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유성기어박스의 캐리어 핀홀 위치 오차의 위상에 따른 유성기어의 하중 분할 연구

김정길1, 박영준2,#, 이근호3, 오주영4, 김영주1

A Study on the Load Sharing among Planet Gears according to the Phase of Carrier Pinhole Position Error in the Planetary Gearbox

Jeong Gil Kim1, Young-Jun Park2,#, Geun Ho Lee3, Joo Young Oh4, Young Joo Kim1
Journal of the Korean Society for Precision Engineering 2017;34(6):377-382.
Published online: June 1, 2017

1 한국생산기술연구원 융복합농그룹

2 서울대학교 바이오시스템·소재학부

3 한국기계연구원 시스템신뢰성연구실

4 한국생산기술연구원 건설기계부품그룹

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#E-mail: yjpark95@snu.ac.kr, TEL: +82-2-880-4602, FAX: +82-2-873-2049
• Received: February 22, 2017   • Revised: March 23, 2017   • Accepted: April 12, 2017

Copyright © The Korean Society for Precision Engineering

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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  • The planetary geartrain can be reduced in size and weight, and has excellent durability since the input torque is divided by the number of planet gears when the power is transmitted. In order to improve its durability, the load sharing among planet gears must be even. However, of the various manufacturing errors possible, the carrier pinhole position error has the greatest influence on load sharing. This study compared and analyzed the load sharing and the gear safety of planetary gears, according to the phase of the carrier pinhole position error. We confirmed that load sharing among the planet gears varied, depending on the phase of the carrier pinhole position error. The mesh load factor is inversely related to the gear safety factor for bending and contact, and affects the durability of the planetary geartrain. Also, in the design of the planetary geartrain, the load sharing among planet gears is directly affected by the carrier pinhole position error and its phase. Therefore, the geometric tolerance must be managed efficiently, which needs to be reflected in the production drawings.
  • KEYWORDS: Planetary gearbox, Load sharing, Carrier pinhole position error, Mesh load factor
  • KEYWORDS: 유성기어박스, 하중 분할, 캐리어 핀홀 위치 오차, 하중 분할 계수

u

Gear ratio

d 1

Reference diameter of pinion (mm)

Ft

Nominal transverse tangential load at reference cylinder per mesh (N)

KA

Application factor

KFα

Transverse load factor for root stress

KFβ

Face load factor for root stress

KHα

Transverse load factor for contact stress

KHβ

Face load factor for contact stress

KV

Dynamic factor

Kγ

Mesh load factor

mn

Normal module

NCP

Number of planet gears

Tin

Input torque (Nm)

Tbranch

Torque in branch with heaviest load (Nm)

YB

Rim thickness factor

YDT

Deep tooth factor

YF

Tooth form factor

YNT

Life factor for root stress

YRrelT

Relative surface factor

YS

Stress correction factor

YST

Stress correction factor for reference test gear

YX

Size factor for root stress

Yβ

Helix angle factor for root stress

YδrelT

Relative notch sensitivity factor

Z B,D

Single pair tooth contact factor

ZE

Elasticity factor (N/mm2)

ZH

Zone factor

ZL

Lubricant factor

ZNT

Life factor for contact stress

ZR

Roughness factor

ZX

Size effect factor for contact stress

ZV

Velocity factor

ZW

Work hardening factor

Zβ

Helix angle factor for contact stress

Zε

Contact ratio factor

σF

Tooth root stress (MPa)

σ F0

Nominal tooth root stress (MPa)

σFG

Tooth root stress limit (MPa)

σ Flim

Nominal stress number for bending (MPa)

σH

Contact stress (MPa)

σ H0

Nominal contact stress (MPa)

σFG

Pitting stress limit (MPa)

