Análisis de la oferta

Lowering the load; emergency stop

This can be a dangerous situation. A crane is lowering a load; and an emergency stop is required – the crane driver then pushes the emergency

button. The hoisting mechanism does not brake electrically: it is an emergency stop. The load is now pulled down by gravity and acceler- ated sharply during the short time that it is needed to activate the brake. The activated brake starts braking the load, but is starting from a higher speed than the normal lowering speed. This means that the necessary time for braking towards zero-speed becomes longer than normal. Assuming that it is a container crane with the reeving shown in Fig. 4.2.1 (schematic).

Fig. 4.2.1 Wire rope scheme

Example

1. Weight of spreader plus load:

Q (kg) Q G66 000 kg

2. Force on the wire ropes on the drum: L (kg) (see Fig. 4.2.1) L G(Q : 2) ·ηs(kg) LG(66 000 : 2) · 0,95 G_{31 350 kg} ηsGηsheavesCdrumGn · 0,99 (nG5) 3. Torque on motorshaft: M1G

冢

L ·Ddrum 2 : igb

冣

·ηgb M1G

冢

31 350 · 1,2 2 : 24,6

冣

· 9,81(Nm) · 0,94 · 9,81 G_{7051 Nm} Drum diam. DdrumG1,2 m

Gearbox reduction igbG24,6

4. Lowering speed of the load:

û_(m兾min) û G_{60 m}兾min 5. Wire rope speed on the drum:

û_dG2 · û (m兾min) û_dG2 · 60G120 m兾min G(2 · û) : 60 (m兾sec) G_{120 : 60 G2 m}兾sec 6. Nos. of rev兾min of the drum:

ndGûd: (π · Dd) (rev兾min) ndG120 : (π · 1,2)

G_{31,84 rev}兾min 7. Nos. of rev兾min of the

motor:

nmotorGnd· igb(rev兾min) nmG31,84 · 24,6

G_{783 rev}兾min 8. Inertia moment on the

motorshaft from: motor(s); brakesheave(s) and gearbox: JrotGJmCJbCJgb(kg m 2 ) JrotG24C16C6 G_{46 kg m}2 9. Reduced inertia moment on

the motorshaft from the weight of the spreader plus load: JLG(L · û2d·ηgb) :ω21(kg m2) JLG(31 350 · 22· 0,94):

冢

783 · 2 ·π 60

冣

2 JLG117 876 : 81,952 G_{17,55 kg m}2 10. JtotalGJrotCJL(kg m2) JtotG46C17,55

11. After pushing the emergency button, the load is

accelerated by M1during∆t

sec (activating time for the brake) with ∆ω2(rad兾sec):

∆ω2G∆t · M2

Jrot

(rad兾sec) ∆ω2G(0,3 · 7051)

46 G46 rad兾sec 12. The activated brake starts

mechanical braking after ∆t sec with a rotational speed on the motorshaft of:

ω3G(ω1Cω2)(rad兾sec) ω₃G

冢

783 · 2π 60

冣

C46 ω1G(nm: 60) · 2π (rad兾sec)

G_81,95C46 G_{127,95 rad}兾sec 13. The numbers of rev兾min of

the motor- and brake-shaft is then: n2Gω3· 60 2π(rev兾min) n2G128 · 60 2πG1223 rev兾min 14. The wire rope speed on the

drum is then: û_d2Gn2 nm · ûd(m兾sec) ûd2G 1223 783 · 2 G3,123 m兾sec 15. The effective brake moment

is:

MbeGηb· Mb(Nm) MbeG0,95 · 19 000

G_{18 050 Nm} 16. The effective braking time is:

tbrakeG ω 3· Jtotal MbeAM1 (sec) tbrG 128 · 63,55 18 050A7051G0,740 sec 17. Total braking time:

18. Wire rope displacement on the drum during braking:

SdG∆S1C∆S2(m) ∆S1Gdisplacement on the drum during∆t (m) ∆S2Gdisplacement on the drum during deceleration whilst braking in tbrsec. ∆S1G û_dCû_d2 2 ·∆t (m) ∆S1 G2C3,123 2 · 0,3 G0,768 m ∆S2G 3,123 2 · 0,74 G1,155 m ∆S2G û_d2 2 · tbr(m) SdG0,768C1,155 G1,923 m 19. Total displacement of spreader and load during emergency stop: in lowering direction (see Fig. 4.2.2)

SsprCLGSd: 2 (m) SsprCLG1,923 : 2 G0,96 m

Note:

– The winch has: 2 motors; 2 brakes; 1 gearbox; 2 drums.

