Tiêu Chuẩn Iso 00230-7-2015.Pdf

© ISO 2015 Test code for machine tools — Part 7 Geometric accuracy of axes of rotation Code d’essai des machines outils — Partie 7 Exactitude géométrique des axes de rotation INTERNATIONAL STANDARD IS[.]

General concepts

3.1.1 spindle unit tool or workpiece carrying device providing a capability to rotate the tool or the workpiece around an axis of rotation

Note 1 to entry: A machine tool may have one or more spindle units.

3.1.2 rotary table swivelling table component of a machine tool carrying a workpiece and providing a capability for changing angular orientation of the workpiece around an axis of rotation

Note 1 to entry: If a rotary table of a machining centre can be used for turning operations, the rotary table can be seen as a spindle unit for these operations.

3.1.3 rotary head swivelling head component of a machine carrying a tool holding spindle unit and providing a capability for changing the angular orientation of the spindle unit around an axis of rotation

Note 1 to entry: Sometimes multiple axes of rotations may be combined in a machine component.

3.1.4 spindle rotor rotating element of a spindle unit (or rotary table/head)

3.1.5 spindle housing stator stationary element of a spindle unit (or rotary table/head)

3.1.6 bearing element of a spindle unit (or rotary table/head) that supports the rotor and enables rotation between the rotor and the stator

3.1.7 axis of rotation line segment about which rotation occurs

Note 1 to entry: See Figure 1 a).

During rotation, this line segment generally experiences translation in radial and axial directions and tilting within the reference coordinate frame These movements are caused by inaccuracies in the bearings and bearing seats' structural motion or axis shifts, as illustrated in Figure 1 a) and b).

3.1.8 positive direction in accordance with ISO 841, the direction of a movement that causes an increasing positive dimension of the workpiece

3.1.9 perfect spindle (or rotary table/head) spindle or rotary table/head having no error motion of its axis of rotation relative to its axis average line

3.1.10 perfect workpiece rigid body having a perfect surface of revolution about a centreline

3.1.11 functional point cutting tool centre point or point associated with a component on the machine tool where cutting tool would contact the part for the purposes of material removal

3.1.12 axis average line straight line segment located with respect to the reference coordinate axes representing the mean location of the axis of rotation

Note 2 to entry: The axis average line is a useful term to describe changes in location of an axis of rotation in response to load, temperature, or speed changes.

Note 3 emphasizes that, unless specified otherwise, the axis average line's position and orientation should be determined by connecting the least-squares centers of two data sets of radial error motion taken at axially separated locations (see 3.4) This method ensures accurate alignment and measurement consistency in analyzing radial error motion.

ISO 841 defines the Z-axis of a machine as being parallel to the principal spindle, implying that the machine’s Z-axis aligns with the axis average line of the principal spindle However, since the axis average line applies to other spindles and rotary axes as well, not all axes of rotation are necessarily parallel to the machine Z-axis An axis average line should only be parallel to the machine Z-axis when it is associated with the principal spindle.

quasi-static relative angular and linear displacement, between the tool side and the workpiece side, of the axis average line due to a change in conditions

Note 1 to entry: See Figure 1 c).

Causes of axis shift include thermal influences, load variations, and changes in speed and direction Accurate measurement of axis of rotation errors requires conducting tests over multiple revolutions under conditions that prevent axis shift, ensuring reliable results Properly accounting for these factors is essential for precise axis alignment and maintaining system performance.

3.1.14 structural loop assembly of components which maintains the relative position and orientation between two specified objects (i.e between the workpiece and the cutting tool)

A typical pair of specified objects in machining processes involves a cutting tool and a workpiece mounted on a machine tool, such as a lathe The structural loop includes key components like the workpiece holding fixture (e.g., chuck), spindle, bearings, spindle housing, machine headstock, machine bed, slideways, carriages, and the tool holding fixture Critical considerations include reference coordinate axes, the axis of rotation, the axis average line, and error motions of the spindle, along with error motions of the axis of rotation Additionally, the position and orientation errors, such as axis shifts of the axis average line, are essential for ensuring machining accuracy and quality.

1 spindle (rotor) E AC tilt error motion of C around X-axis

2 error motion trajectory of axis of rotation at varying angular positions of the spindle E BC tilt error motion of C around Y-axis

3 axis average line E CC angular positioning error motion of C

4 axis of rotation (at a given angular position of the spindle) E XOC error of the position of C in X-axis direction

5 spindle housing (stator) E YOC error of the position of C in Y-axis direction

E XC radial error motion of C in X-axis direction E A(OY)C error of the orientation of C in A-axis direction; squareness of C to Y

E YC radial error motion of C in Y-axis direction E B(OX)C error of the orientation of C in B-axis direction; squareness of C to X

E ZC axial error motion of C E C0C zero position error of C-axis a Reference axis.

Figure 1 — Reference coordinate axes, axis average line, and error motions of an axis of rotation shown for a C spindle or a C rotary axis

Radial throw of a rotary axis at a specific point refers to the distance between the geometric axis of a part or test artifact connected to the rotary axis and the average line of the axis, particularly when the two axes do not coincide This measurement is essential for accurately assessing deviations and ensuring precise alignment in rotary machinery Proper evaluation of radial throw helps in detecting misalignments and optimizing performance of rotary systems.

3.1.16 run-out of a functional surface at a given section total displacement measured by a displacement sensor sensing against a moving surface or moved with respect to a fixed surface

Note 1 to entry: The terms “TIR” (total indicator reading) and “FIM” (full indicator movement) are equivalent to run-out.

Measured run-out of a rotating surface encompasses surface profile (form) errors, radial axis throw, axis of rotation error motions, and dynamic excitation-induced surface motion relative to the axis of rotation It also includes structural error motions, providing a comprehensive assessment of rotational surface accuracy crucial for quality control.

A stationary point run-out total displacement is measured using a displacement sensor that detects movement against a specific point on a rotating surface When both the sensor and the surface rotate together, with negligible lateral motion relative to the sensor, the sensor effectively captures the total displacement caused by surface irregularities or deviations This measurement is essential for ensuring the accuracy and quality of rotating machinery, as it helps identify real surface deviations from false signals caused by lateral motion.

Note 1 to entry: See Figure 2 and ISO 230-1:2012, 10.2.2.

Figure 2 — Schematics of sample applications for use of stationary point run-out

(radial test for concentricity and face test for parallelism)

The 3.1.18 squareness error refers to the angular deviation from a perfect 90° between the average axes of two rotating machine components This measurement assesses the accuracy of the alignment between the axis average line of one rotating part and that of another Ensuring minimal squareness error is essential for optimal machine performance and to prevent undue wear or vibration Proper calibration and alignment procedures can help maintain the correct angular relationship between rotating components, ensuring reliable operation and extending equipment lifespan.

The 3.1.19 squareness error measures the angular deviation from a perfect 90° between a linear axis of motion and the average rotational axis of the machine This error is determined by assessing the angular discrepancy between a reference straight line on a linear moving component and the axis average line of a rotating component Ensuring minimal squareness error is essential for maintaining accurate alignment and optimal machine performance Proper calibration and alignment procedures can reduce this error, enhancing the precision of the entire system.

According to ISO 841, the positive direction for linear motion resulting from an axis of rotation is determined by the right-hand rule Specifically, it is aligned with the positive direction associated with the axis of rotation This standardized approach ensures consistent interpretation of rotational movement and linear displacement in engineering and mechanical contexts.

3.1.20 play condition of zero stiffness over a limited range of displacement due to clearance between elements of a structural loop

3.1.21 hysteresis linear (or angular) displacement between two objects resulting from the sequential application and removal of equal forces (or moments) in opposite directions

Note 1 to entry: Hysteresis is caused by mechanisms, such as drive train clearance, guideway clearance, mechanical deformations, friction, and loose joints.

3.1.21.1 setup hysteresis hysteresis of various components in a test setup, normally due to loose mechanical connections

3.1.21.2 machine hysteresis hysteresis of the machine structure when subjected to specific loads

Error motion terms

Axis of rotation error motion refers to unwanted variations in the position and orientation of the rotation axis relative to its average line, influenced by the angular position of the rotating component These errors can impact the precision and performance of rotating machinery, highlighting the importance of accurate measurement and control to minimize deviations and ensure optimal operation Understanding the relationship between the angular position and axis deviation is essential for improving machine accuracy and reducing mechanical faults.

