Advanced data analysis with Magcam's unique magnetic field measurement systems

This article will show how Magcam inspects a radial flux permanent magnet rotor from a servo motor.  
Specifically, multiple analysis methods for detecting magnetic issues with the rotor will be presented. These methods are included in MagScope, Magcam’s in-house developed software. The magnetic data can be obtained with either Magcam’s Rotor Scanner or Magcam’s Combi Scanner for flat magnets and rotor assemblies.  

The analyses in this article include the following:  

- Magnetic field plot analysis 
- Pole analysis (1D cutout analysis) 
- Average 1D analysis 
- Average peak variations 
- Fourier analysis 
- Cogging torque analysis 

Let’s dive right in. 

Before the magnetic measurement, a laser measurement is performed to define the rotor’s angular position and to be able to correct for runout.  

Angular positioning

Laser measurements

  • Angular positioning: The 0° angular position is defined on the plane between two neighboring magnets, as shown in the picture below.  Using the laser as a visual aid, the rotor was manually clamped to the reference position. The laser and magnetic measurement data can thus be linked to the physical position of the rotor sample.  

Runout correction
  • Runout correction: MagScope’s runout correction feature is used to actively correct for runout caused by tolerances in the rotor geometry and the clamping. Laser measurements are performed at 1 or 2 axial positions using the shaft or the rotor body as a reference, as shown in the image below. From the measured surface measurements, the runout is extracted and actively compensated during subsequent movements. After correction, the runout is generally below 1 µm and, therefore, negligible for most applications. 

Laser sweeps on the rotor body
  •  Laser sweeps: Magcam’s scanner with the add-on laser sensor allows for laser sweeps, i.e., measuring the rotor surface distance while sweeping along a line. Multiple configurations are possible:  

    • ϕ-sweeps, rotating the rotary axis while measuring at one or more axial positions,  

    • Z-sweeps, sweeping along the axial direction at one or more angular positions, 

    • X-sweeps for Magcam’s Combi Scanner, measuring along the X-axis at one or more axial positions. 

Additionally, doing multiple sweeps in subsequent steps along another direction makes complete 2D surface mapping possible. 


Magnetic measurements

The entire rotor surface is measured with the MiniCube 3D magnetic field camera while compensating for runout.  
The rotor diameter input parameter is set to 40.4 mm. The measurements are done at a radial offset of 0.5 mm from the rotor surface. The picture below shows a clamped rotor during measurement. 
A high angular resolution of 0.1° is used in these measurements to provide a detailed mapping of the magnetic field. The standard MiniCube3D axial resolution of 0.1 mm is used.  

Rotor analysis

Magnetic field plot analysis for all three components

Magnetic field plot analysis

Different plots can be used to visualize the magnetic field. The standard plot is a 2D plot expressed in cylindrical coordinates, as shown in the example below. The 2D plot shows the magnetic field (color scale) as a function of the angular position (Φ-axis) and the axial position (Z-axis). This clearly shows the 4 North (red) and 4 South (blue) poles. 

  • 2D Plot of the Br (radial) component - red window 

  • 2D Plot of the Bt (tangential) component - black window 

  • 2D Plot of the Ba (axial) component - blue window 

Surface plot example

Besides the standard 2D color plots, surface plots are also used to visualize the data in a 3-axes plot. An example is shown in the screenshot below. 

Image statistics results

Image statistics

In MagScope, the image statistics provide the general characterization of the measured magnetic field. Some of the key parameters include:

  • Min/Max; the overall extrema on the 2D color plot

  • Range; the peak-to-peak value or the difference between min and max

  • Mean value; an average of all data points, expected to be 0 if there is perfect north-south symmetry

  • Mean Abs value; an average of the absolute value of all data points

  • NS-asymmetry; characterizing the asymmetry between the overall North and South field

  • RMS; the root-mean-squared value of the plot, characterizing the strength of a periodic signal

  • Shape factor, i.e., form factor, characterizing the shape of a periodic signal – independent of the amplitude

Pole analysis

Pole analysis (1D cutout analysis)

For pole analysis, a 1D cutout of the 2D magnetic field on the centerline of the rotor is typically used. Alternatively, the integrated or averaged field over the entire axial range can also be used, as is shown further in the article.

Firstly, the amplitude and angular position of the extrema are automatically extracted. Secondly, the pole widths are precisely determined by the deltas between the automatically detected zero-crossings on the graph. Variations of the pole width around the expected 45° delta can be identified from these results, often used in Quality Control (QC).

