A Synchronous Measurement System for Dual-Rotary Axis Geometric Errors of a Five-Axis Machine Tool Using a Scanning Probe
1. Research Objective
With the advancement of modern manufacturing technology and the increasing demand for high-precision and high-efficiency machining, five-axis machine tools have been widely applied in aerospace, automotive manufacturing, and other fields. However, high-precision machining also introduces complex challenges in error control, directly affecting product quality and machine longevity. Therefore, geometric error measurement of five-axis machine tools has become a critical research topic.
Among various error sources, geometric errors arise from non-ideal geometric deviations during machine manufacturing and assembly—such as axis displacement, angular deviation, and linearity errors—which significantly impact machining quality and tend to accumulate. Thus, accurate measurement and compensation of these errors are essential.
Commercial instruments currently face two main limitations: (1) most systems measure only a few geometric error components at a time, neglecting the coupling effects among different error sources and the compounded errors during simultaneous multi-axis motion; and (2) existing devices often measure only installation errors or single-axis motion errors, without considering position-dependent variations.
Previous studies have examined single-axis motion and installation errors during dual-axis rotation, but few have addressed both simultaneously. Hence, this research aims to develop a high-precision geometric error measurement technique for five-axis machine tools. The proposed system is capable of simultaneously analyzing 20 geometric error components of dual rotary axes while considering coupling and dynamic effects.
2. Research Methodology
(1) Experimental Equipment and Setup
The experimental platform used in this study is a compact vertical five-axis machining center, as shown in Figure 1. This machine adopts a full rotary table configuration, providing synchronized five-axis machining capability. The A-axis and C-axis rotary functions increase the freedom of workpiece positioning, allowing the cutting tool to approach the workpiece from nearly any angle. Such flexibility makes the system suitable for machining aerospace components, complex automotive parts, and high-precision molds.
Figure 1. Vertical Five-Axis Machine Tool
The measuring instrument used is an on-machine probing system, which plays a vital role in ensuring machining accuracy, improving productivity, and optimizing manufacturing processes. By precisely detecting the position of the workpiece and cutting tool, the probing system enables high-performance operation of the five-axis machining center.
Common touch-trigger probes detect the workpiece surface upon contact, providing high-precision positional data. They are generally categorized into single-point contact probes and scanning probes. Single-point probes are ideal for simple, precise point measurements, while scanning probes continuously move along the surface, collecting a large volume of data points and detailed surface profiles—ideal for complex geometries.
This study employs the OSP60 scanning probe system (Figure 2). Compared with touch-trigger probes, it rapidly scans along the workpiece surface to gather extensive spatial and directional data, capturing the detailed contour and complex geometry of the workpiece more effectively. This contributes to higher measurement accuracy, improved quality control, reduced measurement time, and enhanced analytical precision.
Figure 2. OSP60 Scanning Probe System
(2) Measurement System and Procedure
The developed system utilizes the OSP60 scanning probe to measure a precision flat block and a calibration sphere. The goal is to minimize measurement uncertainty from the sphere’s radius error and surface flatness deviation. During the experiment, the calibration sphere is magnetically mounted on the cradle (A-axis), while the block is fixed on the rotary table (C-axis). The probe is installed on the spindle, as shown in Figure 3.
The system first detects the reference positions of the calibration sphere center and block contact points, then rotates both rotary axes to measure the new sphere center position and the block’s surface profile. All measurements are executed automatically via NC code, and the acquired data are processed through the proposed mathematical model to compute geometric errors. Temperature control and compensation calibration ensure the highest accuracy.
Figure 3. Experimental Setup
The measurement principle involves both the block and the calibration sphere.
As shown in Figure 4, the block is mounted on the C-axis rotary table. Installation inaccuracies induce mounting errors, causing radial and tilt deviations in both A- and C-axes. The coupling of these dual-axis errors displaces the block to Position 1, generating a volumetric error dP(PIGE). Additional motion errors from component imperfections cause further displacement to Position 2, resulting in an overall volumetric error dP(PDGE).
By establishing the relationship between volumetric error and rotary axis geometric error, both installation and motion errors can be extracted. Plane normal vectors and corner coordinates are obtained from scanning data through least-squares fitting of multiple measured planes.
Figure 4. Block Deformation under Rotary Axis Geometric Error
Similarly, Figure 5 shows the calibration sphere displacement caused by geometric errors of the A-axis. As the A-axis rotates, the sphere center first moves due to mounting errors (Position 1) and then further due to motion errors (Position 2). This design isolates A-axis errors, simplifying error separation from the C-axis block data and supporting path planning.
