Source-linked AI summary
Evaluation of servo, geometric and dynamic error sources on five axis high-speed machine tool
Loïc Andolfatto, Sylvain Lavernhe, René Mayer
TL;DR
Approximations at multiple manufacturing stages and structural changes under high-speed dynamic loads contribute to tool-center-point errors. The paper measures and decomposes these errors across feed rates, finding that dynamic errors can approach 5% of total volumetric error by the mean norm and that RMS errors follow a logarithmic trend in this experiment.
Problem
Approximations in tool-path generation and increasing structural dynamic loads at higher velocities can contribute to errors in the machined tool position.
Source: §1 · p. 1Method
The method compares controller-based nominal positions and encoder signals with CapBall measurements, decomposing volumetric error into contouring, quasi-static geometric, and dynamic geometric contributions.
Source: §1 · p. 2, §3.2 · p. 3, §3.3.1 · p. 5Results
Dynamic errors can reach nearly 5% of total volumetric error by the mean value of the norm, and RMS errors in this experiment evolve approximately logarithmically with programmed feed rate.
Source: §6 · p. 12Takeaways & Limitations
The method measures dynamic errors directly at the tool tip and can be used to validate models of structural dynamic behavior with in-situ measurements on five-or-more-axis machine tools.
Source: §6 · p. 12The fitted RMS-error relation reflects this experimental trajectory and conditions, so it does not support general conclusions about machine dynamic stiffness.
Source: §5.4 · p. 12
Abstract
from arXiv · showhide
Many sources of errors exist in the manufacturing process of complex shapes. Some approximations occur at each step from the design geometry to the machined part. The aim of the paper is to present a method to evaluate the effect of high speed and high dynamic load on volumetric errors at the tool center point. The interpolator output signals and the machine encoder signals are recorded and compared to evaluate the contouring errors resulting from each axis follow-up error. The machine encoder signals are also compared to the actual tool center point position as recorded with a non-contact measuring instrument called CapBall to evaluate the total geometric errors. The novelty of the work lies in the method that is proposed to decompose the geometric errors in two categories: the quasi-static geometric errors independent from the speed of the trajectory and the dynamic geometric errors, dependent on the programmed feed rate and resulting from the machine structure deflection during the acceleration of its axes. The evolution of the respective contributions for contouring errors, quasi-static geometric errors and dynamic geomet- ric errors is experimentally evaluated and a relation between programmed feed rate and dynamic errors is highlighted.
1. Introduction
The path from a part model to a machined surface introduces approximations and multiple sources of tool-position error. This paper evaluates those sources at different feed rates by separating contouring, quasi-static geometric, and dynamic geometric errors.
1. Introduction
- Complex part geometry can be interpolated and discretized when generating a tool path, and further approximations may occur when converting that path into CNC commands.The conversion transforms the path from the workpiece coordinate system to the joint coordinate system.Source: §1 · p. 1
- Axis follow-up errors, quasi-static link and motion errors, thermal variation, and cutting forces can each contribute to tool or machined-surface errors.Follow-up errors affect tool position and orientation, while cutting forces can deflect the tool.Source: §1 · p. 1
- As programmed feed rate and actual velocity increase, acceleration raises structural dynamic solicitations that may alter machine geometry and add tool-position and orientation errors.These errors are distinct from the quasi-static link, motion, and thermal sources.Source: §1 · p. 1
- The paper evaluates volumetric errors at different programmed feed rates by decomposing them into contouring, quasi-static geometric, and dynamic geometric contributions.The evaluation can quantify the relative impact of dynamic errors and the relevance of a model for corrective actions.Source: §1 · p. 2
2. Principle of the method
The method compares the nominal tool-center-point position calculated from controller inputs with its actual position measured by CapBall. It separates contouring error from quasi-static and dynamic geometric errors by using encoder data and measurements at different feed rates.
