The modelling of volumetric errors of machine tools has been widely used by the method of Homogeneous Transformation Matrix (HTM) based on rigid body kinematics analysis for a long time. Without spindle induced errors and thermal errors, to establish a closed-loop HTM for a three-axis machine tool, the total of 21 geometric errors are the primary elements to be known. It is well known that the measured points of translational errors are directly related to the volumetric error at the tool cutting point through rigid body kinematics. In the generalized HTM method, however, this relationship is missing. This report, therefore, proposes a new comprehensive approach to formulate the volumetric errors based on the famous Abbe principle in order to derive the error term in the motion direction, and Bryan principle to derive the error terms in orthogonal to the motion direction. The proposed methodology is simple in concept, rational in physical meaning and easy in implementation. Experimental results, including faster multi-degree-of-freedom error measurements, volumetric error analysis and compensation on a testbed of small machine tool, validate the correctness and effectiveness of this method.

A novel modeling of volumetric errors of three-axis machine tools based on Abbe and Bryan principles

Abstract A tracking interferometer is a laser interferometer with the mechanism to steer the laser direction to automatically follow a target retroreflector. This paper experimentally investigates the performance of the tracking interferometer prototype, developed by a part of the authors, in estimating the volumetric accuracy of a machining center based on the multilateration principle. Then, the prototype's technical issues are discussed based on the measurement uncertainty analysis. This paper briefly reviews the direct algorithm to calculate the three-dimensional position of the target, as well as the indirect algorithm to estimate geometric error parameters of the machine's kinematic model. Their comparison is also presented based on the uncertainty analysis.

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Title Estimation of three-dimensional volumetric errors of machining centers by a tracking interferometer

The measurement and identification of the four position-independent geometric errors (PIGEs) and six position-dependent geometric errors (PDGEs) in the rotary axis are necessary to reduce their contributions to the overall machining errors of a multi-axis machine tool. In this paper, a new geometric error identification method using a tracking interferometer is presented by considering the rigid-body motion constraint in multilateration. The rigid-body motion constraint is introduced to establish a new coordinate calculation model for the measurement points, and an identification process is presented to separately identify the PIGEs and PDGEs by deriving identification models based on established geometric error models. The main novelty of the proposed method lies in the consideration of the rigid-body motion constraint, which makes the identification more robust against random factors. Monte Carlo simulations and verifying experiments were performed for validation. The results show that the PIGEs and PDGEs in the rotary axis can be successfully separated and identified by the new method. Improved identification accuracy compared with the traditional method is achieved. The maximum angular positioning error was reduced by 84% after compensation. A lower uncertainty in the identified errors compared with those obtained by the traditional method and instrument software is achieved. The proposed method is validated by comparing the identification results with those obtained by the instrument software and laser interferometers.

Geometric errors identification considering rigid-body motion constraint for rotary axis of multi-axis machine tool using a tracking interferometer

An innovative geometric error compensation of the multi-axis CNC machine tools with non-rotary cutters to the accurate worm grinding of spur face gears

The thermal deformation of a machine tool, typically caused by environmental temperature variations or the heat generated by a rotating spindle, often changes the position and orientation errors of the rotary axis average lines. By applying kinematic modeling of a five-axis machine tool, this paper shows that they can be estimated from the finished geometry of any test piece, provided that the test piece contains the features that are sufficiently sensitive to them. Based on the kinematic analysis of their influence, a new machining test is proposed to evaluate the thermal influence on the position and orientation errors of the rotary axis average lines. By inversely solving the five-axis kinematic model, this paper shows that the position and orientation errors of the rotary axis average lines can be analytically identified by the finished test piece geometry. An experimental case study demonstrates that the position and orientation errors of the rotary axis average lines, which change due to the thermal influence, can be observed from the finished test piece geometry.

A machining test to evaluate thermal influence on the kinematics of a five-axis machine tool

To improve the machine tool accuracy, geometric error identification is required for volumetric error compensation. This paper presents a method for the geometric error identification of a five-axis machine tool that considers the optimised distribution of measurement points and accurate description of geometric errors. The measurement is performed using a laser tracker that permits rapid error data collection over a large measurement range. In the volumetric error modelling, the geometric errors are described as position-dependent Chebyshev polynomials. Hence, the identification of geometric errors is converted into the identification of polynomial coefficients. In the identification process, a distribution method for measurement points is proposed to improve the identification accuracy by minimising the influence of measurement error on the identification result. At the same time, an adaptive approach is introduced to accurately define the polynomial orders of geometric errors to improve the identification accuracy. Simulations and experiments are conducted to verify the geometric error identification method. In addition, the proposed method is compared with other methods. Based on the identification result of geometric errors and the volumetric error model, the volumetric error of any position in a workspace can be predicted and further compensated.

Measurement method for volumetric error of five-axis machine tool considering measurement point distribution and adaptive identification process

In recent years, a series of uncertain events, including the spread of COVID-19, has affected the Chinese stock market. When people face uncertainty, they often turn to internet search engines to obtain more information to support their investment decisions. This paper uses the uncertainty index, investor sentiment reflected by search engine data, and Chinese stock return data during the pandemic to examine the relationships among the three. Using daily data from March 2, 2020, to March 2, 2021, our empirical findings reveal that stock returns during a pandemic lead to an increase in investor retrieval of search engine data and that uncertainty affects stock returns during a pandemic. However, the reverse is not true. Therefore, in the face of an uncertainty such as market volatility caused by the spread of the pandemic, the active release of favorable information by regulators can help guide investor sentiment, prevent sharp stock market volatility, and improve the effectiveness of policy governance.

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Uncertainty, Search Engine Data, and Stock Market Returns During a Pandemic

The invention provides a machine tool processing self-adaptive data acquisition method based on the component contour morphology, and belongs to the technical field of intelligent manufacturing. The problems that a traditional common data acquisition method is cumbersome in process, too high in operation cost, and single in data source and the like are solved. A machining path of the component isdivided into equal spacing micro arc, a speed calculation method of a spindle passing through each path is put forward, analyzing and judging are conducted in real time by relying on the calculated data, the change slow situation of the sampled data is judged, and the sampling period is continuously corrected accordingly, so that the sampling period can quickly and accurately adapt to the dynamicchange of the speed of cutter feeding so as to ensure that the valuable data is not lost while the too much low-valuable data does not collected. The machine tool processing self-adaptive data acquisition method combines the data theory with the actual data, and plays an active role in the extension of the data acquisition theory method, the data evaluation process strengthening and the data acquisition self-adaptive ability improving and the like.

Rui Shen

Papers

Measurement method for volumetric error of five-axis machine tool considering measurement point distribution and adaptive identification process

Uncertainty, Search Engine Data, and Stock Market Returns During a Pandemic

Machine tool processing self-adaptive data acquisition method based on component contour morphology