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# Measuring Resonances

Klipper has built-in support for the ADXL345, MPU-9250 and LIS2DW compatible accelerometers which can be used to measure resonance frequencies of the printer for different axes, and auto-tune input shapers to compensate for resonances. Note that using accelerometers requires some soldering and crimping. The ADXL345/LIS2DW can be connected to the SPI interface of a Raspberry Pi or MCU board (it needs to be reasonably fast). The MPU family can be connected to the I2C interface of a Raspberry Pi directly, or to an I2C interface of an MCU board that supports 400kbit/s fast mode in Klipper.

When sourcing accelerometers, be aware that there are a variety of different PCB board designs and different clones of them. If it is going to be connected to a 5V printer MCU ensure it has a voltage regulator and level shifters.

For ADXL345s/LIS2DWs, make sure that the board supports SPI mode (a small number of boards appear to be hard-configured for I2C by pulling SDO to GND).

For MPU-9250/MPU-9255/MPU-6515/MPU-6050/MPU-6500s there are also a variety of board designs and clones with different I2C pull-up resistors which will need supplementing.

## MCUs with Klipper I2C fast-mode Support

MCU Family | MCU(s) Tested | MCU(s) with Support
--- | --- | ---
Raspberry Pi | 3B+, Pico | 3A, 3A+, 3B, 4
AVR ATmega | ATmega328p | ATmega32u4, ATmega128, ATmega168, ATmega328, ATmega644p, ATmega1280, ATmega1284, ATmega2560
AVR AT90 | - | AT90usb646, AT90usb1286

## Installation instructions

### Wiring

An ethernet cable with shielded twisted pairs (cat5e or better) is recommended for signal integrity over a long distance. If you still experience signal integrity issues (SPI/I2C errors):

- Double check the wiring with a digital multimeter for:
  - Correct connections when turned off (continuity)
  - Correct power and ground voltages
- I2C only:
  - Check the SCL and SDA lines' resistances to 3.3V are in the range of 900 ohms to 1.8K
  - For full technical details consult chapter 7 of the I2C-bus specification and user manual UM10204 for fast-mode
- Shorten the cable

Connect ethernet cable shielding only to the MCU board/Pi ground.

Double-check your wiring before powering up to prevent damaging your MCU/Raspberry Pi or the accelerometer.

### SPI Accelerometers

Suggested twisted pair order for three twisted pairs:

    GND+MISO
    3.3V+MOSI
    SCLK+CS

Note that unlike a cable shield, GND must be connected at both ends.

#### ADXL345

##### Direct to Raspberry Pi

Note: Many MCUs will work with an ADXL345 in SPI mode (e.g. Pi Pico), wiring and configuration will vary according to your specific board and available pins.

You need to connect ADXL345 to your Raspberry Pi via SPI. Note that the I2C connection, which is suggested by ADXL345 documentation, has too low throughput and will not work. The recommended connection scheme:

ADXL345 pin | RPi pin | RPi pin name
--- | --- | ---
3V3 (or VCC) | 01 | 3.3V DC power
GND | 06 | Ground
CS | 24 | GPIO08 (SPI0_CE0_N)
SDO | 21 | GPIO09 (SPI0_MISO)
SDA | 19 | GPIO10 (SPI0_MOSI)
SCL | 23 | GPIO11 (SPI0_SCLK)

Fritzing wiring diagrams for some of the ADXL345 boards:

##### Using Raspberry Pi Pico

You may connect the ADXL345 to your Raspberry Pi Pico and then connect the Pico to your Raspberry Pi via USB. This makes it easy to reuse the accelerometer on other Klipper devices, as you can connect via USB instead of GPIO. The Pico does not have much processing power, so make sure it is only running the accelerometer and not performing any other duties.

In order to avoid damage to your RPi make sure to connect the ADXL345 to 3.3V only. Depending on the board's layout, a level shifter may be present, which makes 5V dangerous for your RPi.