[SOURCE: ISO 230-1:2012, 3.5.4 — modified to improve clarity]

Note 1 to entry: See Figure 3

This error motion can be measured by assessing the surface movements of an ideal cylindrical or spherical test artifact, with its centerline aligned with the axis of rotation.

Error motions are defined by their location and direction, as illustrated in Figure 3 a), excluding those caused by axis shifts from temperature variations, load changes, or rotational speed fluctuations These errors can manifest in various forms, including axial error motion, face error motion, radial error motion, and tilt error motion Understanding these different types of error motions is essential for accurate assessment and correction of axis rotation inaccuracies, ensuring optimal machine performance and precision.

3 axis average line 8 radial location

Figure 3 — General case of axis of rotation error motion and axial, face, radial, and tilt error motions for fixed sensitive direction

3.2.2 structural error motion error motion caused by internal or external excitation and affected by elasticity, mass, and damping of the structural loop

Note 2 to entry: Structural error motion can be reaction to the rotation of the spindle/rotary table/head that can influence the measurements.

3.2.3 bearing error motion error motion due to imperfect bearing between stationary and rotating components of a rotary axis Note 1 to entry: See Annex A

3.2.4 static error motion special case of error motion in which error motion is sampled with the spindle (or rotary table/head) at rest at a series of discrete rotational positions

Note 1 to entry: This is used to measure error motion exclusive of any dynamic influences.

Consequences of axis of rotation error motion

The measurement of axis of rotation error motion considers the intended use of the axis, reflecting the overall three-dimensional movement of the axis relative to its average line The impact of this error on machining accuracy varies depending on the operation, with simple processes like single-point turning primarily affected by error components in the tool's direction In contrast, complex machining tasks such as milling with multiple cutting edges require awareness of error motion across multiple directions Accurate measurement of axis of rotation error is crucial for applications like axial drilling on rotary tables, where the deviation impacts the hole pattern, and for turning non-round surfaces, where error motion in the cutting tool direction does not fully describe its effect on the machined profile These definitions underpin the measurement and analysis methods for axis of rotation error motion tailored to specific machining applications, ensuring optimal accuracy and performance.

3.3.1 sensitive direction direction perpendicular to the workpiece surface at the functional point

While many machining and measurement applications focus on a single sensitive direction, some scenarios involve multiple sensitive directions of interest For testing purposes, considering only one sensitive direction is usually sufficient unless specified otherwise, ensuring effective and accurate assessments in most cases.

3.3.2 non-sensitive direction direction perpendicular to the sensitive direction

3.3.3 fixed sensitive direction sensitive direction where the functional point in machine coordinate system does not change with the angular position of the rotating component

Note 2 to entry explains that, for a fixed sensitive direction, measuring the relative displacement between the tool and the workpiece reflects the shape error of the manufactured surface This measurement is essential for assessing the accuracy and quality of the workpiece’s surface in manufacturing processes Understanding this relationship helps in diagnosing surface deviations and improving machining precision.

Note 3 to entry: A single-point turning operation has a fixed sensitive direction However, this is not the case for turning non-round surfaces.

Note 4 to entry: A rotary table may have multiple fixed sensitive directions For example, rotary table used for single point turning in X or Y directions, may have two fixed sensitive directions.

Figure 4 — Illustration of fixed sensitive directions in facing, turning, and chamfering

3.3.4 rotating sensitive direction sensitive direction that rotates synchronously with the angular position of the rotating component Note 1 to entry: See Figure 5.

Note 2 to entry: A jig borer has a rotating sensitive direction A milling spindle with multiple-teeth milling cutter has multiple rotating sensitive directions.

Figure 5 — Illustration of rotating sensitive direction at two instants in time in jig-boring a hole

The sensitive direction in this context varies based on the angular position of the rotating component This variation occurs due to changes in the surface normal, which are influenced by the shape of the workpiece surface Understanding how the sensitive direction shifts with rotation is crucial for accurate surface analysis and measurement in manufacturing processes Recognizing the dependence of sensitive direction on the workpiece's geometry can enhance precision in sensor calibration and surface inspection.

Note 2 to entry: For example, single point turning of non-round workpiece, or machining a polygon on a turning machine, or cam grinding.

Figure 6 — Illustration of varying sensitive direction for cam turning operation

The 2D effect of axis of rotation error significantly impacts the position of the functional point within the plane perpendicular to the average line of the axis Understanding this error motion is essential for precise control and calibration in rotational systems Correcting axis of rotation errors enhances system accuracy by minimizing deviations in the functional point's position Analyzing the 2D effects of these errors enables better prediction and compensation, ensuring optimal performance in applications requiring high precision.

Drilling a circular hole pattern on a workpiece mounted on a rotary table can be affected by axis rotation errors, which lead to inaccuracies in the positioning of the holes These rotation error motions in the setup can compromise the precision of the drilled holes, highlighting the importance of minimizing axis errors for high-accuracy machining Proper calibration and error compensation are essential to ensure precise hole placement during such drilling operations.

Directional decomposition of axis of rotation error motion

Error motions of axes of rotation are decomposed into components along the three orthogonal axes, similar to the approach used for linear axes as outlined in ISO 230-1:2012, 3.4.3 Only the components of axis rotation error along the sensitive directions impact the geometry of the machined part Therefore, error motion in three-dimensional space is measured and analyzed specifically along these sensitive directions The provided definitions facilitate the directional decomposition of rotation axis error motions, ensuring accurate assessment of their influence on machining accuracy.

3.4.1 radial error motion error motion in a direction perpendicular to the axis average line and at a specified axial location Note 1 to entry: See Figure 3 d).

Note 2 to entry explains that this error motion refers to the radial movements of the surface of a perfect cylindrical or spherical test artifact, with its centerline aligned with the axis of rotation Measuring these radial motions is essential for assessing the accuracy and performance of rotating test artifacts, ensuring precision in testing and calibration processes This measurement provides critical data for understanding deviation from ideal geometry, aiding in quality control and maintenance of high-precision equipment.

Note 3 to entry: The term “radial run-out” includes additional errors due to centring and artefact out-of-roundness, and hence is not equivalent to radial error motion.

3.4.2 pure radial error motion error motion in which the axis of rotation remains parallel to the axis average line and moves perpendicular to it in the sensitive direction

Pure radial error motion refers to the radial error motion when tilt error motion is absent, and it is important to note that there should be no attempt to measure this parameter.

3.4.3 tilt error motion error motion in an angular direction relative to the axis average line

Note 1 to entry: See Figure 3 e).

Note 2 to entry: This motion may be evaluated as the difference between two simultaneous measurements of the radial error motion in two radial planes separated by a distance along the axis average line, divided by the axial separation distance.

Note 3 to entry: “Coning,” “wobble,” “swash”, “tumbling”, and “towering” errors are non-preferred terms for tilt error motion.

The term "tilt error motion" was specifically chosen instead of "angular motion" to prevent confusion with device rotation or angular positioning errors, such as those found in rotary tables This precise terminology helps differentiate between tilt-related inaccuracies and other forms of angular deviations, ensuring clarity in measurement and communication within the field Using "tilt error motion" enhances understanding and accuracy in the context of device calibration and error analysis.

3.4.4 axial error motion error motion coaxial with the axis average line

Note 1 to entry: See Figure 3 b).

Axial error motion is measured as the movement along the axial direction, aligned with the axis of rotation, of the surface of a perfect flat disk or spherical test artifact with its centerline coinciding with the axis This measurement helps assess deviations in rotational accuracy and surface stability It is important to note that terms like “axial slip,” “end-camming,” “pistoning,” and “drunkenness” are non-preferred nomenclature for describing axial error motion Understanding and accurately measuring axial error motion is essential for ensuring the precision and reliability of rotating components and test artifacts.

3.4.5 face error motion error motion parallel to the axis average line at a specified radial location

Face error motion encompasses a combination of axial and tilt error motions, impacting the precision of machine faces Unlike face run-out, which is analogous to radial run-out, face error motion refers specifically to the combined deviations in face positioning It is important to distinguish between face run-out and face error motion, as the former relates to radial displacement (see 3.4.2), while the latter involves combined axial and tilt deviations that can affect machining accuracy Understanding these terms is crucial for maintaining optimal surface quality and dimensional accuracy in manufacturing processes.

