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INTRODUCTION • The dynamic dynamic structur structural al calculation calculation allows to determine determine the stress of the elevator during its operation. • Phases: 1.
Find the exte Find externa rnall forces forces and and their their comb combina inatio tion, n, that that act act on the the structure.
2.
Displacem Displa cement ent,, stress stress and and reacti reaction on calcu calculat lation ion of of each each of the the components applying the adequate calculation process.
3.
Verificat Verifi cation ion of the the obtai obtained ned valu values es of elast elastici icity, ty, resis resistan tance ce and and stability.
Nowadays: Finite element element programs are used
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INTRODUCTION • Lo Load adss to to be be con consi side dere red: d: –
–
–
–
Principal loads acting acting on the structure for for the motionless motionless elevator. elevator. The worst loads are: •
Norma No rmall oper operatio ation n load load:: serv service ice loa load d + acce accesso ssorie riess
•
Selff weight Sel weight:: crane crane compo componen nents ts weig weight ht (set (set aside aside oper operati ation on load load))
Loads due to vertical movements: movements: •
Acc ccel eler erat atio ions ns or de dece cele lera rati tion onss
•
Vert Ve rtic ical al im impa pact ctss due due to th thee rol rolle lers rs
Loads due to horizontal movements: movements: •
Acc ccel eler erat atio ions ns or de dece cele lera rati tion onss
•
Centrifugal force
•
Lat ater eral al ef effe fect ctss due due to ro roll llin ing g
•
Impact effects
Loads due to changes in climate: climate: •
–
Win ind, d, sno snow w and and tem tempe pera ratu ture re ef effe fect ctss
Various loads: loads: •
Dime Di mens nsio ioni ning ng of ra rail ilss and and ai aisl sles es
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STRUCTURAL CALCULATION: CASE I •
CASE I: Without wind: –
The next loads are considered: static due to self weight S G, forces due to service load S L multiplied by the dynamic coefficient ψ and the two most unfavourable horizontal effects S H, set aside impact effects, multiplied by an increase factor γ c:
γ c ( SG +ψSL +SH ) –
Increasing factor γ c [UNE 58132-2] : Depends on the elevator classification group
Elevator group
A1
A2
A3
A4
A5
A6
A7
A8
γc
1,00
1,02
1,05
1,08
1,11
1,14
1,17
1,20
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STRUCTURAL CALCULATION: CASE I
γ c ( SG + ψSL + +S SH ) •
Dynamic coefficient ψ ψ: takes into account – – –
The service load lifting. The accelerations and decelerations de celerations in the lifting lifti ng process. The vertical impacts due to the rolling ro lling in the track.
Ψ=1+ξVL VL is the lift speed in m/s
ξ is an experimental experimental coefficient obtained by carrying out several tests in different elevators
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STRUCTURAL CALCULATION: CASE I Bridge and gantry crane
Jib crane
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STRUCTURAL CALCULATION: TOWER CRANE G: crane weig weight ht
Jib pendants
Jib pendants Cat head
Jib Counterweight jib
Pi=Q+Pc (load+trolley) Gc: counterweigh counterweightt weigh weightt
Mast
It is important to know the maximum load depending on the position: its values val ues are usually specified in points A and B
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STRUCTURAL CALCULATION: TOWER CRANE
Above Abo ve str struct ucture ure The jib pe The pend ndant antss ar aree su subje bject ct to tracti tra ction, on, wh while ile the ca catt hea head d is subjecte subj ected d to com compres pression, sion, flex flexure ure and she shear ar Tract Tr action ion fo force rcess in th thee jib tie tiess PB ψ ⋅ PB T1 = T1 = sen ( β ) sen ( β )