ADXL345 pin | Pico pin | Pico pin name
--- | --- | ---
3V3 (or VCC) | 36 | 3.3V DC power
GND | 38 | Ground
CS | 2 | GP1 (SPI0_CSn)
SDO | 1 | GP0 (SPI0_RX)
SDA | 5 | GP3 (SPI0_TX)
SCL | 4 | GP2 (SPI0_SCK)

Wiring diagrams for some of the ADXL345 boards:

### I2C Accelerometers

Suggested twisted pair order for three pairs (preferred):

    3.3V+GND
    SDA+GND
    SCL+GND

or for two pairs:

    3.3V+SDA
    GND+SCL

Note that unlike a cable shield, any GND(s) should be connected at both ends.

#### MPU-9250/MPU-9255/MPU-6515/MPU-6050/MPU-6500

These accelerometers have been tested to work over I2C on the RPi, RP2040 (Pico) and AVR at 400kbit/s (fast mode). Some MPU accelerometer modules include pull-ups, but some are too large at 10K and must be changed or supplemented by smaller parallel resistors.

Recommended connection scheme for I2C on the Raspberry Pi:

MPU-9250 pin | RPi pin | RPi pin name
--- | --- | ---
VCC | 01 | 3.3v DC power
GND | 09 | Ground
SDA | 03 | GPIO02 (SDA1)
SCL | 05 | GPIO03 (SCL1)

The RPi has buit-in 1.8K pull-ups on both SCL and SDA.

Recommended connection scheme for I2C (i2c0a) on the RP2040:

MPU-9250 pin | RP2040 pin | RP2040 pin name
--- | --- | ---
VCC | 36 | 3v3
GND | 38 | Ground
SDA | 01 | GP0 (I2C0 SDA)
SCL | 02 | GP1 (I2C0 SCL)

The Pico does not include any built-in I2C pull-up resistors.

##### Recommended connection scheme for I2C(TWI) on the AVR ATmega328P Arduino Nano:

MPU-9250 pin | Atmega328P TQFP32 pin | Atmega328P pin name | Arduino Nano pin
--- | --- | --- | ---
VCC | 39 | - | -
GND | 38 | Ground | GND
SDA | 27 | SDA | A4
SCL | 28 | SCL | A5

The Arduino Nano does not include any built-in pull-up resistors nor a 3.3V power pin.

### Mounting the accelerometer

The accelerometer must be attached to the toolhead. One needs to design a proper mount that fits their own 3D printer. It is better to align the axes of the accelerometer with the printer's axes (but if it makes it more convenient, axes can be swapped - i.e. no need to align X axis with X and so forth - it should be fine even if Z axis of accelerometer is X axis of the printer, etc.).

An example of mounting ADXL345 on the SmartEffector:

Note that on a bed slinger printer one must design 2 mounts: one for the toolhead and one for the bed, and run the measurements twice. See the corresponding section for more details.

Attention: make sure the accelerometer and any screws that hold it in place do not touch any metal parts of the printer. Basically, the mount must be designed such as to ensure the electrical isolation of the accelerometer from the printer frame. Failing to ensure that can create a ground loop in the system that may damage the electronics.

### Software installation

Note that resonance measurements and shaper auto-calibration require additional software dependencies not installed by default. First, run on your Raspberry Pi the following commands:

    sudo apt update
    sudo apt install python3-numpy python3-matplotlib libatlas-base-dev libopenblas-dev

Next, in order to install NumPy in the Klipper environment, run the command:

    ~/klippy-env/bin/pip install -v numpy

Note that, depending on the performance of the CPU, it may take a lot of time, up to 10-20 minutes. Be patient and wait for the completion of the installation. On some occasions, if the board has too little RAM the installation may fail and you will need to enable swap.

#### Configure ADXL345 With RPi

First, check and follow the instructions in the RPi Microcontroller document to setup the "linux mcu" on the Raspberry Pi. This will configure a second Klipper instance that runs on your Pi.

Make sure the Linux SPI driver is enabled by running `sudo raspi-config` and enabling SPI under the "Interfacing options" menu.

Add the following to the printer.cfg file:

    [mcu rpi]
    serial: /tmp/klipper_host_mcu

    [adxl345]
    cs_pin: rpi:None

    [resonance_tester]
    accel_chip: adxl345
    probe_points:
        100, 100, 20  # an example

It is advised to start with 1 probe point, in the middle of the print bed, slightly above it.