Decomposition of measured axis of rotation error motion based on

3.5.1 total error motion error motion as recorded over multiple revolutions, composed of the synchronous and asynchronous components of the axis of rotation and structural error motions

3.5.2 synchronous error motion portion of the total error motion that occurs at integer multiples of the rotation frequency

Note 1 to entry: It is the mean contour of the total error motion polar plot averaged over the number of revolutions.

3.5.3 fundamental error motion sinusoidal portion of the total error motion that occurs at the rotation frequency

Fundamental radial error motion is typically considered negligible since, in cases where there is a single fixed or rotating sensitive direction, this error does not impact the form accuracy of machined workpieces, such as the roundness of turned or bored cylinders Additionally, most measurements of apparent fundamental radial error motion are influenced by the radial throw of the reference artefact, which can affect the accuracy of the assessment.

Note 4 emphasizes that when the fundamental radial error motion differs between the X- and Y-directions, it becomes significant and cannot be ignored This is especially important in situations where the sensitive direction varies or when assessing two-dimensional effects on the position of the functional point Accurate consideration of these differences is essential for precise positioning and measurement accuracy.

3.5.4 residual synchronous error motion portion of the synchronous error motion that occurs at integer multiples of the rotation frequency other than the fundamental

3.5.5 asynchronous error motion portion of the total error motion that occurs at frequencies other than integer multiples of the rotation frequency

Note 1 to entry: Asynchronous error motion is the deviations of the total error motion from the synchronous error motion.

Asynchronous error motion refers to error components that are not strictly tied to the rotation frequency It includes non-periodic errors, errors that are periodic but occur at frequencies different from the rotation frequency and its integer multiples, and errors at sub-harmonic frequencies of the rotation These various types of asynchronous errors can impact the accuracy and stability of rotating machinery, making their identification and mitigation essential for precise operation.

Terms for axis of rotation error motion polar plots

The error motion of machine axes can be effectively represented using polar plots, which display the displacement versus the rotation angle of the spindle or rotary table This polar coordinate approach enables a clear visualization of error motions associated with axes of rotation By plotting these parameters, engineers can identify specific error characteristics and analyze the precision of machine movements Utilizing this method enhances the accuracy of error detection and supports optimal machine calibration, ensuring high-quality manufacturing outcomes.

3.6.2 total error motion polar plot polar plot of the total error motion as recorded

3.6.3 synchronous error motion polar plot polar plot of the synchronous error motion

Note 1 to entry: See 3.5.2 and Figure 7 b).

Creating the synchronous error motion polar plot can be achieved by averaging the total error motion polar plot over multiple revolutions, providing a clear visualization of error behavior Key concepts include total error motion, synchronous error motion, asynchronous error motion, inner error motion, and outer error motion, each representing different aspects of motion accuracy and deviation in rotating systems This method allows for accurate assessment of synchronous errors, which are crucial for maintaining precision in mechanical and engineering applications Understanding these error motions and their polar plots enhances diagnostic capabilities and helps optimize machinery performance.

Figure 7 — Error motion polar plots

3.6.4 asynchronous error motion polar plot polar plot of the asynchronous error motion

3.6.5 fundamental error motion polar plot best-fit circle passed through the synchronous axial or face error motion polar plot about a specified polar profile centre

3.6.6 residual synchronous error motion polar plot polar plot of the residual synchronous error motion

3.6.7 inner error motion polar plot contour of the inner boundary of the total error motion polar plot

Note 1 to entry: See Figure 7 d).

3.6.8 outer error motion polar plot contour of the outer boundary of the total error motion polar plot

Note 1 to entry: See Figure 7 e).

Terms for axis of rotation error motion polar plot centres

Since axis of rotation error motions are visualized using polar plots, the assessment of error motion values depends on the centers of these plots This article defines these centers to ensure accurate error measurement Table 1 specifies the preferred polar plot centers for various types of error motions, and in the absence of a specified center in a test description, the default assumption is to use the preferred center.

Table 1 — Preferred polar plot centres for various error motion types

Error motion type Preferred centre Radial error motion

Tilt error motion Axial error motion Face error motion

3.7.1 error motion polar plot centre centre defined for the assessment of error motion polar plots

PC centre centre of the polar chart

3.7.3 polar profile centre centre derived from the polar profile by a mathematical or graphical technique

LSC centre centre of a circle that minimizes the sum of the squares of a sufficient number of equally spaced radial deviations measured from it to the error motion polar plot

Note 1 to entry: See Figure 8.

2 error motion value for LSC centre

Figure 8 — Error motion polar plot, PC (polar chart) centre and LSC (least-square circle) centre, and error motion value for LSC centre

MRS centre centre that minimizes the radial difference required containing the error motion polar plot between two concentric circles

MIC centre centre of the largest circle that can be inscribed within the error motion polar plot

MCC centre centre of the smallest circle that will just contain the error motion polar plot

Note 1 to entry: Unless otherwise specified, the polar profile centre is determined using the synchronous error motion polar plot.

Note 2 to entry: A workpiece is centred with zero centring error when the polar chart centre coincides with the chosen polar profile centre.

Terms for axis of rotation error motion values

In most cases, the error motion value corresponds to the difference in radii of two concentric circles that enclose the error motion polar plot, with the specific value depending on the position of the circles' common center Clear definitions are provided to facilitate understanding of the phenomena and the related calculations Mathematical analysis enables the computation of these values directly, eliminating the need to create physical error motion polar plots.

3.8.1 error motion value magnitude assessment of an error motion component over a specified number of revolutions

3.8.2 total error motion value scaled difference in radii of two concentric circles from a specified error motion centre just sufficient to contain the total error motion polar plot

Note 1 to entry: Four total error motion values are defined: total radial error motion, total tilt error motion, total axial error motion, and total face error motion.

3.8.3 synchronous error motion value scaled difference in radii of two concentric circles from a specified error motion centre just sufficient to contain the synchronous error motion polar plot

Note 1 to entry: See Figure 9.

Key a asynchronous error motion value based on PC centre b synchronous error motion value based on LSC centre c synchronous error motion plot

Figure 9 — Error motion polar plot, asynchronous error motion, and synchronous error motion values

3.8.4 asynchronous error motion value maximum scaled width of the asynchronous error motion polar plot, measured along a radial line through a specified polar profile centre

The asynchronous error motion value is determined from the total error motion polar plot by identifying the maximum radial width of the “cloud band” at any angular position around the circumference Unlike other measurements, it does not use concentric circles but focuses on radial variation at specific angles To ensure accuracy, the asynchronous error motion should be measured along a radial line from the polar chart center, rather than from a best-fit center, although this approach may seem counterintuitive.

3.8.5 fundamental axial error motion value value equivalent to twice the scaled distance between the PC centre and a specified polar profile centre of the synchronous error motion polar plot

The amplitude of the measured synchronous error at the rotational frequency serves as a key indicator of system performance According to Note 1, this measurement provides essential insight into the magnitude of errors occurring during rotation It is important to note, as highlighted in Note 2, that the fundamental radial error motion is neglected when evaluating single fixed or rotating sensitive directions, as detailed in section 3.5.3 Understanding these parameters is crucial for accurate assessment of rotational system accuracy and stability.

3.8.6 residual synchronous error motion value scaled difference in radii of two concentric circles from a specified error motion centre just sufficient to contain the residual synchronous error motion polar plot

3.8.7 inner error motion value scaled difference in radii of two concentric circles from a specified error motion centre just sufficient to contain the inner error motion polar plot

3.8.8 outer error motion value scaled difference in radii of two concentric circles from a specified error motion centre just sufficient to contain the outer error motion polar plot

Terms for structural error motion

Structural error motion with a rotating spindle or rotary table involves measuring the relative movement between elements of a structural loop during rotation Specifically, it refers to the displacement or deviation observed between one component and another as the spindle or rotary table moves, which is crucial for assessing accuracy and stability in machining and manufacturing processes This measurement ensures precise alignment and minimizes errors in CNC machining, maintaining the quality of the finished product Understanding and controlling this error motion is essential for optimizing machine performance and ensuring high-precision operations.

Note 1 to entry: In some machines, the spindle drive system may transmit large deflections to the structure.

