Theoretical Analysis of a Relationship between Master/Wheel Cylinder Diameter Ratio and Brake Efficiency. PMB 1011, Esa-Oke, Osun State, Nigeria.

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1 Theoetial Analysis of a Relationship between aste/heel Cylinde Diaete Ratio and Bake Effiieny. I.A. Lateef, B.Teh., B.A. Hassan,.Ed., and A.E.A. Kaee,.S. Depatent of ehanial Engineeing, Osun State College of Tehnology, B 0, Esa-Oke, Osun State, Nigeia. Copute Siene Depatent, Osun State College of Tehnology, B 0, Esa-Oke, Osun State, Nigeia. E-ail: bale_i@yahoo.o ABSTRACT In any bake syste of an autoobile o passenge vehile, an inease in aste/heel ylinde diaete atio leads to an inease in bake effiieny. This pape fouses on aste/heel ylinde diaete effet on the bake effiieny. A VISUAL BASIC opute ode was developed fo oputation of aste/heel ylinde diaete atio oesponding to beak effiieny. Aided by the developed softwae, the effet of ineasing the aste/heel ylinde atio on the bake was investigated. Results obtained fo ase studies exained, at vaying Foe on the Contol pedal, showed that bake effiieny ineases with inease with aste/heel ylinde diaete atio. The nueial esults wee futhe poessed with the EXCELL pakage, whih yields a elationship of fo: η = a + b whee a, b, and ae eal onstants; iplying that the aste/heel ylinde diaete atio has a non-linea elationship with the bake effiieny of a oto vehile. (Keywods: aste ylinde diaete, wheel ylinde diaete, bake effiieny, foe on ontol pedal, foe on atuating ehanis, adii on pedal) INTRODUCTION Road aidents as a ajo auses of isey, obidity, and otality in Afia, patiulaly in Nigeia, have been of onsideable onen to the + geneal publi; howeve, the inteelationship of the host (oad uses), agent (oto vehiles), and envionent (oad onditions) has not been well exained (Igohe and Kwaina, 99), hene, the need fo futhe studies. Vehiles as a ajo agent of oad tanspotation ontibute iensely to the loss of invaluable life, goods, and popeties. It woth noting that oto vehile onditions ae to a geat degee, the deteinant of aident ouene. It is established that vehiles defets an ade the the agent of deise on the oad. These defets an inlude bad ties, inopatibility of vehile pats, bake failue, absene of font lights, and alfuntioning bake lights, just to ention few (Igohe and Kwaina, 99). oto vehiles ae oplex ahines that ontain vaious syste inluding ignition, lubiation, bakes, steeing, and suspension systes. Bake systes ay be ehanially, pneuatially, o hydaulially opeated. It is neessay to etad o stop the vehile duing opeations. The hydauli bake is noted fo sall atuating tie, siple design, sall oveall diensions, sall ass, and low ost of poueent and aintenane. Aong the ajo oponents of hydauli bake ae aste ylinde, wheel ylinde, bake shoes and thei ehanis, bake lines, bake pedal, and bake fluid (Salai, 986; Dolan,98; and Hillie and ittuk, 97). oden baking systes eploy eithe a otating du o dis. The neessay fition is obtained by passing a stationay shoe o pad against the otating ebe. The foe felt at eah shoe is govened by the piston aea in the wheel ylinde; the lage the aea the geate the thust exeted The aifi Jounal of Siene and Tehnology 55 Volue 9. Nube. ay-june 008 (Sping)