#### Configure ADXL345 With Pi Pico

##### Flash the Pico Firmware

On your Raspberry Pi, compile the firmware for the Pico.

    cd ~/klipper
    make clean
    make menuconfig

Now, while holding down the `BOOTSEL` button on the Pico, connect the Pico to the Raspberry Pi via USB. Compile and flash the firmware.

    make flash FLASH_DEVICE=first

If that fails, you will be told which `FLASH_DEVICE` to use. In this example, that's `make flash FLASH_DEVICE=2e8a:0003`.

##### Configure the Connection

The Pico will now reboot with the new firmware and should show up as a serial device. Find the pico serial device with `ls /dev/serial/by-id/*`. You can now add an `adxl.cfg` file with the following settings:

    [mcu adxl]
    # Change <mySerial> to whatever you found above. For example,
    # usb-Klipper_rp2040_E661640843545B2E-if00
    serial: /dev/serial/by-id/usb-Klipper_rp2040_<mySerial>

    [adxl345]
    cs_pin: adxl:gpio1
    spi_bus: spi0a
    axes_map: x,z,y

    [resonance_tester]
    accel_chip: adxl345
    probe_points:
        # Somewhere slightly above the middle of your print bed
        147,154, 20

    [output_pin power_mode] # Improve power stability
    pin: adxl:gpio23

If setting up the ADXL345 configuration in a separate file, as shown above, you'll also want to modify your `printer.cfg` file to include this:

    [include adxl.cfg] # Comment this out when you disconnect the accelerometer

Restart Klipper via the `RESTART` command.

#### Configure LIS2DW series

    [mcu lis]
    # Change <mySerial> to whatever you found above. For example,
    # usb-Klipper_rp2040_E661640843545B2E-if00
    serial: /dev/serial/by-id/usb-Klipper_rp2040_<mySerial>

    [lis2dw]
    cs_pin: lis:gpio1
    spi_bus: spi0a
    axes_map: x,z,y

    [resonance_tester]
    accel_chip: lis2dw
    probe_points:
        # Somewhere slightly above the middle of your print bed
        147,154, 20

#### Configure MPU-6000/9000 series With RPi

Make sure the Linux I2C driver is enabled and the baud rate is set to 400000 (see Enabling I2C section for more details). Then, add the following to the printer.cfg:

    [mcu rpi]
    serial: /tmp/klipper_host_mcu

    [mpu9250]
    i2c_mcu: rpi
    i2c_bus: i2c.1

    [resonance_tester]
    accel_chip: mpu9250
    probe_points:
        100, 100, 20  # an example

#### Configure MPU-9520 Compatibles With Pico

Pico I2C is set to 400000 on default. Simply add the following to the printer.cfg:

    [mcu pico]
    serial: /dev/serial/by-id/<your Pico's serial ID>

    [mpu9250]
    i2c_mcu: pico
    i2c_bus: i2c0a

    [resonance_tester]
    accel_chip: mpu9250
    probe_points:
        100, 100, 20  # an example

    [static_digital_output pico_3V3pwm] # Improve power stability
    pins: pico:gpio23

#### Configure MPU-9520 Compatibles with AVR

AVR I2C will be set to 400000 by the mpu9250 option. Simply add the following to the printer.cfg:

    [mcu nano]
    serial: /dev/serial/by-id/<your nano's serial ID>

    [mpu9250]
    i2c_mcu: nano

    [resonance_tester]
    accel_chip: mpu9250
    probe_points:
        100, 100, 20  # an example

Restart Klipper via the `RESTART` command.

## Measuring the resonances

### Checking the setup

Now you can test a connection.

- For "non bed-slingers" (e.g. one accelerometer), in Octoprint, enter `ACCELEROMETER_QUERY`
- For "bed-slingers" (e.g. more than one accelerometer), enter `ACCELEROMETER_QUERY CHIP=<chip>` where `<chip>` is the name of the chip as-entered, e.g. `CHIP=bed` (see: bed-slinger) for all installed accelerometer chips.

You should see the current measurements from the accelerometer, including the free-fall acceleration, e.g.

