500 lines
25 KiB
Markdown
500 lines
25 KiB
Markdown
# Resonance Compensation
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Klipper supports Input Shaping - a technique that can be used to reduce ringing
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(also known as echoing, ghosting or rippling) in prints. Ringing is a surface
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printing defect when, typically, elements like edges repeat themselves on a
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printed surface as a subtle 'echo':
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Ringing is caused by mechanical vibrations in the printer due to quick changes
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of the printing direction. Note that ringing usually has mechanical origins:
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insufficiently rigid printer frame, non-tight or too springy belts, alignment
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issues of mechanical parts, heavy moving mass, etc. Those should be checked
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and fixed first, if possible.
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[Input shaping](https://en.wikipedia.org/wiki/Input_shaping) is an open-loop
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control technique which creates a commanding signal that cancels its
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own vibrations. Input shaping requires some tuning and measurements before it
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can be enabled. Besides ringing, Input Shaping typically reduces the vibrations
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and shaking of the printer in general, and may also improve the reliability
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of the stealthChop mode of Trinamic stepper drivers.
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## Tuning
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Basic tuning requires measuring the ringing frequencies of the printer
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by printing a test model.
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Slice the ringing test model, which can be found in
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[docs/prints/ringing_tower.stl](prints/ringing_tower.stl), in the slicer:
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* Suggested layer height is 0.2 or 0.25 mm.
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* Infill and top layers can be set to 0.
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* Use 1-2 perimeters, or even better the smooth vase mode with 1-2 mm base.
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* Use sufficiently high speed, around 80-100 mm/sec, for **external** perimeters.
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* Make sure that the minimum layer time is **at most** 3 seconds.
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* Make sure any "dynamic acceleration control" is disabled in the slicer.
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* Do not turn the model. The model has X and Y marks at the back of the model.
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Note the unusual location of the marks vs. the axes of the printer - it is
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not a mistake. The marks can be used later in the tuning process as a
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reference, because they show which axis the measurements correspond to.
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### Ringing frequency
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First, measure the **ringing frequency**.
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1. If `square_corner_velocity` parameter was changed, revert it back
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to 5.0. It is not advised to increase it when using input shaper
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because it can cause more smoothing in parts - it is better to use
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higher acceleration value instead.
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2. Increase `max_accel_to_decel` by issuing the following command:
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`SET_VELOCITY_LIMIT ACCEL_TO_DECEL=7000`
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3. Disable Pressure Advance: `SET_PRESSURE_ADVANCE ADVANCE=0`
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4. If you have already added `[input_shaper]` section to the printer.cfg,
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execute `SET_INPUT_SHAPER SHAPER_FREQ_X=0 SHAPER_FREQ_Y=0` command. If you
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get "Unknown command" error, you can safely ignore it at this point and
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continue with the measurements.
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5. Execute the command:
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`TUNING_TOWER COMMAND=SET_VELOCITY_LIMIT PARAMETER=ACCEL START=1500 STEP_DELTA=500 STEP_HEIGHT=5`
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Basically, we try to make ringing more pronounced by setting different large
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values for acceleration. This command will increase the acceleration every
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5 mm starting from 1500 mm/sec^2: 1500 mm/sec^2, 2000 mm/sec^2, 2500 mm/sec^2
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and so forth up until 7000 mm/sec^2 at the last band.
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6. Print the test model sliced with the suggested parameters.
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7. You can stop the print earlier if the ringing is clearly visible and you see
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that acceleration gets too high for your printer (e.g. printer shakes too
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much or starts skipping steps).
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8. Use X and Y marks at the back of the model for reference. The measurements
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from the side with X mark should be used for X axis *configuration*, and
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Y mark - for Y axis configuration. Measure the distance *D* (in mm) between
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several oscillations on the part with X mark, near the notches, preferably
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skipping the first oscillation or two. To measure the distance between
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oscillations more easily, mark the oscillations first, then measure the
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distance between the marks with a ruler or calipers:
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9. Count how many oscillations *N* the measured distance *D* corresponds to.
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If you are unsure how to count the oscillations, refer to the picture
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above, which shows *N* = 6 oscillations.
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10. Compute the ringing frequency of X axis as *V* · *N* / *D* (Hz),
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where *V* is the velocity for outer perimeters (mm/sec). For the example
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above, we marked 6 oscillations, and the test was printed at 100 mm/sec
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velocity, so the frequency is 100 * 6 / 12.14 ≈ 49.4 Hz.
