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Numerical evaluation of geometrical errors of three-axes CNC machine tool due to cutting forces—case: milling

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Abstract

The quality of the workpiece produced by CNC machine tool is primarily due to the degree of precision and stability of the machines themselves. In general, the quality measures the degree of conformity of a part with predefined dimensions and geometric specifications. However, a simple measure does not identify the contribution of each source of error affecting the room. It is therefore important to analyze the technological aspects of machine tools, numerical control and the influence of the process. In order to give the issues of precision machine tools a conceptual dimension, it is preferable to classify the affecting factors. Errors can be classified according to the working phase during which the sources that generate them are active. During the preparation phase, errors can be associated with setting procedures, errors in the programming, and machining programs converted into machine language. During the machining phase, the sources of error which affect the accuracy are much more varied. Their effects can be considered as the combination of the individual contributions of all the elements constituting the system machine tool cutter, as well as the interaction of this system with the process. The purpose of this article is to present a study on the evaluation of the geometrical errors of a machine tool EMCO PC MILL 155 that exists within our laboratory, which are due to cut efforts.

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Abbreviations

R P :

The piece reference

R 1 :

The carriage reference along the X axis

R 2 :

The table reference along the Y axis

R 3 :

The turret reference along the Z axis

R 4 :

The tool reference

σ xx :

Linear straightness deviations according to X (mm)

σxy, σxz :

Horizontal linear deviations along Y and Z (mm)

εxy, εxz, εxx :

Angular yaw deviations, pitch angular deviations, and rolled angular deviations

σpx, σpy, σpz :

Errors due to the initial placement of the piece along the X, Y, and Z axes

σox, σoy, σoz :

Linear deviation due to changing the length of the tool according to X, Y, and Z

V C :

Cutting speed (mm mn−1)

R P :

The piece radius (mm)

D :

The tool diameter (mm)

f a :

The advance by tooth (mm)

H m :

Chip Thickness (mm)

V f :

Feeding speed (mm mn−1)

Z :

Number of teeth

FC, FA, FR :

The cutting force, the advance effort, and the penetration effort (N)

K C :

Specific resistance to compression failure (N mm−2)

S c :

Chip section (mm2)

a p :

The depth of pass (mm)

\( {H}_{R_0{R}_1} \) :

Represents the carriage coordinate transformation matrix relative to the frame of the machine tool

\( {H}_{R_1{R}_2} \) :

Is the coordinate transformation matrix of the table relative to the carriage

\( {H}_{R_2{R}_3} \) :

Represents the coordinate transformation matrix of the vertical turret by a table

\( {H}_{R_3{R}_4} \) :

Represents the coordinate transformation matrix of the tool/probe relative to the vertical turret

\( {H}_{R_0{R}_P} \) :

Represents the coordinate transformation matrix of the workpiece relative o the machine frame

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Acknowledgments

The support and interest of our sponsors are gratefully acknowledged.

Funding

This research was supported by the Mechanical Engineering, Materials and Structures Laboratory approved in 2020 by Ministerial Order N° 05 on 18 February 2020, a laboratory of excellence at the University Center of Tissemsilt.

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Authors and Affiliations

  1. Laboratory of Mechanical Engineering, Materials and Structures, University Center of Tissemsilt, 38000, Tissemsilt, Algeria

    Sidi Mohammed Merghache & Amine Hamdi

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  1. Sidi Mohammed Merghache
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  2. Amine Hamdi
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Correspondence to Sidi Mohammed Merghache.

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Merghache, S.M., Hamdi, A. Numerical evaluation of geometrical errors of three-axes CNC machine tool due to cutting forces—case: milling. Int J Adv Manuf Technol 111, 1683–1705 (2020). https://doi.org/10.1007/s00170-020-06211-y

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