General Test Definitions

Open Loop Unidirectional Positioning Repeatability and Reversal Error of an Axis
This test quantifies the two parameters Unidirectional Positioning Repeatability and Reversal Error. The
Unidirectional Positioning Repeatability describes the system's ability to achieve a commanded motor position
over many attempts. The Reversal Error (or "backlash") is the slop in any toothed or threaded drive system:
when a stage is moved to a position and then returned to its original position, some motion may be lost. This loss
is a result of relative movement between interacting mechanical parts of a drive system that does not produce
output motion. If the magnitude of the Reversal Error is known, it may be compensated for by always
approaching the final position from the same direction, that is Unidirectional Positioning.

The JJ X-RAY Test Procedure
The motor is commanded to move from one position to another in a number of intervals, each step referred to as
a Target Position. At every Target Position, the corresponding Actual Position is measured by a measuring
device, and the Unidirectional Positioning Deviation of the position (Actual Position − Target Position) is
calculated. The measuring device may be an encoder, a laser interferometer or a digital dial gauge. The data is
collected in accordance with a standard test cycle: 10 Target Positions distributed along the full range of motion
are attained 6 times in each direction (positive/negative). The Positioning Repeatability at each Target Position is
calculated as ± 2 standard deviations of the measured Positioning Deviations. The reported Unidirectional
Positioning Repeatability of the axis is the maximum value of the Target Position Positioning Repeatability.
The reversal error at a position is the difference between the mean Unidirectional Positioning Deviations obtained
from the two directions of approach at a position. The reported Reversal Error of the axis is the maximum of the
absolute reversal errors at all Target Positions along the axis.

The JJ X-RAY Test Sheet Content
The Unidirectional Positioning Repeatability Test Sheet contains a summary of the applied test cycle (number of
target points, number of cycles), the motor controller settings and information about the relevant measuring
device. The data is included as a viewgraph displaying the measured Positioning Deviations as function of the
Target Positions. On the viewgraph, full lines indicate the mean Unidirectional Positioning Deviations and dashed
lines mark ± 2 standard deviations of the measured Positioning Deviations. For completeness, results for both
mean and maximum values of the Unidirectional Positioning Repeatability are included for each direction of
approach. In the summary sheet only one number is reported for the Unidirectional Positioning Repeatability of
the axis: that is the maximum value of the Unidirectional Positioning Repeatability at any position included in the
test cycle.

Open Loop Positioning deviation of an Axis
This test quantifies the ability of an axis to respond to a commanded move input, in terms of the two parameters
Progressive and Periodic Pitch Error. These parameters are derived from measurements of the Unidirectional
Positioning Deviation at Target Positions closely spaced compared to the axis spindle pitch.
A curve visualizing the Unidirectional Positioning Deviations as function of the Target Positions is called a Pitch Error curve. A
typical Pitch Error curve has both a linear and a sinusoidal component. These components are explained below
and are referred to as Progressive and Periodic Pitch Error respectively.

Progressive Pitch Error
The Progressive Pitch Error is a linear error component introduced by an inaccuracy of the lead screw pitch
and/or a misalignment of the Measuring Device to the stage axis of motion. The Progressive Pitch Error is
identified as the slope of a linear fit to the Pitch Error curve. The Progressive Pitch Error has the unit μm/mm for
linear stages and mdeg/deg for rotary stages. A positive Pitch Error indicates a measured range which exceeds
the commanded range, and it may be concluded that the actual lead screw pitch exceeds the nominal lead screw
pitch.
If the measuring device is a Dial Gauge, a misalignment between the Dial Gauge and the stage axis is likely.
Such a misalignment will unavoidably increase the Pitch Error uncertainty. For example, a misalignment of 2° will
introduce an apparent Progressive Pitch Error of +0.6 μm/mm.

Periodic Pitch Error
This periodic error is introduced when successive portions of the thread are either longer or shorter than the mean.
The period is directly related to the lead screw pitch.

The JJ X-RAY Test Procedure
The motor is commanded to move from one position to another in a number of intervals, each step referred to as a
Target Position. At every Target Position, the corresponding Actual Position is measured by a measuring device, and the
Unidirectional Positioning Deviation of the position (Actual Position − Target Position) is calculated. The measuring
device may be an encoder, a laser interferometer or a digital dial gauge. The data is collected in accordance with a
standard test cycle: the Target Positions are distributed along the full range of motion with a spacing corresponding to 5
to 10% of the axis spindle pitch.

The JJ X-RAY Test Sheet Content
The Open Loop Positioning Test Sheet presents the Pitch Error curve with a linear fit for identification of the Progressive
Pitch Error. The Periodic Pitch Error is calculated by subtraction of the Progressive Pitch Error from the Pitch Error. The
Periodic Pitch Error amplitude is estimated as √2 times the standard deviation of the Periodic Pitch Error.
The quantity Open Loop Positioning is defined ± the estimated Periodic Pitch Error amplitude.

Mechanical Resolution of an Axis
The Mechanical Resolution is the smallest possible movement of an axis.

The JJ X-RAY Test Procedure
The motor is commanded to move to a number of Target Positions with identical spacing. The spacing between the
Target Positions is called the Target Step Size. At every Target Position, the corresponding Actual Position is measured
by a measuring device. The spacing between two successive Actual Positions, that is the Actual Step Size, is calculated.
The measuring device may be an encoder, a laser interferometer or a digital dial gauge. The data is collected in
accordance with a standard test cycle: for each Target Step Size the number of Target Positions is 75. The minimum
Target Step Size corresponds to 1 microstep (1/16 full step). Three other values of the Target Step Size is probed,
corresponding to 1/2, 1 and 2 full steps.

The JJ X-RAY Test Sheet Content
The Axis Mechanical Resolution Test Sheet contains a summary of the applied test cycle (number of target points), the
motor controller settings and information about the relevant measuring device. The data is included as a viewgraph
displaying the measured Actual Step Size as function of the Target Positions. The mean value of the Actual Step Size is
compared to the Target Step Size. If the ratio Actual/Target Step Size is close to unity, typically within 3%, the Actual
Step size is reported as the Mechanical Resolution of the axis.

Examples of test reports for particular instruments can be obtained by request: info@jjxray.dk