2. Principle of the method
- The nominal TCP position relative to the workpiece is calculated from controller inputs using the nominal direct kinematic transformation, while CapBall measures the actual relative position.CapBall is a non-contact sensor that measures a ball mounted on the machine table relative to the TCP.Source: §2 · p. 2
- The nominal-to-actual position difference combines contouring error, quasi-static geometric error, and dynamic geometric error.The total difference includes servo errors of the machine axes and geometric defects of the machine structure.Source: §2 · p. 2
- Contouring error is evaluated by comparing the tool–workpiece relative positions derived from controller inputs and actual machine encoder values.At low velocity, dynamic geometric error is considered negligible, so the remaining error after accounting for contouring error is defined as quasi-static geometric error.Source: §2 · p. 2
- Dynamic geometric error is evaluated at increased feed rates by removing contouring and quasi-static geometric error contributions from total geometric error along a trajectory.The method attributes the remaining contribution to machine-structure alterations under dynamic load.Source: §2 · p. 2
3.1. Decomposition of the total errors
The measurement procedure forms a sequence of CapBall readings and a corresponding nominal-position sequence calculated from controller inputs. Their difference expresses the combined contouring and geometric errors.
3.1. Decomposition of the total errors
- At each of n equally distributed trajectory points, CapBall records three components of the measured difference between the actual TCP and master-ball center.The readings are represented as τ for each recorded point and assembled into an n × 3 matrix χ.Source: §3.1 · pp. 2–3
- The effect of master-ball and sensing-head setup-positioning errors is identified using a prior method and removed from χ.Each τ_k is the CapBall reading for the k-th trajectory point.Source: §3.1 · p. 3
- The nominal difference τ_nom is calculated from controller inputs using the nominal direct kinematic transformation for the TCP and master-ball center.The transformation uses nominal machine geometry for both positions.Source: §3.1 · p. 3
- Subtracting the nominal difference matrix χ_nom from the measured matrix χ gives the combined contouring, quasi-static geometric, and dynamic geometric errors.Fig. 2 depicts these three contributions as the decomposition of total error.Source: §3.1 · p. 3, Figure 2 · p. 3
3.2. Contouring error
Contouring error captures the orthogonal deviation of the actual tool path from the controller-input path, rather than the follow-up error of each axis alone. The method compares synchronized nominal and encoder-derived volumetric differences to evaluate this contribution.
3.2. Contouring error
- Smaller axis-by-axis follow-up errors can still produce a larger contouring error, because contouring error is the orthogonal path deviation in part coordinates.The schematic contrasts two cases in which the case with smaller follow-up errors has the larger contouring error.Source: §3.2 · p. 3
- The contouring error is evaluated as the difference between nominal and encoder-derived volumetric difference matrices.The controller inputs and encoder values are synchronized by shifting encoder values backward by 18 ms, the recorded delay.Source: §3.2 · p. 4
- The resulting comparison decomposes the measured difference into contouring, quasi-static geometric, and dynamic geometric contributions.The figure illustrates the three Cartesian components in the machine frame at F = 5,000 mm/min.Source: Figure 3 · p. 4, §3.2 · p. 5
3.3. Quasi-static geometric errors
Quasi-static geometric error is defined as independent of machine velocity and comprises link, motion, and thermal-drift contributions. The section models link and motion errors and treats thermal drift as a test-level offset.
3.3.1. Definition
- Quasi-static geometric error is independent of machine velocity and comprises link errors, motion errors, and thermal drift.These are respectively represented by δl, δm, and δtd.Source: §3.3.1 · p. 5
3.3.2. Link errors
- The five-axis machine's link errors are represented by eight geometric parameters, whose volumetric contribution is modelled using a pose-specific Jacobian.CapBall data are used to identify the model's eight parameters.Source: §3.3.2 · p. 5
3.3.3. Motion errors
- At low programmed feed rate, dynamic geometric error is negligible compared with link and motion errors, and appears only locally along the trajectory.The motion-error polynomial fit is intended to predict the motion contribution; its main weakness is using time rather than actual machine pose, though the small differential rate reduces the approximation's effect.Source: §3.3.3 · p. 6
3.3.4. Thermal drift
- Thermal drift is modelled as a constant offset across each test's measurement points, estimated relative to a reference thermal state.The trajectory takes less than 15 seconds and is treated as instantaneous relative to sensing-head movement from thermal drift.Source: §3.3.4 · pp. 6–7
3.4. Dynamic geometric errors
Dynamic geometric errors are the additional errors that occur as programmed feed rate and dynamic forces on the machine structure increase. They are defined as the contribution absent at low speed.
