Thermal behavior of friction clutch disc based on uniform pressure and uniform wear assumptions

Transcription

1 Fcton 4(3): (2016) ISSN DOI /s z CN /TH RESEARCH ARTICLE Themal behavo of fcton clutch dsc based on unfom pessue and unfom wea assumptons Oday I. ABDULLAH 1,2,*, Josef SCHLATTMANN 1 1 System Technologes and Mechancal Desgn Methodology, Hambug Unvesty of Technology, Hambug 21073, Gemany 2 Depatment of Enegy Engneeng, College of Engneeng, Unvesty of Baghdad, Baghdad-Aljada 47024, Iaq Receved: 11 May 2016 / Revsed: 22 June 2016 / Accepted: 04 July 2016 The autho(s) Ths atcle s publshed wth open access at Spngelnk.com Abstact: Hgh tempeatues appea n the contactng sufaces of a sngle-dsc clutch system (fcton clutch dsc, flywheel and pessue plate) due to the elatve moton between these pats dung the sldng peod. These hgh tempeatues ae esponsble fo seveal dsadvantages such as nceasng wea ate, suface cacks and pemanent dstotons. In some cases, these dsadvantages may lead the contactng sufaces to falue befoe the expected lfetme. In ths wok, mathematcal models of the fcton clutch system (sngle-dsc clutch) wee bult to fnd the tempeatue feld dung the sldng peod (sngle engagement). Analyss has been completed usng developed axsymmetc models to smulate the fcton clutch system dung the engagement. The suface tempeatues ae found based on unfom pessue and unfom wea assumptons. Keywods: dy fcton clutch; themal analyss; fnte element analyss; unfom wea assumpton; unfom pessue assumpton 1 Intoducton The sldng systems such as automotve bakes and clutches consst of two o moe bodes whch pess togethe and slde aganst each othe. One of the contact bodes must be a conducto to dsspate the heat and have a good esstance to wea, whle the othe body should be an nsulato and have a hgh value of coeffcent of fcton. The nteacton between the heat geneated appeas between the contact sufaces due to the elatve speed between them, and themal defomaton and the elastc contact wll change the contact pessue dstbuton. Ths nteacton n some cases wll lead to change the status of the sldng system fom stable zone to unstable zone. In ode to keep the fcton system n the stable zone, t should avod themal falue easons such as excessve sldng speed, wong selecton of fcton mateal, etc. Newcomb [1] pesented an analytcal soluton to * Coespondng autho: Oday I. ABDULLAH. E-mal: odaya2006@yahoo.com obtan the suface tempeatue wth tme dung the bakng pocess assumng a unfom deceleaton. He studed the effect of a non-unfom pessue dstbuted ccumfeentally along the lnng. Hs appoach showed lagely ageement wth the expemental esults. Afte one yea, Newcomb [2] nvestgated the toque capacty and the amount of heat dsspated of the dy clutch dung a sngle engagement assumng a unfom wea of the clutch sufaces. He calculated the tempeatues at vaous depths nsde the contactng elements of the clutch and at any tme dung the slppng peod. The eseach esults showed that the maxmum tempeatue of the fctonal suface affected the pessue plate. El-Shebny and Newcomb [3] used fnte dffeence method to set up equatons to expess the heat balance at evey egon n the clutch system. He detemnes the tempeatues at vaous elements when band contact occus between the ubbng sufaces dung the opeaton of an automotve clutch. Tempeatue dstbutons wee detemned of the contact aea fo dffeent bands wdth on the two clutches facng. Both