T2 =
Gc
T2 =
sen ( α )
σ1 =
Gc
σ2 =
sen ( α )
T1 A1
Von Misses
T2
σc =
A2
Forc Fo rces es in the the ca catt he head ad ar are: e:
σ f =
V=T1 ⋅ sen ( β ) +T2 ⋅ sen ( α ) H=T1 ⋅ cos (β ) -T2 ⋅ cos ( α )
τ=
M=H ⋅ h
V A M W f
H⋅m b ⋅ Iz
2
σT = σ +3τ
2
2
σ T = (σ f + σ c ) +3 + 3τ
2
m: first first mome moment nt of the the principal area
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STRUCTURAL CALCULATION: TOWER CRANE
Above Abo ve str struct ucture ure The ji The jib b is su subj bjec ecte ted d to fl flex exur uree an and d shearr for shea forces ces::
Von Misses M
l,f
=PA ⋅ L3
V pl,c =PA
M
l,f
=ψ ⋅ PA ⋅ L 3
V pl,c =ψ ⋅ PA
σ f = τ =
ψ ⋅ PA ⋅ L3 W pf
ψ ⋅ PA ⋅ m
σ T = σ f 2 +3τ 2
b ⋅ Iz
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STRUCTURAL CALCULATION: TOWER CRANE
Mast Mf =PB ⋅ L1 − G c ⋅ L 2 + G ⋅ e
Thee mas Th astt is su subj bjec ecte ted d to fl flex exur uree an and d compression comp ression forces Jib tie
Jib tie
Vc =PB + G c + G
Cat head Jib
Mf =ψ ⋅ PB ⋅ L1 − G c ⋅ L 2 + G ⋅ e Vc =ψ ⋅ PB + G c + G
Counterweight jib Vc
L2
Mf e
L
L1=L+e σ f = σc =
Tower
ψ ⋅ PB ⋅ L1 − G c ⋅ L 2 + G ⋅ e Wmf
σ T =σ =σ f + σ C
ψ ⋅ PB + G c + G Am
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STRUCTURAL CALCULATION: CASE I
γ c ( SG +ψSL +SH ) •
Load Lo adss du duee to ho hori rizon zontal tal move moveme ment nts: s: –
Accelerations and decelerations decele rations due to translations translat ions movements of the crane
–
Acceleration or decelerations decelerati ons due to movements of the load
–
Centrifugal force
–
Lateral effects due to rolling rollin g (loads due to obliquity)
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STRUCTURAL CALCULATION: CASE I γ c ( SG +ψSL +SH )
• Acce Accelerat lerations ions or decelera decelerations tions of moveme movements nts : –
Accelerations/decelerati ons due to translation Accelerations/decelerations translatio n movements of the crane
H= –
a
g
⋅V
The acceleration/deceleration acceleration/decelera tion value depends on: on : • • •
The desired speed Tim Ti me to to acc accel eler erat ate/ e/de dece cele lera rate te Usage of of th the el elevator
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STRUCTURAL CALCULATION: CASE I
Desired speed [m/s [m/s]]
(a) Low and me mediu dium m spe speed ed wi with th largee trav larg travellin elling g Time to accelerate [s]
Acceleration [m/s2]
(b) Medium Med ium and hig high h spe speeds eds (u (usua suall applications)
(c) High Hi gh spe speed ed wit with h gr great eat accelerations
Time to accelerate [s]
Acceleration [m/s2]
Time to accelerate [s]
Acceleration [m/s2]
4,00
8,00
0,50
6,00
0,67
3,15
7,10
0,44
5,40
0,58
2,50
6,30
0,39
4,80
0,52
2,00
9,10
0,22
5,60
0,35
4,20
0,47
1,60
8,30
0,19
5,00
0,32
3,70
0,43
1,00
6,60
0,15
4,00
0,25
3,00
0,33
0,63
5,20
0,12
3,20
0,19
0,40
4,10
0,098
2,50
0,16
0,25
3,20
0,078
0,16
2,50
0,064
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STRUCTURAL CALCULATION: CASE I γ c ( SG +ψSL +SH )
• Accelerat Accelerations ions or deceler deceleration ationss of the load load movement: –
Inertia force of the load (with (wit h weight W): F=
–
Wa g
=ma
Rotational movement: T: Inertia Inertia moment moment J: Inertia Inertia polar polar moment moment = α: Angular acceleration
T=Jα
∑m d i
2 i
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STRUCTURAL CALCULATION: CASE I Inert In ertia ia fo forc rces es du duee to ro rota tati tion on::
F=me ⋅ a Equ Equival ivalen entt mass ass me =
∑
Tan Tangen gencial cial acce ccelera lerati tion on
mi di2
a=α ⋅ D
D2
F=α ⋅
∑
mi d i2 D
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STRUCTURAL CALCULATION: CASE I γ c ( SG +ψSL +SH )
•
Loads due to obliquity: – –
Tangential forces between the wheels wheels and the rail track. Guide forces.