σ Hlim

Allowable stress number for contact (MPa)
유성기어트레인은 여러 개의 유성기어에 의해 입력 토크가 분할되어 동력을 전달함으로 소형화 및 경량화가 가능하고, 내구성이 뛰어나다. 유성기어트레인의 내구성을 향상시키기 위해서는 유성기어간의 하중 분할이 균일하여야 한다. 그러나 유성기어트레인을 구성하는 기어, 베어링, 유성핀, 캐리어 등의 부품들은 오차가 존재하며, 이로 인하여 유성기어간의 하중 분할을 균일하게 하는 것이 쉽지 않다. 기어의 제작 오차는 치형 오차, 피치 오차, 런아웃 오차가 있으며, 베어링 제작에 의한 내륜과 외륜, 전동체의 오차, 유성핀을 캐리어에 억지 끼움시 조립 오차, 캐리어 런아웃 및 핀홀 위치 오차 등에 의해 유성기어간의 하중 분할이 불균일하게 발생한다.1 또한 이러한 오차들은 기어의 미스얼라인먼트를 유발하여 유성기어트레인의 요구 수명을 만족시키지 못하는 결과를 초래할 수 있다.
이전 연구는 유성기어 3 - 6개를 가진 1단 유성기어트레인 시뮬레이션 모델을 해석적으로 입력 토크 증가, 캐리어의 핀홀 위치 오차를 핀홀 여러 개 중에 1개의 핀홀에 원주 방향의 핀홀 위치 오차를 고려하여 유성기어간의 하중 분할을 연구하였다.2,3
본 연구는 유성기어트레인의 하중 분할에 영향을 미치는 여러 제작 오차 중에 캐리어의 핀홀 위치 오차를 산업용 유성기어박스 시뮬레이션 모델에 반영하여 유성기어간의 하중 분할을 해석하고 유성기어트레인의 내구성에 미치는 영향을 연구하였다. 개발된 시뮬레이션 모델은 상용 프로그램4을 이용하였으며, 이 모델은 Kim5의 이전 연구에서 검증되었다. 해석 조건인 캐리어의 핀홀 위치 오차는 핀홀 6개로 구성된 캐리어6의 3차원 측정을 통해 얻은 원주 방향의 핀홀 위치 오차 중에 최대값을 이용하여 핀홀 4개로 구성된 캐리어에 반영하여 해석을 수행하였다.
2.1 유성기어트레인의 구조
유성기어트레인은 선기어, 유성기어, 링기어, 캐리어로 구성된 1단 유성기어 구조로 유성기어의 개수는 4개이다. 동력은 링기어로 입력되어 선기어로 출력되며, 캐리어는 고정이다.
Fig. 1은 유성기어트레인의 구조를 나타낸 것이며, Table 1은 유성기어트레인의 제원이다.
Fig. 1

Structure of planetary geartrain

KSPE_2017_v34n6_377_f001.jpg
Table 1

Specification of planetary geartrain

Table 1
Items Stage 1
Sun Planet Ring
Module (mm) 3.5
Pressure angle (deg) 20
Center distance (mm) 142.75
Number of teeth 50 31 114
Tip diameter (mm) 182.29 117.15 389.05
Pitch circle diameter (mm) 176.23 109.26 392.13
Root diameter (mm) 166.60 101.45 404.79
Facewidth (mm) 74 72 74
Number of gear 1 4 1
2.2 유성기어간의 하중 분할
유성기어트레인에서 유성기어간의 하중 분할은 하중 분할 계수, Kγ로 나타낸다.7 하중 분할 계수가 1에 가까울수록 유성기어간의 하중 분할이 균일하며, 여러 개의 유성기어 중에 하중 분할 계수가 1이상인 경우에 유성기어간의 하중 분할이 균일하지 않음을 의미한다. 즉, 유성기어트레인의 입력 토크(Tin)가 유성기어의 개수(NCP)로 나누어질 때, 하중 분할 계수가 1.5인 경우, 토크를 크게 받는 유성기어는 1.5·Tin/NCP가 된다. 유성기어간의 하중 분할 계수는 식(1)과 같이 계산한다.
(1)
Kγ=TbranchTin/NCP
2.3 기어 강도 평가
기어 강도 평가는 ISO 규격8을 이용하여 기어의 굽힘 강도와 면압 강도를 평가하였다. 유성기어간의 하중 분할은 기어의 굽힘 강도와 면압 강도에 영향을 준다.
기어의 굽힘 강도는 이뿌리 응력 한도, σFG와 이뿌리 응력, σF의 비로 계산한다. 기어 이뿌리부에서 발생하는 응력이 이뿌리 응력 한도보다 크면, 이뿌리부에서 균열이 발생하여 균열이 진전하여 기어 이의 절손을 유발한다.9
기어의 공칭 이뿌리 응력, σF0는 식(2)와 같이 계산한다.
(2)
σF0=FtbmnYFYSYβYBYDT
기어의 이뿌리 응력, σF는 식(3)과 같이 계산한다.
(3)
σF=σF0KAKγKVKFβKFα
기어의 이뿌리 응력 한도, σFG는 식(4)와 같이 계산한다.
(4)
σFG=σFlimYSTYNTYδrelTYRrelTYX
기어의 면압 강도는 기어의 접촉 응력 한도, σHG와 접촉 응력, σH의 비로 계산하며, 두 기어 사이에서 발생하는 접촉에 의한 강도이다. 기어 치면에서 발생하는 응력이 접촉 응력 한도보다 크면 기어 치면에서 아주 작은 조각이 떨어져 나와 작은 구멍인 피트(Pits)가 발생한다. 피트가 증가하고 커짐에 따라 피팅이 되며, 이는 기어 치면의 내구성에 영향을 준다.9
기어의 공칭 접촉 응력, σH0는 식(5)와 같이 계산한다.
(5)
σH0=ZHZEZεZβFtu+1d1bu
기어의 접촉 응력, σH는 식(6)과 같이 계산한다.
(6)
σH=ZB,DσH0KAKγKVKHβKHα
기어의 접촉 응력 한도, σHG는 식(7)과 같이 계산한다.
(7)
σHG=σHlimZNTZLZVZRZWZX
2.4 캐리어 핀홀 위치 오차의 위상에 따른 해석 조건
본 연구는 Kim6의 이전 연구에 소개된 캐리어의 핀홀 위치 오차를 시뮬레이션 모델에 반영하여 해석하였다. 이전 연구에서 캐리어는 핀홀 6개로 구성하였으며, 실제 산업 현장에서 제작된 캐리어의 오차를 반영하기 위하여 3차원 측정을 통해 핀홀 위치 오차를 측정하였다. 측정된 캐리어 핀홀 위치 오차는 원주 방향의 최대값이 +80 μm, 최소값이 -80 μm로 나타났다.
본 연구는 핀홀 4개로 구성된 캐리어에 핀홀 1은 핀홀 위치 오차가 존재하지 않는 것으로 가정하였으며, 핀홀 2 - 4는 측정된 핀홀 위치 오차의 위상을 변화시키면서 해석을 수행하였다.
Fig. 2는 캐리어 핀홀 위치 오차의 위상을 나타낸 것으로, 핀홀을 기준으로 시계 방향은 (+)의 오차를, 반시계 방향은 (-)의 오차를 나타낸 것이다.
Fig. 2

