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원격무장 고저 시스템용 사이클로이드 감속기 설계에 관한 연구

박진석1,2, 김기훈1,2, 김래성3, 류성기1,#

A Study on Design of Cycloid Reducer for Remote Weapons Systems

Jin Seok Park1,2, Ki Hun Kim1,2, Lae Sung Kim3, Sung Ki Lyu1,#
Journal of the Korean Society for Precision Engineering 2017;34(6):405-410.
Published online: June 1, 2017

1 경상대학교 대학원 기계시스템공학과, 항공연

2 SG Servo㈜ 기술연구소

3 경상대학교 항공IT기계융합사업단

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#Email: sklyu@gnu.ac.kr, TEL: +82-55-772-1632, FAX: +82-55-772-1578
• Received: February 22, 2017   • Revised: March 22, 2017   • Accepted: April 16, 2017

Copyright © The Korean Society for Precision Engineering

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  • An essential mechanical element in an industrial machine is a reducer, which transfers the rotation of an electrical motor or engine to another part with amplified torque. Some reducers, such as planetary reduction gears, a harmonic reducer, or a cycloid reducer, have been applied in various industries. Given the increase of demand for reducers with high precision, compact size, and high load capacity for use in industrial robots, the cycloid reducer has stood out. The cycloid reducer, compared with planetary reduction gears, has some merits, which include a larger reduction gear ratio at only one stage, higher durability, improved efficiency, and a larger torque because of its high tooth-contact ratio despite its being small. This paper presents a design technique for a cycloid reducer intended, because of those merits, for use in remote weapons systems of armed vehicles. In order to verify the performance of the cycloid reducer, we carried out experiments and analyzed the results systematically.
  • KEYWORDS: Cycloid reducer, Cycloid gear, Remote weapons systems, High precision, Planetary reduction gears
  • KEYWORDS: 사이클로이드 감속기, 사이클로이드 기어, 원격무장 시스템, 고정밀, 유성감속기어
원격 무장시스템은 최근 다양한 형식의 차량이나 다른 플랫폼에 장착할 수 있는 경량과 중간 중량의 구경을 가지며 무장을 위한 원격 조작식 무장 탑재대이다. 이런 장비들은 사수가 안전하게 무장을 운용할 수 있도록 해주기 때문에 최근 들어 많은 현대식 군용 차량에 도입되고 있다. 또한 기존의 차량에 손쉽게 장착할 수 있다는 장점을 가지고 있기 때문에 방위 산업 선진국에서는 개발을 완료하여 실전에 배치하여 군 전력 증강을 도모하고 있다.