• A simple simple translati translation on mechani mechanical cal model model is needed: needed: – –
n pairs of wheels in line. p coupled pairs. Individual (I)
Coupled (C) Fixed/Fixed (F/F) Fixed/Mobile (F/M)
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STRUCTURAL CALCULATION: CASE I γ c ( SG +ψSL +SH )
•
Load Lo adss du duee to ce cent ntri rifu fuga gall fo forc rces es:: –
Effects of the cable inclination Fc =
WR πn
2
g 30
W: Load R: Radius n: Rotating Rotating speed g: gravity acceleratio acceleration n
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STRUCTURAL CALCULATION: CASE II •
CASE II: Nor CASE Normal mal ope operat ration ion wit with h ser servic vicee lim limit it wind –
To th thee lo load adss con onssid ideere red d in CAS ASE E I it is add dded ed th thee effect of service limit wind Sw and and,, if if nee needed ded,, the the load loa d due to var variat iation ion in temp temper eratur ature: e: γc ( SG +ψSL +SH ) + S
–
Over Ov erlo load adin ingg du duee to sn snow ow is no nott co cons nsid ider ered ed..
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STRUCTURAL CALCULATION: CASE II γc ( SG +ψSL +SH ) + S
•
Wind Wi nd ef effe fect ct F=A ⋅ p ⋅ Cf
•A is the net surface, in m 2, of the considered element, that is, the solid surface projection over a perpendicular plane in the wind direction. •Cf is a shape factor, in the wind direction, for the considered element. •p is the wind pressure, in kN/m 2, and it is calculated by means of the following equation: -3 2 p = 0, 613 ⋅ 10 ⋅ vs [kPa] where vs is the calculated wind speed in m/s
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STRUCTURAL CALCULATION: CASE II Cf : Shape fact factor or [UNE 58-113-85] 58-113-85] Type
Simple elements
Simple lattice work Machine room, etc
Aerodynamic drag coefficient l/b or l/D
Description 5
10
20
30
40
50
Metal section in L, in U and flat plates
1,3
1,35
1,6
1,65
1,7
1,9
Circular metal sections in which Dvs < 6 m2/s in which Dvs ≥ 6 m2/s
0,75 0,60
0,80 0,65
0,90 0,70
0,95 0,70
1,0 0,75
1,1 0,8
1,55 1,40 1,0 0,8
1,75 1,55 1,2 0,9
1,95 1,75 1,3 0,9
2,1 1,85 1,35 1,0
2,2 1,9 1,4 1,0
Square metal sections of more than 350 mm side and rectangular of more than 250 mm x 450 mm
b/d ≥2 1 0,5 0,25
Flat side metal section
1,7
Circular metal sections in which Dvs < 6 m2/s in which Dvs ≥ 6 m2/s
1,2 0,8
Square structures filled (air cannot flow beneath the structure )
1,1
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STRUCTURAL CALCULATION: CASE II
Wind
Aerodynamic coefficient=
Section proportion=
Element length S ec ec titi on on hei gh ght f ac aci ng ng wi nd nd
=
1 b
Sect Sectio ion n hei heigh ghtt faci facing ng wind wind Sectio Section n width width para parall llel el to wind wind
or
=
1 D
b d
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STRUCTURAL CALCULATION: CASE II Spee Sp eeds ds an and d pre pressu ssure ress of se serv rvic icee wi wind nd [U [UNE NE 5858-11 1133-85] 85]
Type Type of cran cranee
Wind Wind speed speed m/s
Wind pressure pressure kPa/m2
Cranes which can be protected against wind and designed exclusively for light wind (for example, low height cra nes with an easily folding jib to the ground)
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0,125