3.4. Dynamic geometric errors
- Dynamic geometric error is the additional contribution that does not appear at low speed, arising as higher feed rates increase dynamic forces and alter machine components.The described alterations include machine-structure deflection under dynamic forces.Source: §3.4 · p. 7
4. Experimental setup and conditions
The experiments use a five-axis KX8 machine, CapBall TCP measurement, and a segmented trajectory designed to generate dynamic loads across six feed rates.
4.1. Machine tool
- The Huron KX8-five records controller inputs and encoder positions for X, Y, Z, A, and C; the recorded values include backlash compensation.Controller inputs remained the same across executions, so they could be recorded separately.Source: §4.1 · p. 7
4.2. External measuring instrument
- CapBall measures a table-mounted master ball against a spindle-mounted three-sensor head, whose orthogonal axes intersect at the virtual TCP.Within the specified ±300 µm sensor ranges, standard type A uncertainty was evaluated below 0.4 µm.Source: §4.2 · pp. 7–8
4.3. Experimental trajectory
- A nearly square, 17-segment G01 trajectory creates acceleration peaks at block transitions and was run at six feed rates from 1,000 to 18,896 mm/min.The axes were synchronized with linear interpolation and corner rounding set to a 10 µm axial tolerance; the trajectory was limited to 15 seconds at 1,000 mm/min by the NC recording buffer.Source: §4.3 · pp. 8–9
5. Results
Across the tested trajectory, the combined contouring and dynamic-error contribution rose with feed rate, while acceleration-linked dynamic errors became prominent at high rates. The fitted feed-rate relationship is specific to the experimental trajectory.
5.3. Contributions along the trajectory
- Linear block-transition acceleration peaks produce sudden dynamic loads; dynamic-error peak-to-peak magnitude exceeded 5 µm along y.The machine was not equally affected in all directions; high X-axis acceleration appeared to have little dynamic effect.Source: Figure 10 · p. 10, §5.3 · p. 11
5.1. Mean value of the norm
- Thermal drift increased across tests, but its trend may not reflect feed rate because the spindle only regulated its angular position, not actual machining use.The authors expect more sizeable errors under heavier spindle use.Source: §5.1 · p. 10
- The mean combined contouring and dynamic contribution rose from 1.7% at 1,000 mm/min to 14.3% at 18,896 mm/min.The reported source share is the mean proportion of total error attributable to that source along the trajectory.Source: §5.1 · pp. 9–10, Table 1 · p. 10
5.2. Maximum errors
- Link-error maxima depend on machine pose, can be calculated offline for a tool path, and may be higher elsewhere in the working volume.Table 2 reports maximum quasi-static geometric errors along the experimental trajectory.Source: Table 2 · p. 11, §5.2 · p. 11
- Dynamic errors were non-negligible above 10,000 mm/min, and their magnitude increased with programmed feed rate.Dynamic errors also occurred at 1,000 mm/min, but only locally at the trajectory’s sharp corner.Source: Table 3 · p. 11, §5.2 · p. 11
5.4. Root mean square of the dynamic errors
- The RMS dynamic errors were fitted against feed rate, but the fitted parameters depend on the trajectory and do not establish general machine dynamic stiffness.The authors suggest the results may provide a performance indicator under dynamic load when using a standard trajectory designed for that purpose.Source: Figure 11 · p. 11, §5.4 · p. 12
6. Conclusion
The conclusion presents a method for evaluating dynamic errors directly at the tool tip under high dynamic loads. In the experiments, dynamic errors reached nearly 5% of total volumetric error, and RMS error evolution with feed rate was approximated by a logarithmic law.
6. Conclusion
- The method measures volumetric error at the tool tip and evaluates dynamic geometric errors under high-acceleration loads that may disrupt rigid-body behavior.Source: §6 · p. 12
- High-feed-rate experiments were enabled by the non-contact CapBall, redesigned for greater stiffness under high dynamic loads.Source: §6 · p. 12
- Dynamic errors reached nearly 5% of total volumetric error by mean norm, quantifying their relative impact alongside contouring and quasi-static geometric errors.Source: §6 · p. 12
- In this particular case, RMS errors versus programmed feed rate were approximated by a logarithmic law.Source: §6 · p. 12
- The method applies to five-or-more-axis machines, can validate structural dynamic models in situ, and can investigate interpolation and controller command laws.The study also reports that linear interpolation generates acceleration and dynamic-error peaks.Source: §6 · p. 12