Publication result detail

Numerical Aspects of Multilateration for Volumetric Error Calculation

HOLUB, M.; ZATOČILOVÁ, J.; MAREK, T.; BLECHA, P.; HEINRICH, P.

Original Title

Numerical Aspects of Multilateration for Volumetric Error Calculation

English Title

Numerical Aspects of Multilateration for Volumetric Error Calculation

Type

WoS Article

Original Abstract

We discuss two approaches to multilateration with a particular focus on numerical aspects for a given dataset. More precisely, we calculate the volumetric errors of the MCV 754 milling machine from the data measured by a LaserTRACER and provide criteria showing which numerical method is appropriate for the solution of the multilateration problem with respect to a given measurement dataset. In the first case, we consider two cost functions of the optimisation problem; in the second, we use the extremal principle method. We discuss the calculation accuracy depending on the matrix condition number. Our results are compared to the reference results produced by the Trac-Cal software, which is a standard used by most producers for error compensations.

English abstract

We discuss two approaches to multilateration with a particular focus on numerical aspects for a given dataset. More precisely, we calculate the volumetric errors of the MCV 754 milling machine from the data measured by a LaserTRACER and provide criteria showing which numerical method is appropriate for the solution of the multilateration problem with respect to a given measurement dataset. In the first case, we consider two cost functions of the optimisation problem; in the second, we use the extremal principle method. We discuss the calculation accuracy depending on the matrix condition number. Our results are compared to the reference results produced by the Trac-Cal software, which is a standard used by most producers for error compensations.

Keywords

multilateration; numerical model; volumetric errors; machine tool error

Key words in English

multilateration; numerical model; volumetric errors; machine tool error

Authors

HOLUB, M.; ZATOČILOVÁ, J.; MAREK, T.; BLECHA, P.; HEINRICH, P.

RIV year

2023

Released

21.09.2022

Publisher

MDPI

ISBN

2075-1702

Periodical

Machines

Volume

10

Number

833

State

Swiss Confederation

Pages from

1

Pages to

15

Pages count

15

URL

https://www.mdpi.com/2075-1702/10/10/833

Full text in the Digital Library

http://hdl.handle.net/11012/208691

BibTex

@article{BUT179249,
  author="Michal {Holub} and Jitka {Zatočilová} and Tomáš {Marek} and Petr {Blecha} and Petr {Heinrich}",
  title="Numerical Aspects of Multilateration for Volumetric Error Calculation",
  journal="Machines",
  year="2022",
  volume="10",
  number="833",
  pages="1--15",
  doi="10.3390/machines10100833",
  url="https://www.mdpi.com/2075-1702/10/10/833"
}

Documents

machines-10-00833
machines-10-00833-v3