Every normal crane installed in exteriors
20
0,25
28,5
0,50
Dock cranes that should continue operation in case of strong wind
-3 2 p = 0,613 ⋅10 ⋅ vs [kPa]
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STRUCTURAL CALCULATION: CASE II γc ( SG +ψSL +SH ) + S
•
Snow overloading: –
•
It is not considered
Temperature effect: Only when the elements cannot freely f reely expand – Temperatur Temperaturee limit -20 ºC º C + 45 ºC –
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STRUCTURAL CALCULATION: CASE III •
CASE III: Elevator subjected to exceptional loads a)
Elevato Ele vatorr out out of ser service vice subje subjecte cted d to maxi maximum mum win wind. d.
b)
Elevator in service subject to t o impact.
c)
Elevato Ele vatorr subjec subjected ted to stat static ic and dyna dynamic mic test tests. s.
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STABILITY
Wm d m > Wb d b + W d
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STABILITY
Wm
Rotation axis
Wm d m + Wf ( d o − d f ) > Wb d b + Wr d
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COUNTERWEIGHT CALCULATION It is usu usual ally ly cal calcu cula lated ted so th that at it co coun unte tera ract ctss the ha half lf of the ma mater teria iall mo mome ment nt and th thee ji jib b mo mome ment nt
Moment:
G c ⋅ d=G ⋅ e+(Pc +
2
) ⋅L
M f =(Pc + Qi ) ⋅ L+G ⋅ e-G c ⋅ d
M f =(Pc + Qi ) ⋅ L+G ⋅ e- G ⋅ e+(Pc +
P=Qi+Pc (Load+hoist)
Q
Most unfavourable situations:
Q 2
) ⋅ L = Qi −
Q
⋅ L
2
Without Wit hout load load:: Q i=0 Q M f =- ⋅ L 2 With Wit h load load:: Qi=Q
M f =
Q 2
⋅L
With this type of counterweight the mast, with and without load, has a uniform solicitation in a favourable way
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CLASSIFICATION Crane and elevators classification allows to establish the design of the structure and of the mechanisms It is used by manufacturers and clients so that a specific elevator operates within certain required service conditions.
Elevator Eleva tor class classificat ification ion Used by the client and the manufacturer to achieve a fixed elevators service conditions
Mechanism classification It gives the manufacturer information of how to design and verify the elevator so that it has the desired service life for the operation service conditions
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CLASSIFICATION OF THE EQUIPMENT CLASSIFICATION OF THE EQUIPMENT (standard 58-112-91/1) Numb Nu mber er of cyc cycle less of of a man manoe oeuv uvre re
Load Lo ad sp spec ectr trum um co coef effi fici cien entt
A manoeuvre cycle begins when the load is prepared to be lifted and finishes when the elevator is prepared to lift the next load
• The total total number number of manoeuvre manoeuvre cycles cycles is is the sum of all of the cycles cycles carried carried out during the elevator life. • The user expects expects that that the elevator’ elevator’ss manoeuvre manoeuvre number number of cycles cycles is achieved achieved during its life. • The total total numbe numberr of manoeuv manoeuvre re cycles cycles has has a relatio relationship nship with with the the usage factor: –
The manoeuvre spectrum has been conveniently divided in 10 usage classes.