원격 무장에 적용되는 감속기는 소형으로 큰 토크 전달이 가능하고, 구조의 최적화(Compact)가 요구되며, 높은 부하 용량과 고정밀도의 위치 제어가 요구되는 품목으로, 이러한 요구조건을 충족시키기 위해서는 사이클로이드(Cycloid) 감속기와 같은 낮은 백래시(Backlash), 고정밀도, 높은 과부하 대응, 고강성, 고효율이 요구되는 감속기가 필요하다. 산업기계에서 모터나 엔진의 회전력을 피구동부까지 전달하는데 필요한 핵심 기계 요소는 증속이나 감속의 기능을 수행하는 감속기(Reducer)이다. 때로는 증속의 용도로 사용하기도 하지만, 대부분의 기계장치에서는 구동축보다 피구동축이 회전수 조건보다는 동력전달 조건을 요구하기 때문에 더 많은 힘을 얻기 위해 감속기를 사용한다.1
감속기는 엔진이나 모터 등으로부터 출력되는 고속회전을 입력으로 하여, 로봇, 자동화 및 정밀제어기기 등에서 요구되는 안정도 및 정밀도를 구현할 수 있도록 일정비율로 감속하여 출력시키는 장치로, 일반적으로 다수의 기어를 조합하여 기어의 잇수 차이로 인한 감속을 도모하고 있으며, 유성 기어가 선기어의 주위를 회전하면서 감속이 이루어지는 유성기어 시스템이 대표적인 예이다.2-4 또한 외국 선진업체의 피치감속기는 유성기어구조의 감속기를 사용하고 있다. 국내 H사는 피치감속기의 중량을 줄이기 위해 사이클로이드 기어형태의 감속기를 채택하고 있다.5 사이클로이드 감속기는 기존 동력전달 장치에서 많이 사용되고 있는 유성기어 감속기에 비하여 1단으로도 큰 감속비를 가지고 있으며 치물림률이 크므로 소형으로 큰 토크 전달이 가능하며 콤팩트한 구조로 높은 부하 용량과 위치 제어 시 고정밀도가 요구되는 로봇 분야에서 주로 사용되고 있다.
본 연구에서는 일반 유성 기어에 비하여 내구성 및 효율을 향상시키고, 소형화의 장점을 가지고 있는 새로운 사이클로이드 모델을 개발하고자 한다.
따라서 사이클로이드 치형의 장점을 이용한 원격 무장 고저 시스템용 감속기설계에 관하여 연구하고자 한다. 각종 기계장치의 구동기는 대부분 모터와 감속 장치로 구성되어 있으며 이러한 장치의 동특성이 시스템의 성능에 큰 영향을 미치게 된다. 특히 정확한 위치 제어를 요하는 장치의 경우에는 이러한 구동 부분의 정밀도와 동특성이 장치의 정밀도를 결정하기 때문에 감속기는 기계 장치의 정도와 진동 및 소음 특성에 영향을 미치는 부품으로 기계적 구성 장치의 핵심부품이다.
사이클로이드 감속기는 소치수차식 감속기로 기본원리는 내접하는 원의 구름 운동시에 안쪽 원의 회전 운동을 이용하는 것이다. 감속비는 내기어와 외기어의 기어수의 차에 비례하고 보통 1 - 2개의 잇수 차로 감속기를 구성하기 때문에 소치수차식 감속기라 부르고 있다. 감속비는 1단의 기구로 상당히 커지며, 소형으로 부하 용량을 크게 할 수 있기 때문에 로봇을 비롯한 정밀 구동부에 주로 사용된다. 소치수차식 감속기는 구조적으로 내접 유성식과 주족식 감속기로 구분한다.6
사이클로이드 감속기는 사이클로이드 곡선을 이용한 감속기로 일반 유성 기어와 달리 높은 감속비를 가질 경우 구조상 일반 유성기어 감속기에 비해 소형화의 장점을 가지고 있다.
따라서 본 연구에서는 유성기어 감속기보다 콤팩트한 사이클로이드 감속기 설계 시 고려되어야 할 사항들을 면밀히 검토하고 적용함으로써 무인 정찰용 전차에 사용되는 원격 무장 고저시스템용 사이클로이드 감속기의 요구조건인 감속비 127 : 1, 백래시 1 Arcmin(1/60 deg) 이하, 감속기 효율 70% 이상에 준하는 사이클로이드 감속기를 설계하였다. 또한 요구조건을 만족하는지 평가하기 위하여 정격출력 토크 및 속도, 감속비, 백래시, 로스트모션을 측정하였다.
2.1 사이클로이드 기어 및 유성기어 설계
감속비는 식(1)과 식(2)를 활용하여 계산된다.
(1)
R=1+Z2Z1-Z4
(2)
i=1R
여기에서 R은 속도비를 나타내고, Z1은 입력축의 선기어 잇수, Z2는 유성기어의 잇수, Z3는 사이클로이드 기어의 잇수, Z4는 핀의 수, i는 감속비를 나타낸다.
사이클로이드 감속기 기어 설계의 구성도와 사이클로이드 감속기 형상을 각각 Figs. 1과 2에 나타냈다.
Fig. 1

Reducer design configuration

KSPE_2017_v34n6_405_f001.jpg
Fig. 2

Shape of cycloid reducer

KSPE_2017_v34n6_405_f002.jpg
Table 1에 식(1)과 식(2)를 통하여 핀 직경 및 선기어, 유성기어, 사이클로이드기어, Pin의 잇수를 정리 하였으며 최종 감속비 결과값을 나타냈다.
Table 1

