DESIGN AND RESEARCH INTO THE NONLINEAR MAIN VIBRATION SPRING IN DOUBLE-MASS HIGH ENERGY VIBRATION MILLING

Transcription

1 0 X. Yang et al.: Desgn and research DESIGN AND RESEARCH INTO THE NONLINEAR MAIN VIBRATION SPRING IN DOUBLE-MASS HIGH ENERGY VIBRATION MILLING Xaolan Yang,* Jfeng Lu, Yajun Zhou Zhen Wang College of Mechancal Engneerng, Nanjng Insttute of Technology, 00, Chna Huanghe Scence and Technology College, , Chna ARTICLE INFO Artcle hstory: Receved: Receved n revsed form: Accepted: Keywords: Double - mass Vbraton mll Nonlnear Sprng stffness Vbraton ntensty Introducton Vbraton mll, also known as a reactor, s the typcal mass - energy converson equpment whch can convey vbraton energy nto partculate matter. Ths one pece equpment can carry out everythng from partculate matter refnng and reuntng to modfyng. Therefore, t has broad applcaton prospects n the ndustry [-]. Currently, the most commonly adopted man vbraton sprng desgn n a double - mass structure s employng an equal - ptch cylndrcal helx sprng whch s of a lnear type. The reason for ths s due to the easness of lnear sprng n desgn and producton. The lnear sprng stffness cannot be changed along wth the dynamc load, so lnear sprng cannot save more Abstract: Due to the shortcomngs of one - mass vbraton mll such as neffcency, hgh energy consumpton and bg nose, a double - mass hgh energy vbraton mll, n whch transent hgh vbraton ntensty s produced, s nvestgated by applyng the non - lnear vbraton theory. The nonlnear hard - feature varable-ptch sprng 0s used n the man vbraton system whch has the characterstc of the stffness that can be vared along wth the dynamc load. In ths way, the goals of operaton stablzaton and energy savng wll be acheved. Results from the feld test show that the effcency s obvously mproved,.e. a 8% ncrease n the vbraton ntensty, 0% decrease n energy consumpton and 4% decrease n nose. That verfes the correctness of the man vbraton system constructon. Ths system can be used by others as a reference desgn for ths feld. energy than that wth nonlnear sprng. Based on the exstng problems, the experence from actual producton and the new nonlnear technology theory and the constructon of nonlnear vbraton dryer and nonlnear vbraton screener, we come up wth adoptng the hard - feature varable - ptch cylndrcal helcal sprng n the vbraton mll desgn to take a full advantage of the nonlnear vbraton theory [-4]. The desgn of the nonlnear man vbraton system n double - mass hgh energy vbraton mll The structure of the double-mass hgh energy vbraton mll s shown n Fg.. The upper mass s * Correspondng author. Tel.: E-mal address: yxhh00@6.com

