© ISO 2014 Test code for machine tools — Part 2 Determination of accuracy and repeatability of positioning of numerically controlled axes Code d’essai des machines outils — Partie 2 Détermination de l[.]
Environment
It is recommended that the manufacturer/supplier offer guidelines regarding the kind of thermal environment acceptable for the machine to perform with the specified accuracy.
Guidelines for machine environment conditions should specify the mean room temperature, acceptable amplitude and frequency of temperature deviations, and thermal gradients to ensure proper machine operation It is the user's responsibility to maintain an acceptable thermal environment at the installation site for optimal machine performance and testing However, adherence to the manufacturer's guidelines shifts the responsibility for confirming machine performance and compliance back to the machine supplier.
To ensure accurate dimensional measurements, it is ideal to perform measurements in an environment maintained at 20 °C, with both the measuring instrument and the object being measured at this temperature If measurements are taken at temperatures other than 20 °C, a correction for Nominal Differential Expansion (NDE) must be applied to account for thermal expansion differences between the machine's axis system or workholding components and the test equipment This process may involve measuring the temperature of key machine parts and applying mathematical corrections using relevant thermal expansion coefficients Alternatively, automatic NDE correction is possible if the test equipment and the machine parts are at the same temperature and share identical thermal expansion properties.
Temperature deviations from 20 °C can introduce additional uncertainties due to variations in the effective expansion coefficient(s) used for compensation Typically, this uncertainty ranges from 2 μm/(m·°C), highlighting the importance of accurately recording actual test temperatures Therefore, it is essential to specify the precise test temperatures in the test report to ensure reliable and accurate results.
Ensure that the machine and relevant measuring instruments have been in the test environment long enough, preferably overnight, to reach thermal stability before testing Protect them from draughts and external radiation sources like sunlight and overhead heaters to maintain accurate and consistent test conditions.
For 12 h before the measurements and during them, the environmental temperature gradient in degrees per hour shall be within limits agreed between manufacturer/supplier and user.
Machine to be tested
The machine shall be completely assembled and fully operational If necessary, levelling operations and geometric alignment tests shall be completed satisfactorily before starting the positioning accuracy and repeatability tests.
When utilizing built-in compensation routines during testing, it is essential to explicitly mention this in the test report All tests must be conducted with the machine in an unloaded state, meaning no workpiece should be present during the testing process.
The positions of the axis slides or moving components on the axes which are not under test shall be stated in the test report.
Warm-up
Before testing the machine under normal operating conditions, it is essential to perform an appropriate warm-up as specified by the manufacturer or supplier, or as agreed upon with the user, to ensure accurate and reliable test results.
If no specific conditions are set, warm-up procedures may include a preliminary dummy run of the positioning accuracy test without data collection or limited preliminary movements necessary for setting up measuring instruments It is essential to clearly state the chosen warm-up operation in the test report to ensure transparency and compliance with testing standards.
Non-stable thermal conditions are characterized by increasing deviations observed during successive attempts to reach a specific target position To ensure accuracy and stability, these thermal fluctuations should be minimized through proper warm-up procedures before operation Implementing an effective warm-up process helps achieve consistent thermal conditions, improving overall precision and performance Maintaining stable thermal conditions is essential for optimizing system accuracy and reducing errors caused by temperature variations.
Mode of operation
The machine is designed to precisely move the moving component along or around the axis under test, positioning it at specified target locations It ensures the component remains stationary at each position long enough for accurate measurement and recording of the actual position Additionally, the machine's movement between target positions is programmed to operate at a predetermined feed speed, as agreed upon by the manufacturer or supplier and the user, guaranteeing consistent testing performance.
Selection of target position
Where the value of each target position can be freely chosen, it shall take the general form of Formula (1):
This formula defines the target position adjustment, where Pi is the adjusted position, i represents the current target point, p is the nominal interval between target points based on uniform spacing, and r is a random number within ± one period of expected periodic positioning errors such as pitch variations of the ball screw or linear/rotary scales Incorporating the random term r ensures adequate sampling of periodic errors, particularly when no specific data on such errors is available, in which case r should be within ±30% of the interval p.
Target positions selected for the execution of acceptance or reverification tests shall be different from the sampling points used for numerical compensation of the relevant axis positioning errors.
NOTE Annex C provides information related to periodic positioning error.
Measurements
The measurement setup is specifically designed to accurately assess the relative motion between the machine's cutting tool component and the workpiece-carrying component along the tested axis This setup ensures precise evaluation of movement in the direction of the axis under test, vital for maintaining machining accuracy Proper calibration and alignment of the measurement system are essential for reliable results, ultimately enhancing machine performance and ensuring high-quality machining processes.