– The spreader and the load are suspended by eight ropefalls; 4 of which are fixed on the boom end; the other 4 falls run via wire rope sheaves to the 2 wire rope drums.

– ∆t can be taken as ∆tG0,3 sec the worst case for∆tG0,5 sec.

– The maximal peripherical speed of the brake disc must be controlled.

The allowed number of brake cycles in an emergency stop can be calcu- lated as follows:

Dissipated energy per brake cycle: WB GMbr·

n2

9,55·

tbr

Fig. 4.2.2 Lowering: emergency stop

Nos. of kWh per brake cycle: kWh G kJ

3593(kWh) Allowed numbers of emergency

Z G ûB· 2

kWh · 30(nos) brake cycles; approximately:

where

û_BG_{98 100 mm}3_{for SB23 brakes (for a certain brakepad material )} û_BG_{244 800 mm}3_{for SB28 brakes (for a certain brakepad material )} 30 Gbrakepad wear per kWh.

The maximum circumference speed of the brake disc which is allowed is: û G85 m兾sec for a brake disc of Fe52.3 (S 355 J2 G3).

4.3

Hoisting brakes

Lowering the load; braking by full motor torque

The crane driver is lowering the load and wants to halt the load by stopping the winch by ‘electric braking’. The full motor torque is to be

Fig. 4.3.1 Wire rope scheme

taken as the brake moment. The reeving scheme in Fig. 4.3.1 is assumed for a container crane.

Example

1. Weight of spreader plus

Load: Q (kg) Q G66 000 kg

2. Force on the wire ropes on the drum: L (kg) (see Fig. 4.3.1) L G(Q : 2) ·ηs(kg) LG(66 000 : 2) · 0,95 G_{31 350 kg} ηsGηsheavesCdrumGn · 0,99 (nG5) 3. Torque on motorshaft: M1G

冢

L ·Ddrum 2 : igb

冣

·ηgb M1G

冢

31 350 · 1,2 2 : 24,6

冣

· 9,81 (Nm) · 0,94 · 9,81 G_{7051 Nm} Drum diam. DdrumG1,2 m

Gearbox reduction igbG24,6

4. Lowering speed of the load:

û_(m兾min) û G_{60 m}兾min 5. Wire rope speed on the drum:

û_dG2 · û (m兾min) û_dG2 · 60G120 m兾min G_{(2 · û): 60 (m}兾sec) G_{120 : 60 G2 m}兾sec 6. Nos. of rev兾min of the drum:

ndGûd: (π · Dd) (rev兾min) ndG120 : (π · 1,2)

G_{31,84 rev}兾min 7. Nos. of rev兾min of the

motor:

nmotorGnd· igb(rev兾min) nmG31,84 · 24,6

G_{783 rev}兾min 8. Inertia moment on the

motorshaft from:

Motor(s); brake sheave(s) and gearbox:

JrotGJmCJbCJgb(kg m2) JrotG24C16C6

G_{46 kg m}2 9. Reduced inertia moment on

the motorshaft from the weight of the spreader plus load: JLG(L · û2d·ηgb) :ω12(kg m2) J_LG(31 350 · 22· 0,94) :

冢

783,2π 60

冣

2 JLG117 876 : 81,952 G_{17,55 kg m}2 10. JtotalGJrotCJL(kg m2) JtotG46C17,55

11. Braking is immediately started with the electric current, delivering the nominal motor torque. (The 2 motors deliver in total