Pinhole position error of carrier

KSPE_2017_v34n6_377_f002.jpg
Table 2는 시뮬레이션 모델에 반영한 캐리어 핀홀 위치 오차의 위상에 따른 해석 조건이다. Table 2에서 Case A는 캐리어의 핀홀 위치 오차가 존재하지 않는 경우와 핀홀 위치 오차가 핀홀 1개에 존재하는 경우이다. Case B는 캐리어의 핀홀 위치 오차가 핀홀 2개에 존재하는 경우이고, Case C는 캐리어의 핀홀 위치 오차가 핀홀 3개에 존재하는 경우이다.
Table 2

Analysis condition of pinhole position error

Table 2
Case Pinhole position error (μm)
Pinhole 1 Pinhole 2 Pinhole 3 Pinhole 4
A 1 0 0 0 0
2 0 0 0 80
3 0 0 0 -80
B 4 0 0 80 80
5 0 80 0 80
6 0 0 80 -80
7 0 80 0 -80
8 0 0 -80 -80
9 0 -80 0 -80
C 10 0 80 80 80
11 0 80 80 -80
12 0 80 -80 80
13 0 -80 80 80
14 0 80 -80 -80
15 0 -80 80 -80
16 0 -80 -80 80
17 0 -80 -80 -80
3.1 캐리어 핀홀 위치 오차의 위상에 따른 유성기어간의 하중 분할 해석
유성기어트레인 시뮬레이션 모델을 활용하여 캐리어 핀홀 위치 오차의 위상에 따른 유성기어간의 하중 분할을 해석하였다. 유성기어트레인의 입력 토크 및 속도는 18,238.5 Nm@85.9 RPM이며, 회전 방향은 링기어를 기준으로 반시계 방향이다.
Fig. 3은 핀홀 위치 오차가 존재하지 않는 경우와 핀홀 1개에 핀홀 위치오차가 존재하는 경우에 대한 해석 결과이다. Case A-1모델은 핀홀 위치 오차가 존재하지 않는 조건으로 각 유성기어의 핀홀 위치에 따른 중력의 영향을 제외하면, 유성기어간의 하중 분할 계수는 1로 균일하였다. Case A-2모델은 핀홀 4에 (+) 위상의 핀홀 위치 오차가 존재함으로 유성기어 4에서 가장 먼저 기어 물림이 발생하여 가장 높은 하중이 작용하였다. 유성기어 4의 양쪽 측면에 위치한 유성기어 1과 3은 가장 작은 하중이 작용하며, 유성기어 4의 180°위치에 존재하는 유성기어 2는 유성기어 1과 3보다는 큰 하중이 작용하였다. Case A-3모델은 핀홀 4에 (-) 위상의 핀홀 위치 오차가 존재함으로 유성기어 4에서 기어 물림이 발생하지 않고, 유성기어 4의 양쪽 측면에 위치한 유성기어 1과 3에서 먼저 기어 물림이 발생하여 큰 하중이 작용하고, 유성기어 4의 180° 위치에 존재하는 유성기어 2에 상대적으로 작은 하중이 작용하였다.
Fig. 3