This analysis contains the following elements, as indicated in the figure below:

  • 2D Plot of the Br component – red window

  • 1D Plot of the Br component at the axial center position of the rotor - black window

  • Automatic minimum, maximum, zero-crossings, and pole angle detections - blue window

  • Image statistics of the 1D plot, including the RMS and shape factor – green window

Average 1D analysis

Average 1D Analysis

Further processing is done to provide more averaged results that are less susceptible to local variations. Therefore, the actual magnetic part is cut out from the 2D plot. Next, the data is averaged over the Z-axis. This provides a 1D Plot (like the plot analysis) of the average field over the magnet surface as a function of the angular position on the rotor. This can be identified in the screenshots in the following elements, as indicated in the figure below:

  • 2D Plot of the Br component on the magnet surface - red window

  • 1D Plot of the average Br component on the magnet surface - black window

  • Automatic minimum, maximum, and zero-crossings detection - blue window

  • Image statistics of the 1D Plot, including RMS and shape factor - green window

    The same analysis of the poles as described above (pole analysis) can be performed now on the average values.

Average peak variations

Average peak variations

The figure below shows the absolute value of the same average 1D plot. Then, the scale is zoomed in only to show the average peak of each of the poles. This is shown in the image below, containing the following elements:

  • 2D Plot of the Br component on the magnet surface - red window

  • 1D Plot of the absolute value of the average Br component on the magnet surface - black window

  • Scaling parameters, zoomed in to the peak values on the graph - blue window

This can be used as a visual aid to identify variations, such as 1st, 2nd, or higher-order harmonics that can be linked to peak imbalances. This view can also visualize North-South asymmetries, where all North/South poles would be larger or smaller. The following sections provide more detailed analysis methods for quantifying these possible defects.

Fourier analysis

Fourier Analysis

On the averaged 1D Plots, a Fourier analysis is furthermore performed. The amplitude spectrum of the FFT output is shown in the figure below. This contains the following elements:

  • 2D Plot of the Br component on the magnet surface - red window

  • 1D Plot of the average Br component on the magnet surface - black window

  • 1D Plot of the FFT (Br) amplitudes of the average 1D plot - blue window

  • THD parameter of the average 1D plot - green window

This allows for comparing the amplitude of certain harmonics between different rotors. If certain higher harmonics are known to cause NVH issues, these can be checked in the magnetic data. This can be done either by their measured amplitude or the amplitude relative to the main harmonic. In this example, the main harmonic is the 4th order signal, i.e., a sine wave that appears four times in 1 rotation of the sample (360°).

A parameter used to characterize the cumulated distortion in the field caused by higher harmonics is the Total Harmonic Distortion (THD). The THD for this sample is 4.83 %, whereby the reference frequency is taken to be the 4th-order harmonic.

In a more detailed analysis, each harmonic amplitude can be plotted as a function of the axial position. This feature can pinpoint the exact axial location of a certain frequency component, which in turn could point to a local defect on the rotor or in one of the magnets.

Cogging torque analysis

Cogging torque analysis

MagScope’s cogging torque analysis uses measurement data and a basic stator model to simulate the cogging torque that the rotor would cause. For example, the analysis’ output signal is proportional to the cogging torque the measured rotor would produce in a simplified, perfect stator with the same parameters as the actual stator. This stator model is based on the following parameters:

Cogging torque stator model parameters


Used value

Number of stator teeth


Slot width

4.20 mm

Tooth width

7.58 mm

Stator length

26.50 mm


This relates to a duty cycle of 64.332 %, with a duty cycle defined as 
Duty cycle = (tooth width) (slot width+tooth width)


The figure below shows the cogging torque analysis in MagScope, constructed by the following elements:

  • 1D Plot of the average Br component on the magnet surface - red window

  • 1D Plot of the calculated cogging torque signal, proportionate to the actual cogging torque - black window

  • 1D Plot of the FFT amplitudes of the cogging torque signal, with max extrema - blue window

  • Cogging torque settings - green window

These results can be compared between different samples. In many use cases, the amplitude of the FFT output provides significant differences between rotor samples with known cogging torque differences. One of the following parameters is often detected to have a higher value: (A) the main harmonic in the cogging torque signal, (B) the peak-to-peak value, or (C) the amplitude of other harmonics relative to the main harmonic. Once such a defect is observed, the other magnetic and geometric data can be used to identify plausible causes of the higher cogging torque (e.g., tangential misalignment of magnets, NS-asymmetry, angle deviations in the individual magnets, …)

Using the standard MagScope features, all the parameters and analysis data mentioned above can be exported automatically for further analysis, e.g., statistical analysis of large datasets, or can be directly used for pass/fail classification in production applications. For more information about MagScope features, please check out the MagScope page below or contact us.