Mechanical Faigue and Load-Induced Aging of Loudspeaker Suspension Wolfgang Klippel, Insiue of Acousics and Speech Communicaion Dresden Universiy of Technology presened a he ALMA Symposium 2012, Las Vegas Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 1
Absrac The mechanical suspension becomes more and more complian over ime changing he loudspeaker properies e.g. resonance frequency significanly. This aging process is reproducible and he decay of he siffness can be modeled by accumulaing he apparen power supplied o he suspension par and using an exponenial relaionship. The free parameers of his model are esimaed from empirical daa provided by on-line monioring or inermien measuremens during regular power ess or oher kinds of long-erm esing. The idenified model can be used o predic he load-induced aging for music or es signals having arbirary specral properies. New characerisics are being inroduced which simplify he qualiy assessmen of suspension pars and separae mechanical faigue from he iniial break-in effec. Pracical experimens are performed o verify he model and o demonsrae he diagnosic value for selecing opimal suspension pars providing sufficien long-erm sabiliy. Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 2
Quesions addressed in he paper Why is he suspension he weakes loudspeaker par? How o measure he long-erm sabiliy of sof pars? How o consider he influence of he mechanical load on he aging? How o separae he early break-in process from faigue? How o predic he final loss of siffness? How o design and selec good suspension pars? Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 3
Road Map Inroducion problem, hisory Modeling of load-induced aging Measuremen echniques Pracical applicaion diagnosics Conclusion Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 4
Variaion of Suspension Siffness K versus Measuremen Time Performing a power es wih pink noise of consan ampliude break-in Siffness raio afer 1 h and 100 h power esing faigue R 100h K 100h K 1h Disadvanages of : measuremen resuls depends on he properies of he simulus assumes consan exciaion during power es can no be ransferred o oher simuli neglecs he slope of he siffness variaion accumulaed load Idea: Replacing ime by a quaniy describing he dosage of he mechanical load Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 5
Convenional Measuremen of Faigue S-N Curves Wöhler show he sinusoidal sress S and number of cycles N causing a failure Sress 1 1000 100000 number of cycles N before break Couresy by Coldwork.com canno be direcly applied o loudspeaker suspensions because we are ineresed in he siffness variaion before a faal break occurs Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 6
Loudspeaker Suspension The load-induced variaion of he siffness depends on he poenial energy emporarily sored in he suspension considering he nonlinear force-deflecion characerisic, energy dissipaed ino hea by losses in he maerial, frequency cycles of an alernaing simulus, accumulaed power ransferred o he suspension par during life ime of he suspension, oher unknown facors Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 7
How o define he Mechanical Load? 90 degree phase shif Apparen mechanical power P Fk v velociy v resoring force F k reacive power Apparen mechanical work performed on he suspension over life ime m W m P d Pm. 0 Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 8
Consan Load Model loss of siffness Measuremen Condiion: same simulus of consan ampliude during he power es Siffness of loudspeaker suspension versus accumulaed work W Kˆ W K W 0 K W K W N i1 C i 1 e W / w N=2 sufficien for mos cases i Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 9
1 s Characerisic: Relaive Aging Raio Definiion: a W K W 0 K W 100 N C i i1 % describes he progress of he ageing process in percen approaches 100 % for infinie work Derived Characerisics: K W 0 K W N i1 C i final value of siffness Kˆ W Kˆ K0 N C i i1. Toal loss of siffness during life ime V a N i1 C i K W 100% 0 a W 50 % 50% a W 90 % 90% Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 10
2 nd Characerisic: Break-in Raio Definiion: R b C1 C C 1 2 100% N 2 w 1 C 1 1 e W / w 1 C 1 C1 C 2 The simple model for N=2 is a good approximaion of mos suspension pars and separaes he breakin effec generaing he seep decay a he beginning of he aging process from he faigue causing a much slower decay a large values of accumulaed work W. w 1 describes he amoun of work required o complee 63% of he break-in phase. Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 11
