Sa se efectueze calculul dinamic pentru un autoturism de teren echipat cu motor cu aprindere prin comprimare, cu puterea maxima de 113 kW si turatia maxima de 3900 rot/min.

Pm= 113 kWnm= 3900 rot/minGu= 500 kg

Alegerea dimensiunilor autovehiculului

Dimensiuni de gabarit

Lungimea autovehiculului A= 4950 mmLatimea autovehiculului l= 1900 mmInaltimea autovehiculului H= 1400 mmAmpatamentul L= 3000 mmConsola fata c1= 850 mmConsola spate c2= 1100 mmUnghiul de atac α1= 30 °Unghiul de degajare α2= 27 °Ecartament B= 1650 mmGarda la sol (lumina) c= 250 mm

Parametrii de greutate

Greutatea totala Ga=G0+Gu= 2000 kgGreutatea proprie G0= 1500 kgGreutatea utila Gu= 500 kgCoeficientul de utilizare a greutatii ηG=Gu/G0= 0,333333Greutatea maxima admisa pe puntea fata G1= 1000 kgGreutatea pe fiecare roata a puntii din fata G1`=G1/2= 500 kgGreutatea maxima admisa pe puntea spate G2= 1000 kgGreutatea pe fiecare roata a puntii din spate G2`=G2/2= 500 kg

Calculul pozitiei centrului de greutate in plan longitudinal

b=G1*L/Ga= 1250 mma=G2*L/Ga= 1250 mma+b= 2500 mm

Alegerea pneurilor

Se aleg pneuri: 225/50 R17

Balonajul B= 225 mmDiametrul jentii d= 416,5 mmPresiunea de regim p= 2,3 barViteza maxima v max= 180 km/hR - Constructie radiala

Sarcina maxima pe anvelopa Simplu= 5200 kg

Diametrul exterior al rotii D= 646 mmRaza statica rs= 295 mmRaza libera r0=rn=d/2+H= 323 mm

D=d+2*H H=(D-d)/2= 114,75 mm

rs=d/2+H*(1-K)= 311,525 mmCoeficientul care ia in K=0,1…0,16 pentru pneuri conventionalecalcul incarcarea K=0,2…0,3 pentru pneuri specialeSe adopta K= 0,1Raza dinamica r=λ*rn= 300,39 mmCoeficientul de deformare al pneului λ= 0,93

Calculul dinamic al autovehiculului

Determinarea caracteristicii externe a mototrului

α1=(3-4*c)/2*(1-c)= 0,75α2=2*c/2*(1-c)= 1,5α3=-1/2*(1-c)= -1,25

Coeficientul de elasticitate c=nM/nm= 0,6Verificare α1+α2+α3= 1Turatia la moment maxim nM=c*nm= 2340Coeficientul de adaptabilitate k=MM/Mm= 1,2

Pe=Pm*[(α1*ne/nm)+(α2*(ne/nm)^2)+(α3*(ne/nm)^3)]

Me=Mm*[α1+(α2*ne/nm)+(α3*(ne/nm)^2)]

Pm=Mm*ωm Mm=Pm/ωm= 276,68475ωm=2*π*nm/60= 408,40704

MM=Mm*[α1+(α2*nM/nm)+(α3*(nM/nm)^2)]= 332,0217

ce=c min*MM/Me

Consumul specific minim c min=270…340 g/kWh pentru m.a.c.Se adopta c min= 280 g/kWh

Ce=Pe*ce/1000

Determinarea Caracteristicii externe

n [rot/min] Pe [kW] Me [Nm] ce [g/kWh] Ce [kg/h]1000 30,49356 291,19205 319,260347 9,73538461100 34,218699 297,05864 312,955297 10,7089231200 38,009558 302,47046 307,355886 11,6824621300 41,851852 307,4275 302,4 12,6561400 45,731292 311,92976 298,035282 13,6295381500 49,633591 315,97726 294,217617 14,6030771600 53,544463 319,56997 290,909919 15,5766151700 57,44962 322,70792 288,081172 16,5501541800 61,334775 325,39109 285,70566 17,5236921900 65,18564 327,61948 283,762354 18,4972312000 68,98793 329,3931 282,234433 19,4707692100 72,727355 330,71195 281,108911 20,4443082200 76,389631 331,57602 280,376354 21,4178462300 79,960468 331,98531 280,030685 22,3913852340 81,36 332,0217 280 22,78082400 83,42558 331,93984 280,069051 23,3649232500 86,770681 331,43959 280,491767 24,3384622600 89,981481 330,48456 281,302326 25,3122700 93,043696 329,07476 282,507463 26,2855382800 95,943037 327,21018 284,117304 27,2590772900 98,665217 324,89083 286,145577 28,2326153000 101,19595 322,11671 288,609911 29,2061543100 103,52095 318,88781 291,53223 30,1796923200 105,62592 315,20414 294,939258 31,1532313300 107,49659 311,06569 298,863158 32,1267693400 109,11866 306,47247 303,342336 33,1003083500 110,47784 301,42447 308,42245 34,0738463600 111,55985 295,9217 314,157676 35,0473853700 112,35041 289,96416 320,612296 36,0209233800 112,83522 283,55184 327,862711 36,9944623900 113 276,68475 336 37,968

Caracteristica externa

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120Me [Nm] Pe [kW] ce*10 [g/kWh] Ce [kg/h]