N G720 kW at n G783 rev兾min) MnomG N · 9550 n (Nm) Mnom G720 · 9550 783

MnomGMel.braking torque MnomGMebG8781 Nm

12. ωmotG n 60· 2π (rad兾sec) ωmot G783 60 · 2π (rad兾sec) G_{81,95 rad}兾sec 13. The effective braking time is:

tbrakeG ω

mot· Jtotal

MebAM1

(sec) tbrG

81,95 · 63,55

8781A7051sec G3 sec

14. Wire rope displacement on the drum during braking:

SdG12· ûd· tbr(m) SdG12· 2 · 3 G3 m

15. Total displacement of spreader and load during electric braking in hoisting direction:

SsprCLGSd: 2 (m) SsprCLG3 : 2 G1,5 m

4.4

Hoisting brakes

Hoisting the load; braking by full motor torque

The crane driver is hoisting the load and wants to stop the load by stopping the hoisting winch by ‘electric braking’. We take now the full motor torque as brake moment. Consider a container crane with the reeving shown in Fig. 4.4.1 (schematic).

Example

1. Weight of spreader plus

load: Q (kg) Q G66 000 kg

2. Force on the wire ropes on the drum: L (kg) (see Fig. 4.4.1) L G(Q : 2) ·ηs(kg) LG(66 000 : 2) · 0,95 G_{31 350 kg} ηsGηsheavesCdrumGn · 0,99 (nG5) Fig. 4.4.1

3. Torque on motorshaft: M1G

冢

L ·Ddrum 2 : igb

冣

·ηgb M1G

冢

31 350 · 1,2 2 : 24,6

冣

· 9,81 (Nm) · 0,94 · 9,81 G_{7051 Nm} Drum diam. DdrumG1,2 m

Gearbox reduction igbG24,6

Efficiency gearbox ηgbG0,983

4. Hoisting speed of the load:

û_(m兾min) û G_{60 m}兾min 5. Wire rope speed on the drum:

û_dG2 · û (m兾min) û_dG_{2 : 60 G120 m}兾min G(2 · û) :60 (m兾sec) G_{120 : 60 G2 m}兾sec 6. Nos. of rev兾min of the drum:

ndGûd: (π :Dd) (rev兾min) ndG120 : (π · 1,2)

G_{31,84 rev}兾min 7. Nos. of rev兾min of the

motor:

nmotorGndr· igb(rev兾min) nmG31,84 · 24,6

G_{783 rev}兾min 8. Inertia moment on

motorshaft from:

motor(s); brake sheave(s) and gearbox:

JrotGJmCJbCJgb(kg m2) JrotG24C16C6

G_{46 kg m}2 9. Reduced inertia moment on

the motorshaft from the weight of the spreader plus load: JLG(L ·ν2d·ηgb) :ω12(kg m2) J_LG(31 350 · 22· 0,94):

冢

783,2π 60

冣

2 JLG117 876 : 81,952 G_{17,55 kg m}2

10. JtotalGJrotCJL(kg m2) JtotG46C17,55

G_{63,55 kg m}2 11. Braking is immediately

started with the electric current, delivering the nominal motor torque. (The 2 motors deliver in total N G720 kW at n G783 rev兾min) MnomG N · 9550 n (Nm) Mnom G720 · 9550 783

MnomGMel.braking torque MnomGMebG8781 Nm

12. ωmotG n 60· 2π (rad兾sec) ωmotG 783 60 · 2π (rad兾sec) G_{81,95 rad}兾sec 13. The effective braking time is:

tbrakeG ω mot· Jtotal MebCM1 (sec) tbrG 81,95 · 63,55 8781C7051sec G_{0,329 sec} 14. Wire rope displacement on

the drum during braking:

SdG12· ûd· tbr(m) SdG12· 2 · 0,329 G0,329 m

15. Total displacement of spreader and load during electric braking in hoisting direction:

Fig. 4.4.2 Hoisting: electrical braking by full motor torque

4.5

Hoisting brakes

Hoisting the load; emergency stop

This is not as dangerous as in the lowering situation. The crane is hoist- ing the load and something occurs so that the crane driver must use the emergency push-button. Again, the hoisting mechanism does not brake electrically, it is an emergency stop. The load is at first decelerated by gravity, during the short time that is needed to activate the brake. The activated brake starts braking the load, but is starting from a lower speed than the normal hoisting speed. Assuming again that it is a con- tainer crane, with the reeving system shown in Fig. 4.5.1 (schematic).