Gear teeth numbers and gear ratio

Table 1
Division Z1 Z2 Z3 Z4 Gear ratio
Gear teeth 36 30 41 42 127 : 1
2.2 사이클로이드 치형 설계
사이클로이드 치형은 기본 원 위를 다른 반경을 가진 구름 원이 미끄럼 없이 구를 때 구름 원의 내부, 외부 또는 원주상에 위치한 고정된 점의 이동 궤적에 의해 생성된다. 구름 원의 중심이 기본 원의 내부에 존재하는지, 외부에 존재하는지에 따라 외피 사이클로이드(Epi-Cycloid) 곡선과 내피 사이클로이드(Hypo-Cycloid) 곡선으로 분류된다.
사이클로이드 곡선은 Fig. 3에 나타낸 바와 같이 점 P의 운동에 의해 생성된다는 것을 알 수 있다. 이 때, 점 P의 운동은 회전 운동과 직선 운동으로 이루어져 있으므로 사이클로이드 곡선을 구하기 위해, 점의 운동을 회전 운동과 직선 운동으로 분해하고, 그 두 운동의 합으로 점 P의 운동으로 정의한다.
Fig. 3

Shape of point P that performs rotational motion

KSPE_2017_v34n6_405_f003.jpg
Fig. 4에 사이클로이드 치형 설계를 나타내었으며 3D 모델링 작도 및 시뮬레이션 결과 구동하는 것을 확인하였다.
Fig. 4

Shape of cycloid tooth design

KSPE_2017_v34n6_405_f004.jpg
사이클로이드 치형 설계는 사이클로이드 곡선이 사이클로이드핀의 사이클로이드 곡선과 겹쳐지거나 떨어짐 없이 연결이 되어야 한다.
크랭크 샤프트를 45°씩 회전을 시키며, 사이클로이드 기어는 원주의 336등분한, 1.0714° 위치의 사이클로이드 핀을 크랭크샤프트 1 회전시 사이클로이드 기어 잇수 1 개 회전하고 사이클로이드 핀 42 개 중 1 개를 회전 이동하여 작도하였다.
크랭크 샤프트는 각 45° 회전하는 위치마다 반복하고 사이클로이드 핀의 위치를 작도를 하였으며, 반복 작도 결과 사이클로이드 핀 중심 이동 곡선과 사이클로이드 핀 외경과 사이클로이드 기어와 접촉면의 이동 곡선을 작도 하였다.
2.3 유성기어 치형 설계
Fig. 5는 기어 설계프로그램인 HEXGON을 활용하여 치형을 작도하여 표현한 형상을 나타내었으며, 선기어와 유성기어의 모듈, 압력각, 잇수, 전위계수, 중심거리, 치폭 값을 Table 2에 나타냈다.
Fig. 5

Shape of planetary gear tooth

KSPE_2017_v34n6_405_f005.jpg
Table 2

Specification of planetary gear

Table 2
Division Module Each
pressure		 Teeth Potential
coefficients		 Center
distance
(mm)		 Face
width
(mm)
Sun gear 1.5 20 10 0.3 30 7.5
Planetary
gear		 1.5 20 30 -0.3 30 7.5
2.4 기어 강도설계
본 연구에서 유성기어열의 강도 해석을 수행하기 위하여 기어 전문 설계/해석 프로그램인 HEXGON을 사용하였으며, Table 3에 유성기어열의 이뿌리 파괴 강도 해석결과를 나타내었고, Fig. 6은 해석 프로그램을 이용한 결과를 확인하였다. 이론적인 강도 해석을 통해 계산된 원격 무장 고저각 감속기의 유성기어 열에 대하여 치형 설계 및 강도 해석을 수행하여 강도 조건을 만족함을 확인하였다.
Table 3

Tooth root fracture strength

Table 3
Division Safety factor
Sun gear 2.58
Planetary gear 2.45
Fig. 6

Tooth root fracture strength

KSPE_2017_v34n6_405_f006.jpg
3.1 주요 구성품 및 특징
사이클로이드 감속기는 기본적으로 선기어, 유성기어, 사이클로이드 기어 및 캐리어로 구성되며, 입력축의 요소와 사이클로이드 기어의 요소에 따라 회전속도 및 감속비가 결정된다.
Fig. 7은 원격무장 고저시스템용 감속기 구조 및 형상을 나타낸 것으로 3D 디자인 프로그램인 Autodesk Inventor를 사용하여 3D 모델링을 하였다.
Fig. 7

Structure of cycloid reducer

KSPE_2017_v34n6_405_f007.jpg
Fig. 8에 2차 사이클로이드 기어의 제품 및 모델링을 나타내었으며, 사이클로이드 감속기의 핵심부품으로 기어감속부 출력축의 메인 기어 역할을 한다.
Fig. 8