2 Fcton 4(3): (2016) 229 sngle and epeated engagements made at egula nteval ae consdeed. Yevtushenko et al. [4] appled one-dmensonal tansent heat conducton to study the contact poblem of a sldng of two sem-spaces, whch nduces the effects of fcton and the heat geneated dung the bakng. In the analyss, they assumed that the capacty of the fctonal souce on the contact plane depends on the tme of bakng. The poblem s solved exactly usng Laplace tansfom technque. The numecal esults of the tempeatue ae obtaned fo dffeent values of nput paametes, whch chaacteze the duaton of the ncease of the contact pessue dung bakng fom zeo to the maxmum value. An analytcal fomula fo the abasve wea of the contact plane s obtaned assumng that the wea coeffcent s a lnea functon wth the contact tempeatue. Gzes [5] pefomed a tansent themal analyss of dsc bake n a sngle bake applcaton to examne the effect of the angula speed and the contact pessue on the tempeatue feld of dsc bake. A paabolc heat conducton equaton fo the two-dmensonal model was used to obtan the numecal smulaton. The esults showed that both otatng speed of the dsc and the contact pessue wth specfc mateal popetes geatly affect the tempeatue felds of the dsc bake. Ivanovć et al. [6] pesented a pagmatc semphyscal appoach to model the themal dynamc behavo of wet clutch. The themal enegy balance was consdeed the base to nvestgate the heat tansfe mechansms n the sepaato plate. The coeffcent of fcton and the themal popetes ae consdeed the most mpotant paametes whch effect on the wet clutch dynamcs esponse. Moeove, the effects of the coeffcent of fcton on the slppng speed of the clutch, the appled foce, and the fctonal suface tempeatues have been studed. The esults of the dynamc themal model wee expementally valdated. Yevtushenko and Kucej [7] nvestgated a tansent themal poblem of thee-elements (dsc/pad/calpe) wth tme-dependent. The effects of Bot numbe and the duaton of the pessue nceasng fom zeo at the ntal moment of tme to nomnal value at the moment of a stop on the values of the tempeatue of the cast on dsc/metal ceamc and pad/steel calpe have been studed. The eseach esults showed that the effect of Bot numbe wll educe the heat tansfe though the contact suface. Abdullah and Schlattmann [8 15] study the themoelastc behavo of a sngle and mult-dsc fcton clutches dung the begnnng of the engagement. They also nvestgated the effect of pessue between contact sufaces when t s vayng wth tme on the tempeatue feld and the ntenal enegy of clutch dsc usng two appoaches; heat patton ato appoach computes the heat geneated of each pat ndvdually wheeas the second appoach apples the total heat geneated of the whole model usng the contact model. Futhemoe, they studed the effect of engagement tme, sldng speed functon, themal load, and dmensonless dsc adus (nne dsc adus/oute dsc adus) on the themal behavo of the fcton clutch dung the sldng peod. They concluded that the estcton condton and mateal popety modulus of elastcty ae vey effectve on the contact pessue dstbuton and tempeatue feld dung the sldng peod. The objectve of ths wok s to develop mathematcal models of a sngle-dsc clutch based on unfom pessue and unfom wea assumptons to fnd the tempeatue dstbuton dung the sldng peod. Futhemoe, compasons have been made between the esults obtaned when assumng a unfom pessue between the contact sufaces and those obtaned assumng unfom wea. The esults showed that each assumpton has dffeent tempeatue dstbuton dung the sldng peod. 2 Enegy dsspaton based on fctonal foce Heat geneated due to the sldng between two bodes wll ase the tempeatues of the contact sufaces as a esult of fcton phenomenon, as shown n Fg. 1. The fst law of themodynamc states that the change n the nput enegy to the sldng system U n s equal to the sum of the ntenal enegy of the system U accumulated (accumulated o stoed ntenally) and the enegy output to the suoundng U out (dsspated extenally) [16]. U U U (1) n out accumulated The nput enegy n the fcton case s the poduct of