Example

1. Weight of spreader plus load:

Q (kg) Q G66 000 kg

2. Force on the wire ropes on the drum:

L (kg) (see Fig. 4.5.1)

L G(Q : 2) ·ηs(kg) LG(66 000 : 2) · 0,95

G_{31 350 kg} ηsGηsheavesCdrumGn · 0,99 (nG5)

Fig. 4.5.1 3. Torque on motorshaft: M1G

冢

L ·Ddrum 2 : igb

冣

:ηgb M1G

冢

31 350 · 1,2 2 : 24,6

冣

· 9,81 (Nm) · 0,94 · 9,81 G_{7051 Nm} Drum diam. DdrumG1,2 m

Gearbox reduction igbG24,6

Efficiency gearboxηgbG0,983

4. Hoisting speed of the load:

û_(m兾min) û G_{60 m}兾min 5. Wire rope speed on the drum:

û_dG2 · û (m兾min) û_dG2 · 60G120 m兾min G(2 · û) :60 (m兾sec) G_{120 : 60 G2 m}兾sec 6. Nos. of rev兾min of the drum:

ndGûd: (π · Dd) (rev兾min) ndG120 : (π · 1,2)

G_{31,84 rev}兾min 7. Nos. of rev兾min of the

motor:

nmotorGnd· igb nmG31,84 · 24,6

8. Inertia moment on the motorshaft from:

motor(s); brake sheave(s) and gearbox:

JrotGJmCJbCJgb(kg m2) JrotG24C16C6

G_{46 kg m}2 9. Reduced inertia moment on

the motorshaft from the weight of the spreader plus load: JLG(L · û2d·ηgb) :ω21(kg m2) JLG(31 350 · 22· 0,94):

冢

783 · 2 ·π 60

冣

2 JLG117 876 : 81,952 G_{17,55 kg m}2

10. JtotalGJrotCJL(kg m2) JtotG46C17,55 G63,55 kg m2

11. After pushing the emergency button, the load is

decelerated by M1 during∆t

sec (activating time for the brake) with ∆ω2(rad兾sec):

∆ω2G∆t · M1

Jrot

(rad兾sec) ∆ω2G0,3 · 7051

46 G_{46 rad}兾sec ∆ω2is here negative (negative)

12. The activated brake starts mechanical braking after ∆t sec with a rotational speed on the motorshaft of:

ω3Gω1Aω2(rad兾sec)— ω3G

冢

783 · 2π

60

冣

A46 ω1G(nm: 60) · 2π (rad兾sec) G81,95A46

13. Nos. of rev兾min of the motor- and brake-shaft is then: n2Gω3· 60 2π(rev兾min) n2G36 · 60 2πG344 (rev兾min) 14. The wire rope speed on the

drum is then: û_d2Gn2 nm · ûd(m兾sec) ûd2G 344 783· 2 G0,88 m兾sec 15. The effective brake moment

is:

MbeGηb· Mb(Nm) MbeG0,95 · 19 000

G_{18 050 Nm} 16. The effective braking time is:

tbrakeG ω 3· Jtotal MbeCM1 (sec) tbrG 36 · 63,55 18 050C7051G0,091 sec 17. Total braking time:

t G(∆tCtbr) (sec) t G0,3C0,091 G0,391 sec

18. Wire rope displacement on the drum, during braking:

SdG∆S1C∆S2(m) ∆S1Gdisplacement on the drum during∆t (m) ∆S2Gdisplacement on the drum during deceleration while braking in tbrsec ∆S1G û_dCû_d2 2 ·∆t (m) ∆SG 2C0,88 2 · 0,3 G0,432 m ∆S2G û_d2 2 · tbr(m) ∆S2G 0,88 2 · 0,091 G0,04 m SdG0,432C0,04 G0,472 m

19. Total displacement of the spreader and load during emergency stop in hoisting direction (see Fig. 4.5.2):

SsprCLGSd: 2 (m) SsprCLG0,472 : 2 G0,236 m

Fig. 4.5.2 Hoisting: emergency stop

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