Structural error motion with a non-rotating spindle or rotary table refers to the unintended relative movement of one or more elements within a structural loop concerning the axis of rotation, measured while the spindle or rotary component remains stationary This phenomenon can impact machining accuracy by causing deviations in part dimensions and surface quality, making it essential to monitor and control for precise manufacturing outcomes Understanding and identifying these errors help maintain system stability and ensure high-precision operations in CNC machining and rotational equipment.

Note 1 to entry: In many applications, it is important to isolate sources of structural motion to external sources, i.e coolant or hydraulic pumps, or excitation caused by floor vibration.

3.9.3 structural error motion plot time-based rectilinear displacement plot or polar plot for recording structural motion

Note 1 to entry: A polar plot may be desired in order to resolve which component of the total structural error motion is synchronous with the spindle rotation.

3.9.4 structural error motion value range (max − min.) of displacement measured over a defined time and specified operating conditions

Terms for axis shift

3.10.1 radial shift axis shift in the direction perpendicular to the axis average line

3.10.2 tilt shift axis shift in an angular direction relative to the axis average line

3.10.3 axial shift axis shift in the direction parallel to the axis average line measured on a functional surface (e.g E Z0, TABLE , E Z0,SPINDLENOSE )

3.10.4 face shift combination of axial and tilt shifts in the axis of rotation measured at a specified radial location

3.10.5 speed-induced axis shift plot rectilinear graph of the shift in the axis of rotation as rotational speed is varied

The speed-induced axis shift value refers to the difference between the maximum and minimum displacement measurements of the axis of rotation, obtained using a single displacement sensor or a combination of sensors for tilt and face measurements, at various specified rotational speeds This measurement is crucial for understanding how rotational speed impacts the axis stability and precision of displacement sensors during operation Analyzing the variation in axis shift across different speeds helps optimize sensor performance and ensures accurate tilt and face measurements under dynamic conditions Monitoring these differences at various speeds provides insights into the sensor's reliability and the effects of rotational velocity on measurement accuracy.

Measuring units

In ISO 230, all linear dimensions, deviations, and tolerances are specified in millimeters, ensuring precision and consistency Angular dimensions are expressed in degrees, while angular deviations and tolerances are primarily represented as ratios; however, microradians or arcseconds may be used in certain situations for clearer measurement The standard provides clear equivalences for converting angular deviations and tolerances between different units, facilitating accurate communication and measurement across various applications.

Recommended instrumentation and test equipment

The recommended measuring instruments serve as examples; other devices capable of measuring the same parameters with equal or lesser measurement uncertainty can be used For spindle measurements, a non-contact linear displacement sensor that is insensitive to metallographic variations of the test artifact should be employed, ensuring adequate range, resolution, thermal stability, accuracy, and bandwidth The bandwidth requirement depends on the number of undulations per revolution to be resolved and the spindle's speed range.

A 10 kHz bandwidth displacement sensor is suitable for rotational speeds up to 6,000 r/min, capable of detecting up to 50 undulations per revolution at this speed Since high numbers of undulations are typically not expected in machine tool spindles, higher spindle speeds can be measured using sensors with greater bandwidths beyond 10 kHz, especially for higher spindle speeds and undulation counts (see Table H.1) For rotary table or head measurements, contact-type linear displacement sensors are also applicable Essential components include data acquisition systems, such as computers for sampling and storing displacement data, along with a test-mandrel designed according to machine-specific standards or agreements (ISO 230-1:1996, A.3), and a fixture for mounting the displacement sensors.

Long-term accuracy of the measuring equipment shall be verified, for example, by transducer drift tests.The measuring instruments shall be thermally stabilized before starting the tests.

Environment

Ensure that the machine and measuring instruments have been in the test environment long enough, preferably overnight, to reach thermal stability before testing Protect them from drafts, external radiation like sunlight, and overhead heaters to maintain accurate and consistent measurement conditions.

Rotary component to be tested

The rotary component shall be completely assembled and fully operational Axis of rotation tests shall be carried out in the unloaded condition.

Please note that this is not a diagnostic test for the spindle unit or rotary table/head Variations in test results across different machines using the same spindle unit or rotary table/head can occur due to factors such as mounting conditions, thermal effects, and vibration influences.

Rotary component warm-up

The tests shall be preceded by an appropriate warm-up procedure as specified by the manufacturer and/or agreed between the supplier/manufacturer and the user.

Preliminary movements should be limited to essential adjustments needed to set up measuring instruments for rotary heads, rotary tables, and swiveling tables It is important to test the spindle after allowing it to warm up at half of its maximum rotational speed for at least 10 minutes to ensure accurate performance.

Structural error motion tests

General

These tests are designed to point out relative motion between the tool and the workpiece, which is caused by the machine structure and the environment.

Test procedure

First, measure structural error motion with the machine’s power and auxiliary systems on, but with the machine drives off, that is, the emergency stop position.

To accurately assess the structural error motion, measure it while the machine is operational, incorporating the power and auxiliary systems like hydraulics, and ensure measurements are taken with the machine drives active in feed-hold mode.

Analysis of results

The structural error motion value is the peak-to-valley (range of) displacement observed over a relatively short time period (e.g 1 s).

5 Error motion test methods for machine tool spindle units

General

Error motions of machine spindle units in a single sensitive direction directly impact machining accuracy by causing one-for-one form and finish errors on the workpiece, making them critical for evaluating machine tool performance While error motions in non-sensitive directions are typically not assessed, potential second-order effects in these directions can become significant, especially when turning small-diameter parts, highlighting the importance of comprehensive spindle error analysis for precision manufacturing.

Test parameters and specifications

When documenting measurement procedures, it is essential to specify the measurement locations (radial, axial, or face), identify all artefacts, targets, and fixtures used, and detail the setup position The report should include the position of any linear or rotary stages connected to the device under test and the direction angle of the sensitive measurement axis, such as axial or radial Results must be presented clearly, whether as error motion values, polar plots, or frequency content plots, along with the spindle's rotational speed (or zero for static errors) and measurement duration in seconds or spindle revolutions Proper warm-up or break-in procedures should be followed and documented Instrumentation frequency response—including bandwidth, filter roll-off, and digital resolution—is critical The structural setup, including sensor placement relative to the spindle housing and reference objects, must be specified All measurements should be timestamped, noting the type and calibration status of testing equipment, and other operating conditions like ambient temperature should be recorded if they influence the results.

Spindle axis of rotation tests — Rotating sensitive direction(s)

General

These tests are applicable to the machining operations with rotating tools, for example, boring, milling, drilling, and contour grinding.

Radial error motion

Figure 10 illustrates a test setup for measurement, featuring a precision test sphere or suitable artifact like a cylinder mounted on the machine spindle Displacement sensors are positioned orthogonally on the workholding table to accurately capture data The test sphere is carefully centered on the rotational axis to minimize radial throw, ensuring precise measurements An angle-measuring device, such as a rotary encoder, is used to determine the spindle's angular position, contributing to accurate assessment of machine performance.

You can determine the spindle’s angular position without a rotary encoder by mounting a test sphere slightly eccentric, which creates a 90° phase-shifted sinusoidal signal with each revolution These sinusoidal signals, superimposed on the displacement sensor outputs, enable accurate calculation of the spindle’s angular position for polar plotting It is essential to remove this one-per-revolution error component during data analysis to ensure precise measurements.

Figure 10 — Schematic of test setup for radial error motion with rotating sensitive direction using angular position measuring device and centred reference artefact (sphere)

The oscilloscope is most effectively used for radial error motion measurement with a rotating sensitive direction, following the method outlined by Tlusty A schematic diagram (Figure 11) illustrates the setup, featuring horizontal and vertical displacement sensors that detect radial deviations against a reference test sphere These sensor signals are amplified and transmitted to the horizontal and vertical axes of the oscilloscope, enabling precise analysis of radial errors.

Using a wobble plate, the reference sphere is intentionally made eccentric to the axis average line, enabling precise measurement of radial error motion In an ideal scenario with a perfect axis of rotation, the error motion would form a perfect circle as the axis rotates; however, imperfections cause deviations that are detectable through oscilloscope displays Radial error motion along the direction of the reference sphere's eccentricity alters the shape of the oscilloscope's display, providing a direct measurement of the radial error; motion perpendicular to this eccentricity has negligible effect This setup allows for accurate assessment of radial error motion parallel to a line from the axis's average line to the geometric center of the eccentric reference sphere When mounting tools or sensors in a fixed angular orientation, the eccentricity of the reference sphere should be aligned in that specific direction for optimal measurement accuracy.