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11. Do (8) - (10) for Y mark as well.
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Note that ringing on the test print should follow the pattern of the curved
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notches, as in the picture above. If it doesn't, then this defect is not really
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a ringing and has a different origin - either mechanical, or an extruder issue.
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It should be fixed first before enabling and tuning input shapers.
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If the measurements are not reliable because, say, the distance
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between the oscillations is not stable, it might mean that the printer has
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several resonance frequencies on the same axis. One may try to follow the
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tuning process described in
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[Unreliable measurements of ringing frequencies](#unreliable-measurements-of-ringing-frequencies)
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section instead and still get something out of the input shaping technique.
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Ringing frequency can depend on the position of the model within the buildplate
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and Z height, *especially on delta printers*; you can check if you see the
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differences in frequencies at different positions along the sides of the test
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model and at different heights. You can calculate the average ringing
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frequencies over X and Y axes if that is the case.
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If the measured ringing frequency is very low (below approx 20-25 Hz), it might
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be a good idea to invest into stiffening the printer or decreasing the moving
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mass - depending on what is applicable in your case - before proceeding with
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further input shaping tuning, and re-measuring the frequencies afterwards. For
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many popular printer models there are often some solutions available already.
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Note that the ringing frequencies can change if the changes are made to the
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printer that affect the moving mass or change the stiffness of the system,
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for example:
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* Some tools are installed, removed or replaced on the toolhead that change
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its mass, e.g. a new (heavier or lighter) stepper motor for direct extruder
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or a new hotend is installed, heavy fan with a duct is added, etc.
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* Belts are tightened.
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* Some addons to increase frame rigidity are installed.
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* Different bed is installed on a bed-slinger printer, or glass added, etc.
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If such changes are made, it is a good idea to at least measure the ringing
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frequencies to see if they have changed.
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### Input shaper configuration
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After the ringing frequencies for X and Y axes are measured, you can add the
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following section to your `printer.cfg`:
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```
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[input_shaper]
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shaper_freq_x: ... # frequency for the X mark of the test model
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shaper_freq_y: ... # frequency for the Y mark of the test model
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```
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For the example above, we get shaper_freq_x/y = 49.4.
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### Choosing input shaper
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Klipper supports several input shapers. They differ in their sensitivity to
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errors determining the resonance frequency and how much smoothing they cause
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in the printed parts. Also, some of the shapers like 2HUMP_EI and 3HUMP_EI
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should usually not be used with shaper_freq = resonance frequency - they are
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configured from different considerations to reduce several resonances at once.
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For most of the printers, either MZV or EI shapers can be recommended. This
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section describes a testing process to choose between them, and figure out
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a few other related parameters.
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Print the ringing test model as follows:
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1. Restart the firmware: `RESTART`
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2. Prepare for test: `SET_VELOCITY_LIMIT ACCEL_TO_DECEL=7000`
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3. Disable Pressure Advance: `SET_PRESSURE_ADVANCE ADVANCE=0`
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4. Execute: `SET_INPUT_SHAPER SHAPER_TYPE=MZV`
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5. Execute the command:
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`TUNING_TOWER COMMAND=SET_VELOCITY_LIMIT PARAMETER=ACCEL START=1500 STEP_DELTA=500 STEP_HEIGHT=5`
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6. Print the test model sliced with the suggested parameters.
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If you see no ringing at this point, then MZV shaper can be recommended for use.
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If you do see some ringing, re-measure the frequencies using steps (8)-(10)
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described in [Ringing frequency](#ringing-frequency) section. If the frequencies
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differ significantly from the values you obtained earlier, a more complex input
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shaper configuration is needed. You can refer to Technical details of
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[Input shapers](#input-shapers) section. Otherwise, proceed to the next step.
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Now try EI input shaper. To try it, repeat steps (1)-(6) from above, but
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executing at step 4 the following command instead:
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`SET_INPUT_SHAPER SHAPER_TYPE=EI`.
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Compare two prints with MZV and EI input shaper. If EI shows noticeably better
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results than MZV, use EI shaper, otherwise prefer MZV. Note that EI shaper will
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cause more smoothing in printed parts (see the next section for further
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details). Add `shaper_type: mzv` (or ei) parameter to [input_shaper] section,
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e.g.:
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```
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[input_shaper]
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shaper_freq_x: ...
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shaper_freq_y: ...
