Tension Profile

7/23/2019 Tension Profile

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TENSION PROFILE

DYNAMIC TENSION CLAMPS

Marco WishartEngineering ManagerRockwell Automation

Drive Systems


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TENSION PROFILE - DYNAMIC TENSION CLAMPS

Tension profile and dynamic tension clamps attempt to keep the tensions in all the zones of a process to the

desired tension references without bridle slip or horsepower limitations.

An independent zone must be determined in a process. This zone will only be limited by the minimum and

maximum tensions set forth from the mill builder. All the other zones will have dynamic clamps dependent onthis zone. The clamps will work out from the independent zone.

An example of a line is shown in drawing 1. The pickle tank tension is the independent zone. The tensionlimits are based upon the mill builders minimum and maximum values for this zone. The tension reference is

calculated based on strip width and thickness to keep a catenary loop in the tanks. The exit looper tension zone,which is to the right of the pickle tank, is dependent on the tank tension. If the tension reference to the looper

exceeds the maximum T or horsepower limits of bridle 4, the looper tension reference will be clamped to the

maximum allowable tension based on the tension seen on the entry side of bridle 4 (pickle tank tension). The exit

tension (or tension reel tension) is dependent on the looper tension. The exit tension is clamped to the maximumslip and horsepower capabilities of bridle 5. These capabilities are dependent on bridle 5 entry tension which isexit looper tension (plus losses). Exit looper tension is dependent on bridle 4 entry tension (pickle tank tension).This cascading effect protects the independent zone. This also is true of the entry side of the pickle tank starting

at leveler tension through payoff tension.

BRIDLE 1 BRIDLE 2 BRIDLE 3 BRIDLE 4 BRIDLE 5TENSION

REEL

PAYOFF

REEL

Entry (payoff)

tension zonePickle tank

tension zone

Independent

Zone

Exit (tension reel)

tension zone

Exit looper

tension zone

Leveler

tension zone

Entry looper

tension zone

B1E B4EB3XB3EB2XB2EB1X B4X B5Elosses

Line Overview

Drawing 1

If the tension references are correct and the operator does not change the tension references, the dynamictension clamping will not have any effect on the zone tensions. The only purpose of dynamic tension clamping isto prevent a bad tension senddown or operator error from adversely affecting the process.

DYNAMIC TENSION CLAMPS (DTC)

The dynamic tension clamps limit all zone tension references that may cause a bridle to slip or go into a

horsepower limit, based on the independent zone tension. The following zones are explained for the pickle lineexample.


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ENTRY TENSION DYNAMIC CLAMPING

+

x

motoring (slip)

multiplication factorfrom calculations

B1X tension

(entry side of bridle)

motoring HP

maximum delta tension

value from calculation

-regenerating (slip)

multiplication factor

from calculations

B1X tension


regenerating HP



Maximum entry

tension

(from mill builder)

Minimum entry

tension

(from mill builder)

To Exit Side of Payoff

Reel and Entry Side of

Bridle 1 Tension

Reference

Reference Select

entry tension reference

Thread tension

Stall tension

Looper tension not on tension *

Entry Tension Zone

* Entry tension is limited to fixed

value if looper tension is Off to

prevent bridle 1 slippage

Entry Tension

Ref

from level 2

Bridle 1

entry losses

-

entry

losses

-

entry

losses

B1X

Minimum

Select

Maximum

Select

Drawing 2

Entry Tension Zone- drawing 2Payoff Reel

The payoff (or unwind) reel will always have zero entry tension (since no strip is coming into the reel). Thepayoff is typically current/tension regulated. The limits for the payoff are dependent on the exit tension of bridle1.

The upper tension reference limit is bridle 1 slip/horsepower motoring limit minus the entry losses (remember,losses always add in the direction of strip travel). The lower tension reference limit is the bridle 1 slip/hp

regenerating limit minus entry losses. The entry losses are subtracted because they are seen at the entry side ofthe bridle but are not produced by the payoff reel. The entry loss value may change if equipment like levelers,

pinch rolls, etc. are in and out of the passline. This may necessitate changing the loss value as the losses change.

The payoff tension may also limited if the entry looper (strip accumulator) tension is not on. If the entry loopertension is off, the tension at the exit side of bridle 1 is zero. Many times, a pinch roll is placed on the last roll of

the entry bridle, but the pinch roll may not provide enough entry tension to allow the payoff to go to maximumtension so a reduced entry tension may be used in this situation.

Bridle 1 - entry side

Bridle 1 is the pacer for the entry end. It has a speed regulator with an outer position loop to regulate tower

position. The entry side tension reference for the bridle is entry tension reference plus entry losses. Since bridle 1is a speed regulator, the tension reference to the bridle is only used as a current regulator feedforward signal. If

the feedforward signal contains all the correct tensions and losses for the bridle, the speed regulator output should


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be zero or near zero. Examining the output of the speed regulator can indicate if there are additional losses not

accounted for.

