A Practical Calculating Method on Spring Characteristics and Stresses of Coiled Wave Springs Hideki TAKAHASHI, Naoko KAWAMURA, Takahiko KUN

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1 35 A Practical Calculating Method on Sring Characteristics and Stresses of Coiled Wave Srings Hideki TAKAHASHI, Naoko KAWAMURA, Takahiko KUNOH Coiled wave srings (CWS) are considered as multile layered waved washers. They are light but owerful in limited saces. In recent years, CWS have been alied to clutches of automobiles and exected to be alied to other uses. The formulas on the sring rates and stresses of CWS have been resented by an American sring maker of Smalley Steel Ring Comany, Nishio, and Jaan Sring Manufacturers Association (for short, JSMA). But none of them are ractical, because the accuracy is not enough. Moreover the derivations of the formulas are not clear in the case of Smalley and JSMA. It has been observed that CWS show nonlinear sring characteristics in large deflection, however, the cause has not been made clear. In this research, sring rates and stresses for CWS are analyzed theoretically. A cause of the nonlinear sring characteristics is made clear, too. Then emirical formulas on the sring rates and stresses are derived by comaring the theoretical results with exeriments and FEM analysis. Key Words : Coiled wave sring, Nonlinear sring, Sring characteristics, Stress analysis, FEM analysis 1 CWS Fig. 1 CWS 1 CWSSmalley 3) JSMA 5 CWS 678 CWS CWS FEM Fig.1 Coiled wave sringcws b mm t mm D mm R mm Keio University

2 36 ID mm OD mm H mm h 1H/nt mm N 1 n l 1/Fig. 6 mm r Fig. 6 mm Fig. 6 rad Fig. 5 rad /N rad CWSFig. Table 1 CWSTable Table JSMA CWS 1Fig. 3 JSMA Smalley SmalleyJSMA P N 1P/N N M b Nmm M t Nmm I mm Z mm 3 J 9 mm U b 1/ Nmm U t 1/Nmm CWS mm b 1/ mm B 1 mm t 1/ mm T 1 mm k N/mm k max N/mm k min N/mm 1 MPa 1max MPa b MPa t MPa k s a,b,c 3 E GPa G GPa v Fig.3 Fig. Test srings Load-deflection diagramcws 1 Test sring No Material of CWS High carbon steel wire SWRH Young's modulus EGPa Shear modulus GGPa Width bmm Thickness tmm Mean diameter of coil Dmm Free length Hmm Number of waves / turn N Active coils n Table Table 1 Secification of test srings Stainless steel SUS Formulas on sring rates and stresses of CWS 1 k min 1 10 N

3 CWS Fig. 1/ / M b1 M b M b1 cosx 1 Fig. 5/ CWS /Fig. 5 M t M t R1cos U t J U b1 0 M R 3 3 sin t Rdsin 9 GJ 8GJ Jbt t tanh b 3 5 b t 10 M b coslrsinrsin1cos U b1 U b 1 l U b1 Mb1 l 3 cos dx 3 EI 0 EI 1 U b Mb rd EI 0 r lcosr sin rlcosr sincos1 8EI rsin r t l x Fig. b1 b U b1 b1 l 3 cos 6EI 5 Fig. Plane bending of 1/ wave segment b U b r EI lcosr sin rlcosr sincos1 rsin 6 1 B B b1 b r rlcosr l 3 cos sin rlcosr sin EI 3 rsin 3 cos1 7 R Fig.5 b Torsion of 1/ wave segment

4 38 Fig. 5 t U R 3 t t 3 sin sin GJ 1 T t R 3 GJ 71CWS CWSP 3 sin sin n B T 13 PN 1 P N k n B T N 1 l 3 cos n rlcosr sin EI 3 rsin rlcosr sincos1 R 3 3 sin sin 15 GJ 15lr Fig lr l r Fig. 6 r sinl cosr l Rr sin cos CWS 0cossin Fig N k 3 1 Rr sin cos n EI cos 3 JSMATable CWSTable Table JSMA CWS 1 Fig. 7 Table SmalleyJSMA Fig. 7 Fig. 7SmalleyJSMA cos1sin0 17 N n R 3 3 EI 19EIN 3 nd 3 16Ebt 3 N 18 3 nd 3 Fig. r l r sinl cosr Fig.6 1/ wave segment in lane r h Fig.7 StressLoad diagramcws 1

5 39 M b M b coslrsinrsin1cos lcosrsin 19 b M b b P Z 3lcosrsin 0 bt N Fig. 6lr R R 3P 3D 1 bt N bt N b P SmalleyJSMA Table Fig. 5/ M t 8 M t R 1cos t 1 M t PD1 t 3 bt bt N CWS 1 b b 1 t b CC-33A UCAM-0PC UCS10A CWS 13 3 a b c 1 1 CWS CWS 5 E 1 1 a c 1 1 a b b c 6 1 tan 1 b a c 7 a c 5FEM MARC MENTAT 005r Fig. 8CWS 1CWS CWS 3 CWS CWS 5 9/7CWS Fig. 8a Linear contactfig. 8b Point contact D 1 b P 5 bt N.1 HTC-A0K 5CWS 1 5. KFG-1-10-D17-11L1M 0/5/ mm5mm 10 k s.1 Fig.8 FEM analysis models

6 0 CWSFig CWS 15 FEMFig. 10 Linear contactfem Linear contactfem DRAGONI 1 CWSFig. 11 Linear contactpoint contact Fig. 11 FEMFig. 8b Fig. 10FEMLinear contactpoint contact Point contact Point contactlinear contact Linear contact 18Point contactfig. 1Linear contact CWS 15 FEMFig. 10FEM Fig. 13 Linear contactpoint contact FEM Fig. 10Linear contactpoint contact FEM FEM CWS Fig.9 Loading and constraint condition of FEM analysis model max 16Ebt3 N 3 nd Ebt 3 N min nd Point contactlinear contact CWS 1CWS CWS 550 CWS CWS 335 1ND ND/bCWS Fig.13 Fig.11 Point contact of CWS Distribution of maximum rincial stress

7 1 Fig.10 Sring characteristics and stresses of CWS

8 Fig.1 Formulas on sring rates and stresses of CWS

9 3 Fig max 7 CWS CWS CWS 3D bt N P CWS FEM Smalley Steel Ring ComanyWave/Comression SringsCatalog No.WS No JSMA SB No No Wang C. T Budynas Richard G.Advanced Strength and Alied Stress Analysis McGRAW-HILL KOGAKUSHA DRAGONI E.Journal of Strain Analysis for Engineering Design

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