Approximate Solution for Constant Velocity of Archimedean Spiral for Abrasion Testing of Rock Cutting Tools

Hoon Kang; Dae-ji Kim; Changheon Song; Joo-Young Oh; Jung-Woo Cho

doi:10.7474/TUS.2020.30.3.181

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2020 Vol.30, Issue 3 Next Page

Technical Note

Approximate Solution for Constant Velocity of Archimedean Spiral for Abrasion Testing of Rock Cutting Tools 암석공구 마모시험을 위한 아르키메데스 나선의 등속도 운동 근사해 조사

30 June 2020. pp. 181-192

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Abstract

Pin-on-disk test is a suggested abrasion testing method by ASTM (American Society for Testing and Materials). This briefly illustrated the Archimedean spiral motion of a pin type specimen on a disk. To apply this method to rock cutting tools, a constant linear velocity (CLV) is precisely maintained during the test. We defined the two velocity vectors (RPM and horizontal speed) which connected to the resultatnt velocity. We derived a differential equations for the two parameters under CLV condition. It was difficult to find a exact solution. Previous literatures had been reviewed, and an approximate solution was investigated. We mathematically simulated the result for a certain parameter, and examine the accuracy of the solution.

Keywords

Abrasion test

Archimedean spiral

Constant linear velocity

Approximate solution

accuracy

Pin-on-disk 시험방법은 ASTM에서 제안한 마모시험방법 중 하나이다. 이 시험법에서는 Pin-on-disk 시험에서 나타나는 핀의 나선운동을 간략히 설명하고 있다. 이 방법을 암석공구의 마모성능을 평가하는 데 적용하기 위해서는 핀의 등속도 운동을 수학적으로 구현하여야 한다. 먼저 합산속도에 관여하는 2가지 속도성분(핀의 선형이동속도, 디스크의 회전운동)을 정의하였다. 각각의 성분에 대해 아르키메데스 나선방정식의 등속도 조건을 만족하는 미분방정식을 전개하여 수학 해를 도출하여, 풀이의 난해함을 설명하였다. 이를 해결하기 위한 기존 문헌의 근사해를 조사하고, 정확도와 한계점을 분석하였다.

키워드

마모시험

아르키메데스 나선

등속도

근사해

정확도

References

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Information

Publisher :Korean Society for Rock Mechanics and Rock Engineering
Publisher(Ko) :한국암반공학회
Journal Title :Tunnel and Underground Space
Journal Title(Ko) :터널과 지하공간
Volume : 30
No :3
Pages :181-192
Received Date : 2020-04-27
Revised Date : 2020-05-12
Accepted Date : 2020-05-12
DOI :https://doi.org/10.7474/TUS.2020.30.3.181

Tunnel and Underground SpaceISSN:1225-1275(Print) 2287-1748(Online)한국암반공학회

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