2 Engneerng Revew, Vol. 7, Issue, 0-6, 07. drven by the centrfugal force, whch s produced by the rotatng eccentrc block n the vbraton motor. The power s passed on to the grndng cylnder whch contans abrasves and stanless steel balls wth the dameter of 4, 6, 8 and 0 mm respectvely. The strong longtudnal vbraton s produced by the cylnder whch wll create mpact and frcton between materal and grndng medum lke steel balls. In ths way, the goal of materal smashng and fne grndng s acheved. The granularty and the productvty are controlled by adjustng the offset of the eccentrc block and granular composton of the grnd medum [5-7]. system becomes larger accordngly. Therefore, the power drawn from the vbraton source s reduced and the energy s therefore saved. It s especally sutable for varable-load system. The vbraton mll s just a varable load system because of the materal thrown up and down constantly. Accordng to reference [8], n the varable - load system, the natural frequency s set up as k m When mass m changes and stffness remans unchanged, the wll vary wth m. If the changes wth m, then mantans n a constant whch wll make the system have a more stable vbraton ampltude durng operaton. By adjustng preload of the nonlnear sprng, the operatng pont of the system can be set easly to ensure steady operaton near the pont of resonance. The exctng force wll be reduced whch mproves the system effcency by consumng less power and havng more powerful drve. k k. a. The choce of the nonlnear sprng The nonlnear sprng has many types and the common ones are lsted below [8, 0-]. Fgure. Structural representaton of the vbraton mll (. eccentrc block,. vbraton motor,. cylnder, 4. mountng plate, 5. nonlnear sprng, 6. lower mass, 7. vbraton-solaton sprng). Comparng wth lnear sprng, nonlnear sprng has the followng features [8-9]: The load and deformaton that change n nonlnear can ft nto the lnear relaton n terms of load and stffness. That s to say, when the load s small, the stffness of the system s small too, and when the load becomes larger, the stffness of the system becomes larger accordngly. Therefore, the power drawn from the vbraton source s reduced and the energy s therefore saved. It s especally sutable for varable-load system. The vbraton mll s just a varable load system because of the materal thrown up and down constantly. Load and deformaton that change n nonlnear can ft nto the lnear relaton n terms of load and stffness. That s to say, when the load s small, the stffness of the system s small too, and when the load becomes larger, the stffness of the ) Unequal-ptch cylndrcal spral sprng When the sprng s compressed to the pont when neghborng cols begn to contact wth each other, the characterstc lne becomes nonlnear. The stffness and the natural vbraton frequency all come to varable whch helps elmnate or mtgate the mpact of the resonance. It s used to support hgh-speed varable load structure. ) Taper spral sprng When the sprng s compressed to the pont when neghborng cols begn to contact wth each other, the characterstc lne becomes nonlnear. The natural vbraton frequency s varable. In comparson wth the varable-ptch compress sprng, the taper spral sprng ablty of ant-resonance s stronger. Because of ts compact structure and good stablty, t s usually used to support large load and absorb shock.

3 X. Yang et al.: Desgn and research ) Bellevlle sprng The Bellevlle sprng was nvented by J. Bellevlle, a French engneer, 00 years ago. The sharp of the Bellevlle sprng s a concal dsk. Compared wth tradtonal sprng, t has specal features lke large load, short stroke, lttle space, convenent use, easness to nstall and mantan, and t s less expensve and safer. It s wdely used n precson heavy machnery whch has small space and large load. Its maxmum compress stroke spans from 0 to 75%. Actng as the sprng to support the upper mass whose vbraton s large, the varable-ptch cylndrcal helcal sprng offers better features and s more sutable for beng applcable as the man vbraton sprng of the vbraton mll than other sprngs. b. Desgn of the nonlnear man vbraton sprng The overall performance of the vbraton mll s decded by the non-lnear desgn of the man vbraton sprng. The stffness of the sprng should be ncreased along wth an ncrease n the load. Meanwhle, the stffness of the sprng should be dentfed as drect lnear varaton because t has a lnear relatonshp to stablze the system. The ptch of the varable-ptch cylndrcal helcal sprng can be arranged n the order of small to large or can be placed large n the mddle and small n ends. The latter s used n ths desgn... Condton and assumpton of the feld processng Accordng to the condton n the feld, when the system s of no-load type, the total mass m ncludng the upper mass, vbraton excter and cylnder s 0 kg. The mass m of the materal s about 0 kg. So, the total of upper mass s 40 kg. In the feld there are 6 equal - ptch sprngs whose orgnal length s 0 mm. The length of the sprng wll be compressed to 6 mm due to the gravty of the upper mass (the deformaton of the length s 4 mm). The expected vbraton ampltude of the sprng wll be 6 and mm. The maxmum deformaton of the sprng s (4 + 6) mm when the sprng s forced by maxmum dynamc load (the maxmum vbraton dsplacement of the system). The deformaton of the sprng s 7 mm when the system s forced by the maxmum statc load, and the deformaton of the sprng s 4 mm when t s a not-load type. Supposng that the non-lnear characterstcs lne equaton of the man vbraton sprng s: F af bf c, () where, F s the load, N; f s the deformaton, mm... The nonlnear characterstc equaton Consderng the load condton and the abovementoned mass, when the system s of no - load type, the load on each sprng s as follows: m F 0 g 96 N. () 6 When the system s of full - load type, the load on each sprng s expressed as: ( m m ) g F 8.7 N. () 6 Consderng the addtonal load caused by the non - unform load on each sprng, takng non - unform coeffcent of load on each sprng s.4, accordngly, the maxmum statc load on each sprng s: F.4F 0. N. (4) max Takng 5 tmes of maxmum statc load as the maxmum dynamc load: F F N. (5) max 5 max One can fgure out that the ponts of the non - lnear curve s C (4,96), C (7,0.) and C (0, 600.5). After nsertng those nto Equaton (), load deformaton equaton of the nonlnear hard sprng wll be: 96 96a 4b c 0. 89a 7b c a 0b c. (6)

