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

Huang, Yubin; Fan, Kui; Lou, Zhifeng; Sun, Wei

doi:10.1016/j.ijmachtools.2020.103527

Cited by 65 publications

(19 citation statements)

References 36 publications

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“…A more important contribution is that the Abbe principle was extended to the straightness motion error of the linear stage [9]. In other words, when we deal with or analyze the error of an instrument or machine tool, the straightness motion error corresponds to Bryan's proposal, while the angular motion error corresponds to the traditional Abbe principle [10].…”

Section: Summary Of the Relationship Between Slider Motion Error And mentioning

confidence: 99%

Analysis of Motion Errors of Linear Guide Pair Based on Parallel Mechanism

Lei

2021

Machines

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This paper systematically summarized the technical state of art and research results on the motion error of a linear guideway, corrected some misconceptions, and further clarified the relationship between the straightness error of the guide rail itself and the motion error of the linear stage. Moreover, a new method based on parallel mechanism is provided to study the motion errors of the linear guide pair. The basic idea is to abstract the structural relationship between the stage and the guide rail into a 4-bar parallel mechanism. Thus, the stage can be considered as a moving platform in the parallel mechanism. Its motion error analysis is also transferred to moving platform position analysis in the parallel mechanism. The straightness motion error and angular motion error of the stage can be analyzed simultaneously by using the theory of parallel mechanism. Some experiments were conducted on the linear guideway of a self-developed parallel coordinate measuring machine. The experimental data and analysis verify the feasibility and correctness of this method.

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Section: Summary Of the Relationship Between Slider Motion Error And mentioning

confidence: 99%

Analysis of Motion Errors of Linear Guide Pair Based on Parallel Mechanism

Lei

2021

Machines

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“…Unluckily, the positional relationship between the measurement and actual processing points was not taken into account in previous findings. While the center line of the motion axis is inconsistent with the moving direction of the working point of the measuring system, the Abbé deviation will occur [21][22][23][24]. The errors primarily come from the fact that the deflection errors can be amplified by the Abbé deviation.…”

Section: Introductionmentioning

confidence: 99%

Modeling method of CNC tooling volumetric error under consideration of Abbé error

Chen

Zhang

Wang

et al. 2022

Int J Adv Manuf Technol

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The Abbé error is a key factor for high-precision CNC machine tools. Unluckily, it is not taken into account in traditional machine tool volumetric error models. In this respect, based on the traditional machine tool volumetric error models, a new machine tool volumetric error model containing Abbé error is performed by analyzing the mechanism of Abbé error formation tool volumetric and based on 21-item geometric error measurement data, Abbé arm, and angle functional relationship. Moreover, integrated qualitative and quantitative simulation method for evaluation of machine tool space precision are correspondingly presented. Finally, an example was utilized to further verify the value of our model by means of analysis and comparison of the tooling precision prior to and after performance of compensation, and its validity and feasibility were proved. This study provides an important modeling method for high-precision machine tools and has very important theoretical significance and practical value.

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“…The famous Abbe principle and the Bryan principle were applied based on the above analysis to derive the error terms in the parallel and perpendicular directions of motion, respectively. On this basis, a high-precision error model was established [23].…”

Section: Introductionmentioning

confidence: 99%

High-precision modeling of CNCs’ spatial errors based on screw theory

et al. 2022

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A method for establishing machine tool’s spatial error model is put forward based on screw theory, which is different from the traditional error modeling method. By analyzing the position relationship between the ideal coordinate vector and the actual coordinate vector jointly affected by linear errors and angular errors, a single-axis screw conversion matrix error expression is brought up based on screw theory. Meanwhile, the comprehensive spatial error model of the CNC machine tool is derived by considering the influence of the workpiece motion chain and the tool motion chain on the model. Further, to compensating spatial errors of CNCs, such screw theory-based model is embedded in the error compensation system by means of integration of a few specific application examples. And in order to evaluate the compensation effects, an integrated evaluation method of quantitative spatial diagonal calculation and MATLAB simulation is proposed. Application results show that the screw theory-based spatial error model of tool has a very substantial compensation effect, which makes the position error of the machine tool decreased by about 80%.

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

Cited by 65 publications

References 36 publications

Analysis of Motion Errors of Linear Guide Pair Based on Parallel Mechanism

Analysis of Motion Errors of Linear Guide Pair Based on Parallel Mechanism

Modeling method of CNC tooling volumetric error under consideration of Abbé error

High-precision modeling of CNCs’ spatial errors based on screw theory

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