A Complete Review of Planetary Gear Dynamics and Vibrations Researches

Transcription

1 "#$ *8/ 01) ,6 07$ *8'(") *+,-.,- *2 *29,: 6 6 -, -. / / , -. / / ,; " * 7 424, ;2 =;7 > : / 3 3 FGH; < 4E D 3 A C; B/ 6A / 19 /?@ => 4; <3 :3 / 43 4; :, C;N F../ 43 4O I 4;<3?.: 2 3 / C;N F J8 M;. JK I D 3 C; 5 1 UJV 4;=T S R/ A R, 3 / O I 4;<3 2 A QH >>P 4 /?.: 2 / [/ XK ZH 3. 6/ 49/ Y5 CV/ A I XK F W FH; /. <; 3. 6/ A F ^>P 4 / FH 4;. \ ] XK 4/RH, <; 6.; C. 43 4O I 4;< ;=?.: O I 4;<3:*; *8?2+ A Complete Review of Planetary Gear Dynamics and Vibrations Researches M. Karimi Khoozani M. Poursina A. Pourkamali Anaraki Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran Department of Mechanical Engineering, Isfahan University, Isfahan, Iran Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran Abstract Planetary gear boxes are widely used in power transmission systems with high torque to weight ratio, high speed reduction in low space and access to deceleration in several stages. The main objective of this research is an overview on the dynamics and vibrations of the planetary gear systems. This research provides a comprehensive study of relevant resources published in various journals for researchers who wish to work on the dynamics of planetary gear systems. For this reason, these topics have been expressed in several sub-sections that cover all the dynamics and vibrations of planetary gear systems. In the end, a summary of the issues discussed and suggestions for further research in this field are expressed. Keywords: Planetary gear systems, Dynamic, Vibration, Dynamic models. >>P 4 / / 43 4O I 4;<3?.: 43 4O I 4;<3 2 A QH 1 UJV 4;=T S R/ A J 3 / / <; 3. [1],92 G504,D *8=(BC3) 247A 34*8G Z5 3; 69A S =3 ^>P 2 ;O I 2 73 d 4;= /. ( 1970 =3 A 43 4;O I 2 4 / :] 2 A 4A?>>P! 6 A :/. 9 A`.: 4; ao Q. 43 4;O I?.: GV A 4H 1 Q... Z5 ]O ` 2 FGH; 4;O I?.: 2 A. 1 4;>.; 61 O = ;;. ;1 1 Q. H /, / 2 A > 14 A H > 10 Q@K ; 3 K F., 43 4;O I 1990 ; / A F. 1 4;> : 2000 : / / / ;> : Y O = / / 3 / ;=3 F/ =3 10 =b 3 ;>.3 3 ci 2 J. 2 5 ^>P F J8 M; * poursina@eng.ui.ac.ir : 95/01/24 :! 95/11/18 :) *!

2 / : F 9 W 6/ 9 4;Z, = 4 / :[9]./ A Q. / J K K Ω Ω Ω ( 1) Ω c3 T w 3 w B/ : / K HD?nV / A/ CO I D 3 ]3 / P HD,O 19 6/ u 73 w u / Ω. 5 => 4]O CO I ]3 / 73 w w 6@../. 5 A/ 4+" =2 G ED ZH O ED 6/ uj8 d = p F / G uj` ;= F. 9 W *M]: F 9Y/ =K F /.; J K Q.../?3P A / <5K P 6H 4;= ud. 73 S3 3 P 6H = ; H ) A O 4;^>P 4 0 6>>P.[165] 3 w [17] 6 - Q Q. 73 P../ [18] 6HJ3/ /. Z5?:] 2003 =3 Y g.[2] 3 /A/ ;O I ]O ` 4;= 4 ;^>P A H :. ;1 ;> F 3 / /.[3]., > F 43 4;O I 2 A 4;O I 2 / S > [2] R, =i 6D /., > -I S> Y [3] R,., / 4 / 7JV 4;= O 4;=3 =b 4;= F.. j 43 4O I 4;<3 4, 7JV 4;4/3 ^>P M; /, / 6 ]O 3 / 4;= 9 2 A =i 6D/ A. <> ]O ` 4/<> P 6H = 9 4;Z, = 3. 3 / Z 9 CV/ F.[4] 6 *8J, G Q. ) 43 O I <3 4ED H; 9 F 9 Z,?8/ (A/ O O I 6A A Q>) ; ^ b A 9 4;Z,.. = = O I 4 9 ;6@ (6A / m 4 *M]: S> = p F.. Qn 0 / ; o / 4 *M]: = ;6@ O I 4;, : 3 / ;= F.. 9 <3 ED :. 4/ <> 9 A 3 / 4A R, 3 /...?.: 2 A 9?8 4;^>P 4 [16] 4+" =2 GA 42M 01)2-3 <3 :b 4; ;w F: Q. A?.: x :b. 0 <; XP F../ x 4,?.:!3 F 4 / <; <; 4 / W.. 73 / ;3 6> O3 A F 9 2H / 6-4;w 3P 4 / / Z 2 4.O O I 1G = A 73 / 3 3 / 43 <3 2 :b = y / ^>P F y > /.[6] ; j so 1G ) 6/ d D G F.. ;O :b w zy/ { > 4 / :3 d D G = / [6] R, 6 - JJP ) / 3 y -I 3 / H3 W FH; /.[9] / - 3 / u / 4 4;J8. > 0 *N2 01)2 4;) Q. 4,?.: / [/ XK H@ F /!3 ]O ` 4;nV1 QK K=9 DB G. 9 W ED 1O I K S> = F F A >>P. 4A, 2 S> ED ; 49/ [7 6] 6 - [5] 6H; ; Q. 73 =../ [8] 63 L,>-DB G / ED 1G K F 9 W / rd ;= FI 6 P / HD P78 d D 4; K 6 P >>P. 4A, 3 ED ; F //. 9 W Y 39 [9] F Q. 73 = H F A../ [11] 6 - [10] /3 *1- G-3 9 W 4:/ 3 4E <3 4ED = F, 3 : 4A, C. ED ; F //.. 73 = p F A >>P 6 A.>, 3.. [14] Q [13] g [12] 6 - / 6 4 / d D G so 1G 4;= J b / 4 / 4:/3 =. / 3 4;O I / 4;<3../ u3 v O I / 4;<3 6 = 358