ENTRY LOOPER ZONE DYNAMIC CLAMPING

+

x

-

motoring (slip)


from calculations

B2X tension

(exit side of bridle)

motoring HP


value from calculation bending losses

- -regenerating (slip)


from calculations

B2X tension


regenerating HP


value from calculation bending losses

Maximum entry

looper tension

(from mill builder)

Minimum entry

looper tension

(from mill builder)

Entry Side of Entry looper and

Entry Side of Bridle 2 TensionReference

and

Exit Side of Bridle 1 Tension

Reference

Reference Select

entry looper tension reference

Thread tension

Stall tension

Entry Tension Zone

Bridle 1 Bridle 2

Entry Looper

Tension Ref.

from level 2

B2X

Minimum

Select

Maximum

Select

Drawing 3

Entry Looper Tension Zone- drawing 3Bridle 1 - exit side

Bridle 1 exit side tension reference is looper tension minus half of all bending losses. The T of the bridle is

entry bridle tension reference minus exit bridle tension reference. Inertia compensation for undriven tower rolls

(discussed below) is also added to the reference if needed.

Entry Looper The entry looper tension reference is the looper tension reference value from level 2 limited by bridle 2 exit

tension slip/hp limits minus half of the looper bending losses. It is assumed in this example that the loopertension in the middle strand is the tension desired. Half of all the losses are subtracted from this tension beforethe center strand and half of the losses are added. An accumulator or looper may have some losses that need to be

accounted for in the bridles that border the loop tower or car.


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1. Bending losses - A certain amount of energy is required to make the strip conform the roll in a looper. Success

has been achieved by splitting half the bending losses to the bridle before the looper and half to the bridle after.

Losses, either bending or friction, always add in the direction of strip travel. The bridle before the looper has halfof the bending losses subtracted from the exit side tension of the bridle (which is the looper tension reference).The bridle following the looper has half the bending losses added to the entry side of the bridle tension (alsolooper tension reference).

2. Inertia compensation for undriven looper (accumulator) rolls - The rolls in the loopers are typically undriven.

Any speed change on either side of the looper must be accounted for. An undriven roll acts like a regeneratingmotor on acceleration i.e. tension after the roll is higher than tension in front of the roll. The roll acts like amotoring motor during deceleration i.e. tension in front of the roll is higher than tension past the roll. By taking

the derivative of the strip speed on both sides of the looper and adding them together and multiplying that valueby the total tower tension change, a inertia comp value for the bridles can be determined. See drawing below.

T1 T2 T3 T4

entry exit

entry exit

accel +

decel -

tension change

* = no change

T1 T2 T3 T4

+

-

+

-

*

*

*

*

*

*

*

*

Bridle 2 - entry side Bridle 2 in this example is either a tension or elongation regulator. Bridle 2 and bridle 3 make up the tensionleveler zone in this example. The entry side tension reference is looper tension reference plus half of looper

bending losses (plus any undriven looper roll inertia compensation if needed). When the leveler is in tensionmode, it will regulate to the tension reference sent. In elongation, this bridle reverts to a speed regulating scheme.


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LEVELER ZONE DYNAMIC CLAMPING

+

x

-

motoring (slip)


from calculations

T3 tension


motoring HP

maximum delta

tension


leveler

losses



from calculations

T3 tension


regenerating HP



leveler losses

Maximum leveler

tension

(from mill builder)

Minimum leveler

tension

(from mill builder)

Entry Side of Bridle 3

Tension Reference

and

Exit Side of Bridle 2

Tension Reference

Reference Select

leveler tension reference

Thread tension

Stall tension

Leveler Tension Zone

Bridle 2 Bridle 3

Leveler Tension

Ref.

from level 2

-B3E

B2X

x

Minimum

Select

Maximum

Select

Drawing 4

Leveler Tension Zone - drawing 4

Bridle 2 - exit side Bridle 2 exit side tension reference is leveler tension reference limited by bridle 3 exit side slip/hp limits minus

leveler losses.

Bridle 3 - entry side

Bridle 3 is the process section speed pacer. The tension reference for the entry side is leveler tension referenceplus leveler losses.


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TANK ZONE DYNAMIC CLAMPING

Maximum tank

tension

(from mill builder)

Minimum tank

tension

(from mill builder)

Entry Side of Bridle 4

Tension Reference

and

Exit Side of Bridle 3Tension Reference

Reference Select

leveler tension reference

Thread tension

Stall tension

Tank (Process) Tension Zone

Bridle 3 Bridle 4

Tank Tension

Ref.

from level 2

Drawing 5

Pickle Tank (Process) Tension Zone - drawing 5

Bridle 3 - exit side The tension reference for the exit side of bridle 3 is pickle tank tension reference.