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shaper_type: mzv
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```
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A few notes on shaper selection:
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* EI shaper may be more suited for bed slinger printers (if the resonance
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frequency and resulting smoothing allows): as more filament is deposited
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on the moving bed, the mass of the bed increases and the resonance frequency
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will decrease. Since EI shaper is more robust to resonance frequency
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changes, it may work better when printing large parts.
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* Due to the nature of delta kinematics, resonance frequencies can differ a
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lot in different parts of the build volume. Therefore, EI shaper can be a
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better fit for delta printers rather than MZV or ZV, and should be
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considered for the use. If the resonance frequency is sufficiently large
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(more than 50-60 Hz), then one can even attempt to test 2HUMP_EI shaper
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(by running the suggested test above with
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`SET_INPUT_SHAPER SHAPER_TYPE=2HUMP_EI`), but check the considerations in
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the [section below](#selecting-max_accel) before enabling it.
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### Selecting max_accel
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You should have a printed test for the shaper you chose from the previous step
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(if you don't, print the test model sliced with the
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[suggested parameters](#tuning) with the pressure advance disabled
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`SET_PRESSURE_ADVANCE ADVANCE=0` and with the tuning tower enabled as
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`TUNING_TOWER COMMAND=SET_VELOCITY_LIMIT PARAMETER=ACCEL START=1500 STEP_DELTA=500 STEP_HEIGHT=5`).
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Note that at very high accelerations, depending on the resonance frequency and
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the input shaper you chose (e.g. EI shaper creates more smoothing than MZV),
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input shaping may cause too much smoothing and rounding of the parts. So,
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max_accel should be chosen such as to prevent that. Another parameter that can
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impact smoothing is `square_corner_velocity`, so it is not advisable to increase
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it above the default 5 mm/sec to prevent increased smoothing.
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In order to select a suitable max_accel value, inspect the model for the chosen
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input shaper. First, take a note at which acceleration ringing is still small -
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that you are comfortable with it.
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Next, check the smoothing. To help with that, the test model has a small gap
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in the wall (0.15 mm):
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As the acceleration increases, so does the smoothing, and the actual gap in
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the print widens:
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In this picture, the acceleration increases left to right, and the gap starts
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to grow starting from 3500 mm/sec^2 (5-th band from the left). So the good
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value for max_accel = 3000 (mm/sec^2) in this case to avoid the excessive
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smoothing.
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Note the acceleration when the gap is still very small in your test print.
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If you see bulges, but no gap in the wall at all, even at high accelerations,
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it may be due to disabled Pressure Advance, especially on Bowden extruders.
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If that is the case, you may need to repeat the print with the PA enabled.
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It may also be a result of a miscalibrated (too high) filament flow, so it is
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a good idea to check that too.
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Choose the minimum out of the two acceleration values (from ringing and
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smoothing), and put it as `max_accel` into printer.cfg.
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As a note, it may happen - especially at low ringing frequencies - that EI
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shaper will cause too much smoothing even at lower accelerations. In this case,
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MZV may be a better choice, because it may allow higher acceleration values.
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At very low ringing frequencies (~25 Hz and below) even MZV shaper may create
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too much smoothing. If that is the case, you can also try to repeat the
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steps in [Choosing input shaper](#choosing-input-shaper) section with ZV shaper,
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by using `SET_INPUT_SHAPER SHAPER_TYPE=ZV` command instead. ZV shaper should
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show even less smoothing than MZV, but is more sensitive to errors in measuring
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the ringing frequencies.
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Another consideration is that if a resonance frequency is too low (below 20-25
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Hz), it might be a good idea to increase the printer stiffness or reduce the
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moving mass. Otherwise, acceleration and printing speed may be limited due too
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much smoothing now instead of ringing.
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### Fine-tuning resonance frequencies
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Note that the precision of the resonance frequencies measurements using the
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ringing test model is sufficient for most purposes, so further tuning is not
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advised. If you still want to try to double-check your results (e.g. if you
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still see some ringing after printing a test model with an input shaper of
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your choice with the same frequencies as you have measured earlier), you can
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follow the steps in this section. Note that if you see ringing at different
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frequencies after enabling [input_shaper], this section will not help with that.