Mesh load factor of case A

KSPE_2017_v34n6_377_f003.jpg
Figs. 4와 5는 캐리어 핀홀 위치 오차가 핀홀 2개에 존재하는 경우에 대한 해석 결과이다. Case B-4와 B-8 모델은 캐리어 핀홀 위치 오차가 2개의 핀홀에 연속적으로(핀홀 3과4) 같은 위상을 갖는 경우로 B-4모델은 유성기어 3과 4에, B-8 모델은 유성기어 1과 2에서 기어 물림이 먼저 발생하여 하중 분할 계수가 1.5보다 큰 경향성을 보였다. Case B-5와 B-9 모델은 캐리어 핀홀 위치 오차가 2개의 핀홀에 180° 위치 간격(핀홀 2와 4 또는 핀홀 1과 3)으로 같은 위상을 갖는 경우로, B-5 모델은 유성기어 2와 4에, B-9모델은 유성기어 1과 3에서 기어 물림이 먼저 발생하는 경향성을 보였다. Case B-6과 B-7 모델은 캐리어 핀홀 위치 오차가 원주 방향을 기준으로 2개의 핀홀에 서로 다른 위상을 갖는 경우로, (+) 위상의 핀홀 위치 오차를 갖는 유성기어는 하중 분할 계수가 2.5보다 큰 경향성을 보이며, (-) 위상의 핀홀 위치 오차를 갖는 유성기어는 기어 물림이 발생하지 않았다.
Fig. 4

Mesh load factor of case B-1

KSPE_2017_v34n6_377_f004.jpg
Fig. 5

Mesh load factor of case B-2

KSPE_2017_v34n6_377_f005.jpg
Case B 모델을 보았을 때, 캐리어 핀홀 위치 오차가 동일한 위상으로 핀홀 4개 중 2개에 존재하는 경우, 2개의 유성기어에 하중 분할이 균일하게 발생하는 경향성을 보였으며, 핀홀 위치 오차가 핀홀 2개에 반대 위상으로 존재하는 경우에는 (+) 위상의 핀홀 위치 오차를 갖는 유성기어에서 먼저 물림이 발생하며, (+) 위상의 양쪽 측면에 존재하는 유성기어에서 그 다음 하중을 분할하는 경향성을 보였다.
Fig. 6과 7은 캐리어 핀홀 위치 오차가 핀홀 3개에 존재하는 경우로, Case C-10 모델은 캐리어 핀홀 위치 오차가 모두 (+) 위상을 가지므로 유성기어 2, 3, 4에서 기어 물림이 발생하고 유성기어 1은 물림이 발생하지 않았다. 이는 Case A-3 모델과 유사한 경향성을 보이며, 유성기어의 최대 하중 위치만 변경되었다. Case C-11 - C-13 모델은 캐리어 핀홀 위치 오차가 핀홀 2개에 (+) 위상, 핀홀 1개에 (-) 위상을 가지므로, 연속적으로(핀홀 2와 3 또는 핀홀 3과 4) (+) 위상을 갖는 유성기어는 2개의 유성기어에서 하중을 분할하고, 핀홀 위치 오차가 존재하지 않는 유성기어에서 나머지 하중을 분담하였다. 그러나, 불연속적으로(핀홀 2와 4) (+)의 위상을 갖는 유성기어는 2개의 유성기어에서 하중을 약 50%씩 분할하고, 나머지 유성기어는 하중을 분담하지 않았다. Case C-14 - C-16 모델은 캐리어 핀홀 위치 오차가 핀홀 1개에 (+) 위상, 핀홀 2개에 (-) 위상을 가지므로, (+) 위상이 존재하는 유성기어에서 기어 물림이 먼저 발생하고, 기어 이의 변형량이 증가함에 따라 핀홀 위치 오차가 존재하지 않는 유성기어에 하중이 분할되었다. Case C-17 모델은 캐리어 핀홀 위치 오차가 모두 (-) 위상을 가지므로 유성기어 1에서 먼저 기어 물림이 발생하고, 유성기어 3, 2, 4에 기어 물림이 발생하였다. 이는 Case A-2 모델과 유사한 경향성을 보이며, 유성기어의 최대 하중 위치만 변경되었다.
Fig. 6