    Recv: // adxl345 values (x, y, z): 470.719200, 941.438400, 9728.196800

If you get an error like `Invalid adxl345 id (got xx vs e5)`, where `xx` is some other ID, immediately try again. There's an issue with SPI initialization. If you still get an error, it is indicative of the connection problem with ADXL345, or the faulty sensor. Double-check the power, the wiring (that it matches the schematics, no wire is broken or loose, etc.), and soldering quality.

If you are using a MPU-9250 compatible accelerometer and it shows up as `mpu-unknown`, use with caution! They are probably refurbished chips!

Next, try running `MEASURE_AXES_NOISE` in Octoprint, you should get some baseline numbers for the noise of accelerometer on the axes (should be somewhere in the range of ~1-100). Too high axes noise (e.g. 1000 and more) can be indicative of the sensor issues, problems with its power, or too noisy imbalanced fans on a 3D printer.

### Measuring the resonances

Now you can run some real-life tests. Run the following command:

    TEST_RESONANCES AXIS=X

Note that it will create vibrations on X axis. It will also disable input shaping if it was enabled previously, as it is not valid to run the resonance testing with the input shaper enabled.

Attention! Be sure to observe the printer for the first time, to make sure the vibrations do not become too violent (`M112` command can be used to abort the test in case of emergency; hopefully it will not come to this though). If the vibrations do get too strong, you can attempt to specify a lower than the default value for `accel_per_hz` parameter in `[resonance_tester]` section, e.g.

    [resonance_tester]
    accel_chip: adxl345
    accel_per_hz: 50  # default is 75
    probe_points: ...

If it works for X axis, run for Y axis as well:

    TEST_RESONANCES AXIS=Y

This will generate 2 CSV files (`/tmp/resonances_x_*.csv` and `/tmp/resonances_y_*.csv`). These files can be processed with the stand-alone script on a Raspberry Pi. To do that, run the following commands:

    ~/klipper/scripts/calibrate_shaper.py /tmp/resonances_x_*.csv -o /tmp/shaper_calibrate_x.png
    ~/klipper/scripts/calibrate_shaper.py /tmp/resonances_y_*.csv -o /tmp/shaper_calibrate_y.png

This script will generate the charts `/tmp/shaper_calibrate_x.png` and `/tmp/shaper_calibrate_y.png` with frequency responses. You will also get the suggested frequencies for each input shaper, as well as which input shaper is recommended for your setup. For example:

    Fitted shaper 'zv' frequency = 34.4 Hz (vibrations = 4.0%, smoothing ~= 0.132)
    To avoid too much smoothing with 'zv', suggested max_accel <= 4500 mm/sec^2
    Fitted shaper 'mzv' frequency = 34.6 Hz (vibrations = 0.0%, smoothing ~= 0.170)
    To avoid too much smoothing with 'mzv', suggested max_accel <= 3500 mm/sec^2
    Fitted shaper 'ei' frequency = 41.4 Hz (vibrations = 0.0%, smoothing ~= 0.188)
    To avoid too much smoothing with 'ei', suggested max_accel <= 3200 mm/sec^2
    Fitted shaper '2hump_ei' frequency = 51.8 Hz (vibrations = 0.0%, smoothing ~= 0.201)
    To avoid too much smoothing with '2hump_ei', suggested max_accel <= 3000 mm/sec^2
    Fitted shaper '3hump_ei' frequency = 61.8 Hz (vibrations = 0.0%, smoothing ~= 0.215)
    To avoid too much smoothing with '3hump_ei', suggested max_accel <= 2800 mm/sec^2
    Recommended shaper is mzv @ 34.6 Hz

The suggested configuration can be added to `[input_shaper]` section of `printer.cfg`, e.g.:

    [input_shaper]
    shaper_freq_x: ...
    shaper_type_x: ...
    shaper_freq_y: 34.6
    shaper_type_y: mzv

    [printer]
    max_accel: 3000  # should not exceed the estimated max_accel for X and Y axes

or you can choose some other configuration yourself based on the generated charts: peaks in the power spectral density on the charts correspond to the resonance frequencies of the printer.

Note that alternatively you can run the input shaper auto-calibration from Klipper directly, which can be convenient, for example, for the input shaper re-calibration.