Determinarea vitezei maxime

v max= 41,07745 m/sv max= 147,8788 km/h

A= (Ga*f)/(K*S)= 198,1818B= (η tr*Pv max)/(K*S)= 77453,1

Coeficientul de rezistenta la rulare f= 0,014Coeficientul de rezistenta al aerului K= 1/2*ρ*cx= 0,6Densitatea aerului ρCoeficient de forma al automobilului cxRandamentul transmisiei η tr= 0,85…0,95Se adopta η tr= 0,95Suprafata frontala a autovehiculului S= B1*H= 2,31 m^2Puterea la viteza maxima Pv max= Pm= 113000 W

Determinarea raportului de transmitere al transmisiei principale (reductorul central)

i 0= (π*r*nm)/(30*i CVmax*i CDn*v max)i 0= (π*0,3*3900)/(30*1*1*42,35186)= 2,9865

Raportul de transmitere din cutia de viteze i CVmax= 1Raportul de transmitere din cutia de distributie i CDn= 1

Determinarea rapoartelor de transmitere din cutia de viteze

Determinarea raportului de transmitere din treapta I

Raport din conditia de invingere a rezistentelor maxime la inaintare

(Ga*Ψ max*r)/(MM*η tr*i 0)(19620*0,289*0,3)/(332,02*0,95*2,897)= 1,808725

Coeficientul maxim al rezistentei totale a drumuluiΨ max= f*cos(α max)+sin(α max)= 0,289095

Unghiul care caracterizeaza rampa maxima pe care o poate urca autovehicululα max= 12…16 ° Se adopta α max= 16 °

Raport din conditia de aderenta

(mm*Gm*φ*r)/(MM*η tr*i 0)(1*19620*0,8*0,3)/(332,02*0,95*2,897)= 5,005206

Coeficientul schimbarii dinamice a reactiunilor la puntea motoare mm= 1Greutatea pe puntea motoare Gm= 19620 NCoeficientul de aderenta

φ= 0,2…0,8 Se adopta φ= 0,8

Raportul de transmitere din treapta I: i KI, se alege in intervalul cuprins de raportul de invingere a rezistentelor maxime la inaintare si raportul de aderenta

(Ga*Ψ max*r)/(MM*η tr*i 0)<=i KI<=(mm*Gm*φ*r)/(MM*η tr*i 0)

1,808725 <=i KI<= 5,005206

Se adopta i KI= 3,5

Se adopta numarul de 5 trepte in cutia de viteze a autoturismului

Calculul ratiei progresiei geometrice

q= (i KI)^(1/(n-1))= 1,367782n= 5 nr de trepte de viteza

Calculul rapoartelor de transmitere pentru fiecare treapta de viteza

1 i KI= 3,52 i KII= (1/q)*i KI= 2,5588873 i KIII= (1/(q^2)*i KI= 1,8708294 i KIV= (1/(q^3)*i KI= 1,3677825 i KV= (1/(q^4)*i KI= 1

Diagrama vitezelor (diagrama fierastrau)

n min= nm/q= 2851,3307 rot/min

v1 min= (π*r*n min)/(30*i 0*i KI)= 8,580614 m/sv1 max= (π*r*nm)/(30*i 0*i KI)= 11,73641 m/sv2 min= (π*r*n min)/(30*i 0*i KII)= 11,73641 m/sv2 max= (π*r*nm)/(30*i 0*i KII)= 16,05286 m/sv3 min= (π*r*n min)/(30*i 0*i KIII)= 16,05286 m/sv3 max= (π*r*nm)/(30*i 0*i KIII)= 21,95682 m/sv4 min= (π*r*n min)/(30*i 0*i KIV)= 21,95682 m/sv4 max= (π*r*nm)/(30*i 0*i KIV)= 30,03215 m/sv5 min= (π*r*n min)/(30*i 0*i KV)= 30,03215 m/sv5 max= (π*r*nm)/(30*i 0*i KV)= 41,07745 m/s

n [rot/min] Pe [kW] Me [Nm] v1 [m/s] v2 [m/s] v3 [m/s] v4 [m/s] v5 [m/s]1000 30,49356 291,19205 3,009337        1100 34,2187 297,05864 3,31027        1200 38,00956 302,47046 3,611204        1300 41,85185 307,4275 3,912138        1400 45,73129 311,92976 4,213071        1500 49,63359 315,97726 4,514005        1600 53,54446 319,56997 4,814939        1700 57,44962 322,70792 5,115872        1800 61,33477 325,39109 5,416806        1900 65,18564 327,61948 5,71774        2000 68,98793 329,3931 6,018673        2100 72,72736 330,71195 6,319607        2200 76,38963 331,57602 6,620541        2300 79,96047 331,98531 6,921474        2340 81,36 332,0217 7,041848        2400 83,42558 331,93984 7,222408        2500 86,77068 331,43959 7,523342        2600 89,98148 330,48456 7,824275        2700 93,0437 329,07476 8,125209        2800 95,94304 327,21018 8,426143        

2851,331 97,36338 326,07645 8,580614 11,73641 16,05286 21,95682 30,032152900 98,66522 324,89083 8,727076 11,93674 16,32687 22,3316 30,544773000 101,1959 322,11671 9,02801 12,34835 16,88986 23,10165 31,598043100 103,5209 318,88781 9,328944 12,75997 17,45286 23,87171 32,65133200 105,6259 315,20414 9,629878 13,17158 18,01585 24,64176 33,704573300 107,4966 311,06569 9,930811 13,58319 18,57885 25,41182 34,757843400 109,1187 306,47247 10,23174 13,9948 19,14184 26,18187 35,811113500 110,4778 301,42447 10,53268 14,40641 19,70484 26,95193 36,864373600 111,5599 295,9217 10,83361 14,81802 20,26783 27,72198 37,917643700 112,3504 289,96416 11,13455 15,22964 20,83083 28,49204 38,970913800 112,8352 283,55184 11,43548 15,64125 21,39382 29,26209 40,024183900 113 276,68475 11,73641 16,05286 21,95682 30,03215 41,07745