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CLASSIFICATION OF THE EQUIPMENT: TOTAL NUMBER OF CYCLES
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CLASSIFICATION OF THE EQUIPMENT CLASSIFICACIÓN OF THE EQUIPMENT (standard (standard 58-112-91/1) Numb Nu mber er of cyc cycle less of of a man manoe oeuv uvre re
Load Lo ad sp spec ectr trum um co coef effi fici cien entt
The load condition is the number of times a load is lifted, which is suitable to the elevator capacity
• Depending Depending on the the available available inform information ation of the the number number and weight weight of the the loads to be lifted during the elevator life: – –
Lack of indications: manufacturer and clien t have to achieve an agreement. If the information is available: the load spectrum coe fficient of the elevator can be calculated.
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CLASSIFICATION OF THE EQUIPMENT : LOAD LEVEL
C P 3 K p = ∑ i i CT Pmax Ci is the mean number of cycles of manoeuvre for each different load level. CT is the total of the individual cycles for every load level. Pi are the values of the individual loads characteristic of the equipment service operation. Pmax is the maximum load that the equipment is authorized to lift (safe working load).
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CLASSIFICATION OF THE EQUIPMENT : LOAD LEVEL
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CLASSIFICATION OF THE COMPLETE EQUIPMENT
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CLASSIFICATION OF THE COMPLETE EQUIPMENT
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CLASSIFICATION OF THE MECHANISM CLASSIFICACIÓN OF THE MECHANISMS (standard 58-112-91/1) Usage of work equipment
Mechanism lo l oad level
It is calculated for the planned service duration in hours • Maximum Maximum service service duration duration can can be computed computed by means means of the the mean daily daily service, in hours, of the number of working days per year and the number of the planned years of service. • A mechanism mechanism is conside considered red to be on servic servicee when it it is on movement movement..
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CLASSIFICATION OF THE MECHANISM: USAGE
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CLASSIFICATION OF THE MECHANISM CLASSIFICACIÓN OF THE MECHANISMS (standard 58-112-91/1) Use of work equipment
Loads ap a pplied to t o th t he mechanism
The lo load ad lev level el is a feat featur uree th that at sh show owss how muc much h a mecha mechani nism sm is su subje bject cted ed to a max maximu imum m lo load ad,, or or on only ly to lo low w lo load ads. s.
t k m =∑ i Tt
3 Pi Pmax
ti is the mean service duration of the mechanism when subjected to individual loads. Tt iis the sum of the individual durations in all load level Pi is the individual load level of the mechanism Pmax is the maximum load applied to the mechanism
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CLASSIFICATION OF THE MECHANISM: APPLIED LOAD
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CLASSIFICATION OF THE MECHANISM
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CLASSIFICATION OF THE MECHANISM
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CLASSIFICATION
Cran Cr anee wit with h ho hook ok::
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CLASSIFICATION
Cran Cr anee wi with th ho hook ok:: Us Usag agee cl clas asss U 5
Lift Li ft cyl cylce ce
Load lift Move Mo vem men entt of th thee lo load ad Rotation Lowering Unho Un hook ok th thee lo load ad Unloade Unl oaded d lift Rotation Move Mo vem men entt of th thee lo load ad Unloade Unl oaded d lift To ho hook ok a ne new w lo load ad
tmc=150 s