2 on the du o dis, hene the highe the effiieny of the bake (Hillie and ittuk, 97). The pupose of wheel ylinde is to tansit the aste ylinde pessue to the bake shoe and foe the outwad against the du. The wheel ylinde assebly is siple in onstution; it onsists of ast ion housing, two aluinu pistons, two-ubbe up expande, two push ods and two ubbe dust boots. In the wheel ylinde, the hydauli pessue applied between the two piston ups foes the piston out, thus, the bake shoe atuating pins foe the bake shoes into ontat the bake du. The effiient baking of vehile is one of the pinipal fatos in seuing thei safe opeation. Studies have shown that the typial bake effiieny peentage elated to the ondition of the bakes ae as follows (Table ). Table : eentage Effiieny Coesponding to Bake Conditions (Igohe and Kwaina, 99). 0 / 0 S CONDITION 30 iniu allowable fo any vehile. 50 Fou wheel bakes in good ondition. 60 Fou wheel bake in vey good ondition. 70 Fou wheel bakes in exellent ondition. 80 Safest degee of effiieny. 00 Theoetial liit fo bakes on all wheels. Aoding to Salai, 996 and Hillie and ittuk (97) the stopping distane of a bake (effiieny) depends on: ) oeffiient of fition between the tie and the oad, ) oeffiient of fition between baking sufaes, 3) the foot pedal pessue, 4) the piston aea of the wheel ylinde, 5) and the ethods of atuating the bakes. It has been epoted (Abdahi) that the pesent ondition of ost auto assebly plants and geneal eonoy of Afia, in patiula Nigeia, has ade the duping gounds fo used vehiles oonly alled TOKUNBO in Nigeia. Tokunbo vehile have assoiated pobles of vaious type that an ause geat loss to Afian nations as a esult of elated aidents. Suh pobles ae assoiated with ehanial failues (inluding bake failues) and oveheating. At ties, needs do aise fo the intehange of pats, espeially bake pats, to suit Afian onditions. This is usually done without any onsideation fo bake effiieny, theeby leading to ehanial failue in suh vehiles. The atio of aste ylinde to wheel ylinde diaete whih has geat ipat on the bake effiieny, theeby deteines the stopping distane of the vehile. The ipat of aste ylinde atio to wheel ylinde diaete on the bake effiieny is of paaount ipotane, hene the need to establish the degee of thei influene(s). This will no doubt be a useful tool in geneating the neessay database whih ould aid pefet hangeability of wheel ylinde, aste ylinde, and othe bake pats. The effet of the aste ylinde atio to wheel ylinde on bake effiieny is deteined in this eseah by integating the aste ylinde/wheel ylinde diaete atio into the geneal design equation fo foe on the ontol pedal of a bake (Lukin et al., 989). The esulting expession is developed in the VISUAL BASIC opute ode to geneate peision values of bake effiieny oesponding to seies of aste ylinde/wheel ylinde diaete. ATERIAL AND ETHODS The elationship between the wheel ylinde diaete and developed diving foe is expessed as (Lukin et al., 989): = whee, = 0.5π p K.. heel ylinde diaete () = Diving foe (N) = Fluid pessue in the ylinde with due p K onsideation to the ation of the baking foe egulato. The foe on the ontol pedal is given as: The aifi Jounal of Siene and Tehnology 56 Volue 9. Nube. ay-june 008 (Sping)

3 F p = whee, = F p π 4η k.. Foe on the ontol pedal = Radii on the pedal = aste ylinde diaete () η = Hydauli bake effiieny Fo hydauli dive, the diving foe at the shoes is equal to the su of the diving foe at leading shoe and at tailing shoe: = + l T The diving foe at leading and tailing shoes aoding to Banga and Sing (986) and Chapion (986) is : and F a = R l µ F a = R l µ Theefoe, = 0.5 F a µ R..5 whee, F = a Foe of atuating ehanis (N) = Distane between anho pin and atuating foe (N) µ = Coeffiient of fition ateial R = Bake du adius. Fo Equation : k = π Also fo Equation : η = π 4F p k..7 anipulating Equations 5, 6, and 7: η = 0.5 F a ( µ R).8 F p The atio of aste ylinde ( ) to wheel ylinde diaete ( ). Foe of the atuating ehanis ( F a ), oeffiient of fition ateial (µ ), and foe on ontol pedal ae featues of the design ondition fo deteining the effiieny of oto vehile bakes. Theefoe, if foe on ontol pedal ( the pedal ( F p ), adii of ), the distane fo pivot and atuating ehanis ( ), oeffiient of fition ateial ( µ ), foe on atuating ehanis ( F ), and adius of the bake du ( ) ae a held onstant, the effet of the atio of aste ylinde to wheel ylinde on bake effiieny of a oto vehile an be deteined fo Equation (8). Copute siulation of Equation (8) was aied out in this study. The poga was developed in FORTRAN 77 and was stutued in inteative data input fo. The softwae evaluates the elationship between the atio of aste ylinde to wheel ylinde and effiieny of a oto vehile bake. Data geneated though the poga was then poessed with the EXCEL pakage to obtain atheati expessions, whih desibe the effet of the atio of aste ylinde to wheel ylinde on the bake effiieny. R The aifi Jounal of Siene and Tehnology 57 Volue 9. Nube. ay-june 008 (Sping)