Caracteristica de tractiune

FR= (Me*i 0*i Ki*η tr)/r

Caracteristica dinamica

D= (FR-K*S*v^2)/Ga

Variatia acceleratiei

a= (g*(D-f))/δiδi= 1+0,06*i Ki

δ1= 1+0,06*i KI= 1,21δ2= 1+0,06*i KII= 1,153533δ3= 1+0,06*i KIII= 1,11225δ4= 1+0,06*i KIV= 1,082067δ5= 1+0,06*i KV= 1,06

Inversul acceleratiei

1/a

Treapta I

n [rot/min] Me [Nm] v1 [m/s] FR [N] D a [m/s^2] 1/a [1/(m/s^2)]1000 291,19205 3,009337 9626,051 0,489985 3,859016 0,259133411100 297,05864 3,31027 9819,985 0,499735 3,938065 0,2539318181200 302,47046 3,611204 9998,885 0,508706 4,010798 0,2493269491300 307,4275 3,912138 10162,75 0,516898 4,077215 0,245265471400 311,92976 4,213071 10311,59 0,524311 4,137316 0,2417026091500 315,97726 4,514005 10445,39 0,530945 4,191101 0,2386008081600 319,56997 4,814939 10564,15 0,5368 4,23857 0,235928651700 322,70792 5,115872 10667,88 0,541876 4,279723 0,2336600071800 325,39109 5,416806 10756,58 0,546173 4,31456 0,2317733711900 327,61948 5,71774 10830,25 0,549691 4,34308 0,2302513162000 329,3931 6,018673 10888,88 0,55243 4,365285 0,2290800922100 330,71195 6,319607 10932,48 0,55439 4,381174 0,2282492982200 331,57602 6,620541 10961,04 0,55557 4,390747 0,2277516532300 331,98531 6,921474 10974,57 0,555972 4,394005 0,2275828342400 331,93984 7,222408 10973,07 0,555595 4,390946 0,227741382500 331,43959 7,523342 10956,53 0,554438 4,381571 0,2282286632600 330,48456 7,824275 10924,96 0,552503 4,36588 0,2290489162700 329,07476 8,125209 10878,35 0,549789 4,343873 0,2302093232800 327,21018 8,426143 10816,72 0,546295 4,31555 0,231720185

2851,331 326,07645 8,580614 10779,24 0,544199 4,298558 0,2326361362900 324,89083 8,727076 10740,04 0,542023 4,280911 0,2335951453000 322,11671 9,02801 10648,34 0,536971 4,239956 0,2358515043100 318,88781 9,328944 10541,6 0,531141 4,192685 0,2385106383200 315,20414 9,629878 10419,83 0,524531 4,139098 0,2415985183300 311,06569 9,930811 10283,02 0,517142 4,079195 0,2451463853400 306,47247 10,23174 10131,18 0,508975 4,012977 0,249191593500 301,42447 10,53268 9964,308 0,500028 3,940442 0,2537786573600 295,9217 10,83361 9782,401 0,490302 3,861591 0,258960633700 289,96416 11,13455 9585,46 0,479797 3,776424 0,2648007723800 283,55184 11,43548 9373,485 0,468514 3,684941 0,2713747483900 276,68475 11,73641 9146,477 0,456451 3,587142 0,27877343

Treapta a II-a

n [rot/min] Me [Nm] v2 [m/s] FR [N] D a [m/s^2] 1/a [1/(m/s^2)]1000 291,19205 4,116118 7037,706 0,357504 2,921261 0,3423178751100 297,05864 4,52773 7179,494 0,364479 2,980582 0,3355049691200 302,47046 4,939341 7310,29 0,37087 3,034934 0,3294964111300 307,4275 5,350953 7430,094 0,376677 3,084319 0,3242206461400 311,92976 5,762565 7538,908 0,3819 3,128736 0,3196178431500 315,97726 6,174177 7636,73 0,386539 3,168186 0,3156380461600 319,56997 6,585788 7723,561 0,390594 3,202668 0,3122397141700 322,70792 6,9974 7799,401 0,394064 3,232181 0,3093885681800 325,39109 7,409012 7864,249 0,39695 3,256728 0,3070566851900 327,61948 7,820624 7918,106 0,399253 3,276306 0,3052217852000 329,3931 8,232236 7960,972 0,400971 3,290917 0,303866692100 330,71195 8,643847 7992,847 0,402105 3,30056 0,3029789082200 331,57602 9,055459 8013,73 0,402654 3,305235 0,3025503472300 331,98531 9,467071 8023,623 0,40262 3,304942 0,3025771252400 331,93984 9,878683 8022,523 0,402001 3,299682 0,3030594852500 331,43959 10,29029 8010,433 0,400799 3,289454 0,3040017972600 330,48456 10,70191 7987,351 0,399012 3,274259 0,305412662700 329,07476 11,11352 7953,279 0,396641 3,254095 0,3073051012800 327,21018 11,52513 7908,214 0,393686 3,228964 0,309696875