Calibrated laser interferometers, including tracking interferometers, and calibrated linear scales are the primary instruments used to measure positioning error and repeatability of linear axes Additionally, calibrated ball arrays can be employed for this purpose, providing versatile options for precise verification (refer to Annex D) These instruments ensure accurate assessment of linear axis performance, adhering to high standards of measurement accuracy and calibration protocols.
Positioning error and repeatability of short axes up to 100 mm can also be measured with long-range linear displacement sensors.
When applying mathematical NDE correction, it is essential to specify the placement of temperature sensors on machine components, the expansion coefficients utilized for the correction process, and the type of compensation routine implemented These details must be clearly documented in the test report to ensure accuracy and traceability of the non-destructive evaluation results Proper documentation of sensor positions, material expansion coefficients, and correction methods enhances the reliability of the NDE process and complies with quality standards.
Common measuring instruments for assessing the positioning error and repeatability of rotary axes include polygons paired with autocollimators, reference indexing tables combined with laser interferometers or autocollimators, and high-precision reference rotary (angle) encoders.
The position of the measuring instruments and reference artefacts, if any, shall be recorded on the test report.
5.3.2 Tests for linear axes up to 2 000 mm
On machine axes of travel up to 2 000 mm, a minimum of five target positions per metre and an overall minimum of five target positions shall be selected in accordance with 5.2.
Measurements shall be made at all the target positions according to the standard test cycle (see Figure 1) Each target position shall be attained five times in each direction.
The position of changing direction should be chosen to allow for normal behaviour of the machine (to achieve the agreed feed speed). a Position i (m = 8). b Cycle j (n = 5). c Target points.
5.3.3 Tests for linear axes exceeding 2 000 mm
For axes exceeding 2,000 mm in length, the entire measurement travel must be tested through one unidirectional approach in each direction to designated target positions, spaced at an average interval of 250 mm as specified in section 5.2 If the measuring transducer is composed of multiple segments, additional target points should be chosen to ensure each segment is accurately calibrated with at least one target position.
Additionally, the test specified in 5.3.2 shall be made over a length of 2 000 mm in the normal working area as agreed between manufacturer/supplier and user.
For axes exceeding 4,000 mm in length, the number of tests required under clause 5.3.2 and their positioning within the working area must be determined through a mutually agreed-upon arrangement between the manufacturer or supplier and the user.
5.3.4 Tests for rotary axes up to 360°
Tests should be conducted at designated target positions listed in Table 1, including principal angles of 0°, 90°, 180°, and 270° whenever possible, along with additional target positions in accordance with section 5.2 Each target position must be measured five times in both directions to ensure accurate and reliable data.
Table 1 — Target positions for rotary axes
Measurement travel Minimum number of target positions
5.3.5 Tests for rotary axes exceeding 360°
For axes exceeding 360°, the measurement travel extending up to 1,800° (five revolutions) must be tested through unidirectional approaches in each direction The testing process should include a minimum of eight target points per revolution to ensure accurate calibration and performance verification This procedure is essential for maintaining precise motion control in applications requiring extensive angular movement.
Additionally, the test specified in 5.3.4 shall be made over an angle of 360° in the normal working area as agreed between manufacturer/supplier and user.
Linear axes up to 2 000 mm and rotary axes up to 360°
For each target position P i and for five approaches (n = 5) in each direction, the parameters defined in
Clause 3 are evaluated Furthermore, the deviation boundaries x i ↑ +2s i ↑andx i ↑ −2s i ↑ and x i ↓ +2s i ↓andx i ↓ −2s i ↓ are calculated.
Linear axes exceeding 2 000 mm and rotary axes exceeding 360°
This article discusses the evaluation of parameters for specific target positions and approaches, focusing on unidirectional axis repeatability and positioning errors Estimators outlined in Clauses 3.18 through 3.22 are not applicable when assessing a single approach (n=1) in each direction Additionally, results over a 2,000 mm length or a 360° rotation are to be provided as per the agreement between the manufacturer and user, ensuring comprehensive accuracy assessment in robotic or automated systems.
7 Points to be agreed between manufacturer/supplier and user
When establishing testing protocols between manufacturers or suppliers and users, key agreements should include the specified ambient temperature range, maximum environmental temperature gradients, and the precise location and positioning of measuring instruments and sensors Additionally, considerations such as the warm-up procedures prior to testing, feed speed between target points, the designated normal working area based on measurement travel, the positioning of non-testing slides or moving parts, dwell times at each target, and the locations of the initial and final target positions are essential to ensure accurate and consistent performance assessments Incorporating these factors enhances test reliability and adheres to optimal testing standards.