3 230 Fcton 4(3): (2016) Fg. 1 Schematc vew of fctonal sldng between two bodes. the fctonal foce F f and the sldng speed V s. The ate of the nput enegy at the fctonal nteface s balanced by the heat conducton and the mechancal enegy tansmsson movng away fom the nteface, ethe nto the contact bodes o the suoundng. The patton of enegy dung the fcton unde vaous condtons s yet to be clealy detemned. When the speed nceases less and less fcton enegy pehaps as lttle as 5% consumed o stoed n the mateal as mcostuctual defects such as dslocatons, the enegy poduces phase tansfomatons, suface enegy of new wea patcles and popagatng subsuface cacks, etc. The est of the enegy s dsspated as a heat o melts the sldng nteface. The enegy that cannot be emoved apdly fom the nteface wll cause ases n the values of the tempeatue locally. The tempeatues whch appea n the sldng pocess can be classfed nto two types [16]: The flash tempeatue (localzed): The maxmum fcton-nduced tempeatue of the tps of the nteactng aspetes. Ths tempeatue occus when the sldng sufaces touch at only a few locatons at any nstant. The enegy s concentated thee and the heatng s patculaly ntense. The concept and calculaton of the flash tempeatues ae explaned wth detals n Ref. [17]. The mean suface tempeatue (bulk): The aveage tempeatue ove the nomnal contact zone. The ate of the heat geneated based on the fcton foce dung the slppng between two bodes (e.g., automotve bakes and clutches) s gven as follows [18]: q pv, 0t t (2) f s s whee, pandv ae the coeffcent of fcton, contact s pessue and sldng speed, espectvely. It can be obtaned the ate of the heat geneated dung slppng peod n the fcton clutches unde a unfom pessue condton between the contact sufaces usng the followng fomula: 3 T qf(,) t, 0t t 3 3 2π n ( ) p o whee T, ω,, n p, and o ae toque capacty of clutch, angula sldng speed, dsc adus, numbe of fcton sufaces n clutch system, nne dsc adus and oute dsc adus, espectvely. The heat geneated dung slppng peod n the fcton clutches unde a unfom wea condton s 1 T qf() t, 0t t 2 2 π n ( ) p o Fgue 2 shows the vaaton of the heat geneated (heat flux) wth dsc adus dung the sldng peod fo both cases (unfom pessue and unfom wea condtons). 3 Mathematcal model The statng pont of the tempeatue feld analyss of a clutch system s the paabolc heat conducton equaton n the cylndcal coodnate system ( adal coodnate (m), θ ccumfeental coodnate ( ), and z axal coodnate (m)) [19], as shown n Fg T 1T 1 T T 1 T, z k t,0 2π, 0 z, t 0 o whee k s the themal dffusvty (k = K/(ρc)), s the s s (3) (4) (5)

4 Fcton 4(3): (2016) 231 and thus the heat conducton equaton educes to (Fg. 4) 2 2 T 1T T 1 T, o,0, z t z k t (6) Owng to the symmety n the geomety and the bounday condtons of the clutch dsc n z-axs, t s possble to smulate only the half of the cutch dsc to educe the tme consumpton fo calculaton. The bounday and ntal condtons of a clutch dsc (uppe half) wthout gooves ae gven as follows (Fg. 4): T K h[ T(, z, t) T ], cu 0 o a 0 2π, 0 zt 2, t 0 cu (7) whee T a s the ambent suoundng tempeatue and h s the convecton heat tansfe coeffcent. Fg. 2 Vaaton of heat flux on the sufaces of a clutch dsc dung the sldng peod. Fg. 3 Thee-dmensonal model of a sngle-dsc clutch system. nne dsc adus, o s the oute dsc adus of the clutch, and δ s the thckness of the contactng pats. Hence the dstbuton of heat flow wll be unfom n ccumfeental decton, whch means that the tempeatue and heat flow wll not vay n θ decton, Fg. 4 Axsymmetc model of a clutch system wth bounday condtons.