2851,331 326,07645 11,73641 7880,814 0,391942 3,214134 0,3111257662900 324,89083 11,93674 7852,159 0,390146 3,198865 0,3126108953000 322,11671 12,34835 7785,112 0,386023 3,163798 0,3160757913100 318,88781 12,75997 7707,074 0,381316 3,123764 0,3201266473200 315,20414 13,17158 7618,045 0,376024 3,078762 0,3248059313300 311,06569 13,58319 7518,024 0,370148 3,028792 0,3301646783400 306,47247 13,9948 7407,013 0,363688 2,973854 0,3362639943500 301,42447 14,40641 7285,01 0,356644 2,913949 0,3431769623600 295,9217 14,81802 7152,015 0,349016 2,849075 0,3509910653700 289,96416 15,22964 7008,03 0,340803 2,779234 0,3598113093800 283,55184 15,64125 6853,053 0,332007 2,704426 0,369764253900 276,68475 16,05286 6687,085 0,322626 2,624649 0,381003255

Treapta a III-a

n [rot/min] Me [Nm] v3 [m/s] FR [N] D a [m/s^2] 1/a [1/(m/s^2)]1000 291,19205 5,629953 5145,341 0,260011 2,169805 0,46087097

1100 297,05864 6,192949 5249,003 0,264824 2,212258 0,4520269071200 302,47046 6,755944 5344,629 0,269183 2,250703 0,444305571300 307,4275 7,31894 5432,22 0,273087 2,285141 0,4376096711400 311,92976 7,881935 5511,774 0,276538 2,315572 0,4318586911500 315,97726 8,44493 5583,293 0,279534 2,341996 0,4269862771600 319,56997 9,007926 5646,776 0,282075 2,364412 0,4229381991700 322,70792 9,570921 5702,223 0,284162 2,38282 0,4196707681800 325,39109 10,13392 5749,635 0,285795 2,397221 0,4171496141900 327,61948 10,69691 5789,01 0,286973 2,407615 0,4153487562000 329,3931 11,25991 5820,35 0,287698 2,414002 0,4142499212100 330,71195 11,8229 5843,654 0,287967 2,416381 0,4138420772200 331,57602 12,3859 5858,922 0,287783 2,414752 0,414121152300 331,98531 12,94889 5866,154 0,287144 2,409117 0,4150899272400 331,93984 13,51189 5865,351 0,28605 2,399473 0,416758122500 331,43959 14,07488 5856,511 0,284503 2,385823 0,4191426162600 330,48456 14,63788 5839,636 0,282501 2,368165 0,4222679082700 329,07476 15,20087 5814,725 0,280044 2,346499 0,4261667322800 327,21018 15,76387 5781,778 0,277133 2,320827 0,430880947

2851,331 326,07645 16,05286 5761,745 0,275463 2,306092 0,4336340052900 324,89083 16,32687 5740,795 0,273768 2,291147 0,43646273000 322,11671 16,88986 5691,777 0,269949 2,257459 0,4429759353100 318,88781 17,45286 5634,722 0,265675 2,219764 0,4504983373200 315,20414 18,01585 5569,632 0,260947 2,178062 0,4591238213300 311,06569 18,57885 5496,506 0,255764 2,132352 0,4689657393400 306,47247 19,14184 5415,344 0,250127 2,082635 0,4801609983500 301,42447 19,70484 5326,147 0,244036 2,02891 0,4928754223600 295,9217 20,26783 5228,913 0,237491 1,971178 0,5073107733700 289,96416 20,83083 5123,644 0,230491 1,909439 0,5237140353800 283,55184 21,39382 5010,339 0,223036 1,843692 0,5423898643900 276,68475 21,95682 4888,998 0,215128 1,773938 0,563717513

Treapta a IV-a

n [rot/min] Me [Nm] v4 [m/s] FR [N] D a [m/s^2] 1/a [1/(m/s^2)]1000 291,19205 7,700551 3761,812 0,187545 1,573352 0,6355856561100 297,05864 8,470606 3837,601 0,190528 1,600397 0,6248449231200 302,47046 9,240662 3907,514 0,193128 1,623968 0,61577574

1300 307,4275 10,01072 3971,552 0,195344 1,644064 0,6082487181400 311,92976 10,78077 4029,716 0,197178 1,660686 0,6021606271500 315,97726 11,55083 4082,004 0,198628 1,673834 0,597430691600 319,56997 12,32088 4128,417 0,199695 1,683508 0,5939978021700 322,70792 13,09094 4168,955 0,200379 1,689707 0,5918185111800 325,39109 13,86099 4203,618 0,200679 1,692432 0,5908656191900 327,61948 14,63105 4232,406 0,200597 1,691683 0,591127332000 329,3931 15,4011 4255,319 0,200131 1,687459 0,5926068772100 330,71195 16,17116 4272,356 0,199282 1,679761 0,5953226292200 331,57602 16,94121 4283,519 0,198049 1,668589 0,5993086572300 331,98531 17,71127 4288,807 0,196434 1,653943 0,6046158242400 331,93984 18,48132 4288,219 0,194435 1,635822 0,611313432500 331,43959 19,25138 4281,757 0,192053 1,614227 0,6194915482600 330,48456 20,02143 4269,419 0,189288 1,589158 0,6292641722700 329,07476 20,79149 4251,206 0,18614 1,560614 0,6407734112800 327,21018 21,56154 4227,118 0,182608 1,528596 0,654195026

