Collision Energy Dissipation Calculation and Experiment for Impact Damper with Particles

Transcription

1 Sesors & Trasducers o 59 ssue Noeber 3 pp Sesors & Trasducers 3 by FSA Coso Eergy Dsspato Cacuato ad Experet for pact Daper wth Partces XAO Wag-Qag L We Departet of Mechaca ad Eectrca Egeerg Xae Uersty Xae 365 Cha Schoo of Mechaca Egeerg Uersty of Scece ad Techoogy Bejg Bejg 83 Cha Te: Receed: 7 Noeber 3 /Accepted: 9 Noeber 3 /Pubshed: 3 Noeber 3 Abstract: The suato ode of pact daper wth partces was estabshed based o the theory of coso eergy dsspato to study the dspaceets ad eoctes of the adjacet partces before ad after the coso betwee the partces ad the daper wa The partce paraeters were studed experetay such as the uber of partces the desty of partces the sze of partces the recoery coeffcet of grauar atera ad the ta eocty of daper whch hae a great fuece o the dapg characterstcs The expereta resuts show good agreeet wth the cacuato predcto whch erfes the proposed suato ode The resuts hae show that the pact daper wth partces ca effectey reduce the ketc eergy of structure ad offer cosderabe dapg effect Ths suato ode w prode the egeerg appcatos wth the theoretca gudace ad desg crtera Copyrght 3 FSA Keywords: pact daper Partces Coso Eergy dsspato Expereta study troducto Partce dapg techoogy s a passe brato cotro techoogy The ketc eergy of structura syste s dsspated through the coso ad frcto betwee the partces ad the daper so as to suppress the brato ad the ose [-] Ths brato dapg techoogy has a ot of adatages for exape spe structure ow costs sa odfcato of orga structure ow addtoa ass rearkaby prog the dapg rato of syste appcabe for harsh eroet wthout dapg perforace degradato oer te etc [3-4] Therefore t has wde prospect of egeerg appcatos the feds of aerospace autoobe ad precso achery etc [5-7] Ths cocept of o-obstructe partce dapg (NOPD) was put forward frsty 99 ad had bee successfuy apped to the turbe bades [8] Howeer the echas of brato eergy dsspato the partce daper s ery copex ad oes the echaca behaor of partces eda whch has hdered the appcato of the partce dapg Recety ay studes hae bee carred out based o the partce dapg ad the partcuate atter dyacs The research ethods are ay dded to the theoretca suato ad the experet [9-4] The theoretca ethods ay cude the dscrete eeet ethod (DEM) the coso theory the regresso desg ad the optzato desg etc ad ay ew theores ad ethods are beg troduced to the research of partce dapg [5-9] DEM s used to suate the dyacs of partce syste cotactg wth each other by estabshg the echaca ode of sge partce [-3] Howeer durg the uerca coputato because the oear cotact characterstcs of partces t the te-step of cotact paraeters DEM s usutabe for ay arge suato of the oear cotact ode wth 44 Artce uber P_RP_9

2 Sesors & Trasducers o 59 ssue Noeber 3 pp partce uber ore tha 7 [] Howeer the egeerg appcatos the partce uber the daper s usuay ore tha 8 whch t the appcato of DEM the egeerg fed Accordg to the preset research of echas ad the defects of the exstg ode [4-6] we estabsh the coso ode based o the oeet of aog the partces betwee the partce ut ad the daper boudary ad aog the adjacet partces after codg wth the daper wa The eergy ethod s used to cacuate the eergy dsspato factor whch s copared wth the expereta resuts Ths paper estgates the partce paraeters betwee the partce group ad the daper such as the uber of partces the desty of partces the sze of partces the recoery coeffcet of grauar atera ad the ta eocty of coso whch hae a great fuece o the dapg characterstcs The suato ode of pact daper wth partces whch characterzes the oear dapg w be epoyed the egeerg desg Eergy Dsspato Mode of Coso for Partces Durg the eergy dsspato of pact daper wth partces whe the aptude of the exctato force s ore tha /5 of syste graty [5] the reate oeet aog the partces s oet so that the partces are separated At ths te the brato eergy of syste s dsspated ay by the coso aog the partces ad betwee the partces ad the daper wa Ths paper w estabsh the eergy dsspato ode of pact daper wth partces based o the coso theory [ 6 6] Coso Mode Aog the Partces order to be coeet for aayss ad cacuato t s assued that the partce s the sphere ut The aayss of teracto aog the partces requres judgg the reatoshp of partce postos at dfferet oets The oca coordates are estabshed Fg t s assued that the asses of partce ad partce are respectey ad the radus of partce s r ts posto coordates are ( ) x y z ts eocty s ( ) x y z ad the radus of partce s r ts posto coordates are ( ) x y z ts eocty s ( ) x y z The cotact codtos of partce ad partce ca be expressed as ( ) ( ) ( ) d x x + y y + z z < r + r () Before the cosos happe the eoctes of partce ad partce oca coordates are respectey ( ) ad ( ) t s assued that axs cocdes wth the coectg e for ceters of two partces oca coordates ad cosα cos β cosγ are respectey drecto cose of axs The correspodg reatos of the oeet eocty of partce oca coordates ad orga coordates before the coso are x cosα + y cos β + z cosγ () cos β cosα x y cos α + cos β cos α + cos β cos α cosγ cosβ cosγ x y + cos α+ cos β cos α+ cos β + cos α+ cos β z (3) (4) After the cosos the eocty copoets of partce ad partce oca coordates are respectey ( ) ad ( ) Hece the equatos accordg to the oetu theore are wrtte as (5) The ora Newto recoery coeffcet at the cotact pot of two spheres s ge by e (6) Fg Coso coordates of two partces The frcto coeffcet λ oca coordates s the rato of puses two drectos whch s 443