5 232 Fcton 4(3): (2016) T Kc h[ T( 0 o, z, t) Ta], 0 2π, ( t 2) z( t /2) t, t 0 cu cu c T Kc z( t cu /2) t q c c(,), t z, 0 2π, 0t t o s T Kc h[ T(, z, t) Ta], 0 2π, ( t 2) z( t 2) t, t 0 The ntal tempeatue s T (,, z,0) T, cu cu c, 0 2π, 0 zt ( t /2) o c cu T z T 0, 0 z( t 2), t 0 cu 0,, 0 2π, t 0 z 0 o (8) (9) (10) (11) (12) (13) In ths mathematcal model, the angula sldng angula speed s assumed to decease lnealy wth tme as follows: t t 1, 0 tt t o s s 4 Fnte element fomulaton (14) Axsymmetc model of two dscs n contact Ω 1 and Ω 2 s shown n Fg. 5. One of these dscs sldes ove the othe one. The bounday and ntal condtons of ths model ae descbed as follows: T T on (15) p a T q h( T T ) on (16) cu q h q q on (17) T T at t 0 (18) T p s the pescbed tempeatue. Γ Τ, Γ h, and Γ q ae the boundaes on whch tempeatue, convecton and heat flux ae pescbed of the system. The tempeatue was appoxmated ove space as follows [20]: n T (, zt,) N(, zt ) () t (19) 1 whee N s shape functon, n s the numbe of nodes n an element, and T (t) s the tme dependent nodal tempeatues. The standad Galekn s appoach of Eq. (6) leads to the followng equaton [20]: 2 2 T 1 T T T KN C d z t (20) Usng ntegaton by pats of Eq. (20), t wll obtan ntegal fom of bounday condtons: N T N T N T T K N C d z z t (21) T T KN ld KN nd 0 z q T T KN ld KN nd z Nqd NhT ( T) d q a h h (22) Substtutng Eq. (22) and spatal appoxmaton Eq. (19) to Eq. (21), t can obtan the followng equaton: N N j N N N j N j K T d j z z N CN T N qd h j d j t q NhT ( T)d 0 a h q (23) whee and j epesent the nodes. Equaton (23) can be wtten n matx fom as follows: T C K T R (24) t Fg. 5 Geometc model of the sldng system (two dscs). whee C s the heat capacty matx, K s the heat conductvty matx, and {R} s the themal load.

6 Fcton 4(3): (2016) 233 Also, t can be wtten ths equaton n dffeent fom as follows: Tj C K T R j j j j t (25) whee K j C CN N d j j N N N j K z z N N j Tj hn N d o n matx fom, j N j Tj Tj R qn d N ht d q a h q h T C CN N K d d K B T DB T N N h d d Mesh qualty has a sgnfcant effect on the eos exstng n the numecal esults and the tme step was taken n the model valdaton phase to ensue that the most effcent combnaton of numbe of elements and numbe of nodes was employed, and the esultng mesh was sutable. It s essental to use a sutable mesh to obtan the esults wth hgh accuacy. Theefoe, t s necessay to fnd the elatonshp between the lagest element sze n the decton of heat flow and the smallest tme step sze to mpove the accuacy of the esults. The mnmum tme step s [21] 2 le t (26) 4k whee k s the themal dffusvty, and l e s the value of the conductng length of an element (along the decton of heat flow) n the expectng hghest tempeatue gadent. Fgue 6 shows the axsymmetc fnte element model of fcton clutch system. The Cank-Ncolson method was selected as an uncondtonally stable scheme n ths analyss. Fg. 6 Axsymmetc fnte element model of a sngle-dsc fcton clutch system. 5 Results and dscussons The appoach of pesent wok was compaed wth the numecal esults of Fu et al. [22] to fnd the maxmum tempeatue (T max ) at nne and oute adus of fcton clutch. Table 1 shows the compason between the esults obtaned usng ou appoach wth othe eseache whch used dffeent appoach (Fu et al. [22]). In ths table, the maxmum dffeence not exceeds 1%. The data fo the vefcaton case ae shown n Table 2. Fgue 7 shows the developed axsymmetc fnte element models of a clutch dsc unde unfom pessue Table 1 The values of maxmum tempeatue at nne and oute adus ad. T max at (K) T max at o (K) Pesent wok Fu et al. [22] Dffeence (%) Table 2 The paametes and mateal popetes fo vefcaton case [22]. Steel Popetes Fcton mateal popetes popetes Dmensonal paametes Inteo damete, D 1 = 252 mm; extenal damete, D 2 = 386 mm; thckness, t 2 = 5 mm Thckness t 1 = 10 mm t 3 = 5 mm Modulus of elastcty (MPa) Themal conductvty (W/(m K)) Specfc heat capacty (J/(kg K)) 1, Densty (kg/m 3 ) 1,300 7,800