2851,331 326,07645 21,95682 4212,472 0,180646 1,510812 0,6618958452900 324,89083 22,3316 4197,155 0,178693 1,493104 0,6697457353000 322,11671 23,10165 4161,317 0,174395 1,454137 0,6876929023100 318,88781 23,87171 4119,604 0,169714 1,411697 0,7083674783200 315,20414 24,64176 4072,016 0,164649 1,365782 0,7321814993300 311,06569 25,41182 4018,553 0,159201 1,316392 0,7596520243400 306,47247 26,18187 3959,215 0,15337 1,263529 0,791434443500 301,42447 26,95193 3894,001 0,147156 1,207191 0,8283696183600 295,9217 27,72198 3822,913 0,140559 1,147378 0,8715521043700 289,96416 28,49204 3745,95 0,133578 1,084092 0,9224311133800 283,55184 29,26209 3663,111 0,126214 1,017331 0,9829642813900 276,68475 30,03215 3574,397 0,118467 0,947096 1,055859349

Treapta a V-a

n [rot/min] Me [Nm] v5 [m/s] FR [N] D a [m/s^2] 1/a [1/(m/s^2)]1000 291,19205 10,53268 2750,3 0,132342 1,095217 0,9130606551100 297,05864 11,58595 2805,71 0,13352 1,106123 0,9040583311200 302,47046 12,63921 2856,824 0,134323 1,113552 0,8980268231300 307,4275 13,69248 2903,644 0,13475 1,117505 0,8948505851400 311,92976 14,74575 2946,167 0,134801 1,117981 0,894469704

1500 315,97726 15,79902 2984,396 0,134477 1,11498 0,8968770361600 319,56997 16,85229 3018,329 0,133777 1,108503 0,9021178771700 322,70792 17,90555 3047,967 0,132701 1,098548 0,9102921061800 325,39109 18,95882 3073,309 0,13125 1,085118 0,921559021900 327,61948 20,01209 3094,356 0,129423 1,06821 0,9361452832000 329,3931 21,06536 3111,108 0,127221 1,047826 0,9543567662100 330,71195 22,11862 3123,564 0,124643 1,023965 0,976595472200 331,57602 23,17189 3131,726 0,121689 0,996628 1,0033833822300 331,98531 24,22516 3135,591 0,118359 0,965814 1,0353960842400 331,93984 25,27843 3135,162 0,114654 0,931523 1,0735105112500 331,43959 26,3317 3130,437 0,110573 0,893756 1,1188737632600 330,48456 27,38496 3121,417 0,106116 0,852512 1,173004232700 329,07476 28,43823 3108,101 0,101284 0,807791 1,2379437332800 327,21018 29,4915 3090,49 0,096076 0,759594 1,316493085

2851,331 326,07645 30,03215 3079,782 0,093257 0,733503 1,3633201252900 324,89083 30,54477 3068,584 0,090493 0,70792 1,4125893743000 322,11671 31,59804 3042,383 0,084534 0,652769 1,5319351423100 318,88781 32,6513 3011,886 0,078199 0,594142 1,68309983200 315,20414 33,70457 2977,094 0,071488 0,532038 1,8795654913300 311,06569 34,75784 2938,006 0,064402 0,466457 2,1438192823400 306,47247 35,81111 2894,623 0,05694 0,3974 2,5163566943500 301,42447 36,86437 2846,945 0,049103 0,324866 3,0781922843510 300,89466 36,9697 2841,941 0,048298 0,317421 3,1503863593600 295,9217 37,91764 2794,972 0,04089 0,248855  3700 289,96416 38,97091 2738,703 0,032301 0,169368  3800 283,55184 40,02418 2678,139 0,023336 0,086404  3900 276,68475 41,07745 2613,279 0,013996 0  

Bilantul de putere

Acesta reprezinta echilibrul dintre puterea la roata PR si suma puterilor necesare invingerii rezistentelor la inaintare si se determina cu relatia :

PR= Pe*η tr= Pr+Pp+Pa+Pd=vi*(Ga*f*cosα+Gasinα+K*S*vi^2+δ*Ga*aa)

Pr = puterea consumata pentru invingerea rezistentelor la rulare Pp = puterea necesara invingerii rezistentei la urcarea pantei Pa = puterea necesara invingerii rezistentei aeruluiPd = puterea necesara invingerii rezistentei la demarare

PR= Pe*η trPp+r+a= (vi*(Ga*Ψ+K*S*vi^2))/1000

Ψ= f*cosα+sinαΨ1= 0,289095 α= 16 °Ψ2= 0,272342 α= 15 °Ψ3= 0,187435 α= 10 °Ψ5= 0,101102 α= 5 °Ψ5= 0,014 α= 0 °

      α=16°     α=15°Pe [kW] v1 [m/s] PR [kW] Pp+r+a [kW] v2 [m/s] PR [kW] Pp+r+a [kW]30,49356 3,009337 28,96888223 17,10686362 4,116118 28,96888 22,09051426