3 Sesors & Trasducers o 59 ssue Noeber 3 pp wrtte as equatos becoe λ λ The oetu + λ + λ + λ + λ (7) The frcto coeffcet λ ad λ s defed by sg λ sg( ) sg λ sg( ) where syboc fucto sg[] s expressed as x sg[ x] x t s assued that the ector { } T { } T The eocty equato oca coordates before ad after two partces code ca be wrtte as Coso Mode betwee the Partces ad the Daper Whe the partces oe ecosed space addto to the coso aog the partces they are aso subjected to the restrcto of the daper wa ths paper the cotact betwee the partces ad the daper wa s equaet to the ass-sprgdapg syste t s assued that the ass of partce s ts eocty s ad the cuded age betwee the partce ad the daper wa xoy pae s α durg codg wth the daper wa The coso process s dded to two stages e copresso stage ad recoery stage [4] The eocty of partce eag away fro the daper wa s t after the coso The scheatc represetato of coso s ge Fg [ ] [ ] [ ] A B C (8) Where atrx A ad B are [ A] λ λ [ B] e e λ λ After the adjacet partces teract oe partce w chage to a ew eocty ad posto The cotue codg wth other partce ad chage ts eocty ad posto aga Whe the coso eergy dsspato of pact daper wth partces s cacuated the cyce repeats ad the syste eergy s cotuay dsspated Therefore after oe te step t ew posto coordates of partce are ( x t + x) t x t x+ ( y t + y) t yt y+ ( z t + z) t z t z+ (9) Fg Coso ode of partces ad daper wa ) Copresso stage The eocty of partces before the coso s dded to x y ad z respectey the drecto of taget pae ad ora pae Accordg to the puse theore we obtas where x c x x y y c cx c cy z cz y ad c () z c are the eocty copoets of partce taget pae ad ora pae whe the copresso stage fshes; cx ad cy are the puse copoet taget pae ths stage; cz s the puse copoet ora drecto Defe the tageta dyac frcto factor as µ + cx cy cz 444