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Assuming that you have sliced the ringing model with suggested
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parameters, complete the following steps for each of the axes X and Y:
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1. Prepare for test: `SET_VELOCITY_LIMIT ACCEL_TO_DECEL=7000`
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2. Make sure Pressure Advance is disabled: `SET_PRESSURE_ADVANCE ADVANCE=0`
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3. Execute: `SET_INPUT_SHAPER SHAPER_TYPE=ZV`
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4. From the existing ringing test model with your chosen input shaper select
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the acceleration that shows ringing sufficiently well, and set it with:
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`SET_VELOCITY_LIMIT ACCEL=...`
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5. Calculate the necessary parameters for the `TUNING_TOWER` command to tune
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`shaper_freq_x` parameter as follows: start = shaper_freq_x * 83 / 132 and
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factor = shaper_freq_x / 66, where `shaper_freq_x` here is the current value
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in `printer.cfg`.
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6. Execute the command:
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`TUNING_TOWER COMMAND=SET_INPUT_SHAPER PARAMETER=SHAPER_FREQ_X START=start FACTOR=factor BAND=5`
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using `start` and `factor` values calculated at step (5).
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7. Print the test model.
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8. Reset the original frequency value:
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`SET_INPUT_SHAPER SHAPER_FREQ_X=...`.
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9. Find the band which shows ringing the least and count its number from the
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bottom starting at 1.
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10. Calculate the new shaper_freq_x value via old
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shaper_freq_x * (39 + 5 * #band-number) / 66.
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Repeat these steps for the Y axis in the same manner, replacing references to X
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axis with the axis Y (e.g. replace `shaper_freq_x` with `shaper_freq_y` in
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the formulae and in the `TUNING_TOWER` command).
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As an example, let's assume you have had measured the ringing frequency for one
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of the axis equal to 45 Hz. This gives start = 45 * 83 / 132 = 28.30
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and factor = 45 / 66 = 0.6818 values for `TUNING_TOWER` command.
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Now let's assume that after printing the test model, the fourth band from the
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bottom gives the least ringing. This gives the updated shaper_freq_? value
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equal to 45 * (39 + 5 * 4) / 66 ≈ 40.23.
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After both new `shaper_freq_x` and `shaper_freq_y` parameters have been
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calculated, you can update `[input_shaper]` section in `printer.cfg` with the
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new `shaper_freq_x` and `shaper_freq_y` values.
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### Pressure Advance
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If you use Pressure Advance, it may need to be re-tuned. Follow the
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[instructions](Pressure_Advance.md#tuning-pressure-advance) to find
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the new value, if it differs from the previous one. Make sure to
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restart Klipper before tuning Pressure Advance.
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### Unreliable measurements of ringing frequencies
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If you are unable to measure the ringing frequencies, e.g. if the distance
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between the oscillations is not stable, you may still be able to take advantage
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of input shaping techniques, but the results may not be as good as with proper
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measurements of the frequencies, and will require a bit more tuning and printing
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the test model. Note that another possibility is to purchase and install an
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accelerometer and measure the resonances with it (refer to the
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[docs](Measuring_Resonances.md) describing the required hardware and the setup
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process) - but this option requires some crimping and soldering.
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For tuning, add empty `[input_shaper]` section to your
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`printer.cfg`. Then, assuming that you have sliced the ringing model
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with suggested parameters, print the test model 3 times as
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follows. First time, prior to printing, run
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1. `RESTART`
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2. `SET_VELOCITY_LIMIT ACCEL_TO_DECEL=7000`
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3. `SET_PRESSURE_ADVANCE ADVANCE=0`
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4. `SET_INPUT_SHAPER SHAPER_TYPE=2HUMP_EI SHAPER_FREQ_X=60 SHAPER_FREQ_Y=60`
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5. `TUNING_TOWER COMMAND=SET_VELOCITY_LIMIT PARAMETER=ACCEL START=1500 STEP_DELTA=500 STEP_HEIGHT=5`
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and print the model. Then print the model again, but before printing run instead
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1. `SET_INPUT_SHAPER SHAPER_TYPE=2HUMP_EI SHAPER_FREQ_X=50 SHAPER_FREQ_Y=50`
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2. `TUNING_TOWER COMMAND=SET_VELOCITY_LIMIT PARAMETER=ACCEL START=1500 STEP_DELTA=500 STEP_HEIGHT=5`
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Then print the model for the 3rd time, but now run
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1. `SET_INPUT_SHAPER SHAPER_TYPE=2HUMP_EI SHAPER_FREQ_X=40 SHAPER_FREQ_Y=40`
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2. `TUNING_TOWER COMMAND=SET_VELOCITY_LIMIT PARAMETER=ACCEL START=1500 STEP_DELTA=500 STEP_HEIGHT=5`
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Essentially, we are printing the ringing test model with TUNING_TOWER using
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2HUMP_EI shaper with shaper_freq = 60 Hz, 50 Hz, and 40 Hz.
