Symbrium Encoder-Based Shaft Measurement Methods

Symbrium is expert in dimensional inspection of rotating components such as gears, shafts, rotors, clutch housings and the like.  Most of our inspection centers and precision gauging equipment incorporate sophisticated encoder-based data acquisition and signal processing methods that greatly enhances measurement accuracy, repeatability, and diagnostic capabilities. This enables superior process controls and faster diagnosis and correction of manufacturing issues.


Instrumented Spindles with Smart Tooling

Symbrium employs ultra-precision machine tool grade spindles  our dimensional gauges with many unique features:

  • Servo-Controlled or Manual Rotation
  • Automatic Tool Loading
  • Smart RFID For ID and Error Proofing
  • Integrated Optical Encoders
  • Integrated Torque Sensors



The vast majority of automated shaft runout gauges rotate the part either manually or automatically using a motor running at some nominally constant speed while streaming data from an analog or digital indicator to a PLC or computer.

Typically data is collected over two or more rotational cycles to make sure that enough data is captured to provide a decent representation of radial errors about the circumference of the shaft. The sampling rate may or may not be constant. Filtering may or may not be employed to “smooth” the data. All this leads to inherent errors due to aliasing and phase shift that are beyond the scope of explanation here. Most of the time, there is no correlation between shaft angle and the actual data points.


TIR or Total Indicator Runout represents the entire error associated with the radial characteristics of a shaft and is computed by finding the maximum and minimum probe readings that occur during the testing cycle (TIR = Max – Min).  TIR measurement is highly susceptible to noise and the max or min readings might correspond to a localized bump or divot that can greatly influence the TIR calculation making  TIR an unreliable metric of true shaft quality in many cases.  TIR is definitely not a good diagnostic indicator for figuring out what may be wrong with a turning, grinding or friction welding operation that is producing bad parts.


The Symbrium Encoder Based Method solves many of these issues.  Rather than acquire data points based on time, each data point is triggered by a signal from a high accuracy rotary encoder integral to the drive spindle. For instance, if an encoder having N = 10,000 pulses per revolution is used to trigger probe readings exactly when the encoder produces a pulse, there will be 10,000 data points per revolution that correspond to every 360 / 10,000 = 0.036 degrees. Because the data acquisition is triggered by the encoder and not some time signal that may or may not be synchronized with spindle speed, the data becomes independent of motor speed or hand turning and will also not exhibit timing induced errors associated with the scan time of the PLC. Even large variances in speed such as those due to hand turning have no effect on the quality of the measurement.  This proven technique is known as synchronous sampling.


Synchronous Sampling allows for many desirable outcomes. When data from more than one shaft rotation is synchronously sampled, the respective points from each rotation correspond to the exact same location about the circumference of the shaft. A technique known as ensemble averaging can be employed to dramatically increase signal to noise ratio by averaging data from successive rotations without any distortion of the measured waveform. This cannot be accomplished without encoder based processing.

There are also important implications to spectral analysis when applied to a synchronously sampled signal. The corollary of Frequency when applied to synchronously sampled signals is Orders. Order Domain analysis can be performed on the signal using advanced mathematics that provides an extremely accurate representation of the circular characteristics of the shaft by breaking down the errors in terms of Shaft Order Amplitudes which is very information that allows one to better understand the manufacturing process.

Order 1 = Eccentricity or Runout

Order 2 = Ovality or egg shape

Order 3 = Tri-lobe due to a part being clamped in a three jaw chuck.

Synchronous sampling also allows the correlation of measurements to the exact rotational position on the shaft. After analysis, the spindle can be “clocked” to the exact high or low point associated with each measurement probe. A marker can be used to highlight those locations.  Such information can be very useful for machine set up.

Of course, TIR can still be computed in the usual manner using encoder based data. TIR can also be derived from the Order Domain analysis.


TIR Versus Polar Plotting and Order Analysis: TIR provides very limited information about the actual radial errors present in a shaft. Consider the following simulated outputs from a shaft gauge having Symbrium encoder-based measurement capability with advanced digital signal processing. The upper left-hand graph is a magnified polar plot of the shaft error from ideal. The upper right graph is probe output versus shaft rotation angle. The lower plot shows the amount of eccentricity and out-of-roundness error present in each shaft measurement from order analysis.


The four shafts above read the exact same TIR yet have dramatically different profiles caused by different manufacturing issues.  In fact, every plot on this page corresponds to the exact same TIR value. It is impossible distinguish the type of error using TIR as the sole metric. For most cases, it is impossible or very difficult to deduce the shape of the shaft from the probe versus time plot. However, the situation is immediately apparent by glancing at either the Polar Plot or the Order Diagram, which cannot be accurately produced without using an encoder-based method.

Eccentricity and Circularity:  An eccentric shaft can be perfectly round. The shaft surface is simply offset from the centerline from which it is being measured.  An out-of-round shaft can be egg-shaped or lobed or exhibit a combination of errors.  The most common case for most drive shafts is a mix of centerline eccentricity (run-out) and ovality (non-circularity) as shown below. Both of these simulated outputs  have the exact same TIR.  The left measurement is dominated by eccentricity while the right measurement is dominated by non-circularity. Again, it is impossible to distinguish between the two conditions using TIR alone. The type of error causing the TIR is readily apparent from the polar and order plots, providing machine setup technicians with the necessary information to the correct the problem much faster.

Damage: In addition to providing far superior qualitative analysis and diagnostic capability, automated gauges equipped with Symbrium encoder based measurement systems can rotate the shaft so that the maximum error or a defect can be marked. Consider the measurement below where there is both eccentricity and a “Flat Spot” where the part may have been damaged by a machine fixture or through handling. Again this example has the exact same TIR as all of the other plots presented on this page. The gauge is capable of clocking the spindle so that this flat spot can be marked as well as the high spot of the eccentricity. The machine set-up person now knows what is causing the out-of-range TIR, where it is happening on the shaft, and can correct the problem faster.


Noise Reduction: As a final example, consider noise found in typical time based probe measurements as shown below. Order Domain Analysis using encoder-based measurements provides an extremely effective method to increase the signal to noise ratio without affecting the quality or magnitude of the underlying shaft geometry.


The Symbrium Advantage

Symbrium has expert knowledge in Dimensional Gauging of Rotational Prismatic Parts to micron levels including Diameter, Length, Radial Runout, Axial Runout, Offset and other attributes.  Functional testing of shaft components including Torque to Turn, Joint Articulation Torque, Grease Fill, Weight, and Balance are also our specialties.