34,2187 3,31027 32,50776395 18,82627543 4,52773 32,50776 24,3218931138,00956 3,611204 36,10908056 20,54818022 4,939341 36,10908 26,5596512241,85185 3,912138 39,75925926 22,27280463 5,350953 39,75926 28,8043685345,73129 4,213071 43,44472724 24,00037529 5,762565 43,44473 31,0566249749,63359 4,514005 47,1519117 25,73111885 6,174177 47,15191 33,3170004753,54446 4,814939 50,86723984 27,46526192 6,585788 50,86724 35,5860749757,44962 5,115872 54,57713886 29,20303116 6,9974 54,57714 37,8644283961,33477 5,416806 58,26803596 30,94465319 7,409012 58,26804 40,1526406865,18564 5,71774 61,92635833 32,69035465 7,820624 61,92636 42,4512917668,98793 6,018673 65,53853318 34,44036217 8,232236 65,53853 44,7609615872,72736 6,319607 69,09098771 36,19490239 8,643847 69,09099 47,0822300576,38963 6,620541 72,57014911 37,95420194 9,055459 72,57015 49,4156771279,96047 6,921474 75,96244458 39,71848746 9,467071 75,96244 51,7618827183,42558 7,222408 79,25430132 41,48798559 9,878683 79,2543 54,1214267786,77068 7,523342 82,43214653 43,26292295 10,29029 82,43215 56,4948892189,98148 7,824275 85,48240741 45,04352619 10,70191 85,48241 58,88284999

93,0437 8,125209 88,39151115 46,83002193 11,11352 88,39151 61,2858890295,94304 8,426143 91,14588496 48,62263682 11,52513 91,14588 63,7045862597,36338 8,580614 92,49521249 49,54524967 11,73641 92,49521 64,9523916798,66522 8,727076 93,73195603 50,42159748 11,93674 93,73196 66,1395216101,1959 9,02801 96,13615157 52,22713056 12,34835 96,13615 68,59127501103,5209 9,328944 98,34489877 54,03946269 12,75997 98,3449 71,06042642105,6259 9,629878 100,3446248 55,8588205 13,17158 100,3446 73,54755574107,4966 9,930811 102,1217569 57,68543062 13,58319 102,1218 76,05324293109,1187 10,23174 103,6627223 59,5195197 13,9948 103,6627 78,57806791110,4778 10,53268 104,9539481 61,36131437 14,40641 104,9539 81,12261061111,5599 10,83361 105,9818616 63,21104125 14,81802 105,9819 83,68745097112,3504 11,13455 106,73289 65,068927 15,22964 106,7329 86,27316891112,8352 11,43548 107,1934604 66,93519824 15,64125 107,1935 88,88034439

113 11,73641 107,35 68,8100816 16,05286 107,35 91,50955731    α=10°     α=5°     α=0°

v3 [m/s] PR [kW] Pp+r+a [kW] v4 [m/s] PR [kW] Pp+r+a [kW] v5 [m/s] PR [kW] Pp+r+a [kW]

5,629953 28,96888 20,95139568 7,700551 28,96888 15,90793853 10,53268 28,96888223 4,512611526

6,192949 32,50776 23,1036686 8,470606 32,50776 17,64493012 11,58595 32,50776395 5,337976113

6,755944 36,10908 25,27226532 9,240662 36,10908 19,4236925 12,63921 36,10908056 6,270227397

7,31894 39,75926 27,45866984 10,01072 39,75926 21,24802301 13,69248 39,75925926 7,319082349

7,881935 43,44473 29,66436613 10,78077 43,44473 23,12171898 14,74575 43,44472724 8,494257941

8,44493 47,15191 31,89083819 11,55083 47,15191 25,04857777 15,79902 47,1519117 9,805471146

9,007926 50,86724 34,13956999 12,32088 50,86724 27,03239672 16,85229 50,86723984 11,26243894

9,570921 54,57714 36,41204551 13,09094 54,57714 29,07697317 17,90555 54,57713886 12,87487828

10,13392 58,26804 38,70974875 13,86099 58,26804 31,18610447 18,95882 58,26803596 14,65250616

10,69691 61,92636 41,03416368 14,63105 61,92636 33,36358796 20,01209 61,92635833 16,60503954

11,25991 65,53853 43,38677428 15,4011 65,53853 35,61322099 21,06536 65,53853318 18,74219539

11,8229 69,09099 45,76906454 16,17116 69,09099 37,93880089 22,11862 69,09098771 21,0736907

12,3859 72,57015 48,18251845 16,94121 72,57015 40,34412502 23,17189 72,57014911 23,60924242

12,94889 75,96244 50,62861997 17,71127 75,96244 42,83299071 24,22516 75,96244458 26,35856753

13,51189 79,2543 53,10885311 18,48132 79,2543 45,40919531 25,27843 79,25430132 29,331383

14,07488 82,43215 55,62470183 19,25138 82,43215 48,07653617 26,3317 82,43214653 32,53740582

14,63788 85,48241 58,17765013 20,02143 85,48241 50,83881062 27,38496 85,48240741 35,98635294

15,20087 88,39151 60,76918198 20,79149 88,39151 53,69981602 28,43823 88,39151115 39,68794134

15,76387 91,14588 63,40078137 21,56154 91,14588 56,6633497 29,4915 91,14588496 43,65188799

16,05286 92,49521 64,7676457 21,95682 92,49521 58,22561059 30,03215 92,49521249 45,79167172

16,32687 93,73196 66,07393229 22,3316 93,73196 59,73320902 30,54477 93,73195603 47,88790987

16,88986 96,13615 68,7901187 23,10165 96,13615 62,91319131 31,59804 96,13615157 52,40572395

17,45286 98,3449 71,55082461 23,87171 98,3449 66,20709391 32,6513 98,34489877 57,2150472

18,01585 100,3446 74,35753398 24,64176 100,3446 69,61871418 33,70457 100,3446248 62,32559659

18,57885 102,1218 77,21173081 25,41182 102,1218 73,15184945 34,75784 102,1217569 67,7470891

19,14184 103,6627 80,11489907 26,18187 103,6627 76,81029707 35,81111 103,6627223 73,48924169

