Effects of Position and Orientation Errors of Linear and Rotary Axis Average Lines of Five-Axis Controlled Machining Centre Onto its Motion Errors in Testing Method With Truncated Square Pyramid

In this paper, ‘position and orientation errors of linear and rotary axis average lines’ is newly named ‘geometrical mechanism deviations.’ This paper presents suggestive simulation results of tool motion error caused by geometrical mechanism deviations of a five-axis controlled machine tool. Firstly, there were assumed seven geometrical mechanism deviations consisting of three positional and four angular deviations. As positional deviations, the error of intersection is set to be 0.01 [mm] off-centre, and the squareness errors of the cross axes as angular deviations are 0.01 [°]. Secondly, there was simulated theoretically the shape of machined pyramidal surface according to the virtual cutter movement of a flat end mill along contouring tool paths. Thirdly, the correspondence of geometrical mechanism deviations and simulated flatness error was analysed and found to have two regularities. One of the two indicated that four pyramidal surfaces wave similarly with left half surface up and right half surface down. The other indicated that the centre of a specific pyramidal surface should be concave in the cases of squareness error between B-Z axes. Through the analysis of grouped flatness error, specific geometrical mechanism deviations seem to cause a particular deformation of pyramidal surface due to the misalignment of tool position and orientation.

Characterization and Correction of the Geometric Errors in Using Confocal Microscope for Extended Topography Measurement. Part I: Models, Algorithms Development and Validation

This work presents a method for characterizing and correcting the geometric errors of the movement of the lateral stage of Imaging Confocal Microscope (CM) in extended topography measurement. For an extended topography measurement, a defined number of 2D images are taken and stitched by correlation methods. Inaccuracies due to linear displacement, vertical and horizontal straightness errors, angular errors, and squareness errors based on the assumption of the rigid body kinematics are described. A mathematical model for the scale calibration of the X- and Y- coordinates is derived according to the system kinematics, the axis chain vector of CM, and the geometric error functions and their approximations by Legendre polynomials. The correction coefficients of the kinematic modelling are determined by the measured and certified data of a dot grid target standard artefact. To process the measurement data, algorithms for data partitions, fittings of cylinder centers, and determinations of coefficients are developed and validated. During which methods such as form removal, K-means clustering, linear and non-linear Least Squares are implemented. Results of the correction coefficients are presented in Part II based on the experimental studies. The mean residual reduces 29.6% after the correction of the lateral stage errors.

Measuring and Modeling of Volumetric Errors for Vertical Machining Centers Based on Bi-Directional Laser Sequential Step Diagonal Measurement

This paper proposes a bi-directional laser sequential step diagonal measuring method for three-axis vertical machining centers. Different measure paths are particularly designed for positive and negative directions, and corresponding error decoupling models are established. Based on the laser measuring data along these bi-directional paths, 18 geometric errors can be identified simultaneously, including 6 angular errors, 3 positioning errors, 6 straightness errors and 3 squareness errors. Compared with single directional step diagonal measurements, the proposed bi-directional mothed is more efficient and can identify more error items, namely 6 angular errors. Experimental tests were conducted on a three-axis vertical machining center. Decoupled error items obtained by the proposed bi-direction measurements coincide with those from direct measurements via a laser Doppler displacement meter, which verified the feasibility of the proposed method. Finally, the position error of the machine whole workspace was predicted by building volumetric error model and the machine accuracy was improved.

ENHANCING LASER STEP DIAGONAL MEASUREMENT BY MULTIPLE SENSORS FOR FAST MACHINE TOOL CALIBRATION

The volumetric performance of machine tools is limited by the remaining relative deviation between desired and real tool tip position. Being able to predict this deviation at any given functional point enables methods for compensation or counteraction and hence reduce errors in manufacturing and uncertainties for on-machine measurement tasks. Time-efficient identification and quanitification of different contributions to the resulting deviation play a key role in this strategy. The authors pursue the development of an optical sensor system for step diagonal measurement methods, which can be integrated into the working volume of the machine due to its compact size, enabling fast measurements of the axes’ motion error including roll, pitch and yaw and squareness errors without significantly interrupting the manufacturing process. The use of a frequency-modulating interferometer and photosensitive arrays in combination with a Gaussian laser beam allow for measurements at comparable accuracy, lower cost and smaller dimensions compared to state-of-the-art optical measuring appliances for offline machine tool calibration. For validation of the method a virtual machine setup and raytracing simulation is used which enables the investigation of systematic errors like sensor hardware misalignment.