3 H JD 3 - AO H HP.[12] / 0 W 9 4; : m A. <0 <H: 6A / m <3 2 / ) F g.[22] Q1 / Z <0 6D P 4, U V9,W *8TCD -4 4;< ]O ` 33 QD ^>P FI Y, /../ Aw 43 4O I ]O?8 / 43 4;<3 - [12 5] ]O `?8 / ;<3 ;> >/ /. 9 W H: O I 4;<3 / /1.. 9 W?.:!3 4?8 / 99 ]O ` 4; F.. ;1 43 4O I 4;<3 4, 07. 2; -3!3 C, ) Q. ;../ ` ) / 43 <3 2 ]O `!3 6 - Q / ^>P F Z5 / :] P 6H w ) 2 P w 5 m / 3 5 F 63. ;1!3 6 \d / ) (4 9 Z5 9 4;Z, ) / FH; O ^>P Y ; 2; -I wb/ QK ) A 61>>P -.[21] ) / 3 F 43 4O I 4;<3 4Y A H; = S RA 3 FI S3 S. I 9.. ;O / RA A <-3 ;3, Q/@ ` C3 T O3 A. 4;]O :@.. ;3 6 / / / RA / 5 ;]O F ; [263] R, ;3 6 / RA 4 / JJP 4;= / / RA x ^>P 2 Y / d D G = / 4?8 43 4;O I / RA A ;^>P 1/ R, / 6 =i 4 /.3 9?8 4A3Q R8 43 4;O I / RA.. [ ].3 3 / [31] R, Y J; *,64 X1Y7 61 ;O I 2 / S UJV R/ 3 / P QD 2 6D/ => 4]O ; => 4]O J K.[2] 3. * O I 7, w / / / / R/ 2 u@ d?8 / 4;<3 4 9 FI 6, /.. 6/ ) 4.O O I =K 43 4O I -43 4;O I O 4;O I A O / <; / np 6 F (0 4.O 4;O I u3 6I / 2 P 4;7ƒ 4;<3 AP *8O+?B: QK 4;) CV/ F -4 : 9 j 43 *4>*,6G2,Q2 *8O+-4 4;<3 2 4 / /O/ 4D 4 9= 0 ) QK 4 / ) F y F //. O. 43 4O I 4 y ) A [10] /3 39../ ;<3 F 43 4O I <3 A 1G = 2 QJP 4 / 4 4D 4;) JH, A <; [5] -/ ) >>P S3 / 78 RS- O+-4 K!3 F 4 / 9 b / 2; wb/ ) F. 73 ]O ` ]O 4;<3 4 ; K!3 2 P 3 3 d F / ) / 6A / m u d 2 P QK ) F.; 2; 4 3 4*0, / wo3.. S/ / 6 Q 7?B: <3 nv1 : : / {HD ) Q 4,?B: S> W 3 ; 4;?D 2; wb/ ) 6 /. 9 W 2;?D. 9 W?D 2 A C/ D XP.. 79 D -I 2; wb/ ) 6 / D 2; wb/ ) ; ;O I 2 wb/ ) ; 63.[209]. 73 D -I / 43 4O I <3 2 D 2; 61>>P -.[21] :3 Aw FI F 9 W :/ / O I 4; Aw A. ]O `? }. U8 /. j [19] 6 - ~.FJ/ ^>P D 2; wb/ ) A 61>>P J8 ud :[3] A 3?D 9?x1 2; 3 4;!3 Qi ]O ` 4; A O / ) A 73 / K / 6 2; -3 A ) F 3 6 / 2; -I wb/. F/.3 P { ) G247. O ;w nv1 : / [/ N > x QK / 6 wo3. 3/ 6 6 / 4; :b. V3 <3!3 = ph5 ) A 73 / Q/@ 6A A Q> 4;<3 4 / S> ) F J K <3 2 / ) F <> b/ 6 -../ 73 V3? m O ^>P A. =HD 43 O I 359