19,70484 104,9539 83,06852276 26,95193 104,9539 80,59785439 36,86437 104,9539481 79,56177134

20,26783 105,9819 86,07408584 27,72198 105,9819 84,51831874 37,91764 105,9818616 85,97439503

20,83083 106,7329 89,13307231 28,49204 106,7329 88,57548748 38,97091 106,73289 92,73682972

21,39382 107,1935 92,24696615 29,26209 107,1935 92,77315794 40,02418 107,1934604 99,85879238

21,95682 107,35 95,41725134 30,03215 107,35 97,11512747 41,07745 107,35 107,35

Calculul timpului si spatiului de demarare in functie de viteza

Timpul de demarare

td= ti-1+(1/ai+1/ai-1)(vi-vi-1/2)

Spatiul de demarare

Sd= Si-1+(ti-ti-1)vi-(ti-ti-1)*(vi-vi-1/2)

  v [m/s] 1/a [s^2/m] td [s] Sd [m]Treapta I 3,009337 0,25913341 0,38991 0,586685

  3,31027 0,25393182 0,467109 0,83062  3,611204 0,24932695 0,542833 1,09268  3,912138 0,24526547 0,617253 1,372622  4,213071 0,24170261 0,690525 1,6703  4,514005 0,23860081 0,762795 1,985651  4,814939 0,23592865 0,834196 2,318699  5,115872 0,23366001 0,904853 2,669542  5,416806 0,23177337 0,974886 3,038356  5,71774 0,23025132 1,044405 3,42539  6,018673 0,22908009 1,113519 3,830966  6,319607 0,2282493 1,182332 4,255482  6,620541 0,22775165 1,250945 4,699413  6,921474 0,22758283 1,319458 5,163314  7,222408 0,22774138 1,387969 5,647821  7,523342 0,22822866 1,456577 6,153662  7,824275 0,22904892 1,525383 6,681659

  8,125209 0,23020932 1,594486 7,232739  8,426143 0,23172019 1,663991 7,80794  8,580614 0,23263614 1,699856 8,112913  8,727076 0,23359514 1,733998 8,408378  9,02801 0,2358515 1,804634 9,035454  9,328944 0,23851064 1,87601 9,690574  9,629878 0,24159852 1,948251 10,37537  9,930811 0,24514638 2,02149 11,09167  10,23174 0,24919159 2,095871 11,84153  10,53268 0,25377866 2,171552 12,62726  10,83361 0,25896063 2,248702 13,45147  11,13455 0,26480077 2,32751 14,31711  11,43548 0,27137475 2,408187 15,22755  11,73641 0,27877343 2,490966 16,18662

Treapta II 11,73641 0,31112577 2,490966 16,18662  11,93674 0,31261089 2,553442 16,92613  12,34835 0,31607579 2,68283 18,49722  12,75997 0,32012665 2,813764 20,14099  13,17158 0,32480593 2,946495 21,86195  13,58319 0,33016468 3,081292 23,66518  13,9948 0,33626399 3,218447 25,5564  14,40641 0,34317696 3,35828 27,54212  14,81802 0,35099107 3,501143 29,62967  15,22964 0,35981131 3,647431 31,82747  15,64125 0,36976425 3,797582 34,14512

  16,05286 0,38100326 3,952094 36,59368Treapta III 16,05286 0,433634 3,952094 36,59368

  16,32687 0,4364627 4,0713 38,52361  16,88986 0,44297594 4,31886 42,63517

  17,45286 0,45049834 4,570371 46,95396  18,01585 0,45912382 4,826427 51,49495  18,57885 0,46896574 5,087682 56,27523

  19,14184 0,480161 5,354859 61,31428  19,70484 0,49287542 5,628767 66,63448  20,26783 0,50731077 5,910317 72,26163  20,83083 0,52371403 6,200548 78,22568  21,39382 0,54238986 6,500654 84,56161

  21,95682 0,56371751 6,81202 91,31059Treapta IV 21,95682 0,66189585 6,81202 91,31059

  22,3316 0,66974574 7,061557 96,83637  23,10165 0,6876929 7,584208 108,7092  23,87171 0,70836748 8,12173 121,3338  24,64176 0,7321815 8,676381 134,7879  25,41182 0,75965202 9,250778 149,1632  26,18187 0,79143444 9,847989 164,5694  26,95193 0,82836962 10,47166 181,1383  27,72198 0,8715521 11,12617 199,0308  28,49204 0,92243111 11,81691 218,4452  29,26209 0,98296428 12,55054 239,6303

  30,03215 1,05585935 13,33554 262,9034Treapta V 30,03215 1,36332013 13,33554 262,9034

  30,54477 1,41258937 14,04703 284,4533  31,59804 1,53193514 15,59772 332,6354  32,6513 1,6830998 17,29086 387,0271  33,70457 1,87956549 19,16708 449,2762  34,75784 2,14381928 21,28594 521,8071  35,81111 2,51635669 23,74014 608,4025  36,86437 3,07819228 26,68642 715,4636  36,9697 3,15038636 27,01444 727,573

Franarea autovehiculului

Aprecierea capacitatii de franare se face cu ajutorul deceleratiei maxime si a spatiului de franare minim care se determina cu ajutorul relatiilor :

af= g*(f+φ)Sf= (v^2)/(2*g)*(φ+f)

daca se considera ca viteza initiala de la care se incepe franarea este v max [m/s] si franarea este totala (viteza la sfarsitul franarii va este 0)si are loc pe drum orizontal ( α= 0) cu motorul decuplat si neglijindu-se rezistenta aerului si rezistenta la rulare.