7 234 Fcton 4(3): (2016) Table 3 Model paametes and mateal popetes. Paametes Values Inne dsc adus, (m) Oute dsc adus, o (m) Toque, T (N m) 580 Maxmum pessue, p max (MPa) 0.25 Coeffcent of fcton, μ [1] 0.3 Numbe of fcton sufaces, n p [1] 2 Maxmum angula slppng speed, ω o (ad/s) 220 Conductvty of fcton mateal, K c (W/(m K)) 0.75 Conductvty of pessue plate, flywheel and axal cushon, K p, K f and K cu (W/(m K)) 56 Densty of fcton mateal, ρ c (kg/m 3 ) 1,300 Densty of pessue plate, flywheel and axal cushon, ρ p, ρ f and ρ cu (kg/m 3 ) 7,200 Specfc heat of fcton mateal, c c (J/(kg K)) 1,400 Specfc heat of pessue plate, flywheel and axal cushon, c p, c f and c cu (J/(kg K)) 450 Thckness of fcton mateal, t c (m) Thckness of axal cushon, t cu (m) Fg. 7 Axsymmetc fnte element models of clutch dsc unde dffeent types of load, 8 nodes themal element (PLANE77), numbe of elements=1,776. and unfom wea assumptons. The slppng tme s 0.4 s and the ntal angula sldng speed ω o s assumed to be lnealy decays and fnally eaches zeo at the end of the slppng peod (Eq. (14)). The heat tansfe coeffcent was changed as a functon of the elatve suface speed (V ) accodng to Czél et al. [23]: at a statonay poston the value of heat tansfe coeffcent s 5 W/(m 2 K). At V = 14.8 m/s, the heat tansfe coeffcent s 40 W/(m 2 K). In all computatons, t has been assumed a homogeneous and sotopc mateal; all paametes and mateals popetes ae lsted n Table 3. All values and paametes efeed to the axal cushon, fcton mateal, flywheel and pessue plate n the followng consdeatons wll have bottom ndexes cu, c, f, and p, espectvely. Fgues 8(a) 8(h) show the vaaton of the suface tempeatue wth dsc adus of clutch dsc assumng unfom wea and unfom pessue between the contact sufaces, espectvely. It can be notced that the tempeatue values ae appoxmately unfom dstbuted wth dsc adus (vey small effect of the heat convecton on the values of tempeatues nea the nne and oute dsc ad) at cetan tme assumng unfom wea between the contact sufaces. In case when assumng unfom pessue between the contact sufaces, the values of tempeatues ncease lnealy wth dsc adus at any tme dung the sldng peod. Fgue 9 llustates the vaaton of the maxmum suface tempeatue assumng unfom wea and unfom pessue between the contact sufaces, espectvely. It can be seen fo both assumptons that the tempeatue stats fom an ntal value (T ) at begnnng of slppng (t = 0) and nceases to the maxmum value (T max ) appoxmately at half tme of slppng peod (t s 0.2 s), and then t gadually deceases fom T max to the fnal tempeatue (T f ) at end of slppng peod (t s = 0.4). Also, t can be obseved that the maxmum tempeatues, whch appeaed on the sufaces of clutch dsc assumng unfom pessue ae geate than those obtaned assumng unfom wea at any tme dung the sldng peod. The dffeence between tempeatues obtaned fom both assumptons nceases wth tme at any cetan tme untl appoxmately the md tme of a sldng peod