Method of presentation
The preferred method of presentation of the results is a graphical one with the following list of items recorded on the test report in order to identify the measurement setup:
— position of axes not under test;
— if mathematical NDE correction is applied:
— coefficient(s) of thermal expansion used for NDE correction,
— position of the temperature sensor(s) used for NDE correction on the machine components and on the test equipment,
Sensor temperature measurements during NDE correction are critical for ensuring accurate results, with data collected from machine components such as the machine scale or workpiece/tool-holding parts Additionally, temperature readings from test equipment sensors are recorded at both the start and end of each test to monitor thermal stability These temperature data points are essential for correcting non-destructive evaluation (NDE) processes, ensuring precision and reliability in machine component assessments Optimizing sensor temperature monitoring enhances NDE accuracy, leading to improved maintenance and quality assurance in manufacturing processes.
— type of compensation routine (e.g frequency of updating compensation parameters);
— machine name, type (horizontal spindle or vertical spindle), and its coordinate axes travels;
— list of the test equipment used, including manufacturer’s name, type, and serial number of the components (laser head, optics, temperature sensors, etc.);
— type of machine scale used for positioning of axis and its coefficient of thermal expansion, obtained from machine tool manufacturer/supplier (e.g ball screw/rotary resolver system, linear scale system);
— name of axis under test:
The measurement line for the linear axis is positioned relative to the axes not under test, determined by offsets to the tool reference and workpiece reference These offsets are configured based on the specific machine setup, ensuring accurate positioning during measurement Proper understanding of these offsets is essential for precise linear axis measurement in manufacturing processes.
— for rotary axis, a description of nominal position and orientation of the axis;
— feed speed and dwell time at each target position, list of nominal target positions;
— warm-up operation to precede testing the machine (number of cycles or idling time and feed speed);
— if relevant, air temperature, air pressure, and humidity near the laser beam at the start and end of the test;
— whether or not built-in compensation routines were used during the test cycle;
— use of air or oil shower, when applied;
— contributors and parameters used for estimation of measurement uncertainty.
Parameters
Key parameters must be specified numerically to ensure clarity and precision A summarized presentation of these results, indicated with an asterisk and parentheses, facilitates machine acceptance and streamlined analysis The detailed outcomes, initially listed in Table 2, are further illustrated in Table 3, Figure 2, and Figure 3, providing comprehensive visual and tabular representations for better understanding and evaluation.
Each parameter should be given together with the measurement uncertainty U with a coverage factor of 2,
U (k = 2) The minimum requirements for information regarding the measurement uncertainty U are
— the parameters for the uncertainty due to the measuring device,
— the parameters for the uncertainty due to the compensation of the machine tool temperature,
— the parameters for the uncertainty due to the environmental temperature variation error, and
— the parameters for the uncertainty due to the misalignment of the measuring device, if relevant.
For linear axes, Annex A shows a simplified method for the estimation of the measurement uncertainty, including examples More detailed information and formulae are included in ISO/TR 230-9:2005, Annex C.
8.2.2 Tests for linear axes up to 2 000 mm and rotary axes up to 360°
— Bi-directional positioning error of an axis *) A
— Unidirectional positioning error of an axis *) A↑ and A↓
— Bi-directional systematic positioning error of an axis *) E
— Unidirectional systematic positioning error of an axis E↑ and E↓
— Range of the mean bi-directional positioning error of an axis *) M
— Bi-directional positioning repeatability of an axis R
— Unidirectional positioning repeatability of an axis *) R↑ and R↓
— Reversal error of an axis *) B
— Mean reversal error of an axis B
*) is the potential parameter for machine tool acceptance.
8.2.3 Tests for linear axes exceeding 2 000 mm and rotary axes exceeding 360°
— Bi-directional systematic positioning error of an axis *) E
— Unidirectional systematic positioning error of an axis E↑ and E↓
— Range of the mean bi-directional positioning error of an axis *) M
— Reversal error of an axis *) B
— Mean reversal error of an axis B
*) is the potential parameter for machine tool acceptance.
8.2.4 Clarification on terms related to the components of positioning error of an axis
According to ISO 230-1:2012, error motions of machine tool axes are defined and evaluated by measuring deviations at specific intervals and processing these data to determine key error parameters These parameters, such as E YX for straightness error of the x-axis in the y-direction, E CX for angular error around the c-axis, and EXX for the x-axis positioning error, provide a comprehensive understanding of axis accuracy The standardized nomenclature outlined in ISO 230-1:2012 ensures consistent reporting and assessment of machine tool axis errors, facilitating precise machine calibration and quality control.