4 Engneerng Revew, Vol. 7, Issue, 0-6, 07. a.6 Soluton out b 69. c So, the load deformaton equatons of non - lnear hard characterstcs sprng can be obtaned as follows: F.6 f 69. f (7) The ftted curve s shown n Fg. based on Matlab smulaton []. Then, 8D 8 45 C F d 8 (8) 4 [ ] 647. MPa. ) The stffness p of the sprng wthout load Alterable-ptch cylndrcal screw pressure sprng has the same functon of the nlne combnaton of sprngs wth dfferent ptch; ts stffness s [8]: 4 4 Gd p nf 44.8 N/mm, (9) 8D 8 45 p where, s the shear modulus of the sprng; s the number of actve col of the sprng; s the stffness wthout load on sprng. Accordng to Equaton (7), the relatonshp between the stffness F of the sprng wthout load and the load F can be derved as: G n F Fgure. Load - deformaton dagram of nonlnear hard characterstcs sprng... Calculaton of the nonlnear sprng desgn ) The shear stress of the sprng Accordng to the known condton, alloy steel wre whch has been ol-quenched and tempered s selected as the materal for the sprng. The sprng parameters are as follows: Shear modulus G MPa ; Allowable shear stress; [ ] (0.4 ~ 0.40) (0.5 ~ 0.40) ~ 647. MPa, The mddle dameter of the sprng D 45 mm ; The dameter of the wre: d 8 mm ; The curvature coeffcent: C. 5. b df F. F 7. f (0) df.6 Accordng to the reference [8]: we can get, F F 76 N/mm, () f 6 0 P 44.8 n () F 76 Takng a col on each sde of the sprng as the support sprng, there are a total of 8 cols. ) The stffness and the bearng load of the sprng when the frst col was compressed near the second col

5 4 X. Yang et al.: Desgn and research The ptch of the sprng s n the order that the large s n the mddle and small at ends. When the the col or the( 6 )the col of the sprng s compressed, neghborng cols wll contact wth each other by load. The stffness of the rest F sprng s:. () ' ' F F P So t can be obtaned that: The ptch between the frst col and the second col can be gotten as: t d mm. (8) And so on, the spaces and ptches of result cols are lsted n Table. From Table, due to the maxmum load F max =600.5 N<5.85 N, the sprng wll have no contact wth each other. So the system wll not produce nose. Moreover, the deformaton and spacng of each col has the followng relatonshp: F F P , (4) f n ( n ). (9) F N/mm. (5) Accordng to Equaton (0), we can conclude that: F 77 N/mm. (6) The space between the frst col and the second col can be obtaned as follows: ( F0 F ) P (96 77).05 mm (7) Insertng data from Table nto Equatons () and (9), the revsed equaton has now a new form as follows: F (0) 7.7 f 99. f 0.. Three quarter col of both ends of the sprng was grounded nto a plane as a support col. The revsed total cols of the sprng s.5+6= Free heght s 95 mm, and t s n accordance wth the deal heght. The dameter of the sprng wre s 8 mm. All parameters of the nonlnear sprng have also been determned. The nonlnear sprng CAD model s shown n Fg.. Table. Man parameters for sprng desgn and calculaton No. Each col stffness P (N/mm) Stffness of the doublng up sprng F(N/mm) Loads of the doublng up sprng F (N) Space (mm) Ptch t (mm)