### Bed-slinger printers

If your printer is a bed slinger printer, you will need to change the location of the accelerometer between the measurements for X and Y axes: measure the resonances of X axis with the accelerometer attached to the toolhead and the resonances of Y axis - to the bed (the usual bed slinger setup).

However, you can also connect two accelerometers simultaneously, though the ADXL345 must be connected to different boards (say, to an RPi and printer MCU board), or to two different physical SPI interfaces on the same board (rarely available). Then they can be configured in the following manner:

    [adxl345 hotend]
    # Assuming `hotend` chip is connected to an RPi
    cs_pin: rpi:None

    [adxl345 bed]
    # Assuming `bed` chip is connected to a printer MCU board
    cs_pin: ...  # Printer board SPI chip select (CS) pin

    [resonance_tester]
    # Assuming the typical setup of the bed slinger printer
    accel_chip_x: adxl345 hotend
    accel_chip_y: adxl345 bed
    probe_points: ...

Two MPUs can share one I2C bus, but they cannot measure simultaneously as the 400kbit/s I2C bus is not fast enough. One must have its AD0 pin pulled-down to 0V (address 104) and the other its AD0 pin pulled-up to 3.3V (address 105):

    [mpu9250 hotend]
    i2c_mcu: rpi
    i2c_bus: i2c.1
    i2c_address: 104 # This MPU has pin AD0 pulled low

    [mpu9250 bed]
    i2c_mcu: rpi
    i2c_bus: i2c.1
    i2c_address: 105 # This MPU has pin AD0 pulled high

    [resonance_tester]
    # Assuming the typical setup of the bed slinger printer
    accel_chip_x: mpu9250 hotend
    accel_chip_y: mpu9250 bed
    probe_points: ...

[Test with each MPU individually before connecting both to the bus for easy debugging.]

Then the commands `TEST_RESONANCES AXIS=X` and `TEST_RESONANCES AXIS=Y` will use the correct accelerometer for each axis.

### Max smoothing

Keep in mind that the input shaper can create some smoothing in parts. Automatic tuning of the input shaper performed by `calibrate_shaper.py` script or `SHAPER_CALIBRATE` command tries not to exacerbate the smoothing, but at the same time they try to minimize the resulting vibrations. Sometimes they can make a sub-optimal choice of the shaper frequency, or maybe you simply prefer to have less smoothing in parts at the expense of a larger remaining vibrations. In these cases, you can request to limit the maximum smoothing from the input shaper.

Let's consider the following results from the automatic tuning:

    Fitted shaper 'zv' frequency = 57.8 Hz (vibrations = 20.3%, smoothing ~= 0.053)
    To avoid too much smoothing with 'zv', suggested max_accel <= 13000 mm/sec^2
    Fitted shaper 'mzv' frequency = 34.8 Hz (vibrations = 3.6%, smoothing ~= 0.168)
    To avoid too much smoothing with 'mzv', suggested max_accel <= 3600 mm/sec^2
    Fitted shaper 'ei' frequency = 48.8 Hz (vibrations = 4.9%, smoothing ~= 0.135)
    To avoid too much smoothing with 'ei', suggested max_accel <= 4400 mm/sec^2
    Fitted shaper '2hump_ei' frequency = 45.2 Hz (vibrations = 0.1%, smoothing ~= 0.264)
    To avoid too much smoothing with '2hump_ei', suggested max_accel <= 2200 mm/sec^2
    Fitted shaper '3hump_ei' frequency = 48.0 Hz (vibrations = 0.0%, smoothing ~= 0.356)
    To avoid too much smoothing with '3hump_ei', suggested max_accel <= 1500 mm/sec^2
    Recommended shaper is 2hump_ei @ 45.2 Hz

Note that the reported `smoothing` values are some abstract projected values. These values can be used to compare different configurations: the higher the value, the more smoothing a shaper will create. However, these smoothing scores do not represent any real measure of smoothing, because the actual smoothing depends on `max_accel` and `square_corner_velocity` parameters. Therefore, you should print some test prints to see how much smoothing exactly a chosen configuration creates.