Figure 5. Calibration Sphere Error Behavior
The measurement sequence proceeds as follows:
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Mount the scanning probe on the spindle.
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Place the calibration sphere on the A-axis and the block on the C-axis.
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Measure reference coordinates at zero angles (A=0°, C=0°).
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Run automated NC programs to measure multiple A/C combinations.
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Record geometric data and compute error terms.
The probe automatically performs circular scans, linear scans, and single-point triggers. Fitted data yield deviations in sphere center coordinates (XYZ center error), start-point orientation (Start Point Error), and path inclination (Best Fit Angle).
Table 1 summarizes the 12 combinations of rotary axis positions and measurements. Excluding the initial position, the experiment resolves 110 error parameters, including 4 installation errors and 36 motion errors (6 DOF × 6 positions) for the A-axis, and 4 installation errors and 66 motion errors (6 DOF × 11 positions) for the C-axis.
Table 1. Measurement Positions and Axis Angles
| Measurement No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A-axis (°) | 0 | 0 | 0 | 0 | 0 | 0 | -15 | -30 | -45 | -60 | -75 | -90 |
| C-axis (°) | 0 | 30 | 60 | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 300 | 330 |
| Sphere Measurement | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ✔ | ✔ | ✔ | ✔ | ✔ | ✔ |
| Line Scans | 10 | 10 | 10 | 10 | 10 | 10 | 6 | 6 | 6 | 6 | 6 | 6 |
(3) Kinematic Modeling
To analyze geometric errors, two motion chains were established:
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Probe P → Z → Y → X → A → C → Block B
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Probe P → Z → Y → X → A → Calibration Sphere S
Homogeneous transformation matrices represent each coordinate system’s motion. By multiplying these matrices according to relative geometric relations, both ideal and actual configurations (with errors) are modeled, yielding the probe tip position, sphere center, block vertex, and plane normal vectors.
Equating probe-tip contact conditions (probe tip coinciding with sphere center or block vertex) allows derivation of geometric error relationships for both rotary axes. The resulting nonlinear equations include angular positions (A, C) and coordinate offsets of the block and sphere. These are solved via least-squares optimization with iterative linearization.
Each complete measurement generates about 180 equations, sufficient to simultaneously solve for all A-axis and C-axis geometric errors.
3. Experimental Results
Five experimental runs were averaged to evaluate repeatability. Figures 7–9 present the results.
From Figure 7, the A-axis installation errors were −23.1704 μm, −72.8639 μm, −29.0082 arcsec, and 5.8683 arcsec;
the C-axis installation errors were 7.0554 μm, 5.0641 μm, 3.6991 arcsec, and 51.7812 arcsec.
Significant offset and tilt errors were observed, possibly due to coupling effects from other components, such as linear-axis perpendicularity errors, since the system assumes ideal linear axes.
Figure 7. Installation Error Results (a) A-axis (b) C-axis
Figure 8. A-axis Motion Errors (a–f)
Figure 9. C-axis Motion Errors (a–f)
Because the experimental machine lacked built-in compensation and domestic studies were limited, a numerical comparison method was used for verification.
The calibration sphere method, commonly used by manufacturers, estimates rotary axis deviation by measuring sphere centers at 0° and 180°, then averaging to find offset. Increasing sampling to every 90° allows circular fitting to estimate axis misalignment. Though not highly precise, it effectively captures general rotary behavior.
In this study, due to limited A-axis travel, a 30° interval and four sampled points were used for best-fit circle estimation. The results were consistent with previous dual-axis measurement systems developed in earlier work, confirming validity despite small variations from environmental factors such as temperature and vibration.
4. Conclusion and Future Work
This study presents a novel measurement system capable of simultaneously identifying 20 geometric error components of dual rotary axes in a five-axis machine tool. The system uses a scanning probe for dynamic, automatic, and rapid measurement with minimal setup.
Compared to conventional touch-trigger systems, this method resolves more error parameters with advantages such as low cost, easy setup, short measurement time, and adaptability.
Future work will focus on intelligent, automated, and multifunctional measurement systems. By integrating AI, the probe could perform automatic calibration and error compensation, reducing human intervention and improving efficiency. Additionally, extended measurement parameters—such as workpiece dimensions, shape, and surface roughness—could enable comprehensive quality inspection.
Integration of real-time thermal compensation and active vibration control will further enhance accuracy by dynamically correcting temperature- and vibration-induced errors.