4 Case Study A typial ase study (A) with the following paaete was investigated: =0.007, =0.03, =890 N, F a F p =500 N, µ =0.5, R =0.39, and =0.46. Keeping all othe paaete onstant, the atio of the aste ylinde to wheel ylinde diaete was vaied between ( ) geneating diffeent bake effiieny values. Also fo ase B, C, D, and E using an ineent in foe on ontol pedal at a ate of 0 N and a atio of aste ylinde to wheel ylinde vaiation between (0.83.) to geneate diffeent values fo bake effiieny. RESULTS AND DISCUSSION The esults obtained ae pesented in Tables -6. Fo the tables, the bake effiieny ineases with inease in atio of aste ylinde to wheel ylinde diaete. Aodingly, data fo the output of the opute poga (above tables) wee poessed with the EXCEL pakage to obtain atheatial expession elating bake effiieny to atio of aste ylinde diaete with wheel ylinde diaete in an hydauli bake syste. As evident fo Figues and, the ases onsideed (Case A-E) gave quantitative expession in espetive ode as pesented below with eah having R value equal to. Table : oga Output fo the Vaiations of aste/heel Cylinde Diaete Ratio with Bake Effiieny Results (Foe on Contol edal = 500N). ASTER/HEEL DIAETER RATIO , Table 3: oga Output fo the Vaiations of aste/heel Cylinde Diaete Ratio with Bake Effiieny Results (Foe on Contol edal = 50N). ASTER/HEEL DIAETER RATIO , Table 4: oga Output fo the Vaiations of aste/heel Cylinde Diaete Ratio with Bake Effiieny Results (Foe on Contol edal = 50N). ASTER/HEEL DIAETER RATIO , The aifi Jounal of Siene and Tehnology 58 Volue 9. Nube. ay-june 008 (Sping)

5 Table 5: oga Output fo the Vaiations of aste/heel Cylinde Diaete Ratio with Bake Effiieny Results (Foe on Contol edal = 530N). ASTER/HEEL DIAETER RATIO , Table 6: oga Output fo the Vaiations of aste/heel Cylinde Diaete Ratio with Bake Effiieny Results (Foe on Contol edal = 540N). ASTER/HEEL DIAETER RATIO , ase A;Fp= ASTER/HEEL CYL. RATIO Figue : aste/heel Cylinde Diaete Ratio Vaiation with Bake Effiieny. The aifi Jounal of Siene and Tehnology 59 Volue 9. Nube. ay-june 008 (Sping)

6 y = 0.00x x R = y = 0.00x + 0.8x +.88 R = y = 0.00x x R = y = 0.00x x R = y = 0.009x + 0.5x +.7 R =.5 ase A,Fp=500N ase B,Fp=50N ase C,Fp=50N ase D,Fp=530N ase E,Fp=540N oly. (ase A,Fp=500N) oly. (ase B,Fp=50N) oly. (ase C,Fp=50N) oly. (ase D,Fp=530N) oly. (ase E,Fp=540N) ASTER/HEEL CYL DIA. RATIO Figue : aste/heel Cylinde Diaete Ratio Vaiation with Bake Effiieny at Diffeent Fp Values. η = 0.00 η = 0.00 η = 0.00 η = 0.00 η = η = a + b χ Geneally, these elationships ae non-linea (quadati) and of the fo: η = a + b + whee a, b and ae eal haateisti values of the patiula poble of hydauli baking syste of an autoobile vehile. It an thus be dedued that the lage the atio of aste/wheel ylinde diaete, the geate the bake effiieny, in ageeent with the above elationship, and the faste the ate of etading/stopping the vehile. The oelations above ae fo the speifi ases onsideed. An attept to obtain a single The aifi Jounal of Siene and Tehnology 60 Volue 9. Nube. ay-june 008 (Sping)