In the example above the suggested shaper parameters are not bad, but what if you want to get less smoothing on the X axis? You can try to limit the maximum shaper smoothing using the following command:

    ~/klipper/scripts/calibrate_shaper.py /tmp/resonances_x_*.csv -o /tmp/shaper_calibrate_x.png --max_smoothing=0.2

which limits the smoothing to 0.2 score. Now you can get the following result:

    Fitted shaper 'zv' frequency = 55.4 Hz (vibrations = 19.7%, smoothing ~= 0.057)
    To avoid too much smoothing with 'zv', suggested max_accel <= 12000 mm/sec^2
    Fitted shaper 'mzv' frequency = 34.6 Hz (vibrations = 3.6%, smoothing ~= 0.170)
    To avoid too much smoothing with 'mzv', suggested max_accel <= 3500 mm/sec^2
    Fitted shaper 'ei' frequency = 48.2 Hz (vibrations = 4.8%, smoothing ~= 0.139)
    To avoid too much smoothing with 'ei', suggested max_accel <= 4300 mm/sec^2
    Fitted shaper '2hump_ei' frequency = 52.0 Hz (vibrations = 2.7%, smoothing ~= 0.200)
    To avoid too much smoothing with '2hump_ei', suggested max_accel <= 3000 mm/sec^2
    Fitted shaper '3hump_ei' frequency = 72.6 Hz (vibrations = 1.4%, smoothing ~= 0.155)
    To avoid too much smoothing with '3hump_ei', suggested max_accel <= 3900 mm/sec^2
    Recommended shaper is 3hump_ei @ 72.6 Hz

If you compare to the previously suggested parameters, the vibrations are a bit larger, but the smoothing is significantly smaller than previously, allowing larger maximum acceleration.

When deciding which `max_smoothing` parameter to choose, you can use a trial-and-error approach. Try a few different values and see which results you get. Note that the actual smoothing produced by the input shaper depends, primarily, on the lowest resonance frequency of the printer: the higher the frequency of the lowest resonance - the smaller the smoothing. Therefore, if you request the script to find a configuration of the input shaper with the unrealistically small smoothing, it will be at the expense of increased ringing at the lowest resonance frequencies (which are, typically, also more prominently visible in prints). So, always double-check the projected remaining vibrations reported by the script and make sure they are not too high.

Note that if you chose a good `max_smoothing` value for both of your axes, you can store it in the `printer.cfg` as

    [resonance_tester]
    accel_chip: ...
    probe_points: ...
    max_smoothing: 0.25  # an example

Then, if you rerun the input shaper auto-tuning using `SHAPER_CALIBRATE` Klipper command in the future, it will use the stored `max_smoothing` value as a reference.

### Selecting max_accel

Since the input shaper can create some smoothing in parts, especially at high accelerations, you will still need to choose the `max_accel` value that does not create too much smoothing in the printed parts. A calibration script provides an estimate for `max_accel` parameter that should not create too much smoothing. Note that the `max_accel` as displayed by the calibration script is only a theoretical maximum at which the respective shaper is still able to work without producing too much smoothing. It is by no means a recommendation to set this acceleration for printing. The maximum acceleration your printer is able to sustain depends on its mechanical properties and the maximum torque of the used stepper motors. Therefore, it is suggested to set `max_accel` in `[printer]` section that does not exceed the estimated values for X and Y axes, likely with some conservative safety margin.

Alternatively, follow this part of the input shaper tuning guide and print the test model to choose `max_accel` parameter experimentally.

The same notice applies to the input shaper auto-calibration with `SHAPER_CALIBRATE` command: it is still necessary to choose the right `max_accel` value after the auto-calibration, and the suggested acceleration limits will not be applied automatically.

Keep in mind that the maximum acceleration without too much smoothing depends on the `square_corner_velocity`. The general recommendation is not to change it from its default value 5.0, and this is the value used by default by the `calibrate_shaper.py` script. If you did change it though, you should inform the script about it by passing `--square_corner_velocity=...` parameter, e.g.

    ~/klipper/scripts/calibrate_shaper.py /tmp/resonances_x_*.csv -o /tmp/shaper_calibrate_x.png --square_corner_velocity=10.0

so that it can calculate the maximum acceleration recommendations correctly. Note that the `SHAPER_CALIBRATE` command already takes the configured `square_corner_velocity` parameter into account, and there is no need to specify it explicitly.