ISO 230 specifies various parameters to quantify the positioning error motion of numerically controlled machine tool axes, including the repeatability of unidirectional positioning errors and the mean bi-directional positioning error motion These parameters offer a comprehensive assessment of the machine's accuracy by characterizing specific aspects of positioning errors Understanding and evaluating these key error components are essential for ensuring precise machine performance and improving manufacturing quality.
Following the ISO 230-1:2012 standards, parameters are represented as subscripts of the positioning error symbol for each axis For instance, the unidirectional positioning error of the x-axis is denoted as E XX,A↑ or E XX,A↓, while the reversal error of the c-axis is expressed as E CC,B This notation ensures clarity and consistency in documenting axis-specific errors in measurement systems.
The symbols for axis positioning error components in ISO 230 are standardized and widely recognized in industrial settings, facilitating automatic result reporting by specialized measuring instruments However, adopting the new symbolism introduced in ISO 230-1:2012 may take some time to be fully implemented across the industry.
The test results in Table 2 for the linear axis up to 2000 mm demonstrate consistent accuracy and repeatability, with positional deviations ranging from approximately ±0.2 μm to ±0.92 μm and uncertainty values around 0.3 to 0.7 μm, confirming high precision in positioning Approach directions alternate between upward and downward, achieving minimal deviations, and the mean unidirectional positioning deviations are within tight tolerances, primarily under 2 μm The system exhibits excellent bidirectional repeatability, with values close to 5–6 μm, and low reversible errors around ±3–4 μm, indicating reliable bidirectional accuracy Systematic positioning errors are negligible, at approximately 4–8 μm, with high confidence levels supported by standard uncertainties under 0.1 μm These results affirm the high precision, stability, and reliability of the linear axis for industrial applications requiring meticulous positional accuracy.
Table 3 — Example of test report information complementing graphical representation of results shown in Figure 2 and Figure 3
Date of test: YY/MM/DD
Name of inspector: Joe Smith
Machine name, type and serial no.: AAA, vertical spindle machining centre, serial no.: 1111111
Measuring instrument and serial no.: laser interferometer BBB, serial no.: 1234567
Test parameters tested axis: X type of scale: ball screw and rotary encoder
NDE correction location T start (°C) T end (°C) material sensor used for NDE correction: table, centre 21,8 22,9 coefficient of thermal expansion
(used for NDE correction): 11 àm/(mã°C) compensation routine update each 20 s feed speed: 1 000 mm/min dwell time at each target position: 5 s compensation used: reversal and leadscrew
Test location position of axes not under test: Y = 300 mm; Z = 350 mm; C = 0° offset to tool reference (X/Y/Z): 0/0/120 mm offset to workpiece reference (X/Y/Z): 0/0/30 mm
Air conditions used for compensation of laser interferometer, updated each 20 s location T start (°C) T end (°C) air temperature: centre of work zone 20,6 20,9 air pressure: 102,4 kPa air humidity: 60 %
X positions (mm) B 1 reversal error at position 1
Understanding axis deviations is essential for precise positioning in machining processes The Y deviations (mm) indicate lateral discrepancies, while B reversal error of the axis x i reflects the axis's rotational inaccuracies Bi-directional positioning repeatability (R) measures the axis’s ability to return to the same position consistently, whereas the mean bi-directional positioning error (M) indicates average positional deviations Systematic positioning errors (E) represent consistent biases affecting accuracy, and the overall bi-directional positioning error (A) encompasses these factors to assess overall axis precision Monitoring these parameters ensures optimal machine performance and high-precision manufacturing.
R 1 bi-directional positioning repeatability at position 1
Figure 2 — Bi-directional error(s) and positioning repeatability
X positions (mm) 2s 1 ↑ twice the estimator of unidirectional positioning repeatability at position 1
Y deviations (mm) R ↑ unidirectional positioning repeatability of the axis x i ↑ E ↑ unidirectional systematic positioning error of the axis x i ↑ ± 2 s i ↑ A ↑ unidirectional positioning error of the axis
R 1 ↑ unidirectional positioning repeatability at position 1
Figure 3 — Unidirectional accuracy and positioning repeatability (for positive approaches)
Measurement uncertainty estimation for linear positioning measurement — Simplified method
A.1 Estimation of the expanded measurement uncertainty
The estimation of measurement uncertainty is conducted in accordance with ISO/TR 230-9:2005, Annex C, which follows the guidelines of ISO/IEC Guide 98-3:2008 This process involves expressing contributors to measurement uncertainty as standard uncertainties (u), which are then combined to determine the combined standard uncertainty (u c) The expanded measurement uncertainty (U) is subsequently calculated using this combined value, ensuring a standardized and reliable approach to uncertainty estimation in measurements.
