On-Line Preload Monitoring for Anti-Friction Spindle Beatings of High-Speed Machine Tools

Catastroic andpremate bearing failure caused byexcessive thermally-induced bearing prekad isamajor design problem for spindle bearings ofhigh-speed machine tools. Duetoalack ofalow costandeasytomaintain on-line preload meang tecmique, the traditioal solution istolimit themaximumspiespeed andthe initial bearing preload. Thissolution isincompatbe withtheneed toincrase macining productivity, whichrequirs increasing the spindle speed, andprduct quality (suface finish, dimensional accuracy), which requres incasing (or atleast notdecrasing) the preload tokeepthespindle system stiff. This paperproposes asolution that iscompatible with increased productivity andquality. A dynamic state observer hasbeen developed based onapreload model derived fromphysical lawsof heat transfer andthermoelasticity toestimate thespidle bearing preload vialowcostthermocouples attached tothebeaing outer ring andthespindle housing. A systematic prcedure todetermine the observergains isdeveloped toaccount formodeling errors, unknown parameters, nonhnearities, andmeasurement noise. Themodeling errors arepardcularly significant inthis problem because factors like bearing skidding, wear, andlubricant deterioration arenoteasily modeled, andtheobservermust bedesigned tobeinsensitive tothem. Aunique modeling error conpensator idea isintrouced tonull-ot themodeling errors. Thepreload observer hasbeensuccessfuly validated ontwodifferentbearing configurations for awide range of speeds andrunning conditions. Theresults showta themodelbased monitoring technique that combines themeasurements ofthe outer ring/housing temperare andarobust state observer canbean effective andlow-cost solution forpreload monitoring inhigh-speed machine tools. NOMENCLATURE A System matix ofast-space model B Input matrix ofastate-space model C Output matrix ofasrae-pace model 4123Scalar coeffient eQ) Theerror dynamics .Ax,)Geralsysmstate functio FpO nitial prdadacting ononerollmg elment (N) Fj,Resultant axial peoal (N) F, Tbermally iluced prekod (N) g0 Obwrvergin funtk G System inral noise coupling function h(.) System opufunction K, Ptopoital cnolgi vecinthemodeing loop K, Derivative COrOl gain vecinthemodeing loop K ObSrver gain determined bytheextended Kalnan Filt n Spindle speed (rpm) N(-, ) Normal distri1xton function p(x,F4) Induced preoad asafunction of aturae ndiniti prekad P() Riccati matrix fuction q(x4z) Friction heat function vector. QO Conei heat released toluianfrmtherolig elemes (Was) O) Friton heat itothrolig elements (Waits) Q. Conduon heat frmthiner rmgtotheocrmg(Watts) Qf Total frtion heat genraio (Watts) Qk Convecon heat released totheatmosphere (Watts) Qa Conduction beatfrom the rringtherollingelements (Watts) Q, Convection heareleased tolubricant fromtheinner ring (Watts) 0, Fiction heat itothe inerrg(Watts) ,, Conducin heat frmUtinner ring toheshaft (Watts) Q,, Convecto heat released tolubric:ant fromtheouter ring (Watts) Q,,, Friction heat itUet outr nng(Watts) t CConuction heat into threstofthehousing (Watts) rT Theradius ofthehousing r, TheradusofUtheouter ring T1 Temperate oftherolling clements ('C) T Temperatue atthe innrace(C) T.- Characterstic temeature ofUeouter ring/hsing (CC m) u(t)Input vector ofastate-space model v(t) System internal noise V Varance ofv(t) w(t) Measurement noise W Variance ofw(t) x State vector xo Reference state xI Theouter ring/housing temperature variable X2 Theroling element variable ; Theinner ten m u varble y(t) System output variale z Theinduced prekod p Thepowercoefficient oftheinduced force function &q(x, u)Fricton heatprediction earor El Thennal exansion ofthe rolling elments (m) £io Initial intefenc fit duetotheiniti prload (m) E2 Thermal epansion ofthe oarring andthe housing (m) C3 Thermal expansion ofUtinner ring (m) 4 Resutnt change ofinerfee fit (m)