4 Sesors & Trasducers o 59 ssue Noeber 3 pp c The eocty copoet τ of partce taget pae whe the copresso stage copetes s ge by x + y z () c τ ( ) ( ) µ ) Recoery stage recoery stage the coso puse copoets taget pae ad ora drecto are rx ry ad rz ad the puse equatos becoe ad the partce s statoary after the partce codes wth the daper wa Ad the eocty of the partce s after the partce codes wth the partce Defe the recoery coeffcet of two partces as e Accordg to the oetu theore s wrtte as ( + e ) /( + ) (5) x x y y z c t rx c t ry t rz () The ora recoery coeffcet s ge by e z t z The posto of partce ut betwee the partce ad the daper wa after the coso s ( xt yt z t ) The eocty copoet t τ of partce taget pae whe the recoery stage copetes s ge by x + y z + e (3) tτ ( ) ( ) ( ) µ After oe te step t ew posto coordates of partce are ( x + x t) xt x + t ( y + y t) yt y + t (4) zt zw + r where z w s the ora coordate of partce ut o the daper wa 3 Coso Mode of Adjacet partces after Codg wth the Daper Wa After the partce codes wth the daper wa the coso ode of other partces s show Fg 3 For coso of two partces the asses of partce ad partce are respectey ad t s assued that the eocty of the partce s Fg 3 Coso ode of utpe partces Sary the eergy of partce group the daper s trasferred fro eft to rght After the frst partce codes wth the daper wa t codes wth the secod partce; after the secod partce codes wth the frst partce t codes wth the thrd partce ad the ke t the rghtost partce So the eocty after the - partce codes wth the partce s [ + e( ) ] + Through the recurso we obtaed - ( ) + (6) [ + e ] (7) t s assued that the eoctes of daper before ad after the frst partce codes wth the daper are respectey ad The recoery coeffcet e betwee the frst partce ad the daper s ge by - So the eocty becoes e (8) ( ) + e + [ + e ] [ ] (9) Fro the aboe equato after the coso betwee the partce group ad the daper the 445

5 Sesors & Trasducers o 59 ssue Noeber 3 pp eocty s reated to the uber of partces the ateras of partces the eocty before the coso ad the ature of daper Whe the oto status of partce ut chage t w retur to the aboe cacuato process eter to the ext te step ad cacuate the oeet creet of partce uts aga Through the terate coputato the rea-te trackg of the oeet of each partce ut ca be doe 4 Coso Eergy Dsspato Factor For the coso of ay partce [3 4] t s assued that the eocty before the coso s ad the eocty after the coso s t Accordg to the aw of coserato of oetu the eoctes of ( -) t ad t are wrtte as ( ) + e [ ] ( ) t ( ) ( ) + ( + e) [ ] - t ( ) + () The eergy dsspato factor coud be cacuated by the foowg equato [ + ] [ + ] η ( ) ( ) t t π [ ( ) + ] 3 Coso Eergy Dsspato Mode Aog the Partces 3 Expereta Equpet () A cube daper s used experet whch the atera s 4Cr egth Wdth Heght s 7 4 ad the wa thckess s 4 The scheatc dagra ad photographc pcture of the pact daper wth partces are show Fg 4 The test syste s coposed of the sga acqusto aayzer of N38C CP acceerato sesor of N98 acceerato ad force copoud sesor of CL-YD-33 ad eectroagetc excter of JZ-5 etc The uber of sapg pots wth each brato cyce was ot ess tha 4 ad the experet was repeated 5 tes uder eery ta codto 3 Resuts ad Aayss accordace wth the theoretca ode the reguar sooth sphere partces are used wth 3 daeter ad 9 % fg rate The test ateras are the auu oxde stee ad tugste carbde wth the destes of 34 g/c g/c 3 ad 83 g/c 3 Fg 5 copares theoretca ad expereta resuts of the reatoshp of daper eergy dsspato factor s acceerato uder dfferet destes of partce Fro Fg 5 the eergy dsspato factor of partces aog wth the acceerato s oear Due to ess desty the sae oue the eergy dsspato caused by eastc coso of auu oxde partces s ess ad ts dapg effect s aso ess Wth the crease of partce desty the eergy dsspato caused by eastc coso becoes arger The dapg effect of tugste carbde partce s the ost cosderabe t woud appear fro the data preseted Fg 5 that the theoretca ad expereta resuts are good agreeet Ths proes the ratoaty for eergy dsspato ode of pact daper wth partces addto the eergy dsspato aues of the uerca suato are sghty ess tha the expereta aues Ad the reaso for such deato s that the uerca suato oy cosdered a echas of eergy dsspato e coso howeer ay echass of eergy dsspato ke the coso the frcto the ose the adheso are cuded the experet Eergy dsspato factor ( ) Acceerato (g) Fg 4 The experet syste Fg 5 The effect of acceerato ad desty of partces o eergy dsspato factor 446