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If none of the models demonstrate improvements in ringing, then, unfortunately,
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it does not look like the input shaping techniques can help with your case.
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Otherwise, it may be that all models show no ringing, or some show the ringing
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and some - not so much. Choose the test model with the highest frequency that
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still shows good improvements in ringing. For example, if 40 Hz and 50 Hz models
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show almost no ringing, and 60 Hz model already shows some more ringing, stick
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with 50 Hz.
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Now check if EI shaper would be good enough in your case. Choose EI shaper
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frequency based on the frequency of 2HUMP_EI shaper you chose:
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* For 2HUMP_EI 60 Hz shaper, use EI shaper with shaper_freq = 50 Hz.
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* For 2HUMP_EI 50 Hz shaper, use EI shaper with shaper_freq = 40 Hz.
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* For 2HUMP_EI 40 Hz shaper, use EI shaper with shaper_freq = 33 Hz.
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Now print the test model one more time, running
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1. `SET_INPUT_SHAPER SHAPER_TYPE=EI SHAPER_FREQ_X=... SHAPER_FREQ_Y=...`
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2. `TUNING_TOWER COMMAND=SET_VELOCITY_LIMIT PARAMETER=ACCEL START=1500 STEP_DELTA=500 STEP_HEIGHT=5`
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providing the shaper_freq_x=... and shaper_freq_y=... as determined previously.
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If EI shaper shows very comparable good results as 2HUMP_EI shaper, stick with
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EI shaper and the frequency determined earlier, otherwise use 2HUMP_EI shaper
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with the corresponding frequency. Add the results to `printer.cfg` as, e.g.
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```
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[input_shaper]
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shaper_freq_x: 50
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shaper_freq_y: 50
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shaper_type: 2hump_ei
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```
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Continue the tuning with [Selecting max_accel](#selecting-max_accel) section.
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## Troubleshooting and FAQ
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### I cannot get reliable measurements of resonance frequencies
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First, make sure it is not some other problem with the printer instead of
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ringing. If the measurements are not reliable because, say, the distance
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between the oscillations is not stable, it might mean that the printer has
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several resonance frequencies on the same axis. One may try to follow the
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tuning process described in
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[Unreliable measurements of ringing frequencies](#unreliable-measurements-of-ringing-frequencies)
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section and still get something out of the input shaping technique. Another
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possibility is to install an accelerometer, [measure](Measuring_Resonances.md)
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the resonances with it, and auto-tune the input shaper using the results of
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those measurements.
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### After enabling [input_shaper], I get too smoothed printed parts and fine details are lost
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Check the considerations in [Selecting max_accel](#selecting-max_accel) section.
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|
If the resonance frequency is low, one should not set too high max_accel or
|
|
increase square_corner_velocity parameters. It might also be better to choose
|
|
MZV or even ZV input shapers over EI (or 2HUMP_EI and 3HUMP_EI shapers).
|
|
|
|
|
|
### After successfully printing for some time without ringing, it appears to come back
|
|
|
|
It is possible that after some time the resonance frequencies have changed.
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|
E.g. maybe the belts tension has changed (belts got more loose), etc. It is a
|
|
good idea to check and re-measure the ringing frequencies as described in
|
|
[Ringing frequency](#ringing-frequency) section and update your config file
|
|
if necessary.
|
|
|
|
### Is dual carriage setup supported with input shapers?
|
|
|
|
There is no dedicated support for dual carriages with input shapers, but it does
|
|
not mean this setup will not work. One should run the tuning twice for each
|
|
of the carriages, and calculate the ringing frequencies for X and Y axes for
|
|
each of the carriages independently. Then put the values for carriage 0 into
|
|
[input_shaper] section, and change the values on the fly when changing
|
|
carriages, e.g. as a part of some macro:
|
|
```
|
|
SET_DUAL_CARRIAGE CARRIAGE=1
|
|
SET_INPUT_SHAPER SHAPER_FREQ_X=... SHAPER_FREQ_Y=...
|
|
```
|
|
|
|
And similarly when switching back to carriage 0.
|
|
|
|
### Does input_shaper affect print time?
|
|
|
|
No, `input_shaper` feature has pretty much no impact on the print times by
|
|
itself. However, the value of `max_accel` certainly does (tuning of this
|
|
parameter described in [this section](#selecting-max_accel)).
