Linear Stage Specifications: What Do They Mean?
The specifications of a linear stage can be a little confusing, and the terminology used is often inconsistent between manufacturers. To avoid adding to this confusion, we characterize our stages using the ISO 230-2 standard (Test code for machine tools —Part 2: Determination of accuracy and repeatability of positioning of numerically controlled axes). This standard sets out rigid testing procedures and definitions of terms meaning you can be sure that the values we state are related to a particular property. Characterization according to ISO 230-2 requires that the stage is moved forward and backward to set target positions repeatedly, and the differences between the set target positions and the actual positions recorded.
Reversal error
Reversal errors refers to the difference in final position when approaching the same position from two different directions. For an ideal system, the reversal error will be zero and a stage will move to exactly the target position no matter from which direction it must approach. However, in real linear systems, there will be some degree of backlash - ‘slack’ in the mechanism that must be removed when changing direction. To understand reversal errors, we must first define the positioning deviation (PD). This is simply the difference between the target position the stage is programmed to move (PT), and its actual position (PA) when the move is completed. It is important that the stage approaches the target position from the same direction for each measurement.
For a linear axis, the stage can approach the target position from two possible directions, so we must measure two positioning deviations: the forward unidirectional positioning deviation (PD) and the backward unidirectional positioning deviation (PD). These are often measured multiple times for each target position, and an average taken to get the mean forward and reverse unidirectional positioning deviations of the target position. The reversal error of a target position (eR) is the difference between these two values.
We can also define the mean bidirectional positioning deviation at the target position as the average of the unidirectional deviations.
The reversal error should be measured for multiple positions along the axis, and the stage reversal error (ER) is the maximum value of eR across all measured positions.
Positioning repeatability
Repeatability tells us how closely grouped a set of actual positions will be when approaching the same target position multiple times. It encompasses the reversal error at the position, along with additional factors which can cause a distribution in unidirectional positioning errors at that position.
Repeatability is a key property of linear stages. It defines the differences in actual position we can expect when requesting the stage to move to the same position multiple times. The target position can either be approached from a particular direction (which is used to calculate unidirectional positioning error), or from opposing directions (bidirectional positioning error). A high degree of repeatability (small positioning error) is desirable. This can be achieved by using motion control components with tighter tolerances or using feedback from an absolute position encoder.
The positioning repeatability at a specific position (r) is 4 times the sample standard deviation of the positioning deviation. This is calculated separately for both forward and backwards motions giving two distinct values for each measurement position:
The bi-directional repeatability at a specific measurement position is given by the maximum of the following three values:
- The forward repeatability at the particular measurement position
- The backward repeatability at the particular measurement position
The forward and backward positioning repeatability of the stage are the maximum values of r, over all positions.
The bi-directional positioning repeatability of the stage (R) is the maximum value of the position bi-directional repeatability.
Systematic positioning errors
Systematic positioning errors consider the deviations in positions that could be experienced over the whole length of the stage, rather than at specific positions.
The forward systematic positioning error is the difference between the maximum and minimum mean positioning deviations measured when moving in the forward direction.
The backwards systematic positioning error is the difference between the maximum and minimum mean positioning deviations measured when moving in the backwards direction.
The bi-directional systematic positioning (Ep,s) error is the difference between the maximum value measured at any position, minus the minimum value measured at any position.
Positioning error
Positioning errors consider both the systematic positioning error and positioning repeatability.
The bi-directional positioning error of the stage is calculated using the forward and reverse positioning deviations and the standard deviation of the positioning deviations. Firstly, the following two quantities are calculated for each measurement location:
Next the following two quantities are calculated for each measurement location:
The forward positioning error of the stage is the difference between the maximum value of A and the minimum value of B.
The backward positioning error of the stage is the difference between the maximum value of A and the minimum value of B.
Defining A and B, the bi-directional positioning error (Ep) is then the difference between A and B.
Ep = A - B
The mean bi-directional positioning error of the stage is defined as the difference between the maximum and minimum values of PD.
How we calibrate and characterize the Ossila Linear Stage
Each Ossila linear stage is individually calibrated before being characterized to find the parameters given above. To calibrate a stage, we attach it to an absolute position encoder which allows us to accurately monitor the actual stage position during the calibration and characterization process. The stage first homed to set a reference position, and then sequentially moved to 100 target positions spread out across the length of the stage. The deviation from the target position is recorded and saved into the stage’s memory. When the stage is subsequently homed, it will thereafter correct the target position to an actual position using the calibration points stored in memory (interpolating when the target position lies between two calibration points).
Once calibrated, the stages are characterized, still using the absolute position encoder. The stage is homed, and then sequentially moved to 10 target positions across the length of the stage in the forward direction with the actual position recorded at each step. The direction is then reversed, and the stage moved to the same 10 target positions in the reverse direction and the actual positions again recorded. The calculations outlined above are then performed to find the necessary performance parameters.
Linear Stage
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