If the orientation is arbitrary, then the axis should be tested with the sphere eccentric at least in two directions separated by 90ᵒ.

4 reference sphere offset in direction of tool

Figure 11 — Test method for radial error motion with rotating sensitive direction and sphere mounted eccentric to the spindle (Tlusty method)

Radial error motion measurements should be conducted at three specified spindle rotational speeds, which are defined as percentages of the maximum speed according to machine-specific standards At each speed, displacement sensor readings must be accurately recorded relative to the spindle's angular position to ensure precise assessment of radial errors.

Radial error motion is characterized by capturing the radial displacements of the spindle (rotor) as functions of its angular position relative to a stationary reference point This measurement is typically achieved using two sensors that record the spindle's deviations during rotation Accurate assessment of radial error motion is essential for ensuring precision in machine tools and rotating machinery By analyzing the radial displacement data across various spindle angles, engineers can identify and minimize sources of vibration and misalignment, leading to improved machine performance and reliability.

1) It is recommended that the machine user simply observe the output of the measurement system while changing the spindle speed slowly throughout its total speed range Speeds could be observed where excessive error motion displacement sensors located perpendicular to each other and by computing and displaying the error motion polar plot according to Formula (1): r ( )θ = + r 0 ∆ X ( )θ cos θ+ ∆ Y ( )θ sin θ (1) where θ is the angular position of the spindle; r(θ) – r 0 is the radial error motion at angular position θ; ΔX(θ) is the output of the displacement sensor oriented with the X-axis; ΔY(θ) is the output of the displacement sensor oriented with the Y-axis; r 0 is the value to scale the polar plot for visual representation.

Formula (1) assumes that θ aligns with the rotating sensitive direction, but this alignment may not always be achieved during testing Therefore, it is important to report the zero position of θ relative to the rotating sensitive direction At each spindle speed, a polar plot of the spindle axis of rotation error motion should be generated over multiple revolutions to ensure accuracy A representative example of such a plot at a single spindle speed is depicted in Figure 7a.

According to ISO 230, only two error-motion values—the asynchronous and synchronous radial error motions—are calculated from the error motion plot using the LSC center These radial error motion values must be specified with the axial measurement location and reported for each of the three spindle rotational speeds See Figures 7b), 7c), and 9 for reference.

When turning non-axisymmetric (non-round) parts, the radial error motion along the sensitive direction, denoted as r_n(θ), can be accurately calculated using the specific formula This formula accounts for variations in the radial error caused by spindle imperfections and is expressed as r_n(θ) = r_0 + ∆X(θ) cos θ + ∆Y(θ) sin θ, where these terms represent the dynamic radial deviations during spindle rotation Understanding this calculation is essential for optimizing spindle design and ensuring precision in machining complex parts.

Where, θn is the angle of the surface normal of the workpiece at a given angular orientation of the rotating axis θ It is a function of θ.

When spindles carry tools with multiple cutting tips oriented in various directions, the radial error motion along each orientation is calculated using Formula (2) In these scenarios, the angle θn corresponds to increments of 360° divided by the number of cutting tips, ensuring precise assessment of error effects Accurate analysis of radial error motions in multi-tip tools is essential for optimizing machining accuracy and tool performance.

Tilt error motion

To accurately measure the tilt error motion, it is necessary to record the radial error motion at two spatially separated points, as illustrated in Figure 12 A test artifact, such as two precision test spheres spaced at a specific distance or a cylindrical mandrel, can be mounted on the spindle and aligned with its axis of rotation The minimum recommended distances between the spheres or displacement sensors, which vary according to spindle sizes, are provided in Table 2 to ensure precise measurement.

This article discusses two methods for measuring tilt error motion Method 1 utilizes two displacement sensors, while Method 2 employs four displacement sensors to accurately assess tilt Both techniques are valid; however, synchronization challenges between the data collected at different times can lead to variations in the results obtained by each method.

2) For spindles the minimum is 20 revolutions.

Table 2 — Recommended minimum axial separation between spheres/displacement sensors for tilt error motion measurements

Nominal diameter of spindle at front bearing mm

Minimum axial distance between displacement sensors

Figure 12 — Five-sensor test system for measurement of rotating sensitive direction spindle error motions (used for Method 2 of tilt error motion measurements)

To perform radial error motion measurements, first mount a test sphere or other artefact along with displacement sensors according to section 5.3.2.1 Conduct measurements at three specified spindle speeds, which should be defined as percentages of the maximum speed outlined in the machine's specific standards At each rotational speed, record the displacement sensor readings as a function of the spindle’s angular position to ensure accurate assessment of radial errors.

Re-fixture the ball or artifact at the minimum recommended axial distance from its previous position, as specified in Table 2 Then, conduct a second set of measurements at the same three spindle speeds to ensure consistency and accuracy in the data collection process.

Determine the synchronous radial error motion and asynchronous radial error motion at each spindle speed and axial position following section 5.3.2.3 The synchronous tilt motion error is calculated by dividing the difference in synchronous radial error measurements by the distance between measurement points, expressed in radians Similarly, the asynchronous tilt motion error is obtained by dividing the difference in asynchronous radial error measurements by the length, also expressed in radians These measurements are essential for assessing spindle alignment accuracy and ensuring optimal machine performance.

Mount the test artefact and displacement sensors following section 5.3.3.1, then perform measurements at three designated spindle speeds These speeds should be specified as percentages of the maximum speed outlined in the relevant machine standards At each rotational speed, record the displacement sensor readings corresponding to different spindle angular positions to ensure accurate analysis.

Determine the synchronous and asynchronous radial error motions at each spindle speed and axial position per section 5.3.2.3 Use the differences between sensors 1 and 4, and sensors 2 and 5, as ΔX and ΔY in the radial error calculation, with r₀ set to zero; note that sensor 3 is not required for this measurement.

The synchronous tilt motion, measured in radians, is calculated by dividing the synchronous error by the sensor separation distance in the test setup A polar plot is then constructed and analyzed following the procedures outlined in section 5.3.2.3 Additionally, the asynchronous error motion, also expressed in radians, is determined by dividing the asynchronous error by the same sensor spacing These measurements help evaluate tilt behavior accurately in test environments.

Axial error motion

Figure 13 illustrates a schematic test setup designed for precise measurement In this configuration, a high-precision test sphere is securely mounted in the machine spindle, ensuring accurate alignment A displacement sensor is positioned on the machine table, aligned axially against the test sphere to accurately detect deviations The test sphere is precisely centered on the spindle's axis of rotation to minimize concentricity errors, ensuring measurement accuracy Additionally, an angle-measuring device like a rotary encoder is mounted on the spindle to accurately monitor its angular position during testing, providing reliable data for analysis.

Position the displacement sensor according to the axial position shown in Figure 13 to ensure accurate measurement Conduct axial error motion assessments at three specified spindle speeds to evaluate sensor performance It is essential to specify the rotational speeds used during testing to maintain measurement consistency and reliability.

3) It is recommended that the machine user simply observe the output of the error-indicating system while changing the spindle speed slowly throughout its total speed range Speeds could be observed where excessive error motion results due to structural error motion If such speeds exist, they should be avoided when machining.

4) It is recommended that the machine user simply observe the output of the error-indicating system while changing the spindle speed slowly throughout its total speed range Speeds could be observed where excessive error motion results due to structural error motion If such speeds exist, they should be avoided when machining. as the percentages of the maximum speed in the machine specific standards At each rotational speed, displacement sensor readings shall be recorded as a function of the spindle angular position.

Figure 13 — Setup for axial error motion measurement

The analysis of the axial error motion polar plot is similar to that of radial error motion, with key differences in how the fundamental error motion is treated Specifically, the axial error motion is represented on a linear plot of error versus spindle angular orientation, providing clear visualization The asynchronous axial error motion is determined by measuring the maximum displacement range over multiple spindle revolutions, ensuring accurate assessment of non-synchronous deviations In contrast, the synchronous axial error motion is calculated based on the range of average axial deviations at different spindle angles, highlighting consistent misalignments.