3 rd Characerisic: Toal Faigue Loss Definiion: KW=0 V f C2 K W 100% 0 N 2. C 2 describes he percenage of siffness loss due o faigue If he break-in effec is dominan R b 100 % and faigue negligible V f 0 hen we find he relaionship W 90% 3W 50%. Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 12
Imporan Qualiy Crieria for assessing he sabiliy of suspension pars Crieria Opimal value Prioriy Minimal faigue V f =0% 1 Dominan break-in R b = 100 % W 90% 3W 50% 2 Slow faigue process w 2 >W a 3 a he momen no realisic! Toal aging raio V a =0% 4 Fas break-in process w 1 << W a 5 Nominal value for designing ransducers: K K W 0 C N 2 nom 1 Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 13
Influence of he Power Level P on Load-Induced Aging of he Suspension Measuremen Mehodology: 1. Selecing unis of he same ype wih similar properies 2. Applying a consan bu differen mechanical power P o each uni and measuring he variaion of KW 3. Fiing he consan load model o he KW characerisic of each uni K N i1 W / w k k, i W P C 1 e, i P P cons 1,..., J A se of ageing funcions KW measured a consan mechanical power P Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 14
Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 15 Varying Load Model 1 1 2 1 0 ˆ W K W K W K W K W K J J P P i g J d P g W 1,..., oherwise 0 f 1 1,..., 0 0 0 using muliple saes W accumulaing he power P above he power value P using he window funcion g Obecives: To consider he dependency on insananeous power level To predic he siffness variaion for any simuli
Calculaion of Siffness K for an Arbirary Power Profile P Measuremen Resuls dividing in power levels W 0 W 1 W 2 W 3 W 4 accumulaion in he work variables 0 W 0 g P d 0 1,..., J 1 if P P g 1,..., J 0 oherwise Kˆ W K W 0 J K W K 1 W K1W 1 2 Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 16
Measuremen Technology Par 1: Suspension Pars apparen mechanical power P dx K x x d displacemen sensor nonlinear sysem idenificaion Measuremen of spiders, surrounds and passive radiaors using a laser sensor and sysem idenificaion Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 17
Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 18 Measuremen Technology Par 2: Elecro-dynamical Transducer Sysem idenificaion based on volage and curren signals measured a he loudspeaker erminals apparen mechanical power emf k k u i v x Bl x x Bl x K v x x K v x F P Elecro-mechanical equivalen circui of he loudspeaker sysem
Long-Term Monioring of Loudspeaker Suspension M C model fiing m1 2 K W Kˆ W min. m m Long-erm monioring by looping a sequence of measuremens and pos-processing of he colleced daa. Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 19
Example: Poor Spider Suffering from Long-Term Faigue V a 50% half of he iniial siffness will disappear during he life-cycle of he suspension par. R b 50 % only half of he changes occur during he relaive shor break-in process requiring only w 1 = 0.02 kwh. V f 22 % high faigue raio causes a permanen bu slow decay of he siffness W 90% = 0.42 kwh 11W 50% high value of he accumulaed work is required o approach 90 percen of he final value K =0.9 N/mm prediced Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 20
Example: Loudspeaker A Time Work V a 30 % small aging raio R b 85 % mos of he variaions occur during he dominan break-in process W 90% 0.1 kwh small amoun of work is required o approach 90 % of he final siffness value. Levels are very similar low dependency on power level Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 21
Influence of Ambien Condiion Ambien emperaure and humidiy have a srong influence on he siffness K of he suspension The ambien condiion should be consan during he aging es Fiing algorihm provided wih sufficien daa colleced a high sampling rae can compensae for shor variaion Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 22
Conclusions Load-induced aging of he suspension maerial can be described by a dosage model using mechanical apparen work W as sae variable few aging parameers can be idenified from siffness K and apparen power P recorded in long-erm ess The siffness variaion K versus ime can be prediced for any simulus using he power profile P he model has been verified on a variey of suspension pars and assembled ransducers The model predics he final siffness K and he inensiy and dynamics of he aging process Shor break-in effec can be easily separaed from he long-erm faigue effec The siffness K nom found afer break-in is a useful nominal characerisic of he suspension par A low faigue loss of siffness expressed by V f reveals he long-erm sabiliy of he suspension Klippel: Mechanical Faigue and Aging of Loudspeaker Suspension, 2012, 23