deciding whether to lighten the toolhead, replace a bed plate, stiffen the frame, or lower only one axis in firmware.- Effective moving mass
- The estimated inertial load that the X/Y motion system must reverse during direction changes.
- Theoretical ceiling
- Acceleration predicted from the assumed motor force before safety and rigidity reductions.
- Safety coefficient
- A multiplier below 1.0 that reserves torque and stiffness margin to reduce step loss and ringing.
- Ringing risk
- A qualitative indicator based on the force impulse implied by acceleration and mass.
- SCV
- Klipper square corner velocity, a cornering-speed parameter expressed in millimeters per second.
Result interpretation checklist
Use recommended acceleration as the first firmware or slicer limit.
Use SCV for Klipper and jerk for Marlin-style configuration.
If the effective mass is bed-driven, reduce Y acceleration first on a Cartesian printer.
If the result feels low, inspect loose mechanics before simply raising the number.
Validate with a ringing tower, sharp-corner test, or accelerometer input-shaper measurement.
# Practical Workflow for Reducing Ghosting Without Losing Too Much Speed
Start with honest mass values. Weigh the hotend assembly, fans, probe, extruder, printed shroud, cable strain relief, and any toolhead board. For the bed, include everything that moves in Y. If weighing is inconvenient, use the Ender-style and Voron-style presets as reasonable placeholders, then refine the result later. Presets are intentionally ordinary, not best-case marketing values.Apply the calculator result to firmware or slicer limits, then print a small object with sharp text, vertical holes, and square corners at the target speed. Ringing that repeats at a constant distance after each corner indicates mechanical resonance. If ringing improves but print time becomes unacceptable, raise acceleration in small steps, such as 10 percent at a time. If ringing remains strong even below the recommendation, look for belt slack, loose pulley set screws, moving cables, flexible bed springs, worn wheels, rail preload issues, or hotend wobble.- Measure or estimate toolhead and bed mass before changing firmware.
- Select the kinematic type that matches the moving X/Y architecture.
- Use low rigidity for modified bedslingers with heavy direct-drive heads or visibly flexible frames.
- Use high rigidity only when belts, pulleys, rails, and frame screws are already verified.
- Copy the generated text into Klipper or Marlin using the firmware selector.
- Print a validation model and compare ringing distance and amplitude, not only surface gloss.
- Tune pressure advance separately because corner bulging can be confused with ringing.
- Use input shaping for the final high-speed setup when the firmware supports it.
Why mass reduction is powerful
Acceleration force scales directly with mass. Removing 100 g from a toolhead can have the same first-order effect as adding motor force or reducing acceleration demand. That is why compact toolheads, lighter fans, shorter ducts, and remote-drive extruders can improve ringing behavior before any firmware trick is applied.
# Common Mistakes When Setting Acceleration and Jerk
The most common mistake is tuning by a single number copied from another printer. A Voron, Ender, Prusa-style bedslinger, delta, and enclosed custom CoreXY can all print at 150 mm/s, yet their safe acceleration can differ by several multiples. Print speed alone does not define motion stress. Short features rarely reach full speed, so acceleration and cornering parameters often control surface quality more than the nominal slicer speed.Another mistake is treating jerk or SCV as a way to hide poor acceleration settings. A very high transition value can make corners look sharper in motion, but it can also inject abrupt direction changes into the frame and create echoes. A very low value can make the printer slow and rounded at corners. The best result usually comes from a reasonable acceleration limit, moderate corner velocity, firm belts, mechanically tight axes, pressure advance, and input shaping where available.Do not use zero or negative mass
A mass of zero makes the physics undefined because acceleration from
F / m would approach infinity. The interface blocks absurd values and the calculation clamps inputs to keep the result usable. | Symptom | Likely motion setting issue | Mechanical checks |
|---|---|---|
| Repeated ripples after corners | Acceleration too high for mass and stiffness | Belts, frame screws, toolhead wobble, input shaping. |
| Layer shift during fast travel | Acceleration or jerk/SCV too aggressive | Pulley set screws, motor current, belt tooth engagement. |
| Rounded corners and slow small features | Acceleration or corner velocity too low | Planner limits, slicer minimum layer time, pressure advance. |
| Different ringing on X and Y | One axis has higher moving mass or lower stiffness | Bed mass, rail preload, belt path, gantry squareness. |
# Exporting Values to Klipper or Marlin
The copy button produces plain text so the result can be pasted into a printer configuration note, a Klipperprinter.cfg section, or a Marlin tuning record. For Klipper, the output uses max_accel and square_corner_velocity. For Marlin, the output uses acceleration and X/Y jerk-style values. Treat the copied block as a starting configuration, then adapt names if your firmware file uses a board-specific or version-specific format.If your printer supports per-axis acceleration, a Cartesian bedslinger often benefits from a lower Y acceleration than X because the bed is heavier and the printed part adds mass during the job. CoreXY printers usually use a shared X/Y acceleration value, but individual mechanical faults can still make one direction ring more strongly. Delta printers depend heavily on tower stiffness and effector weight, so accelerometer-based validation is especially valuable.Safe tuning sequence
Calculate a conservative acceleration and corner velocity from mass and kinematics.
Apply the generated Klipper or Marlin text as a starting point.
Print a ringing test at the target speed and compare sharp features.
Raise or lower acceleration in small increments while keeping notes.
Run input shaping or resonance compensation after the mechanical baseline is stable.