6 Sesors & Trasducers o 59 ssue Noeber 3 pp The effect of acceerato ad partce sze o the eergy dsspato factor s show Fg 6 The test atera s the stee t ca be see fro ths pot that the eergy dsspato factor of partces w aost crease wth the crease of the acceerato Wth the crease of partce sze fro 5 to 4 the eergy dsspato factor becoes arger howeer whe the partce sze s ore tha 4 t begs decreasg So for the stee partce too sa or too arge partce sze w both ot obta good dapg effect ad the eergy dsspato of 4 stee partce s the best ths daper The reaso for such tur s that whe the partce sze s too sa the adheso aog the partces w reduce the dapg effect; whe the partce sze s too arge the partce uber of oed the coso decrease whch w aso reduce the dapg effect Therefore the desg of dapers choosg a proper partce sze s ecessary ad the opta partce sze ca be detered by ths suato ode Partce eocty (/s) e e4 e Fg 7 The eocty dstrbuto after coso uder dfferet recoery coeffcets 6 5 Partce uber 5/s 5/s 3/s Eergy dsspato factor ( ) Partce eocty (/s) Acceerato (g) Fg 6 The effect of acceerato ad partce sze o eergy dsspato factor After the cosos of the outer ayer of partces ad the daper copete the reatoshp betwee the eocty of adjacet partces ad the recoery coeffcets s show Fg 7 The recoery coeffcets of coso aog the partces are respectey 4 6 Fro the Fg 7 t ca be obsered that after codg wth the daper the oeet eoctes of the adjacet partces reduce rapdy The ow recoery coeffcets aog the partces resut a faster reducto of eocty a arger eergy dsspato ad a greater dapg effect Whe the oeet s trasferred to the seeth adjacet partces f the recoery coeffcet e s ess tha 4 the eocty w reduce to about 5 % ta eocty after coso So the eocty atteuato of partces s ery obous The brato aptude of daper has great fuece o the dapg effect of pact daper wth partces The reatoshp betwee the eoctes of the adjacet partces ad the brato aptude of the daper after the outer ayer of partce codes wth the daper s show Fg 8 Partce uber Fg 8 The eocty dstrbuto after coso uder dfferet brato aptudes The brato eoctes of the daper are take as 5 / s 5 / s 3 / s t ca be see fro ths pot that the arger aptude of brato eocty of daper w resut a hgher eocty of adjacet partces but a faster eocty atteuato of partces t dcates that the eergy dsspato effect of partce group w greaty crease whe the brato aptude of the daper crease Whe the oeet s trasferred to the eghth adjacet partce a the partce eocty ca reduced to about 3 % ta eocty after coso The eergy dsspato dstrbuto s the recoery coeffcet of partce ad the ta eocty of daper s show Fg 9 t shoud be oted fro ths pot that wth the ta eocty of daper rsg the eergy dsspato of partces creases ad the eergy atteuato becoes faster at hgher eocty t dcates that wth ore oet brato the uber of partces oed the coso creases ad the eergy dsspato effect of s ehaced Wth the recoery coeffcet decreasg the eergy dsspato effect s ehaced the pact daper wth partces 447