Mesh load factor of case C-1

KSPE_2017_v34n6_377_f006.jpg
Fig. 7

Mesh load factor of case C-2

KSPE_2017_v34n6_377_f007.jpg
결과적으로 링기어가 반시계 방향으로 회전할 때 1개의 핀홀 위치 오차가 (+) 위상으로 존재하는 경우, 핀홀 위치 오차가 존재하는 유성기어에서 가장 먼저 기어 물림이 발생하며, 그 다음은 가장 먼저 기어 물림이 발생한 유성기어의180° 위치에 존재하는 유성기어에서 하중을 분담하는 경향성을 보였다. 여러 개의 핀홀 위치 오차가 유성기어의 순번에 따라 연속적으로 (+) 위상을 갖는 경우, 핀홀 위치 오차가 존재하는 유성기어에서 기어 물림이 발생한다. 그러나 여러 개의 핀홀 위치 오차가 유성기어의 순번에 따라 (+)와 (-) 위상으로 존재하는 경우에는 (+) 위상으로 핀홀 위치 오차가 존재하는 유성기어에서 기어 물림이 발생하며, 핀홀 위치 오차가 존재하지 않는 유성기어에서 하중이 분할되었다.
링기어가 반시계 방향으로 회전시 핀홀 위치 오차가 (+)의 위상으로 180° 위치에 존재하는 경우에 비해 90°위치에 존재하는 경우에 유성기어간의 하중 분할이 향상되는 경향성을 나타내었다.
3.2 기어 강도 평가
기어 강도 평가는 3.1절에서 해석을 통해 얻은 하중 분할 계수를 2.3절의 수식에 적용하여 계산하였으며 그 결과는 Table 3에 나타내었다.
Table 3

Gear safety factors

Table 3
Case Gear safety factors
Root Flank
Sun Planet Ring Sun Planet Ring
A 1 3.19 2.29 2.29 1.67 1.80 1.68
2 1.35 0.97 0.97 1.09 1.17 1.09
3 2.32 1.66 1.67 1.43 1.53 1.43
B 4 1.72 1.24 1.24 1.23 1.32 1.23
5 1.59 1.13 1.14 1.18 1.27 1.18
6 1.22 0.88 0.88 1.04 1.11 1.04
7 1.23 0.89 0.89 1.04 1.12 1.04
8 1.73 1.24 1.24 1.23 1.32 1.24
9 1.61 1.16 1.16 1.19 1.28 1.19
C 10 2.30 1.65 1.65 1.42 1.53 1.43
11 1.68 1.20 1.21 1.21 1.30 1.22
12 1.59 1.14 1.14 1.18 1.27 1.18
13 1.66 1.19 1.19 1.21 1.30 1.21
14 1.07 0.77 0.77 0.97 1.04 0.97
15 1.11 0.80 0.80 0.99 1.06 0.99
16 1.09 0.78 0.78 0.98 1.05 0.98
17 1.31 0.94 0.94 1.08 1.15 1.08
캐리어 핀홀 위치 오차의 위상에 따라 유성기어의 하중 분할 계수가 달라짐을 확인할 수 있으며, 하중 분할 계수가 증가할수록 기어의 굽힘 강도와 면압 강도에 대한 안전계수는 감소함을 알 수 있었다. 그러므로 하중 분할 계수는 유성기어트레인의 내구성에 영향을 미침을 확인할 수 있었다.10,11
본 연구는 유성기어트레인의 하중 분할에 영향을 미치는 여러 제작 오차 중에 캐리어 핀홀 위치 오차를 유성기어박스 시뮬레이션 모델에 반영하여 유성기어의 하중 분할이 유성기어트레인의 내구성에 미치는 영향을 분석하였다. 캐리어 핀홀 위치 오차의 위상에 따라 유성기어의 하중 분할과 기어 강도를 비교 분석하였으며, 이를 통해 얻은 결론은 다음과 같다.
캐리어 핀홀 위치 오차의 위상에 따라 유성기어의 하중 분할이 달라짐을 확인할 수 있었다. 하중 분할 계수는 기어의 굽힘 강도와 면압 강도의 안전계수와 반비례 관계이며, 계수의 증가는 유성기어트레인의 안전계수와 수명을 감소시킴을 확인하였다. 또한, 유성기어트레인 설계 시 캐리어 핀홀 위치 오차 및 위상이 유성기어의 하중 분할에 영향을 미치므로 제작 도면에 이를 반영하여 기하 공차를 효율적으로 관리해야 한다.
본 논문은 한국생산기술연구원 기관주요사업 “2017년 중소, 중견기업 타킷형 육성 생산기술 개발 사업(1/3) (KITECH JG-17-0010)”의 지원으로 수행한 연구입니다.
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    Kim, J. G., “Effects Analysis of Gear Design Parameter on Load Sharing of Planetary Geartrain,” Ph.D. Thesis, School of Mechanical Design Engineering, Chungnam National University, 2017.
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A Study on the Load Sharing among Planet Gears according to the Phase of Carrier Pinhole Position Error in the Planetary Gearbox
J. Korean Soc. Precis. Eng.. 2017;34(6):377-382.   Published online June 1, 2017
DOI: https://doi.org/10.7736/KSPE.2017.34.6.377
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A Study on the Load Sharing among Planet Gears according to the Phase of Carrier Pinhole Position Error in the Planetary Gearbox
J. Korean Soc. Precis. Eng.. 2017;34(6):377-382.   Published online June 1, 2017
DOI: https://doi.org/10.7736/KSPE.2017.34.6.377
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A Study on the Load Sharing among Planet Gears according to the Phase of Carrier Pinhole Position Error in the Planetary Gearbox
Image Image Image Image Image Image Image
Fig. 1 Structure of planetary geartrain
Fig. 2 Pinhole position error of carrier
Fig. 3 Mesh load factor of case A
Fig. 4 Mesh load factor of case B-1
Fig. 5 Mesh load factor of case B-2
Fig. 6 Mesh load factor of case C-1
Fig. 7 Mesh load factor of case C-2

