docs: Updated measuring resonances doc on max_accel suggestions

Signed-off-by: Dmitry Butyugin <dmbutyugin@google.com>

docs/Measuring_Resonances.md

@@ -181,12 +181,17 @@ recommended for your setup. For example:
 
 ![Resonances](img/calibrate-y.png)
 ```
-Fitted shaper 'zv' frequency = 37.0 Hz (vibrations = 29.1%, smoothing ~= 0.115)
+Fitted shaper 'zv' frequency = 34.4 Hz (vibrations = 4.0%, smoothing ~= 0.132)
-Fitted shaper 'mzv' frequency = 35.4 Hz (vibrations = 15.9%, smoothing ~= 0.163)
+To avoid too much smoothing with 'zv', suggested max_accel <= 4500 mm/sec^2
-Fitted shaper 'ei' frequency = 42.0 Hz (vibrations = 15.1%, smoothing ~= 0.183)
+Fitted shaper 'mzv' frequency = 34.6 Hz (vibrations = 0.0%, smoothing ~= 0.170)
-Fitted shaper '2hump_ei' frequency = 45.6 Hz (vibrations = 9.7%, smoothing ~= 0.260)
+To avoid too much smoothing with 'mzv', suggested max_accel <= 3500 mm/sec^2
-Fitted shaper '3hump_ei' frequency = 59.0 Hz (vibrations = 7.5%, smoothing ~= 0.235)
+Fitted shaper 'ei' frequency = 41.4 Hz (vibrations = 0.0%, smoothing ~= 0.188)
-Recommended shaper is 3hump_ei @ 59.0 Hz
+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
@@ -195,8 +200,11 @@ The suggested configuration can be added to `[input_shaper]` section of
 [input_shaper]
 shaper_freq_x: ...
 shaper_type_x: ...
-shaper_freq_y: 59.0
+shaper_freq_y: 34.6
-shaper_type_y: 3hump_ei
+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
@@ -252,12 +260,17 @@ Let's consider the following results from the automatic tuning:
 
 ![Resonances](img/calibrate-x.png)
 ```
-Fitted shaper 'zv' frequency = 62.2 Hz (vibrations = 36.9%, smoothing ~= 0.046)
+Fitted shaper 'zv' frequency = 57.8 Hz (vibrations = 20.3%, smoothing ~= 0.053)
-Fitted shaper 'mzv' frequency = 35.6 Hz (vibrations = 18.1%, smoothing ~= 0.161)
+To avoid too much smoothing with 'zv', suggested max_accel <= 13000 mm/sec^2
-Fitted shaper 'ei' frequency = 54.6 Hz (vibrations = 19.3%, smoothing ~= 0.108)
+Fitted shaper 'mzv' frequency = 34.8 Hz (vibrations = 3.6%, smoothing ~= 0.168)
-Fitted shaper '2hump_ei' frequency = 46.2 Hz (vibrations = 9.2%, smoothing ~= 0.253)
+To avoid too much smoothing with 'mzv', suggested max_accel <= 3600 mm/sec^2
-Fitted shaper '3hump_ei' frequency = 50.0 Hz (vibrations = 7.2%, smoothing ~= 0.328)
+Fitted shaper 'ei' frequency = 48.8 Hz (vibrations = 4.9%, smoothing ~= 0.135)
-Recommended shaper is 2hump_ei @ 46.2 Hz
+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
@@ -277,16 +290,22 @@ which limits the smoothing to 0.2 score. Now you can get the following result:
 
 ![Resonances](img/calibrate-x-max-smoothing.png)
 ```
-Fitted shaper 'zv' frequency = 55.2 Hz (vibrations = 34.2%, smoothing ~= 0.057)
+Fitted shaper 'zv' frequency = 55.4 Hz (vibrations = 19.7%, smoothing ~= 0.057)
-Fitted shaper 'mzv' frequency = 33.8 Hz (vibrations = 17.4%, smoothing ~= 0.178)
+To avoid too much smoothing with 'zv', suggested max_accel <= 12000 mm/sec^2
-Fitted shaper 'ei' frequency = 47.4 Hz (vibrations = 17.6%, smoothing ~= 0.143)
+Fitted shaper 'mzv' frequency = 34.6 Hz (vibrations = 3.6%, smoothing ~= 0.170)
-Fitted shaper '2hump_ei' frequency = 52.0 Hz (vibrations = 11.9%, smoothing ~= 0.200)
+To avoid too much smoothing with 'mzv', suggested max_accel <= 3500 mm/sec^2
-Fitted shaper '3hump_ei' frequency = 75.0 Hz (vibrations = 9.7%, smoothing ~= 0.146)
+Fitted shaper 'ei' frequency = 48.2 Hz (vibrations = 4.8%, smoothing ~= 0.139)
-Recommended shaper is 3hump_ei @ 75.0 Hz
+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.
+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
@@ -315,14 +334,27 @@ using `SHAPER_CALIBRATE` Klipper command in the future, it will use the stored
 
 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. Follow
+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](Resonance_Compensation.md#selecting-max_accel) part of
-the input shaper tuning guide and print the test model.
+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](#input-shaper-auto-calibration) with
 `SHAPER_CALIBRATE` command: it is still necessary to choose the right
-`max_accel` value after the auto-calibration.
+`max_accel` value after the auto-calibration, and the suggested acceleration
+limits will not be applied automatically.
 
 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
@@ -345,15 +377,24 @@ frequencies for each input shaper, as well as which input shaper is
 recommended for your setup, on Octoprint console. For example:
 
 ```
-Fitted shaper 'zv' frequency = 56.7 Hz (vibrations = 23.2%)
+Calculating the best input shaper parameters for y axis
-Fitted shaper 'mzv' frequency = 52.9 Hz (vibrations = 10.9%)
+Fitted shaper 'zv' frequency = 39.0 Hz (vibrations = 13.2%, smoothing ~= 0.105)
-Fitted shaper 'ei' frequency = 62.0 Hz (vibrations = 8.9%)
+To avoid too much smoothing with 'zv', suggested max_accel <= 5900 mm/sec^2
-Fitted shaper '2hump_ei' frequency = 59.0 Hz (vibrations = 4.9%)
+Fitted shaper 'mzv' frequency = 36.8 Hz (vibrations = 1.7%, smoothing ~= 0.150)
-Fitted shaper '3hump_ei' frequency = 65.0 Hz (vibrations = 3.3%)
+To avoid too much smoothing with 'mzv', suggested max_accel <= 4000 mm/sec^2
-Recommended shaper_type_y = 2hump_ei, shaper_freq_y = 59.0 Hz
+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.
+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](#selecting-max_accel)
+section.
 
 
 If your printer is a bed slinger printer, you can specify which axis