8 Fcton 4(3): (2016) 235 Fg. 8 Dstbuton of suface tempeatue wth dsc adus (a) at t s = 0.05, (b) at t s = 0.1, (c) at t s = 0.15, (d) at t s = 0.2, (e) at t s = 0.25, (f) at t s = 0.3, (g) at t s = 0.35, and (h) at t s = 0.4. when the hghest tempeatues wll appea, afte ths pont the tempeatue dffeence wll be deceased to the end of the sldng peod. The esults ae obtaned assumng unfom wea between the contactng sufaces ndcatng that the values of tempeatue ae appoxmately equal to the tempeatue at the mean dsc adus assumng unfom pessue between the contact sufaces. Howeve, the

9 236 Fcton 4(3): (2016) Fg. 9 Vaaton of the maxmum suface tempeatue dung the sldng peod. esults obtaned fom second case (unfom pessue) show that the values of tempeatue ae not unfom ove the fctonal facng, whch nceases lnealy wth dsc adus. Thus, the maxmum tempeatue wll occu n the oute dsc adus unde the same bounday condtons. The esults of tempeatue dstbuton assumng unfom pessue between the contact sufaces wll lead the automotve desgnes to obtan moe safe desgn of fcton clutch, and subsequently get accuate estmates fo the lfecycles of fcton clutches. 6 Conclusons and emaks In ths wok, axsymmetc models of a sngle-dsc fcton clutch based on dffeent assumptons ae developed. The esults show the tansent themal behavo of a fcton clutch system dung the sldng peod (heatng phase), when the clutch system stats to engage. The analyss consdes two types of load (heat flux) based on the desgn theoes of the fcton clutches. These theoes ae called unfom pessue and unfom wea. The esults pesented the tempeatue feld of fcton clutch dsc based on unfom pessue and unfom wea assumptons. Ths study hghlghts the eo exstng n the esults and dstbuton of tempeatue feld when assumes a unfom wea between the contact sufaces. The heat flux s unfomly dstbuted ove the contact sufaces of clutch dsc at any tme when assumes a unfom wea. The esults of tempeatues based on ths assumpton appoxmately ae equal to the tempeatue values at the mean dsc adus when assumes a unfom pessue between the contact sufaces. The esults unde ths consdeaton aen t gvng the actual values of the maxmum tempeatue and the tempeatue vaaton wth dsc adus. On the othe hand, when computes the tempeatue feld of clutch dsc based on a unfom pessue assumpton, the heat flux nceases lnealy wth dsc adus. The mnmum tempeatue value wll occu at the nne dsc adus and the maxmum tempeatue value wll occu at the oute dsc adus at any tme dung the sldng peod. A good ageement wth esults of othe eseaches usng dffeent appoaches s obtaned whch poves the numecal model based on a unfom pessue assumpton to deal wth the sldng opeaton of fcton clutches system. The outcomes obtaned fom ths wok showed that the calculaton of the tempeatue dstbuton based on a unfom wea wll lead the automotve desgnes to obtan naccuate estmaton of lfecycles of fcton clutches due to the eo exstng n ths assumpton. Open Access: The atcles publshed n ths jounal ae dstbuted unde the tems of the Ceatve Commons Attbuton 4.0 Intenatonal Lcense ( ceatvecommons.og/lcenses/by/4.0/), whch pemts unestcted use, dstbuton, and epoducton n any medum, povded you gve appopate cedt to the ognal autho(s) and the souce, povde a lnk to the Ceatve Commons lcense, and ndcate f changes wee made. Refeences [1] Newcomb T P. Tansent tempeatues n bake dums and lnngs. Poc IMechE: Automoble Dvson 12(1): (1958) [2] Newcomb T P. Tempeatues eached n fcton clutch tansmssons. J Mech Eng Sc 2(4): (1960) [3] El-shebny M, Newcomb T P. Tempeatue dstbutons n automotve dy clutches. Poc IMechE 190(1): (1976) [4] Yevtushenko A A, Ivanyk E G, Yevtushenko O O. Exact fomulae fo detemnaton of the mean tempeatue and wea dung bakng. J Heat Mass Tansfe 35(2): (1999) [5] Gzes P. Fnte element analyss of dsc tempeatue dung bakng pocess. J Acta Mechanca Et Automatca 3(4):