|
|
|
|
## Technical details
|
|
|
|
### Input shapers
|
|
|
|
Input shapers used in Klipper are rather standard, and one can find more
|
|
in-depth overview in the articles describing the corresponding shapers.
|
|
This section contains a brief overview of some technical aspects of the
|
|
supported input shapers. The table below shows some (usually approximate)
|
|
parameters of each shaper.
|
|
|
|
| Input <br> shaper | Shaper <br> duration | Vibration reduction 20x <br> (5% vibration tolerance) | Vibration reduction 10x <br> (10% vibration tolerance) |
|
|
|:--:|:--:|:--:|:--:|
|
|
| ZV | 0.5 / shaper_freq | N/A | ± 5% shaper_freq |
|
|
| MZV | 0.75 / shaper_freq | ± 4% shaper_freq | -10%...+15% shaper_freq |
|
|
| ZVD | 1 / shaper_freq | ± 15% shaper_freq | ± 22% shaper_freq |
|
|
| EI | 1 / shaper_freq | ± 20% shaper_freq | ± 25% shaper_freq |
|
|
| 2HUMP_EI | 1.5 / shaper_freq | ± 35% shaper_freq | ± 40 shaper_freq |
|
|
| 3HUMP_EI | 2 / shaper_freq | -45...+50% shaper_freq | -50%...+55% shaper_freq |
|
|
|
|
A note on vibration reduction: the values in the table above are approximate.
|
|
If the damping ratio of the printer is known for each axis, the shaper can be
|
|
configured more precisely and it will then reduce the resonances in a bit wider
|
|
range of frequencies. However, the damping ratio is usually unknown and is hard
|
|
to estimate without a special equipment, so Klipper uses 0.1 value by default,
|
|
which is a good all-round value. The frequency ranges in the table cover a
|
|
number of different possible damping ratios around that value (approx. from 0.05
|
|
to 0.2).
|
|
|
|
Also note that EI, 2HUMP_EI, and 3HUMP_EI are tuned to reduce vibrations to 5%,
|
|
so the values for 10% vibration tolerance are provided only for the reference.
|
|
|
|
**How to use this table:**
|
|
|
|
* Shaper duration affects the smoothing in parts - the larger it is, the more
|
|
smooth the parts are. This dependency is not linear, but can give a sense of
|
|
which shapers 'smooth' more for the same frequency. The ordering by
|
|
smoothing is like this: ZV < MZV < ZVD ≈ EI < 2HUMP_EI < 3HUMP_EI. Also,
|
|
it is rarely practical to set shaper_freq = resonance freq for shapers
|
|
2HUMP_EI and 3HUMP_EI (they should be used to reduce vibrations for several
|
|
frequencies).
|
|
* One can estimate a range of frequencies in which the shaper reduces
|
|
vibrations. For example, MZV with shaper_freq = 35 Hz reduces vibrations
|
|
to 5% for frequencies [33.6, 36.4] Hz. 3HUMP_EI with shaper_freq = 50 Hz
|
|
reduces vibrations to 5% in range [27.5, 75] Hz.
|
|
* One can use this table to check which shaper they should be using if they
|
|
need to reduce vibrations at several frequencies. For example, if one has
|
|
resonances at 35 Hz and 60 Hz on the same axis: a) EI shaper needs to have
|
|
shaper_freq = 35 / (1 - 0.2) = 43.75 Hz, and it will reduce resonances
|
|
until 43.75 * (1 + 0.2) = 52.5 Hz, so it is not sufficient; b) 2HUMP_EI
|
|
shaper needs to have shaper_freq = 35 / (1 - 0.35) = 53.85 Hz and will
|
|
reduce vibrations until 53.85 * (1 + 0.35) = 72.7 Hz - so this is an
|
|
acceptable configuration. Always try to use as high shaper_freq as possible
|
|
for a given shaper (perhaps with some safety margin, so in this example
|
|
shaper_freq ≈ 50-52 Hz would work best), and try to use a shaper with as
|
|
small shaper duration as possible.
|
|
* If one needs to reduce vibrations at several very different frequencies
|
|
(say, 30 Hz and 100 Hz), they may see that the table above does not provide
|
|
enough information. In this case one may have more luck with
|
|
[scripts/graph_shaper.py](../scripts/graph_shaper.py)
|
|
script, which is more flexible.
|