The Abbé error is a linear positioning error caused by a combination of an angular error in the bearing ways (way of motion), and an offset distance between the measuring device (lead screw, encoder, etc) and the actual point of interest.
φ=h x tanθ
with h being the distance between the encoder and the tool point.
To minimize the Abbé error, the distance h must be as short as possible.
The accuracy is the difference between the actual position of a mechanical system and the expected position. It is typically specified in micron or arcsec per given travel for a deviation of ±3sigma. For example, an accuracy of ±3µm (±20arcsec), at ±3sigma, per 300mm (300°) travel means that if the axis moves to a position 300 mm (300°) away from the current position, the final position will end between 299.997 (300.0056 deg) and 300.003 (299.9944 deg), 99.7% of the time. The accuracy is influenced by the feedback system (encoder, laser interferometer...), the drive mechanism and the type of bearing.
The axial runout is the positioning error of the top of a rotary table in the vertical direction when the table is rotating in the horizontal plane.
The backlash is an error in positioning caused by the reversal of travel direction. It is caused by a clearance between the elements of the mechanical system. The backlash also affects the bidirectional repeatability. The backlash can be compensated by the position controller.
The coefficient of friction is the ratio of the force required to move load to the magnitude of that load. There are two coefficients: the static and the dynamic one (static coefficient > dynamic coefficient).
For a repetitive cycle, the duty cycle is the ratio of ’on’ time to total cycle time. Duty Cycle = (on time/(on time + off time)) x 100%.
The flatness is a vertical deviation from the plane of travel.
The horizontal straightness is a horizontal deviation from the straight line of travel. An horizontal straightness deviation in the travel of the X-axis will cause a positioning error in the Y direction.
The hysteresis error is a deviation between the actual and the commanded position caused by elastic forces accumulated in the motion system. It affects the accuracy and the bidirectional repeatability.
The orthogonality is the degree of perpendicularity between the line of travel of the two stacked axes. If the two travel lines are not orthogonal, the Y-axis travel creates a positioning error in the X direction (for a X-Y table).
The pitch is a rotation (angular deviation from the ideal straight line of travel) around an axis in the horizontal plane (for the example mentioned below) perpendicular to the direction of travel. For the X-axis travel, a pitch will cause an Abbé error in the X and Z directions.
The radial runout is the positioning error of a rotary table’s centering diameter in the horizontal direction when the table is rotating in the horizontal plane.
The repeatability is the ability of a motion system to reliably achieve a commanded position over many attempts under identical conditions. The unidirectional repeatability is the ability to repeat a movement in one direction only (and ignores the effects of backlash or hysteresis within the system). The bidirectional repeatability is the ability to repeat a movement from both directions. By default, the measurement of the repeatability is made with unloaded system.
The resolution is the smallest possible movement that can be achieved by a system. It can be defined at the electronics, encoder and mechanics level.
The roll is a rotation (angular deviation from the ideal straight line of travel) around an axis in the horizontal plane (for the example mentioned below) parallel to the direction of travel. For the X-axis travel, a roll will cause an Abbé error in the Y and Z directions.
Sigma (s) is the standard deviation. It indicates how far a given process deviates from the nominal value, the lower the better. For a normally distributed movement, which is often assumed for position values, a result of 3s=0.1micron (=2arcsec) guarantees 99.7% of the measurement to be between ±0.1micron (2s=0.1micron leads to 95.4% between ±0.1micron, s=0.1micron leads to 68.3% between ±0.1micron) or ±2arcsec (2s=2arcsec leads to 95.4% between ±2arcsec, s=2arcsec leads to 68.3% between ±2arcsec).
The thermal expansion is a change of the size and shape of a system when the temperature is modified. The amount of change is dependent on the size of the component, the degree of temperature change and the characteristics of the material.
The vertical straightness is a vertical deviation from the straight line of travel. A vertical straightness deviation in the travel of the X-axis will cause a positioning error in the Z direction.
The wobble is the angular error between the perpendicular to the interface plate and the actual axis of rotation, when the beta (b) and gamma (g) angles are corrected.
(a): angle with the fastening surfaces
(b): angle between the actual axis of rotation and the base of the rotary table
(g): angle between the perpendicular to the interface plate and the actual axis of rotation
The yaw is a rotation (angular deviation from the ideal straight line of travel) around an axis in the vertical plane (for the example mentioned below) perpendicular to the direction of travel. For the X-axis travel, the yaw will cause an Abbé error in the X and Y directions.