Dynamically Equivalent Systems. Dynamically Equivalent Systems. Dynamically Equivalent Systems. ME 201 Mechanics of Machines

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1 ME 0 Mechnics of Mchines 8//006 Dynmicy Equivent Systems Ex: Connecting od G Dynmicy Equivent Systems. If the mss of the connecting od m G m m B m m m. Moment out cente of gvity shoud e zeo m G m B Theefoe; m m ( ) m x m x m m ( ) Dynmicy Equivent Systems m G m 3. Moment of ineti, out n xis though G B pependicu to the pne, of oth systems shoud e equ. If the dius of gytion of the oigin system is k, Moment of ineti out G I mk Moment of ineti out G of the equivent system Thus I m m m m mk k 3 ME 0 Mechnics of Mchines Tuning Moment Digm nd Fywhees sng Rtnwee Deptment of Fcuty of Engineeing Univesity of Pedeniy

ME 0 Mechnics of Mchines 8//006 Tuning Moment In gene, tuning moment is toque which ottes shft.

foce of the ecipocting pts Oveview of Inten Comustion Engines Top ded cente Stoke Bottom ded cente Tuning moment 5 6 Exmpe: Fou Stoke Spk Ignition (SI) Engine

doing wok Stoke 4: Poduct gses pushed out of the cyinde though the exhust vve Exmpe: Fou Stoke Spk Ignition (SI) Engine Pessue nd tempetue pidy inceses duing the

2 ME 0 Mechnics of Mchines 8//006 Tuning Moment In gene, tuning moment is toque which ottes shft. Ex: The toque t the cnk shft of n inten comustion engine The toque t the cnk shft of n inten comustion engine gey dependent on; the in-cyinde gs pessue the ineti foce of the ecipocting pts Oveview of Inten Comustion Engines Top ded cente Stoke Bottom ded cente Tuning moment 5 6 Exmpe: Fou Stoke Spk Ignition (SI) Engine Stoke : Fue-i mixtue intoduced into the cyinde though intke vve Stoke : Fue-i mixtue compessed Stoke 3: Comustion (oughy constnt voume) occus nd poduct gses expnd doing wok Stoke 4: Poduct gses pushed out of the cyinde though the exhust vve Exmpe: Fou Stoke Spk Ignition (SI) Engine Pessue nd tempetue pidy inceses duing the comustion nd hence the piston is pushed down. Howeve, the comustion pocess occus ony once in fou stokes o two evoutions. Theefoe, thee is significnt fuctution of enegy duing once engine cyce. 7 In-cyinde pessue Vs. Cnk nge position 8

ME 0 Mechnics of Mchines 8//006 x Ccution of Tuning Moment Top ded cente F P T α θ F Q F T The tuning Moment T; sin θ T Fp sinθ n sin θ Whee n F P Net od on the piston (P) Ineti foces (Q) Lod on the

. The tot Ineti foce Q M x 9 Ccution of Tuning Moment: Ineti foces x n Top ded cente (TDC) T F P α θ F Q F T Piston position fom the TDC [ cosθ cosα ] [ cosθ cosα ] x x ( n ) n sinα sinθ ( n sin θ )

3 ME 0 Mechnics of Mchines 8//006 x Ccution of Tuning Moment Top ded cente F P T α θ F Q F T The tuning Moment T; sin θ T Fp sinθ n sin θ Whee n F P Net od on the piston (P) Ineti foces (Q) Lod on the piston (P) cn e ccuted consideing the in-cyinde gs pessue If the mss of the ecipocting pts is M.. The tot Ineti foce Q M x 9 Ccution of Tuning Moment: Ineti foces x n Top ded cente (TDC) T F P α θ F Q F T Piston position fom the TDC [ cosθ cosα ] [ cosθ cosα ] x x ( n ) n sinα sinθ ( n sin θ ) cosα n x n / ( n ) cosθ ( sin θ ) cos θ cceetion x cosθ n.. Q M x / 0 IC Engines: Tuning Moment sin θ T ( P Q) sinθ n sin θ cos θ Q M cosθ n T The toque t the cnk shft o the tuning moment is gey dependent on; The in-cyinde gs pessue The ineti foce of the ecipocting pts s expined ove the gs pessue fuctutes ove compete cyce The cceetion nd deceetion of the piston ssemy so chnges duing the motion ove cyce Theefoe the Tuning Moment so fuctutes ove n engine cyce Tuning Moment Digm of n SI Engine T ( P Q) sinθ sin θ n sin θ positive egions duing suction nd exhust oops e due to ineti effects cos θ Q M cosθ n 3

ME 0 Mechnics of Mchines 8//006 Tuning Moment Digm of SI Engine The Fuctution Tuning Moment cn e contoed to some extent y incesing nume of cyindes (Muti-cyinde engines)

(depends on the cpcity) Theefoe, compete smoothness cn not e chieved y ony incesing the nume of cyindes fywhee is usuy couped to the cnk shft to imit the fuctution of

FLYWHEEL 3 Two whee tcto Cnk piston ssemy of fou cyinde engine 4 Fywhee Fywhee is mechnic eement widey found in the shpe of disc o puey.