10 Fcton 4(3): (2016) (2009) [6] Ivanovć V, Heold Z, Deu J. Expemental chaactezaton of wet clutch fcton behavos ncludng themal dynamcs. SAE Int J Eng 2(1): (2009) [7] Yevtushenko A, Kucej M. Tempeatue and themal stesses n a pad/dsc dung bakng. J Appl Them Eng 30(4): (2010) [8] Abdullah O I, Akhta M J, Schlattmann J. Investgaton of themo-elastc behavo of multdsk clutches. J Tbol 137(1): 1 9 (2015) [9] Abdullah O I, Schlattmann J. An nvestgaton nto the themal behavo of the gooved dy fcton clutch. J Tbol 136(3): 1 6 (2014) [10] Abdullah O I, Schlattmann J. Computaton of suface tempeatues and enegy dsspaton n dy fcton clutches fo vayng toque wth tme. Int J Automot Technol 15(5): (2014) [11] Abdullah O I, Schlattmann J, Al-Shabb A M. Themomechancal analyss of the dy clutches unde dffeent bounday condtons. Tbol Ind 36(2): (2014) [12] Abdullah O I, Schlattmann J. The effect of dsc adus on heat flux and tempeatue dstbuton n fcton clutches. J Adv Mate Res 505: (2012) [13] Abdullah O I, Schlattmann J. The coecton facto fo ate of enegy geneated n the fcton clutches unde unfom pessue condton. J Adv Theo Appl Mech 5(6): (2012) [14] Abdullah O I, Schlattmann J. Fnte element analyss of tempeatue feld n automotve dy fcton clutch. Tbol Ind 34(4): (2012) [15] Abdullah O I, Schlattmann J. Stesses and defomatons analyss of a dy fcton clutch system. Tbol Ind 35(2): (2013) [16] Blau P J. Fcton Scence and Technology fom Concepts to Applcatons, 2 nd Edton. Boca Raton: CRC Pess/Taylo and Fancs, [17] Bok H. The flash tempeatue concept. Wea 6(6): (1963) [18] Lng F F, La W M, Lucca D A. Fundamentals of Suface Mechancs, 2nd Edton. New Yok: Spnge, [19] Nowack W. Themoelastcty. Oxfod (UK): Pegamon Pess, [20] Lews R W, Nthaasu P, Seethaamu K N. Fundamentals of the Fnte Element Method fo Heat and Flud Flow. John Wley and Sons, [21] ANSYS. Contact Technology Gude. ANSYS, Inc, 13, [22] Fu H, Fu L, Lu A, Zhang G-L. Fnte element analyss of tempeatue feld of clutch n tunnel bong machne. In Poceedngs of the Intenatonal Confeence on Infomaton Engneeng IEEE (WASE), Bedahe, Hebe, Chna, 2010: [23] Czél B, Váad K, Albes A, Mtau M. Fe themal analyss of a ceamc clutch. J Tbol Int 42(5): (2009) Josef SCHLATTMANN. He s a Unv.-Pofesso at the Hambug Unvesty of Technology n the feld of Systems Technology and Poduct Development Methodology. The felds of hs eseach ae systematcally poduct development of machne elements and/o machne systems; tbology nvestgatons; development of an autonomous bped obot, e.g., path plannng, optmzaton of the contol and the mechancal unts; coopeaton eseach wok wth the Geman ndusty. Oday Ibaheem ABDULLAH. He eceved hs Ph.D. degee n mechancal engneeng fom Hambug Unvesty of Technology n He s one of the faculty membes n the Depatment of Enegy Engneeng/ College of Engneeng/Unvesty of Baghdad snce Now he s a eseach assocate n System Technology and Mechancal Desgn Methodology Goup/Hambug Unvesty of Technology. Hs eseach aeas cove the tbology, stess analyss, vbaton analyss, and themal analyss.