Spindle tests — Fixed sensitive direction

General

These tests are applicable to the machining operations with fixed sensitive direction, for example, turning and cylindrical grinding.

Test setup

Figure 14 illustrates test setups for measuring spindle error motions with a fixed sensitive direction, such as a work spindle These tests involve generating a signal proportional to the spindle's angular orientation, enabling the creation of polar plots of error motion versus spindle angle A precision test sphere or suitable artifact is mounted in the spindle, while a displacement sensor is positioned on the tool post or a rigid fixture Centering the artifact around the rotation axis minimizes radial throw, which can be confused with fundamental axial error motion.

Radial error motion

The radial error motion shall be measured by positioning the displacement sensor in the radial direction, as shown in Figure 14.

Radial sensors should be installed in the specified sensitive direction, with only one displacement sensor mounted at each Z position, as shown in Figures 10 and 11 This setup is designed specifically to accurately measure the radial error motion in the designated sensitive direction, ensuring precise assessment of displacement along that axis.

Radial error motion measurements should be conducted at three designated spindle speeds, specified as percentages of the maximum speed according to machine-specific standards During each test, displacement sensor readings must be recorded as a function of the spindle's angular position to accurately assess radial error motion.

Figure 14 — Test setups used for measuring spindle fixed sensitive direction error motion

Using an oscilloscope for measuring radial error motion with a fixed sensitive direction necessitates a separate mechanism to generate the base circle Bryan et al [10] describe a method involving two eccentric circular cams, offset by 0.1 mm in perpendicular directions, which are sensed by low-magnification displacement sensors to produce sine and cosine signals for the base circle Alternatively, a single cam with sensors placed 90° apart can be used Radial error motion is detected by a third high-magnification displacement sensor that measures against a reference test sphere centered on the axis's average line The sine and cosine signals are multiplied by the radial error motion signal and fed into the oscilloscope's two axes, creating a polar plot of radial error versus angular position These eccentric cams and low-magnification sensors can be replaced with a small commercial angular measuring device attached directly to the rotation axis, simplifying the measurement setup.

Determination of angular position by the above described method can also be used for rotating sensitive direction measurements.

Figure 15 — Test method for radial error motion with fixed sensitive direction (Bryan method)

When a displacement sensor is correctly aligned with its fixed sensitive direction, the radial error motion, represented by [r(θ) − r₀], can be accurately determined using a simplified formula Specifically, the displacement in the radial direction, r(θ), is calculated as r₀ plus the product of the sensor output, ΔX(θ), and the displacement measurement This formula highlights how the sensor's output directly reflects the radial displacement, enabling precise measurement of radial errors in mechanical systems with high accuracy and reliability.

When the fixed sensitive direction is inclined at an angle θf relative to the X-axis, the measurement can be conducted either by aligning the sensor with the sensitive direction or by employing a second sensor in the orthogonal Y direction In this scenario, the radial error motion at a given angular position θ is described by the equation r(θ) = r0 + ΔX(θ) cos θf + ΔY(θ) sin θf, where θ is the spindle's angular position The parameter r(θ) represents the radial error motion, ΔX(θ) and ΔY(θ) are displacement sensor outputs along the X and Y axes respectively, θf is the fixed sensitive direction’s angle relative to the X-axis, and r0 is a scaling factor for the polar plot This approach enables accurate measurement of radial error motion even when the sensitive direction is angled.

For each rotational speed, a polar plot of the spindle error motion must be generated over a sufficient number of revolutions, with a typical example shown in Figure 7a Although the plots may appear similar for fixed sensitive and rotating sensitive directions, they represent different quantities; only two error-motion values are calculated from these plots The asynchronous error motion is determined by measuring the maximum scaled width of the total error motion polar plot along a radial line through the center, as illustrated in Figure 9 The synchronous error motion is obtained by averaging the total error motion results over all revolutions, with the polar plot depicted as the dark line in Figures 7b and 9 The synchronous radial error motion is defined as the scaled difference in radii of two concentric circles centered at the LSC, just large enough to encompass the synchronous error motion polar plot These radial error motion values must be specified at the axial location where the measurements are taken, ensuring accurate characterization of the spindle's error motion.

Axial error motion

Axial error motion is measured by positioning a displacement sensor in the axial direction, as illustrated in Figure 13 The measurement should be conducted following the same procedure and at identical spindle speeds specified for rotating sensitive direction axial error motion in section 5.3.4.2 This ensures accurate assessment of axial error motion, which is critical for maintaining machine precision and performance.

The analysis of the axial error motion polar plot is similar to that of radial error motion, with the key distinction that concentricity error should not be removed analytically Axial error motion can be effectively represented on a linear plot showing error versus spindle angular orientation The asynchronous axial error motion is determined by measuring the maximum displacement over multiple spindle revolutions, while the synchronous axial error motion is obtained from the range of average axial deviations at different spindle angular positions.

Tilt error motion

Accurate measurement of tilt error motion in the fixed sensitive direction involves assessing the radial error motion at two spatially-separated points using radial displacement sensors As illustrated in Figure 14, sensors 1 and 2 are positioned to capture the radial displacement To ensure precise results, a test artefact with two spheres spaced apart or a high-precision test mandrel is affixed to the spindle and carefully aligned with the spindle's axis of rotation, minimizing radial throw and enabling accurate tilt error analysis.

Two methods for measuring tilt error motion are discussed: Method 1 utilizes a single displacement sensor, while Method 2 employs two displacement sensors for more comprehensive measurement Both approaches are acceptable; however, synchronization challenges between data sets collected at different times may lead to discrepancies in the results obtained by these methods.

To perform radial error motion measurements, mount the test sphere or mandrel along with a displacement sensor, as specified in section 5.4.3.1, using a single displacement sensor aligned with the sensitive direction Conduct the measurements at three distinct spindle speeds, which should be defined as percentages of the machine's maximum speed according to relevant standards At each rotational speed, record the displacement sensor readings throughout the spindle's angular positions to assess radial error motion accurately.

To ensure accurate measurements, remount the sphere or mandrel and displacement sensor 50 mm to 100 mm away from their previous positions Perform a second set of measurements at the same rotational speeds, recording the displacement sensor readings relative to the spindle's angular position.

The synchronous and asynchronous radial error motion values at each spindle speed and both axial positions should be measured according to section 5.4.3.2 The synchronous tilt motion error is calculated by dividing the difference in radial error motion measurements by the distance between measurement points Similarly, the asynchronous tilt motion error is determined by dividing the difference in asynchronous radial error motion values by the length between points, expressed in radians These measurements are essential for assessing spindle performance and ensuring precision in manufacturing processes.

This analysis assumes that two displacement sensors are positioned on the spheres' equators or along the test mandrel, separated by distance Ld To ensure accurate measurements, the sensors should be calibrated for equal sensitivity, with their outputs either subtracted directly before input into the spindle analyzer or processed through software after gain calibration The spindle is operated for multiple revolutions at three selected speeds, as outlined in section 5.4.5.2 The differences between the two displacement sensor readings are then plotted on a polar plot to analyze the measurement consistency and rotational behavior.

The asynchronous tilt error motion value represents the asynchronous component of total error motion, derived from the difference between two displacement sensor readings along a radial line through the polar chart center It is calculated by dividing this difference by the distance Ld between the sensors Mathematically, this is expressed as β(θ) = [r₂(θ) - r₁(θ)] / Ld, where β(θ) is the tilt error motion in radians, and r₂(θ) and r₁(θ) are the radial error motion values at sensors 2 and 1, respectively.

L d is the distance between the two displacement sensors; θ is the angular orientation of the spindle (angle on polar chart).

The synchronous tilt error motion value is calculated by dividing the difference between two synchronous error motion measurements taken at different positions by the distance between the two displacement sensors This method provides an accurate assessment of tilt errors during operation, ensuring precise alignment and performance Properly analyzing these measurements helps identify potential issues in the system's stability and helps optimize calibration processes Ultimately, understanding the synchronous tilt error motion contributes to improved accuracy and reliability in machinery and measurement systems.

When the displacement sensor is not aligned with the fixed sensitive direction, Formula (5) can be modified similarly as in 5.4.3.2

6 Error motion test methods for machine tool rotary tables/heads

General

Axis of rotation error motions in machine tool rotary tables and rotary heads share similar characteristics with machine spindles, but operate at significantly lower rotational speeds Additionally, their rotational travel is often limited to less than 360°, which influences testing conditions Despite using similar methods and concepts, the testing parameters for these components differ due to these operational distinctions.