4 ME 0 Mechnics of Mchines 8//006 Tuning Moment Digm of SI Engine The Fuctution Tuning Moment cn e contoed to some extent y incesing nume of cyindes (Muti-cyinde engines) Tuning Moment Digm of SI Engine Pcticy it is not possie to uid engines with cyindes eyond cetin nume. (depends on the cpcity) Theefoe, compete smoothness cn not e chieved y ony incesing the nume of cyindes fywhee is usuy couped to the cnk shft to imit the fuctution of tuning moment nd hence the fuctution of speed. FLYWHEEL 3 Two whee tcto Cnk piston ssemy of fou cyinde engine 4 Fywhee Fywhee is mechnic eement widey found in the shpe of disc o puey. When otting, Fywhee cts s n enegy esevoi It stoes enegy duing the peiod when the suppy of enegy is moe thn the equiement nd eeses enegy duing the peiod when the equiement is moe thn the suppy. Kinetic Enegy E I Theefoe, Fywhees e used to minimize the enegy fuctution in mchines when the input o output toque is not unifom. 5 Fywhees: Some moe ppictions FLYWHEEL Sewing mchine Punching pess 6 4

ME 0 Mechnics of Mchines 8//006 Fywhees: Some moe ppictions Eectic moto Roto of n eectic moto cn e teted s fy whee fo mechnic nysis Roto Coss section of n eectic moto 7 Fuctution of Enegy To dive od,

(wokdone is the e (shded e) unde the cuve) Fom to B the engine poduces ess toque thn the equiement nd fom B to C it poduces B C D moe. gin fom C to D it poduces ess.

5 ME 0 Mechnics of Mchines 8//006 Fywhees: Some moe ppictions Eectic moto Roto of n eectic moto cn e teted s fy whee fo mechnic nysis Roto Coss section of n eectic moto 7 Fuctution of Enegy To dive od, the engine hs to poduce toque equivent to T men (men esisting toque) s shown in the figue. (wokdone is the e (shded e) unde the cuve) Fom to B the engine poduces ess toque thn the equiement nd fom B to C it poduces B C D moe. gin fom C to D it poduces ess. Theefoe thee is fuctution of enegy ove ech cyce. Tht wi ed to fuctution of speed 8 Mximum fuctution of enegy Conside the tuning moment digm shown eow Mximum fuctution of enegy Conside the tuning moment digm shown eow If the getest of the enegies is t B nd est is t E. Thus, If the enegy vie t is E Wok foce x distnce moved Wok done is the e unde the cuve (shded e) Thus; Enegy t C E - Enegy t D E - 3 Enegy t E E Enegy t F E Enegy t B E Enegy t F E Mximum enegy E Minimum enegy E Mximum fuctution of enegy; Mximum enegy - Minimum enegy E (E )

6 ME 0 Mechnics of Mchines 8//006 Mximum fuctution of enegy Men kinetic enegy (K.E.) in the fywhee; E I mk whee m mss of the Fywhee in kg, k dius of gytion in metes, I mss moment of ineti out the xis of ottion, Mximum fuctution of enegy (s speed chnges fom to ) I I I ( ) ( )( ) ( ) ( ) I Mximum K.E. Minimum K.E. C s I I I C s Men speed Coefficient of fuctution of speed Coefficient of Fuctution of Enegy The tio of the mximum fuctution of enegy to the wok done pe cyce is ced coefficient of fuctution of enegy: Mximum fuctution of enegy C E Wok done pe cyce Wok done pe cyce T men x θ Whee θ nge tuned in one cyce T men -men toque P 60 P T men πn P 60 n n Nume of woking stokes pe minute P - powe tnsmitted in wtts N speed in ev/min, speed in d/s 6

Electric Potential. and Equipotentials

Electric Potential. and Equipotentials Electic Potentil nd Euipotentils U Electicl Potentil Review: W wok done y foce in going fom to long pth. l d E dl F W dl F θ Δ l d E W U U U Δ Δ l d E W U U U U potentil enegy electic potentil Potentil