If you are doing a shaper re-calibration and the reported smoothing for the suggested shaper configuration is almost the same as what you got during the previous calibration, this step can be skipped.

### Testing custom axes

`TEST_RESONANCES` command supports custom axes. While this is not really useful for input shaper calibration, it can be used to study printer resonances in-depth and to check, for example, belt tension.

To check the belt tension on CoreXY printers, execute

    TEST_RESONANCES AXIS=1,1 OUTPUT=raw_data
    TEST_RESONANCES AXIS=1,-1 OUTPUT=raw_data

and use `graph_accelerometer.py` to process the generated files, e.g.

    ~/klipper/scripts/graph_accelerometer.py -c /tmp/raw_data_axis*.csv -o /tmp/resonances.png

which will generate `/tmp/resonances.png` comparing the resonances.

For Delta printers with the default tower placement (tower A ~= 210 degrees, B ~= 330 degrees, and C ~= 90 degrees), execute

    TEST_RESONANCES AXIS=0,1 OUTPUT=raw_data
    TEST_RESONANCES AXIS=-0.866025404,-0.5 OUTPUT=raw_data
    TEST_RESONANCES AXIS=0.866025404,-0.5 OUTPUT=raw_data

and then use the same command

    ~/klipper/scripts/graph_accelerometer.py -c /tmp/raw_data_axis*.csv -o /tmp/resonances.png

to generate `/tmp/resonances.png` comparing the resonances.

## Input Shaper auto-calibration

Besides manually choosing the appropriate parameters for the input shaper feature, it is also possible to run the auto-tuning for the input shaper directly from Klipper. Run the following command via Octoprint terminal:

    SHAPER_CALIBRATE

This will run the full test for both axes and generate the csv output (`/tmp/calibration_data_*.csv` by default) for the frequency response and the suggested input shapers. You will also get the suggested frequencies for each input shaper, as well as which input shaper is recommended for your setup, on Octoprint console. For example:

    Calculating the best input shaper parameters for y axis
    Fitted shaper 'zv' frequency = 39.0 Hz (vibrations = 13.2%, smoothing ~= 0.105)
    To avoid too much smoothing with 'zv', suggested max_accel <= 5900 mm/sec^2
    Fitted shaper 'mzv' frequency = 36.8 Hz (vibrations = 1.7%, smoothing ~= 0.150)
    To avoid too much smoothing with 'mzv', suggested max_accel <= 4000 mm/sec^2
    Fitted shaper 'ei' frequency = 36.6 Hz (vibrations = 2.2%, smoothing ~= 0.240)
    To avoid too much smoothing with 'ei', suggested max_accel <= 2500 mm/sec^2
    Fitted shaper '2hump_ei' frequency = 48.0 Hz (vibrations = 0.0%, smoothing ~= 0.234)
    To avoid too much smoothing with '2hump_ei', suggested max_accel <= 2500 mm/sec^2
    Fitted shaper '3hump_ei' frequency = 59.0 Hz (vibrations = 0.0%, smoothing ~= 0.235)
    To avoid too much smoothing with '3hump_ei', suggested max_accel <= 2500 mm/sec^2
    Recommended shaper_type_y = mzv, shaper_freq_y = 36.8 Hz

If you agree with the suggested parameters, you can execute `SAVE_CONFIG` now to save them and restart the Klipper. Note that this will not update `max_accel` value in `[printer]` section. You should update it manually following the considerations in Selecting max_accel section.

If your printer is a bed slinger printer, you can specify which axis to test, so that you can change the accelerometer mounting point between the tests (by default the test is performed for both axes):

    SHAPER_CALIBRATE AXIS=Y

You can execute `SAVE_CONFIG` twice - after calibrating each axis.

However, if you connected two accelerometers simultaneously, you simply run `SHAPER_CALIBRATE` without specifying an axis to calibrate the input shaper for both axes in one go.