For low-speed rotary axes such as rotary tables and trunnions, a polar recorder synchronized mechanically or electrically with the axis of rotation effectively measures deviations in both fixed and rotating sensitive directions In the rotating sensitive direction, the test involves supporting the reference sphere from the machine frame and mounting the displacement sensor on the rotating axis, ensuring accurate measurement during axis movement For limited revolutions, coiling the sensor cable around the axis minimizes interference; however, for continuous rotation, solutions like slip rings or wireless data transmission are essential to maintain consistent data collection.

Rotary tables and rotary heads are essential for precise positioning of tools and workpieces, functioning similarly to linear axes in machine tools Their measurement procedures for radial, axial, and tilt error motions adhere to the standards outlined in ISO 230-1 Accurate testing of these components ensures optimal machine performance and manufacturing precision.

In situations involving swivelling tables where centering an artefact such as a small precision sphere on the axis of rotation is challenging, specialized calibrated test artefacts like large partial spheres or cylinders are required To address these challenges, a measurement setup employing three displacement sensors can be utilized to accurately determine the position of a test sphere (R-test), ensuring precise measurement even when direct centering is not feasible.

(see ISO 230-1:2012, 11.3.5.3) However, it should be kept in mind that measurement uncertainty increases due to the contributions of the error motions of linear axes involved in the measurement.

Axial error motion

Test setup

A precision test sphere or suitable artifact is securely mounted on the machine's rotating component using an appropriate fixture to ensure accurate positioning along the axis of rotation The displacement sensor is installed on the non-rotating part in the axial direction, enabling precise measurement of the relative motion between the tool and workpiece Proper centering of the sphere or artifact around the axis of rotation is essential to minimize radial throw and ensure measurement accuracy For reference, see Figure 16.

Test procedure

To accurately test the motion of a rotary machine component, such as the table or head, it must be moved to a series of target positions within its designated travel range The measurement interval between these positions should be carefully maintained, ensuring it does not exceed the specified maximum interval for precise results Proper positioning and controlled measurement intervals are essential for reliable motion analysis and quality assurance of rotary machine components.

For axes with a travel range of 90° or less, the measurement interval should not exceed one-tenth of the axis travel For rotary axes capable of multiple full rotations (360°), the interval must be no greater than 30° When the machine reaches a target position, it should remain stationary long enough to allow accurate measurement data recording Depending on the measuring instrument and application, measurements can be performed in continuous mode to improve efficiency.

For rotary tables, it is essential to perform a minimum of five revolutions in both the clockwise and counter-clockwise directions to ensure proper operation Similarly, rotary heads and swivelling tables require at least five rotations across the full travel range in both directions These calibration procedures help maintain accuracy and reliability in machining and positioning tasks.

Default rotational speed shall be at a level to suit the measuring equipment and setup being used and/or the intended use of the machine tool.

2 radial displacement sensor in X-direction

3 radial displacement sensor in Y-direction

Figure 16 — Setup for measurement of axial and radial error motions of rotary table

Data analysis

Axial error motion is typically represented on a polar or linear plot, illustrating error motion against spindle angular orientation The asynchronous axial error motion is measured as the maximum displacement range over multiple revolutions of the rotating component, indicating the highest deviation during operation Meanwhile, the synchronous axial error motion refers to the error component that is phase-locked with the rotation, impacting the precision of spindle performance and ensuring accurate machining or measurement processes Proper analysis of both error types is essential for optimizing spindle accuracy and ensuring high-quality manufacturing outcomes.

Radial error motion

Test setup

A precision test sphere or suitable artifact like a cylinder is securely mounted in the machine's rotating component using an appropriate fixture to ensure the sphere is aligned on the axis of rotation Displacement sensors are strategically placed on the non-rotating part of the machine in orthogonal orientations, allowing accurate observation of the relative motion between the tool and workpiece Proper centering of the test sphere on the rotation axis minimizes radial throw, ensuring precise measurement accuracy.

Test procedure

To effectively evaluate the rotary machine component, such as the table or head, it must be positioned at a series of target locations across its operational travel range Ensuring precise movement to these positions is essential for accurate measurement results The measurement interval should be maintained at no more than [specified value] to guarantee detailed and reliable data collection during testing Proper positioning and controlled measurement intervals are critical for optimizing rotary machine performance assessments.

For rotary axes with less than or equal to 90° movement, the axis travel range should be limited to one-tenth of its full range In contrast, for rotary axes capable of multiple full rotations (up to 360°), the interval between measurements must not exceed 30° At each target position, the machine must remain stationary long enough to allow accurate measurement data to be recorded Additionally, measurements can be performed in continuous mode depending on the measuring instrument and the specific application of the machine tool.

For rotary tables, it is essential to perform a minimum of four revolutions in both the clockwise and counter-clockwise directions to ensure proper operation Similarly, rotary heads and swivelling tables require at least two rotations in each direction to achieve optimal functionality and accuracy These rotational requirements are crucial for the precise calibration and maintenance of machine components Following these guidelines helps maintain equipment performance and extends the lifespan of rotary machinery.

Data analysis for rotating sensitive direction

Radial error motion is determined by recording the radial displacements of the rotating component as functions of its angular position, measured by two perpendicular displacement sensors These measurements are used to compute and display the error motion polar plot based on Formula (6): r(θ) = r₀ + ΔX(θ) cos θ + ΔY(θ) sin θ, where θ represents the angular position, ΔX(θ) and ΔY(θ) are sensor outputs along the X and Y axes respectively, and r₀ is a scaling factor for visual representation This method provides an accurate assessment of radial errors in rotating machinery, facilitating precise analysis and diagnostics.

The radial error motion typically features a specific plot, as illustrated in Figure 7a For ISO 230 standards, two key error-motion values are derived from this plot using the LSC center: the asynchronous radial error motion and the synchronous radial error motion These values are detailed in Figures 7b, 7c, and 9, providing essential metrics for assessing radial error motion in precision measurements.

The radial error motion values shall be specified with the axial location at which the measurements are taken The synchronous and asynchronous radial error motion values shall be reported.

Radial error motion in rotary tables carrying workpieces significantly impacts the precise positioning of the workpiece in the plane perpendicular to the axis This 2D effect of axis of rotation error motion can be characterized by the displacement components [ΔX(θ), ΔY(θ)], which describe how the workpiece's location varies with the rotation angle θ Understanding and compensating for these errors are crucial for enhancing machining accuracy and ensuring high-quality manufacturing outcomes.

Data analysis for fixed sensitive direction

Radial error motion is determined by recording radial displacements of the rotating component as functions of its angular position using displacement sensors A typical radial error motion plot is illustrated in Figure 7a) For ISO 230, two key error-motion values are calculated from this plot— the asynchronous and synchronous radial error motions—based on the LSC centre, as shown in Figures 7b), 7c), and 9 These radial error motion values must be specified at the axial location where measurements are taken, and both the synchronous and asynchronous error motion values should be reported for accurate assessment.

The asynchronous error motion value represents the maximum scaled width of the total error motion polar plot measured along a radial line through the polar chart center, as illustrated in Figure 9 The synchronous error motion polar plot is calculated by averaging the total error motion results over multiple revolutions, with the typical synchronous error motion depicted as the dark line in Figures 7b) and 9 The synchronous radial error motion value is determined by the scaled difference in radii between two concentric circles centered at the LSC (Largest Single Circle) center, just large enough to contain the entire synchronous error motion polar plot Additionally, the radial error motion values must be specified at the axial locations where the measurements are taken, ensuring accurate representation of the error motion.

Tilt error motion

Test setup

Measuring tilt error motion involves assessing the radial error at two spatially separated points using a test artifact, such as two precision test spheres spaced apart or a cylindrical mandrel This test artifact is attached to the machine's rotating component and precisely aligned along the spindle's axis to ensure accurate tilt error measurement Proper alignment and strategic placement of measurement points are essential for reliable and precise evaluation of tilt errors in rotating machinery.

Both methods that are described in 5.3.3 and 5.4.5 are acceptable.