6 Engneerng Revew, Vol. 7, Issue, 0-6, Fgure. The nonlnear sprng CAD model. Accordng to Table, when the load s normal, the system deformaton s ncreased along wth an ncrease n the system load. Even when the load suddenly reaches a certan level due to two or more sprng cols contactng wth each other, the system exhbts hardly any more deformaton as a result of the load changng. It shows that the sprng carres clearly non-lnear hard-feature characterstcs, whch s good for mprovng the system ampltude stablty. Accordng to Equaton (0), load-stffness dagram can be drawn as Fg.4, and we see that the load-stffness dagram s nearly a straght lne, whch means that the system stffness s lnear along wth the load. The system s energy savng and stable. F/N K/(N/mm) Fgure 4. Load - stffness dagram of nonlnear hard characterstcs sprng. From the analyss of deformaton energy of the sprng, the rate of sprng deformaton energy can be gotten [8]. U U F () where, U s deformaton energy of lnear equal ptch sprng; s nonlnear unequal sprng deformaton energy. Accordng to the above calculaton, the pretghtenng force of the lnear sprng s 4.05 tmes larger than the force of the nonlnear sprng. In ths case, the pre-tghtenng force of the nonlnear sprng s small so that t can be easly used to adjust sprng preloadng amount n order to change the frequency of the machne. Thus, the goal of stablzng the systems and avodng resonance has been acheved. Conclusons U F The varable ptch nonlnear sprng s used n the man vbraton system of the vbraton mll whose stffness can change along wth the load to meet the requrements of dynamc load. A vbraton system whch avods resonance, works stable and saves energy can be obtaned. Operatons n our vbraton mll prove that the vbraton ntensty was ncreased by 8%. Meanwhle, the nose and energy consumpton was reduced by 4% and 0% respectvely, whch verfes the correctness of the man vbraton system desgn. Ths desgn acts as a good reference source for other researchers n ths feld.

7 6 X. Yang et al.: Desgn and research Acknowledgements Ths project s supported by Natonal Natural Scence Foundaton of Chna (Grant No. 575), Key Scentfc and technologcal projects of Henan (4008) and Scentfc and technologcal projects of Zhengzhou Cty (00797) as well as by college students of scence and technology nnovaton projects n Jangsu Provnce ( Z). References [] Xv, B., Wang, S., L, S.: Dynamc analyss and smulaton study on the vbraton mll, Chnese Journal of Mechancal Engneerng, 008, 44(), [] Bernotat, S.: Vrbaton mll results n the lght of stress ntensty and number of stressng eventa, Mneral Processng, 004,74, 9-. [] Feng, R.: The research progress of super fne crushng machnery, S P & BMH Related Engneerng,008, 5, -7. [4] Zhang, S.: Oversze vbraton mll and ts applcaton, Metallurgcal ndustry press, 007. [5] Lou, J.J., Zhu, S.J., He, L. et al.: Applcaton of chaos method to lne spectra reducton. Journal of Sound and Vbraton, 005, 86 (), [6] Lu J., Yang, X., Zou, J.: Research on new technques of superfne grndng for superhard powder by hgh vbraton ntensty, Chnese Journal of Mechancal Engneerng, 008, 44 (7), [7] Yang, X., Lu, J., Zhu, D.: Mult-level partal block monocular vbraton, Chna, , 0, [8] Zhang, Y.:.Sprng.manual, Bejng Machnery Industry Press, 008. [9] Zhang, Y.M., Wang, S., Lu, Q.L. et al. Relablty analyss of mult-degree-of-freedom nonlnear random structure vbraton systems wth correlaton falure modes. Scence n Chna Seres E-Technologcal Scences, 00, 46 (5), [0] Zhang, Y.M., Lu, Q.L., Wen, B.C.: Dynamc research of a nonlnear stochastc vbratory machne. Shock and Vbraton, 00, 9 (6), [] Bandera, N., Braut, S., Žgulć, R.: Desgn of the rotor dynamc test bed wth actve magnetc bearngs. Engneerng revew, 009, 9,, [] Beerle, T.: Usng Matlab for Vbraton Measurements, Sound & Vbraton, 007, 4:5, 6-8.