Shape of cycloid gear

KSPE_2017_v34n6_405_f008.jpg
유성 기어의 시제품 및 모델링 형상을 Fig. 9에 나타내었으며, 1차 감속부의 유성 기어로 선기어로부터 입력된 동력을 크랭크 샤프트로 전달하는 역할을 한다. 선기어는 전동기 및 서보모터의 입력 받을 구동력과 연결이 된다. 선기어의 시제품 및 3D 형상을 Fig. 10에 나타냈으며 1차 유성감속부의 선기어 역할을 담당한다.
Fig. 9

Shape of planetary gear

KSPE_2017_v34n6_405_f009.jpg
Fig. 10

Shape of a sun gear

KSPE_2017_v34n6_405_f010.jpg
4.1 정격 출력 토크와 속도 측정결과 및 고찰
정격 출력 토크 및 속도 측정시험이란 감속기의 핵심 구성품인 기어류를 포함한 모든 구성품이 조립된 감속기 조립체 상태에서 이론적으로 계산한 정격출력 및 토크가 도출되는지 확인하는 시험이다.
감속기 성능시험 장치를 Fig. 11에 나타내었으며, 정격 출력토크 및 속도, 백래시, 로스트모션, 비틀림 강성, 감속비를 확인할 수 있고 시험대상을 기준으로 양끝 단에 입력 및 출력 토크 및 속도를 인가하기 위한 서보모터가 위치하며 이를 측정하기 위한 토크, rpm 센서가 입력 및 출력 단에 각각 위치하고 있다.
Fig. 11

Performance testing equipment

KSPE_2017_v34n6_405_f011.jpg
본 연구에서 원격무장 고저용 사이클로이드 감속기는 20 rpm일 때 정격출력토크는 248 Nm의 이론적인 값을 도출하였고 시험용 시작품에 대한 시험을 실시하여 정격 출력 토크 및 속도를 확인하였다.
Figs. 12와 13은 출력토크 및 속도시험을 각 5 회씩 실시한 결과를 나타내고 있는데, 정격출력 토크는 속도 20 rpm일 때 248 Nm의 값으로 나타났다.
Fig. 12

Performance test results table

KSPE_2017_v34n6_405_f012.jpg
Fig. 13

Test results of reducer rated output

KSPE_2017_v34n6_405_f013.jpg
4.2 감속비 시험 결과 및 고찰
감속비 시험은 감속기의 핵심 구성품인 기어류를 포함한 모든 구성품이 조립된 감속기 조립체 상태에서 이론적으로 계산한 기어비가 도출되는지를 확인하는 시험이다. 감속비 측정은 Fig. 11에 나타낸 감속기 성능시험장치로 측정하였으며 감속비 시험을 각 5회씩 실시하여 결과를 Fig. 14에 나타내었다. 감속비 시험을 각 5회씩 실시한 결과 감속비의 평균값은 127.0으로 나타났다.
Fig. 14

Test results of reducer ratio

KSPE_2017_v34n6_405_f014.jpg
4.3 출력축 백래시 측정결과 및 고찰
백래시 시험은 감속기의 입력축에서 출력축까지의 기어 맞물림 시 발생하는 각도 오차를 확인하는 시험으로써, 출력 단에 유격이 생성될 만큼의 토크를 인가 후 출력축 백래시의 합을 계측하였다.
Fig. 15는 백래시 및 로스트모션 시험을 위한 시험장치를 나타내고 있다. 정격토크의 ±100%의 토크를 정역방향으로 인가한 히스테리시스 곡선을 생성 후 토크가 0인 지점에서 정역방향의 비틀림각 차이를 계측하였다.
Fig. 15

Backlash and lost motion testing equipment

KSPE_2017_v34n6_405_f015.jpg
Fig. 16은 시작품에 대해 5 회 반복시험을 실시하여 백래시를 측정한 시험결과를 나타냈으며, 다섯 번의 백래시 시험을 통하여 백래시의 평균값은 0.842 arcmin으로 나타났다.
Fig. 16