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CLASSIFICATION Total To tal lengt length h us usage age of th thee ma mach chin ine: e: T=
N ⋅ t mc 3600
[h]
tmc= cycle mean length [s] N = Number of cycles
T=
5 5 ⋅10 ⋅150
3600
≈ 20835 horas
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CLASSIFICATION For each of the mechanisms it is defined:
αi =
t mechanism t mc
Load lift Move Mo veme ment nt of th thee lo load ad Rotation Lowering Unho Un hook ok th thee lo load ad Unloaded Unloa ded lift Rotation Move Mo veme ment nt of th thee lo load ad Unloaded Unloa ded lower lowering ing Hook Ho ok a new new lo load ad
tmechanism= usag usagee tim timee of of the me mecha chanism nism dur during ing one cycle cyc le [s] tmc= mean mean dur durati ation on of one cyc cycle le [s]
Liftt me Lif mecha chanism nism Slewin Sle wingg me mecha chanis nism m Movement Movem ent mech mechanism anism
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CLASSIFICATION
Liftt me Lif mecha chanism nism
Load lift Moveme Mov ement nt of the loa load d Rotation Lowering Unhoo Un hook k the loa load d Unloaded Unlo aded lift Rotation Moveme Mov ement nt of the loa load d Unloaded lowering Hook Hoo k a new new loa load d
Slew Sle w me mecha chanis nism m Load lift Moveme Mov ement nt of th thee loa load d Rotation Lowering Unhoo Un hook k the loa load d Unloaded Unlo aded lift Rotation Moveme Mov ement nt of th thee loa load d Unloaded lowering Hook Hoo k a newload
63%
Travelling Trave lling mec mechanism hanism
25%
Load lift Moveme Mov ement nt of th thee loa load d Rotation Lowering Unhoo Un hook k the loa load d Unloaded Unlo aded lift Rotation Moveme Mov ement nt of th thee loa load d Unloaded lowering Hook Hoo k a newload
10%
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CLASSIFICATION Total dur Total durati ation on of the me mecha chanis nism m in hours: Lift mech mechanism anism
αi=0.63
Τi=13126 h
Τ7
Slew mech mechanism anism
αi=0.25
Τi=5209 h
Travelling Trave lling mech mechanism anism Τi=2084 h
Τ5
αi=0.10 Τ4
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ENGINES •
Powerr cal Powe calcul culatio ation: n: Lift mov movements ements G ⋅V Pe = 2 4500 ⋅ η
Power
[CV]
Travelling Travel ling move movements ments (G +G +G 2 ) ⋅ W ⋅ V Pt = 1 45000 500000 00 ⋅ η
[CV]
G1: self weight (trolley,span, etc.) [daN] G2: load + accessories [daN] V: speed [m/min] η: mechanical efficiency W: friction coefficient 7 for rolling bearing 20 for friction bearing
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ENGINES Torque need needed ed to acce accelerate lerate:: Starting Starti ng torque = resistanc resistancee torque + accelerat acceleration ion torque
Thee re Th resi sist stan ance ce tor torqu quee on only ly ha hass to be taken taken in into to ac acco coun untt fo forr tr trav avel elli ling ng en engi gine ness MA = Mw + M b [daNm] Mw =
716 ⋅ Pt n1
[daNm]
n1: engine speed in rpm ΣGD12: inertia torque sum referred to engine axis ta: acceleration time: Lift, Lif t, cierre cierre cucha cuchara ra = 2 s Trolley travelling or bridge crane, rotation = 4 s Gantry travelling = 6 s d=
V π ⋅ n1
M b
∑ GD =
2 1
⋅ n1
375 ⋅ t a
[daNm]
Masses moved linearly GD12 =
(G1 +G 2 ) ⋅ d 2
[daNm2 ]
η
Rotating Rota ting mass GD12 = GD22
n 22 n12
[daNm2 ]
[m]
V: Mass lineal speed
25
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ENGINES
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ENGINES Power Pow er ne need eded ed to ov over erco come me wind re resi sist stan ance ce::
Pv =
S⋅ V 4500 ⋅ η
Fv: wind wind pre pressure ssure [daN [daN/m /m2] S: surf surface ace exp exposed osed to win wind d
⋅ Fv [CV]
To sel selec ectt tr trave avelli lling ng eng engine ine:: Engine power ≥ Pt +Pv
[CV]
Max. Max. moto motorr toruq toruque ue ≥ M w +Mb
[daN [daNm] m]
To se sele lect ct li lift ft en engi gine ne:: Engine power ≥ Pe +Pv
[CV]
26