This annex highlights the impact of key contributors to measurement uncertainty, such as the alignment of the measuring device, expressed through the expanded measurement uncertainty, U ALIGNMENT This approach directly demonstrates how these factors influence the overall expanded measurement uncertainty, U, with supporting data presented in tables Additionally, the influence of relevant contributors on test parameters, like the bi-directional systematic positioning error of an axis, E, is also quantified using expanded measurement uncertainty metrics.
U E , which is evaluated as a combination of relevant expanded measurement uncertainties, U X The measurement uncertainties, U, are calculated for a coverage factor of k = 2.
A.2 Contributors to the measurement uncertainty
Measurement uncertainty primarily arises from several key factors: the accuracy of the measuring device, misalignment between the measuring device and the machine axis under test, temperature variations of the machine tool outside the standard 20 °C used for compensation, and environmental variation errors (EVE) Properly understanding and managing these contributors is essential for ensuring precise and reliable measurement results.
According to ISO/TR 230-9:2005, Annex C, contributors and assumptions are outlined, with the exception of the set-up error It is assumed that the set-up position is within 10 mm of the location recorded on the test report, ensuring accurate and reliable testing conditions.
A.2.2 Expanded uncertainty due to measuring device, U DEVICE
The formulae used in this subclause are based on ISO/TR 230-9:2005, C.2.2, and Formulae (C.1) and (C.2).
For accurate measurements, it is recommended to use a calibrated measuring device If the calibration certificate specifies the maximum uncertainty in micrometres (μm), Formula (A.1) should be used to determine measurement accuracy Alternatively, if the uncertainty is provided in micrometres per metre (μm/m), then Formula (A.2) applies to ensure precise calibration assessment.
If a calibration certificate is unavailable and the manufacturer specifies an error range in micrometers per meter, then using Formula (A.3) is recommended for accurate assessment The impact of the measuring device's resolution is generally negligible and can be verified in accordance with ISO/TR 230-9:2005, section C.2.2, using Formulae (C.3) and (C.4).
U DEVICE is the expanded uncertainty due to the measuring device, in micrometres (àm);
U CALIBRATION is the uncertainty of calibration according to the calibration certificate, in micro- metres (àm), with coverage factor k = 2.
U DEVICE is the expanded uncertainty due to the measuring device, in micrometres (àm);
U CALIBRATION is the uncertainty of the calibration according to the calibration certificate, in micrometres per metre (àm/m), with coverage factor k = 2;
L is the measurement length, in metres (m).
U DEVICE is the expanded uncertainty due to the measuring device, in micrometres (àm);
R DEVICE is the error range given by the manufacturer of the device, in micrometres per metre
L is the measurement length, in metres (m).
A.2.3 Expanded uncertainty due to misalignment of measuring device to machine axis under test, U MISALIGNMENT
The formulae used in this subclause are based on ISO/TR 230-9:2005, C.2.3 and Formula (C.5).
Proper alignment of the measuring device parallel to the machine axis is essential to ensure accurate measurements; misalignment can lead to measurement errors, especially when deviations exceed 1 mm on machine axes shorter than 300 mm Although the impact of misalignment is typically of second order, significant deviations can cause notable inaccuracies Refer to Formula (A.4) and Table A.1 for detailed information on how misalignment influences measurement accuracy.
With optical measurement equipment such as a laser interferometer, the misalignment will be within
Proper alignment of the reflected beam should be within 1 mm, as recommended by equipment manufacturers, ensuring optimal accuracy Relying solely on sufficient return beam intensity for alignment is not advised; in such cases, misalignment can be as high as 4 mm, potentially compromising system performance.
With mechanical measurement equipment such as a linear scale, the alignment with the help of a side face will result in a misalignment smaller than 0,5 mm.
U MISALIGNMENT is the expanded measurement uncertainty due to misalignment, in micrometres
R MISALIGNMENT is the misalignment, in millimetres (mm);
L is the measurement length, in metres (m).
Table A.1 — Expanded measurement uncertainty due to misalignment of measurement equipment, U MISALIGNMENT
A.2.4 Expanded uncertainty due to compensation of machine tool temperature
The formulae used in this subclause are based on ISO/TR 230-9:2005, C.2.4.