Test results of reducer backlash

KSPE_2017_v34n6_405_f016.jpg
4.4 출력축 로스트모션 측정결과 및 고찰
사이클로이드 감속기의 구조적인 특성상 일반기어의 백래시와는 달리 로스트 모션이 존재한다. 이것은 물림률이 일반기어에 비하여 상당히 크기 때문에 백래시는 극히 미소하지만 전달 토크가 작을 때에는 강성이 극히 작아서 백래시와 유사하게 작용한다. 로스트모션의 측정은 먼저 감속기의 입력축을 고정하고 출력축에 정역 전으로 작용하는 정격토크를 가할 경우 가해진 토크와 비틀림 각이 동일 직선상을 왕복하지 않고 히스테리시스 루프 곡선을 그리게 된다.7
Fig. 15의 시험 장치에 감속기를 장착하여 5 회 반복 시험을 실시하여 출력축 로스트모션을 측정하였으며, 측정결과를 Fig. 17에 나타냈다. 다섯 번의 시험을 실시한 로스트모션의 평균값은 0.106 arcmin으로 나타났다.
Fig. 17

Test results of lost motion

KSPE_2017_v34n6_405_f017.jpg
본 연구에서는 원격무장 고저시스템용 사이클로이드 감속기의 핵심기술에 관한 원천기술과 시스템의 구조 설계의 검토를 수행하여 설계를 진행하였고, 이를 토대로 사이클로이드 감속기 성능 검증을 위하여 시험치구를 설계, 제작하고 감속기 성능시험 장치를 사용하여 성능 시험을 수행하여 다음과 같은 결론을 얻었으며, 정밀 소형 감속기의 사이클로이드 치형 제작 등 감속기 설계 및 제작기술을 확보하였다.
(1) 정격 출력 토크 시험은 20 rpm일 때 정격출력 토크는 248 Nm으로 측정되었으며 이는 이론적인 목표값 248 Nm의 요구를 충족하였다.
(2) 감속비 시험을 통한 시험 결과값으로 감속비 127.0를 확인 하였으며, 이론상에서 계산된 감속비인 127 : 1에서 오차범위 ±0.02% 이내로 분석되었다.
(3) 백래시 시험을 통해 백래시 시험 결과값은 0.842 arcmin으로 나타났으며, 이론적 목표 값 1 arcmin 이하의 요구를 충족하였다.
(4) 로스트모션 시험을 통하여 로스트모션은 0.1062 arcmin으로 나타났고, 이론적인 목표 값 1 arcmin 이하의 요구를 충족하였다.
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A Study on Design of Cycloid Reducer for Remote Weapons Systems
J. Korean Soc. Precis. Eng.. 2017;34(6):405-410.   Published online June 1, 2017
DOI: https://doi.org/10.7736/KSPE.2017.34.6.405
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A Study on Design of Cycloid Reducer for Remote Weapons Systems
J. Korean Soc. Precis. Eng.. 2017;34(6):405-410.   Published online June 1, 2017
DOI: https://doi.org/10.7736/KSPE.2017.34.6.405
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A Study on Design of Cycloid Reducer for Remote Weapons Systems
Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image
Fig. 1 Reducer design configuration
Fig. 2 Shape of cycloid reducer
Fig. 3 Shape of point P that performs rotational motion
Fig. 4 Shape of cycloid tooth design
Fig. 5 Shape of planetary gear tooth
Fig. 6 Tooth root fracture strength
Fig. 7 Structure of cycloid reducer
Fig. 8 Shape of cycloid gear
Fig. 9 Shape of planetary gear
Fig. 10 Shape of a sun gear
Fig. 11 Performance testing equipment
Fig. 12 Performance test results table
Fig. 13 Test results of reducer rated output
Fig. 14 Test results of reducer ratio
Fig. 15 Backlash and lost motion testing equipment
Fig. 16 Test results of reducer backlash
Fig. 17 Test results of lost motion

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Fig. 15

Fig. 16

Fig. 17

A Study on Design of Cycloid Reducer for Remote Weapons Systems
Division Z1 Z2 Z3 Z4 Gear ratio
Gear teeth 36 30 41 42 127 : 1
Division Module Each
pressure		 Teeth Potential
coefficients		 Center
distance
(mm)		 Face
width
(mm)
Sun gear 1.5 20 10 0.3 30 7.5
Planetary
gear		 1.5 20 30 -0.3 30 7.5
Division Safety factor
Sun gear 2.58
Planetary gear 2.45
Table 1 Gear teeth numbers and gear ratio
Table 2 Specification of planetary gear
Table 3 Tooth root fracture strength

Table 1

Table 2

Table 3

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