Spatiul real de oprire se determina cu relatia :So= Sf+v*(t1+t0)

in care ultimul termen reprezinta timpul suplimentar parcurs de automobil in timpul intirzierilor (virsta conducatorului auto, intirzierea la actionarea dispozitivului de franare):

t1= 0,5t0= 0,7

Daca se tine cont si de forta rezistenta a aerului atunci Sf si af se calculeaza cu formula:Sf= (Ga/2*g*K*S)*ln(1+(K*S*v^2/(φ*Ga+f*Ga)))af= g*(f+φ+(K*S*v^2)/Ga)

Tipul drumului                         Asfalt uscat v [m/s] Sf [m] Sf cu Fa [m] So [m] af [m/s^2] af cu Fa

φ= 0,8 0 0 0 0 8,02458 8,02458f= 0,018 5 1,557714 1,556034795 7,557713924 8,02458 8,041905

    10 6,230856 6,204104869 18,2308557 8,02458 8,09388    15 14,01943 13,8849592 32,01942532 8,02458 8,180505    20 24,92342 24,50261071 48,92342278 8,02458 8,30178    25 38,94285 37,92823162 68,9428481 8,02458 8,457705    30 56,0777 54,00514145 92,07770126 8,02458 8,64828    35 76,32798 72,55450164 118,3279823 8,02458 8,873505    40 99,69369 93,3813153 147,6936911 8,02458 9,13338    41,07745 105,1368 98,14780651 154,4296895 8,02458 9,193918

Pamant batatorit v [m/s] Sf [m] Sf cu Fa [m] So [m] af [m/s^2] af cu Faφ= 0,6 0 0 0 0 6,13125 6,13125f= 0,025 5 2,038736 2,035860982 8,038735984 6,13125 6,148575

    10 8,154944 8,109201632 20,15494393 6,13125 6,20055    15 18,34862 18,11919185 36,34862385 6,13125 6,287175    20 32,61978 31,90388722 56,61977574 6,13125 6,40845    25 50,9684 49,24867032 80,96839959 6,13125 6,564375    30 73,3945 69,89677138 109,3944954 6,13125 6,75495    35 99,89806 93,56085408 141,8980632 6,13125 6,980175    40 130,4791 119,9346812 178,479103 6,13125 7,24005    41,07745 137,603 125,9424706 186,8959192 6,13125 7,300588

Asfalt umed v [m/s] Sf [m] Sf cu Fa [m] So [m] af [m/s^2] af cu Fa

φ= 0,4 0 0 0 0 4,1202 4,1202f= 0,02 5 3,033833 3,027472661 9,033833309 4,1202 4,137525

    10 12,13533 12,03440779 24,13533324 4,1202 4,1895    15 27,3045 26,80051933 45,30449978 4,1202 4,276125    20 48,54133 46,97817554 72,54133295 4,1202 4,3974    25 75,84583 72,11834736 105,8458327 4,1202 4,553325    30 109,218 101,7012095 145,2179991 4,1202 4,7439    35 148,6578 135,1674332 190,6578321 4,1202 4,969125    40 194,1653 171,946861 242,1653318 4,1202 5,229    41,07745 204,7663 180,2519649 254,0592803 4,1202 5,289538

Zapada batatorita v [m/s] Sf [m] Sf cu Fa [m] So [m] af [m/s^2] af cu Faφ= 0,2 0 0 0 0 2,2563 2,2563f= 0,03 5 5,540043 5,518882078 11,54004343 2,2563 2,273625

    10 22,16017 21,82667153 34,16017374 2,2563 2,3256    15 49,86039 48,21302639 67,86039091 2,2563 2,412225    20 88,64069 83,60421531 112,6406949 2,2563 2,5335    25 138,5011 126,6963294 168,5010858 2,2563 2,689425    30 199,4416 176,0923453 235,4415636 2,2563 2,88    35 271,4621 230,4183788 313,4621283 2,2563 3,105225    40 354,5628 288,4064768 402,5627798 2,2563 3,3651    41,07745 373,9212 301,270896 423,2140868 2,2563 3,425638

Stabilitatea autovehiculului

Se determina cu ajutorul vitezei critice de derapare si de rasturnare:

v cr d= sqrt[(g*R*(φ+tgβ))/(1-φ*tgβ)]v cr r= sqrt[((g*R*B1/2*hg)+tgβ)/((1-B1*tgβ)/2*hg)]

R- Raza de virajφ- Coeficient de aderentaφ= 0,2φ= 0,4φ= 0,6φ= 0,8

β= 0 °

hg- Inaltimea centrului de greutatehg= 0,42 m incarcat

Viteza critica de derapare

φ= 0,8 0,6 0,4 0,2R [m] Vcd β=0 Vcd β=0 Vcd β=0 Vcd β=0

50 19,80909 17,15517 14,00714 9,904544100 28,01428 24,26108 19,80909 14,00714150 34,31035 29,71363 24,26108 17,15517200 39,61818 34,31035 28,01428 19,80909250 44,29447 38,36014 31,32092 22,14723300 48,52216 42,02142 34,31035 24,26108

Viteza critica de rasturnare

  IncaracatR [m] Vcr β=0

50 29,59549100 41,85434150 51,26089200 59,19097250 66,17752300 72,49384

Viteza critica de derapare β=0°

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Viteza critica de rasturnarela autovehiculul incarcat

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