4 / / RA u d QJP / O ^>P 6H; g O v 43 O I DH5 2 4O I <3 2 = QJP 6H; g. ;T.[41] 9 4;Z, = A 73 / /} 4A/ / v 3 / 4 J2 *8'(") * -.0 *2 *89,: 34 ^>P F O CV/ 8 :, R/ 3 / /.. - / 43 4;O I 2 UJV 4;A { > G ;< P 6H 4;= JJP 4;= Q. ;A ZH.3 9?8 ;: / 5 4; FGH; P /, R/ v 43 4;O I 2. j = F R, Y ;> F F/../ Y R, F./ [40] R,, C;N 43 <3 A/ 3. V3 K 4 /?B:? } ^>P F Q FH; /. / /} H; B/ 4;D 3 A/ 6 A. 3 T -, A 4; F // W v 43 4;<3 2 A?:] :3 W / 4:/3 4E?B: V3 A/ ]. ED ; 4 / 4A, 6 F 9 3 T? } 6 43 <3 Y Y H; B/ 4;D 3 A/ 6 A...?B: 43 4;<3 4 / P 6H = 2 j.v / / 5 4; Z5 -, CA Y 2 K b S/ 53P8 v 43 4;O I 4.P 6H = JJP V3 0 O I F 9 W *M]: v 43 <3 / <K?B:.<3!3 4 / F }x 6Y 3 / : ,1 [1] Cooley Christopher G., and Robert G. Parker. A review of planetary and epicyclic gear dynamics and vibrations research, Applied Mechanics Reviews, Vol. 66, No. 4, pp. 1-15, [2] Özgüven H. Nevzat, and Donald Russell Houser. Mathematical models used in gear dynamics a review, Journal of sound and vibration Vol. 121, No. 3, pp , [3] Wang Jianjun, Runfang Li and Xianghe Peng, Survey of nonlinear vibration of gear transmission systems, Applied Mechanics Reviews Vol. 56, No. 3, pp , [4] Yang Jianming and Liming Dai, Survey of dynamics of planetary gear trains, International Journal of Materials and Structural Integrity Vol. 1, No. 4, pp , F./ C;?.: F //. M*K :@ 6D P ao ) Z5 4:/ 3 = 2 / 4 9 :@ }x 6-4 S/ QJP / O ^>P Y.[12] 4 / ]. d?8 / 9 4;O I F/ 2 4 / 2 P 19 F 2 P 4 F 6 M*K A.[32] 3/ / 43 4O I <3 / 6. ;^>P A F 4 0 JH,.. [22] g FGH; [33] F *89,: 34 *+,- S- X>, 02,Z2-7 *2 /.. nv 03 / K : 9 Z 6A A Q>?B:./ Qn 6 =K 4A/ nv1 :./ ;O Y 3 T? } Q. 3 / 43 O I DH5 2 P78 QO?.: 4 / K 9 V3 F S3 3 T? } F 9 W v 43 O I 4:/ 3 = <; Q.[9].: 4; 3 / Z0; 9 W 3 T? }.[34] WM 8 6 A A3 B/ 4;D O I <3 = Y Y 0 ^>P 2 -.[35]. Z5 S3 = =H: ` 3 T 4;<3 N >. ;1 B/ D 3 / 43 4;O I ~B 3 / ,) *8'(") -8 *2 *89,:?.: 2 ^@ / 5 4;^>P../ / R, R/ 43 4;O I 2 4 / / 5 4; O 4;^>P 6 ED ; 4 49/ Z5 43 O I DH5 A, - / F.[39-37] y3. 4: wo3. 3P ED ; 1G >,/, = Y ^ b A 6 / 4; :b 4;w P 6H = 9 4;Z, = y / 3/.[37] > 34 4 J2 *8'(") [+4 *2 *89,: v 43 4;O I 2 A, R/ -9 =.. O - : /./ P S3 /} 4A/ / v 43 < ;Z, R, 3 /.[40]. V ?.: 2 A 9?8 4;^>P 4 360

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