Test procedure

To effectively test the motion of rotary machine components such as the table or head, they should be moved to predefined target positions across their operational range Measurement intervals should be no greater than 10° for axes of 90° or less, ensuring accurate data collection, while for rotary axes capable of full 360° rotation, intervals must not exceed 30° At each target position, the machine must remain stationary long enough to record precise measurement data Measurement procedures can be performed in continuous mode, depending on the measuring instrument used and the specific application of the machine tool.

For rotary tables, it is essential to perform at least four revolutions in both the clockwise and counter-clockwise directions to ensure proper operation In contrast, rotary heads and swiveling tables require a minimum of two rotations in each direction These movement guidelines help maintain equipment accuracy and longevity Following these rotation specifications is crucial for optimal performance and precise machining tasks.

If the test setup with one test sphere is used, then the sphere shall be relocated at a different axial location and test procedure shall be repeated.

Data analysis for rotating sensitive direction

The synchronous and asynchronous radial error motion values at both axial positions should be determined according to section 5.3.2.3 The synchronous tilt motion error is calculated by dividing the difference in synchronous radial error motion measurements by the distance between the positions, expressed in radians Similarly, the asynchronous tilt motion error is obtained by dividing the difference in asynchronous radial error motion values by the length, also expressed in radians These calculations are essential for assessing the tilt errors in the system to ensure precision and alignment.

Using a test setup with two test spheres, the difference in output readings from two displacement sensors along the same axis (X or Y) is utilized to calculate both synchronous and asynchronous (pseudo) radial error motion values These error values are then normalized by dividing them by the distance between the test spheres, yielding precise measurements of the synchronous and asynchronous tilt error motion.

Data analysis for fixed sensitive direction

The synchronous and asynchronous radial error motion values at both axial positions should be determined according to section 5.4.3.2 The synchronous tilt error is calculated by dividing the difference in synchronous radial error motion measurements by the distance between the positions, expressed in radians Similarly, the asynchronous tilt error is obtained by dividing the difference in asynchronous radial error motion values by the length, also expressed in radians.

Using a test setup with two spheres, the difference between the displacement sensor outputs in the same direction (X or Y) is utilized to calculate synchronous and asynchronous radial error motions These values are then divided by the distance between the test spheres to determine the synchronous and asynchronous tilt error motions, providing accurate measurements of tilt errors in precision machinery testing.

Annex A (informative) Discussion of general concepts

This annex provides an overview of the fundamental concepts related to the specification and measurement of the quality of rotation axes in machine tools, based on the CIRP Unification document on axes of rotation [8] While it uses specific examples such as a lathe spindle for clarity, these concepts are applicable to all rotational axes in machine tools, including rotary tables, trunnion tables, and live centres.

A perfect axis of rotation must facilitate pure rotation of a workpiece about a fixed line in space; however, simply stating this is insufficient Key requirements include ensuring precise alignment, stability, and minimal friction to enable smooth and accurate movement Additionally, the axis should support the workpiece securely, preventing unwanted deviations, and accommodate the specific rotational needs of the application Understanding these critical points ensures the selection or design of an optimal rotation axis that meets all functional and precision demands.

A lathe mounted aboard a ship experiencing ocean roll demonstrates that the spindle axis undergoes significant motion in space without affecting workpiece accuracy, highlighting the importance of relative motion between the workpiece and cutting tool This focus on relative motion is maintained through the structural loop, which includes the chuck, spindle shaft, spindle bearings, spindle housing, frame, slides, and tool post Ensuring the stability of this structural loop is crucial for precise machining operations despite the ship's dynamic movements.

In lathe operations, imperfections in spindle bearings can cause small axial movements of the workpiece relative to the cutting tool, resulting in one-for-one errors in the finished surface These axial movements occur in a sensitive direction, which is parallel to a line perpendicular to the surface of revolution at the cutting point Conversely, small tangent motions that are parallel to the face do not introduce cutting errors, indicating these are non-sensitive directions Understanding the distinction between sensitive and non-sensitive directions is essential for achieving precise machining, with the sensitive direction being critical for controlling dimensional accuracy during flat facing cuts.

During a boring operation where the workpiece remains stationary and the cutting tool rotates, the sensitive direction, which is always parallel to a line passing through the machining point, rotates with the tool (see Figure 5) Different testing methods are employed depending on whether the machine's sensitive direction remains fixed or rotates relative to the machine frame Similarly, in milling operations, multiple sensitive directions may exist, corresponding to the number of cutting tips or inserts on the tool, which can also undergo rotation during machining.

When machining a cam on a lathe, the process involves coordinating spindle rotation with cross-slide movement Since the cam's geometry lacks rotational symmetry, its surface normal direction changes with respect to the spindle's angular position Consequently, the cam's sensitive or active direction varies as a function of the spindle's angular position, which is illustrated in Figure 6.

Rotary axes can have multiple sensitive directions depending on their application For instance, a milling spindle equipped with a multi-insert milling cutter exhibits several rotating sensitive axes, each aligned with the inserts' cutting paths Similarly, a rotary table used for single-point turning in two orthogonal directions at different axial positions has two fixed sensitive directions Understanding these sensitive directions is essential for precise motion control and accurate machining operations.

A.2.7 Displacement sensors versus cutting tools

In conclusion, the term “tool” should be understood broadly to include not only cutting tools but also grinding wheels These examples highlight that all related concepts—such as tool selection, maintenance, and application—are equally applicable to measuring devices, where a displacement sensor can replace a traditional cutting tool Understanding this broad interpretation is essential for optimizing machining and measurement processes in manufacturing.

Based on the above discussion, it is possible to give a more precise statement of the requirements for a perfect axis of rotation in a machine tool:

A perfect axis of rotation should ideally allow a workpiece to rotate about a line that remains stationary relative to the tool, ensuring precise machining While the initial definition does not specify restrictions on motion in the non-sensitive direction, practical considerations often justify neglecting this component due to minimal measurement errors and reduced effort However, in applications such as drilling patterns on a workpiece supported by a rotating table, even small errors in non-sensitive directions can lead to significant inaccuracies in hole placement, known as the 2D effect of axis of rotation error To estimate the impact of motion along the non-sensitive direction, a specific formula is used, helping to assess and mitigate potential errors in precision machining processes.

E N = motion in the non-sensitive direction

E S = error in the sensitive direction due to E N

For example, let E N = 0,02 mm and R = 10 mm.

A radius of 10 mm experiencing an error motion of 20 Å in the non-sensitive direction results in a minimal error of just 0.02 Å in the sensitive direction, indicating a second-order error Therefore, neglecting motion in the non-sensitive direction is justified under the assumption that it is comparable to motion in the sensitive direction and that the overall error motion remains small relative to the radius.

Figure A.1 — Second-order error due to relative motion in the non-sensitive direction along a curved surface

A.3 Imperfect axis of rotation — Error motion

For a real axis of rotation, the general term “error motion” is used to describe relative displacements in the sensitive direction between the tool and the workpiece The physical causes of error motion can be thought of as bearing error motion due to factors such as non-round bearings components, and structural error motion due to the finite mass, compliance, and damping of the structural loop in conjunction with internal or external sources of excitation The separation of error motion test data into these two categories is not always possible, although the recording of data on synchronized polar charts is useful in this regard, as will be discussed in A.7.5.

The term “structural error motion” is used rather than “vibration” to emphasize the relationship to the structural loop and to relative motion It would be incorrect, for example, to measure the structural error motion by attaching an accelerometer to the tool post of a lathe and integrating the output twice, since this would yield the absolute motion For a rigid structural loop, the entire loop could undergo virtually the same absolute vibratory motion, resulting in a negligible structural error motion.

The significance of the structural loop lies in its influence on relative motion, similar to how the C-frame and anvil are essential to a hand micrometer’s functionality Including structural error motion from all sources, such as noisy bearings, drive gears, motors, or spindle resonance, provides a comprehensive approach, allowing users to select the most relevant structural loop for their specific objectives This ISO 230 guideline applies equally to testing a spindle as a standalone unit or as part of an entire machine, ensuring clear and unambiguous understanding of the structural loop involved in error motion measurement or specification.

Tiêu đề	Geometric Accuracy Of Axes Of Rotation
Thể loại	tiêu chuẩn
Năm xuất bản	2015
Thành phố	Geneva

Định dạng
Số trang	80
Dung lượng	2,16 MB