7 Sesors & Trasducers o 59 ssue Noeber 3 pp Eergy dsspato (J) Recoery coeffcet eocty (/s) The resuts show that the pact daper wth partces ca effectey reduce the ketc eergy of structure hae a apparet dapg effect Ths suato ode w prode the egeerg appcatos wth the theoretca gudace ad desg crtera Ackowedgeets The authors woud ke to express deep grattude to the Natoa Natura Scece Foudato of Cha (No 5538) ad Bejg Natura Scece Foudato (No 33) for faca support for ths research project Fg 9 aratos of eergy dsspato wth recoery coeffcet ad ta eocty 4 Cocuso Ths paper estabshes a eergy dsspato ode of pact daper wth partces based o the coso theory Through the experet the paraeters of partces are further researched to such as the partce uber the partce desty the partce sze the recoery coeffcet of grauar atera ad the ta eocty of daper whch hae a great effect o the dapg characterstcs The eergy dsspato factor of partces aog wth the acceerato s oear The theoretca ad expereta resuts are good agreeet The eergy dsspato aues of the uerca suato are sghty ess tha the experet Ad the reaso for such deato s that the uerca suato oy cosdered a echas of eergy dsspato e coso howeer ay echass of eergy dsspato ke the coso the frcto the ose the adheso are cuded the experet Wth the crease of partce desty the eergy dsspato caused by eastc coso becoes arger The dapg effect of tugste carbde partce s the ost cosderabe Too sa or too arge partce sze w both ot obta good dapg effect ad the eergy dsspato of 4 stee partce s the best ths daper Therefore the desg of dapers choosg a proper partce sze s ecessary ad the opta sze ca be detered by ths suato ode After codg wth the daper the oeet eoctes of the adjacet partces reduce rapdy The ow recoery coeffcets aog the partces resut a faster reducto of eocty ad a greater dapg effect Whe the recoery coeffcet e s ess tha 4 the eocty atteuato of partces s ery obous The arger aptude of brato eocty of daper w resut a faster eocty atteuato of partces The eergy dsspato effect of partce group w greaty crease whe the brato aptude of the daper crease Refereces [] Ba X Shah B Keer L Wag Q Surr R Partce dyacs suatos of a psto-based partce daper Powder Techoogy 89 9 pp 5-5 [] L K Darby A Experets o the effect of a pact daper o a utpe-degree-of-freedo syste Joura of brato ad Cotro 5 6 pp [3] Fred R D Kra K Partce pact Dapg Joura of Soud ad brato 33 pp 93-8 [4] Saek M Aaytca study of ut-partce dapg Joura of Soud ad brato 8 5 pp [5] Lu Z Lu X L Masr S F Studes of the perforace of partce dapers uder dyac oads Joura of Soud ad brato 39 pp [6] Duca M R Wassgre C R Krousgr C M The dapg perforace of a sge partce pact daper Joura of Soud ad brato 86 5 pp 3-44 [7] Boy M S Day P Ba X M Costructo ad characterzato of a partce-based thrust Joura of Soud ad brato 36 9 pp [8] Paossa H No-Obstructe partce dapg tests o auu beas Proceedgs of the Dapg Coferece Sa Dego CA 99 pp 3-7 [9] Guyoar D Bade A Noear se-passe ut-oda brato dapg: a effcet probabstc approach Joura of Soud ad brato 94 6 pp [] Xe Zh-Y Feg Ju-Xao Nuerca aayss of behaor of acte ayer rotary ks by dscrete eeet ethod Joura of Cetra South Uersty 3 pp [] Je A R Geoffrey R T Aptude Depedet Behaour the Appcato of Partce Dapers to bratg Structures Proceedgs of the 46 th AAA/ASME/ASCE/AHS/ASC Structures Structura Dyacs & Materas Coferece 5 pp 8- [] Laarque C H Ja O Moda aayss of echaca systes wth pact o-eartes: tatos to a oda super posto Joura of Soud ad brato 35 pp

8 Sesors & Trasducers o 59 ssue Noeber 3 pp [3] Boy M S Jerey J N Ke R K Se-acte partce-based dapg systes cotroed by agetc feds Joura of Soud ad brato 33 pp 8-93 [4] Oso S E Deeopet of a atheatca ode to predct partce dapg Uersty of Dayto Oho [5] Ku S M Partce pact dapg: fuece of atera ad sze Texas A&M Uersty 3 [6] Mchae Y Y Deeopet of aster desg cures for partce pact dapers Pesyaa State Uersty 3 [7] Je A R Toso G R Aptude depedet behaor the appcato of partce dapers to bratg structures Proceedgs of the 46 th AAA/ASME/ASCE/AHS/ASC Structures Structura Dyacs & Materas Coferece 5 pp [8] Sh Chog Wag Sheg-Na Lu L Mesoechaca suato of drect shear test o outwash deposts wth grauar dscrete eeet ethod Joura of Cetra South Uersty 3 pp 94- [9] Ryzhko D brato daper for eta cuttg The Egeer s Dgest 4 3 pp 46-5 [] Mshra B K Murty C R O the deterato of cotact paraeters for reastc DEM suatos of ba s Powder Techoogy 5 pp 9-97 [] Wu L Qu Fu-Zheg Dscrete eeet suato of echaca characterstc of codtoed sads earth pressure baace shed tueg Joura of Cetra South Uersty of Techoogy 6 9 pp 8-33 [] Gog Guo-B Zha Xao-Xog DEM suato of quefacto for cohesoess eda at gra scae Joura of Cetra South Uersty 9 pp [3] Che Ju Wag L-Bg Huag Xao-Mg Mcroechaca odeg of asphat cocrete fracture usg a user-defed three-desoa dscrete eeet ethod Joura of Cetra South Uersty 9 pp [4] Mao K Wag M Y DEM suato of partce dapg Powder Techoogy pp [5] Lu W Toso G R Je A R The dyac characterzato of dsk geoetry partce dapers Joura of Soud ad brato 85 5 pp [6] Nase S T argas W L Abata A A Dscrete characterzato toos for cohese grauar atera Powder Techoogy 6 pp Copyrght teratoa Frequecy Sesor Assocato (FSA) A rghts resered ( 449