Multi-probe roundness measurement and harmonic content of Reuleaux polygons

Tuomas Tiainen; Raine Viitala

Multi-probe roundness measurement and harmonic content of Reuleaux polygons

Tuomas Tiainen
, Raine Viitala

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

Abstract

This paper aims to clarify misconceptions present in some literature on roundness measurement related to diameter measurement and the harmonic content of Reuleaux triangles, which are sometimes referred to as shapes of constant diameter and thus implied to exhibit odd lobing. To demonstrate, the paper investigates regular Reuleaux polygons in the angular frequency domain by evaluating their harmonic components numerically. A pattern is observed in the frequency domain representation of the Reuleaux polygons, with harmonic components repeating at intervals corresponding to the number of angles in the polygon. Finally, the paper discusses the implications of mechanical filtration effects and the existence of such geometries for roundness measurement in practice, discussing the limitations of two-point diameter measurement in roundness measurement.

Original language	English
Title of host publication	European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022
Editors	Richard K. Leach, A. Akrofi-Ayesu, C. Nisbet, Dishi Phillips
Publisher	euspen
Pages	429-432
Number of pages	4
ISBN (Electronic)	978-1-9989991-1-8
Publication status	Published - 2022
MoE publication type	A4 Conference publication
Event	International Conference of the European Society for Precision Engineering and Nanotechnology - Geneva, Switzerland Duration: 30 May 2022 → 3 Jun 2022 Conference number: 22

Publication series

Name	European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022

Conference

Conference	International Conference of the European Society for Precision Engineering and Nanotechnology
Abbreviated title	EUSPEN
Country/Territory	Switzerland
City	Geneva
Period	30/05/2022 → 03/06/2022

Funding

This research was perfomed in the 19ENG07 Met4Wind project, which has received funding from the EMPIR programme cofinanced by the Participating States and from the European Union’s Horizon 2020 research and innovation programme. This research was perfomed in the 19ENG07 Met4Wind project, which has received funding from the EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme.

Keywords

Harmonics
Reuleaux
Roundness

Access to Document

https://www.euspen.eu/euspen-knowledge-base/proceedings-search/#!/resource_title=Multi-probe%20roundness%20measurement%20and%20harmonic%20content%20of%20Reuleaux%20polygons

Cite this

Tiainen, T., & Viitala, R. (2022). Multi-probe roundness measurement and harmonic content of Reuleaux polygons. In R. K. Leach, A. Akrofi-Ayesu, C. Nisbet, & D. Phillips (Eds.), European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022 (pp. 429-432). (European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022). euspen. https://www.euspen.eu/euspen-knowledge-base/proceedings-search/#!/resource_title=Multi-probe%20roundness%20measurement%20and%20harmonic%20content%20of%20Reuleaux%20polygons

Tiainen, Tuomas ; Viitala, Raine. / Multi-probe roundness measurement and harmonic content of Reuleaux polygons. European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022. editor / Richard K. Leach ; A. Akrofi-Ayesu ; C. Nisbet ; Dishi Phillips. euspen, 2022. pp. 429-432 (European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022).

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title = "Multi-probe roundness measurement and harmonic content of Reuleaux polygons",

abstract = "This paper aims to clarify misconceptions present in some literature on roundness measurement related to diameter measurement and the harmonic content of Reuleaux triangles, which are sometimes referred to as shapes of constant diameter and thus implied to exhibit odd lobing. To demonstrate, the paper investigates regular Reuleaux polygons in the angular frequency domain by evaluating their harmonic components numerically. A pattern is observed in the frequency domain representation of the Reuleaux polygons, with harmonic components repeating at intervals corresponding to the number of angles in the polygon. Finally, the paper discusses the implications of mechanical filtration effects and the existence of such geometries for roundness measurement in practice, discussing the limitations of two-point diameter measurement in roundness measurement.",

keywords = "Harmonics, Reuleaux, Roundness",

author = "Tuomas Tiainen and Raine Viitala",

note = "Funding Information: This research was perfomed in the 19ENG07 Met4Wind project, which has received funding from the EMPIR programme cofinanced by the Participating States and from the European Union{\textquoteright}s Horizon 2020 research and innovation programme. Funding Information: This research was perfomed in the 19ENG07 Met4Wind project, which has received funding from the EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme. Publisher Copyright: {\textcopyright} European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022. All rights reserved.; International Conference of the European Society for Precision Engineering and Nanotechnology, EUSPEN ; Conference date: 30-05-2022 Through 03-06-2022",