### Input Shaper re-calibration

`SHAPER_CALIBRATE` command can be also used to re-calibrate the input shaper in the future, especially if some changes to the printer that can affect its kinematics are made. One can either re-run the full calibration using `SHAPER_CALIBRATE` command, or restrict the auto-calibration to a single axis by supplying `AXIS=` parameter, like

    SHAPER_CALIBRATE AXIS=X

Warning! It is not advisable to run the shaper auto-calibration very frequently (e.g. before every print, or every day). In order to determine resonance frequencies, auto-calibration creates intensive vibrations on each of the axes. Generally, 3D printers are not designed to withstand a prolonged exposure to vibrations near the resonance frequencies. Doing so may increase wear of the printer components and reduce their lifespan. There is also an increased risk of some parts unscrewing or becoming loose. Always check that all parts of the printer (including the ones that may normally not move) are securely fixed in place after each auto-tuning.

Also, due to some noise in measurements, it is possible that the tuning results will be slightly different from one calibration run to another one. Still, it is not expected that the noise will affect the print quality too much. However, it is still advised to double-check the suggested parameters, and print some test prints before using them to confirm they are good.

## Offline processing of the accelerometer data

It is possible to generate the raw accelerometer data and process it offline (e.g. on a host machine), for example to find resonances. In order to do so, run the following commands via Octoprint terminal:

    SET_INPUT_SHAPER SHAPER_FREQ_X=0 SHAPER_FREQ_Y=0
    TEST_RESONANCES AXIS=X OUTPUT=raw_data

ignoring any errors for `SET_INPUT_SHAPER` command. For `TEST_RESONANCES` command, specify the desired test axis. The raw data will be written into `/tmp` directory on the RPi.

The raw data can also be obtained by running the command `ACCELEROMETER_MEASURE` command twice during some normal printer activity - first to start the measurements, and then to stop them and write the output file. Refer to G-Codes for more details.

The data can be processed later by the following scripts: `scripts/graph_accelerometer.py` and `scripts/calibrate_shaper.py`. Both of them accept one or several raw csv files as the input depending on the mode. The graph_accelerometer.py script supports several modes of operation:

- plotting raw accelerometer data (use `-r` parameter), only 1 input is supported;
- plotting a frequency response (no extra parameters required), if multiple inputs are specified, the average frequency response is computed;
- comparison of the frequency response between several inputs (use `-c` parameter); you can additionally specify which accelerometer axis to consider via `-a x`, `-a y` or `-a z` parameter (if none specified, the sum of vibrations for all axes is used);
- plotting the spectrogram (use `-s` parameter), only 1 input is supported; you can additionally specify which accelerometer axis to consider via `-a x`, `-a y` or `-a z` parameter (if none specified, the sum of vibrations for all axes is used).

Note that graph_accelerometer.py script supports only the raw_data*.csv files and not resonances*.csv or calibration_data*.csv files.

For example,

    ~/klipper/scripts/graph_accelerometer.py /tmp/raw_data_x_*.csv -o /tmp/resonances_x.png -c -a z

will plot the comparison of several `/tmp/raw_data_x_*.csv` files for Z axis to `/tmp/resonances_x.png` file.

The shaper_calibrate.py script accepts 1 or several inputs and can run automatic tuning of the input shaper and suggest the best parameters that work well for all provided inputs. It prints the suggested parameters to the console, and can additionally generate the chart if `-o output.png` parameter is provided, or the CSV file if `-c output.csv` parameter is specified.

Providing several inputs to shaper_calibrate.py script can be useful if running some advanced tuning of the input shapers, for example:

- Running `TEST_RESONANCES AXIS=X OUTPUT=raw_data` (and `Y` axis) for a single axis twice on a bed slinger printer with the accelerometer attached to the toolhead the first time, and the accelerometer attached to the bed the second time in order to detect axes cross-resonances and attempt to cancel them with input shapers.
- Running `TEST_RESONANCES AXIS=Y OUTPUT=raw_data` twice on a bed slinger with a glass bed and a magnetic surfaces (which is lighter) to find the input shaper parameters that work well for any print surface configuration.
- Combining the resonance data from multiple test points.
- Combining the resonance data from 2 axis (e.g. on a bed slinger printer to configure X-axis input_shaper from both X and Y axes resonances to cancel vibrations of the bed in case the nozzle 'catches' a print when moving in X axis direction).

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