7 oelation to genealize the esults fo the elationship between the bake effiieny and atio of aste ylinde diaete to wheel ylinde diaete using line of best fit (Figue 3) geneates an appoxiated quadati funtion: η = y =.757x x R = ase A,Fp=500N ase B,Fp=50N 0.5 ase C,Fp=50N ase D, Fp=530N ase E,Fp=540N 0 oly. (ase C,Fp=50N) ASTER/HEEL CYL. RATIO Figue 3: Satte Diaga of a aste/heel Cylinde Ratio Vaiation against Bake Effiieny. The aifi Jounal of Siene and Tehnology 6 Volue 9. Nube. ay-june 008 (Sping)

8 CONCLUSION Fo the foegoing, it an be infeed that; ) The bake effiieny ineases non-linealy with an inease in the atio of aste ylinde/wheel ylinde diaete ) The bake effiieny at onstant atio of aste ylinde/wheel ylinde diaete value deeases with ineases in foe on the ontol pedal. 3) Fo the elationship between the atio of the aste ylinde/wheel ylinde diaete and bake effiieny: η = a + b +. REFERENCES. Abdahi, A.T., Usan,.L., and Fagbenle, R.O Atosphei ollution: Contibution fo Autoobile in a Nigeia City, Ibadan. Jounal of Life and Envionental Siene. 5(): Banga, T.R and Sinngh, N A Textbook on Autoobile Engineeing. ed. Khanna ublishes: Delhi, India Chapion, R.C. and Anold, E.C oto Vehile Calulations and Sienes. 3d ed. Edwad Anold (publishes) Ltd.: London, UK Dolan, J.A oto Vehile Tehnology and atial ok. at &. st ed. Heineann Eduation Books Ltd.: London, UK Hillie, V.A.. and ittuk, F Fundaentals of oto Vehile Tehnology. nd ed, Huthinson Eduation Books, Ltd.: London, UK Lukin,., Gaspayants, G., and Rodionov Autoobile Chassis-Design and Calulations. st ed. i ublishes: osow, Russia ABOUT THE AUTHORS I.A. Lateef is a ebe of Nigeia Institute of ehanial Enginee (niehe). He holds B.Teh (Hons) in Autoobile Tehnology fo Fedeal Univesity Of Tehnology, inna and GD in ehanial Engineeing Fo Ladoke Akintola Univesity of Tehnology, Ogbooso both in Nigeia. He is uently a letue in the Depatent of ehanial Engineeing, Osun State College of Tehnology, Esa- Oke, Nigeia. His eseah aea lies in autootive engineeing, theodynais, infoation tehnology, and ateial siene. B.A. Hassan is a ebe of Nigeia Institute of ehanial Enginee (niehe). He holds a B.Teh (Hons) in etal Tehnology fo Fedeal Univesity Of Tehnology, inna and an.ed. in ehanial Tehnology fo Univesity of Benin both in Nigeia. He is uently a letue in the Depatent of ehanial Engineeing, Osun State College of Tehnology, Esa-Oke, Nigeia. His eseah inteests lie in theodynais, infoation tehnology, and ateial siene. A.E.A. Kaee eeived his B.Teh (Hons) and.s. in Copute Siene fo the Fedeal Univesity of Tehnology, Akue, Nigeia and the Univesity of Ibadan, Nigeia, espetively. He is a hateed IT speialist and ebe of Nigeia Copute Soiety (NCS) and Copute ofessionals Registation Counil of Nigeia (CN). He is also an Assoiate ebe of Nigeia Institute of anageent (NI). Cuently, he is the Ating Head of the Copute Siene Depatent of Osun State College of Tehnology, Esa- Oke, Nigeia. His eseah inteests ae in opute ouniation, netwoking, and the anageent of ICT Infastutues. SUGGESTED CITATION Lateef, I.A., B.A. Hassan, and A.E.A. Kaee Theoetial Analysis of a Relationship between aste/heel Cylinde Diaete Ratio and Bake Effiieny. aifi Jounal of Siene and Tehnology. 9():55-6. aifi Jounal of Siene and Tehnology The aifi Jounal of Siene and Tehnology 6 Volue 9. Nube. ay-june 008 (Sping)