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Tiainen, T & Viitala, R 2022, Multi-probe roundness measurement and harmonic content of Reuleaux polygons. in RK Leach, A Akrofi-Ayesu, C Nisbet & D Phillips (eds), European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022. European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022, euspen, pp. 429-432, International Conference of the European Society for Precision Engineering and Nanotechnology, Geneva, Switzerland, 30/05/2022. <https://www.euspen.eu/euspen-knowledge-base/proceedings-search/#!/resource_title=Multi-probe%20roundness%20measurement%20and%20harmonic%20content%20of%20Reuleaux%20polygons>

Multi-probe roundness measurement and harmonic content of Reuleaux polygons. / Tiainen, Tuomas; Viitala, Raine.
European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022. ed. / Richard K. Leach; A. Akrofi-Ayesu; C. Nisbet; Dishi Phillips. euspen, 2022. p. 429-432 (European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Multi-probe roundness measurement and harmonic content of Reuleaux polygons

AU - Tiainen, Tuomas

AU - Viitala, Raine

N1 - Conference code: 22

PY - 2022

Y1 - 2022

N2 - This paper aims to clarify misconceptions present in some literature on roundness measurement related to diameter measurement and the harmonic content of Reuleaux triangles, which are sometimes referred to as shapes of constant diameter and thus implied to exhibit odd lobing. To demonstrate, the paper investigates regular Reuleaux polygons in the angular frequency domain by evaluating their harmonic components numerically. A pattern is observed in the frequency domain representation of the Reuleaux polygons, with harmonic components repeating at intervals corresponding to the number of angles in the polygon. Finally, the paper discusses the implications of mechanical filtration effects and the existence of such geometries for roundness measurement in practice, discussing the limitations of two-point diameter measurement in roundness measurement.

AB - This paper aims to clarify misconceptions present in some literature on roundness measurement related to diameter measurement and the harmonic content of Reuleaux triangles, which are sometimes referred to as shapes of constant diameter and thus implied to exhibit odd lobing. To demonstrate, the paper investigates regular Reuleaux polygons in the angular frequency domain by evaluating their harmonic components numerically. A pattern is observed in the frequency domain representation of the Reuleaux polygons, with harmonic components repeating at intervals corresponding to the number of angles in the polygon. Finally, the paper discusses the implications of mechanical filtration effects and the existence of such geometries for roundness measurement in practice, discussing the limitations of two-point diameter measurement in roundness measurement.

KW - Harmonics

KW - Reuleaux

KW - Roundness

UR - https://www.scopus.com/pages/publications/85145562908

M3 - Conference article in proceedings

AN - SCOPUS:85145562908

T3 - European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022

SP - 429

EP - 432

BT - European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022

A2 - Leach, Richard K.

A2 - Akrofi-Ayesu, A.

A2 - Nisbet, C.

A2 - Phillips, Dishi

PB - euspen

T2 - International Conference of the European Society for Precision Engineering and Nanotechnology

Y2 - 30 May 2022 through 3 June 2022

ER -

Tiainen T, Viitala R. Multi-probe roundness measurement and harmonic content of Reuleaux polygons. In Leach RK, Akrofi-Ayesu A, Nisbet C, Phillips D, editors, European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022. euspen. 2022. p. 429-432. (European Society for Precision Engineering and Nanotechnology, Conference Proceedings - 22nd International Conference and Exhibition, EUSPEN 2022).

Multi-probe roundness measurement and harmonic content of Reuleaux polygons

Abstract

Publication series

Conference

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Met4Wind: Metrology for enhanced reliability and efficiency of wind energy systems

Cite this

Multi-probe roundness measurement and harmonic content of Reuleaux polygons

Abstract

Publication series

Conference

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Met4Wind: Metrology for enhanced reliability and efficiency of wind energy systems

Cite this