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

A Study on the Load Sharing among Planet Gears according to the Phase of Carrier Pinhole Position Error in the Planetary Gearbox
Items Stage 1
Sun Planet Ring
Module (mm) 3.5
Pressure angle (deg) 20
Center distance (mm) 142.75
Number of teeth 50 31 114
Tip diameter (mm) 182.29 117.15 389.05
Pitch circle diameter (mm) 176.23 109.26 392.13
Root diameter (mm) 166.60 101.45 404.79
Facewidth (mm) 74 72 74
Number of gear 1 4 1
Case Pinhole position error (μm)
Pinhole 1 Pinhole 2 Pinhole 3 Pinhole 4
A 1 0 0 0 0
2 0 0 0 80
3 0 0 0 -80
B 4 0 0 80 80
5 0 80 0 80
6 0 0 80 -80
7 0 80 0 -80
8 0 0 -80 -80
9 0 -80 0 -80
C 10 0 80 80 80
11 0 80 80 -80
12 0 80 -80 80
13 0 -80 80 80
14 0 80 -80 -80
15 0 -80 80 -80
16 0 -80 -80 80
17 0 -80 -80 -80
Case Gear safety factors
Root Flank
Sun Planet Ring Sun Planet Ring
A 1 3.19 2.29 2.29 1.67 1.80 1.68
2 1.35 0.97 0.97 1.09 1.17 1.09
3 2.32 1.66 1.67 1.43 1.53 1.43
B 4 1.72 1.24 1.24 1.23 1.32 1.23
5 1.59 1.13 1.14 1.18 1.27 1.18
6 1.22 0.88 0.88 1.04 1.11 1.04
7 1.23 0.89 0.89 1.04 1.12 1.04
8 1.73 1.24 1.24 1.23 1.32 1.24
9 1.61 1.16 1.16 1.19 1.28 1.19
C 10 2.30 1.65 1.65 1.42 1.53 1.43
11 1.68 1.20 1.21 1.21 1.30 1.22
12 1.59 1.14 1.14 1.18 1.27 1.18
13 1.66 1.19 1.19 1.21 1.30 1.21
14 1.07 0.77 0.77 0.97 1.04 0.97
15 1.11 0.80 0.80 0.99 1.06 0.99
16 1.09 0.78 0.78 0.98 1.05 0.98
17 1.31 0.94 0.94 1.08 1.15 1.08
Table 1 Specification of planetary geartrain
Table 2 Analysis condition of pinhole position error
Table 3 Gear safety factors

Table 1

Table 2

Table 3

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