Bridle 4 - entry side Bridle 4 is responsible for tension in the tank (the independent tension zone). Tank tension controls the heightof the catenary in the tank. The tension reference calculation is based on gauge and width to keep a desiredcatenary height. The upper and lower limits for this bridle are only the mill builder set limits. The reference to

the entry side of bridle 4 is the calculated tension references plus tank losses. An outer tension loop is alsoemployed based on a load cell that measures tank tension.

It is interesting to note that without true tension feedback, a bridle is not a good tension regulator. The only

thing a bridle is good at regulating is

T across the bridle. The tension in front of the bridle is determined by thetension after the bridle and T of the bridle.


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EXIT LOOPER ZONE DYNAMIC CLAMPING

+

x

-

motoring (slip)


B4E tension


motoring HP

maximum delta

tension

value from calculationbending losses



from calculations

B4E tension


regenerating HP



Maximum exit

looper tension

(from mill builder)

Minimum exitlooper tension

(from mill builder)

Entry side of Exit Looper and

Bridle 5 Tension Reference

and

Exit Side of Bridle 4 Tension

Reference

Reference Select

exit looper tension reference

Thread tension

Stall tension

Exit Looper Tension Zone

Bridle 4Bridle 5

Exit Looper Tension Ref.

from level 2

B4E

+

+

bending losses

Minimum

Select

Maximum

Select

Drawing 6

Exit Looper Tension Zone- drawing 6Bridle 4 - exit side Bridle 4 exit side tension reference is looper tension minus half of all exit looper bending losses. Inertiacompensation for undriven tower rolls is also added to the reference if needed.

Exit Looper The exit looper tension reference is the looper tension reference value limited by bridle 4 entry tension slip/hplimits plus half of the looper bending losses. It is assumed in this example that the looper tension in the middle

strand is the tension desired. An accumulator or looper may have some losses that need to be accounted for bythe bridles that border the loop tower or car.

Bridle 5 - entry sideBridle 5 entry side tension reference is exit looper tension limited by bridle 4 slip/hp limits plus half of the exitlooper bending losses.


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EXIT TENSION DYNAMIC CLAMPING

+

x

motoring (slip)


B5E tension


motoring HP



-regenerating (slip)


from calculations

B5E tension


regenerating HP



Maximum exit

tension

(from mill builder)

Minimum exit

tension

(from mill builder)

To Entry Side of Tension

Reel and Exit Side of

Bridle 5 Tension

Reference

Reference Select

exit tension reference

Thread tension

Stall tension

Looper tension not on tension *

Exit Tension Zone

* Exit tension is limited to fixed

value if looper tension is Off to

prevent bridle 6 slippage

Exit Tension Ref.

from level 2

Bridle 5

B5E

Minimum

Select

Maximum

Select

Drawing 7

Exit Tension Zone- drawing 7Bridle 5 - exit side

Bridle 5 is the speed pacer for the exit end. It has a speed regulator with an outer position loop to regulatetower position. The exit side tension reference for the bridle is exit tension reference. Since bridle 5 is a speedregulator, the tension reference to the bridle is only used as a current regulator feedforward.

Tension Reel - entry side

The tension (or rewind) reel will always have zero exit tension (since no strip is coming out of the reel). Thetension reel is typically current/tension regulated. The limits for the tension reel are dependent on the entrytension of bridle 5. The upper tension reference limit is bridle 5 slip/horsepower motoring limit plus the bending

losses (remember, losses always add in the direction of strip travel). The lower tension reference limit is thebridle 5 slip/hp regenerating limit plus bending losses. The bending losses are added because they are seen by the

tension reel but do not add to strip tension.


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The overall dynamic tension clamping scheme is represented in drawing 8. The dynamic tension clamps shown

below the dotted line in the drawing 8 are also shown in drawings 2 through 7. The tension reference grid give

reference information for the whole line.

Bridle 5

E X

T

PayoffReel

E X

T

Bridle 1

E X

T

EntryLooper

E X

T

Bridle 4

E X

T

Bridle 3

E X

T

Bridle 2

E X

T

TensionReel

E X

T

ExitLooper

E X

T

00

0 0

+

++

Entrylosses

(-)

1/2 oftotal

looperbendinglosses

+++

Levelerroll

losses

PI

loadcell

Tanklosses

1/2 oftotal

looperbendinglosses

(-)

++

Bendinglosses

PayoffTension

Reference

Exit LooperTension

Reference

Tank (process)Tension

Reference

LevelerTension

Reference

Entry LooperTension

Reference

Tension ReelTension

Reference

max.

min

Independentzone

DYNAMIC TENSION CLAMPINGOVERVIEW

E = Entry Side Tension Reference

X = Exit Side Tension Reference

DynamicClamps

DynamicClamps

DynamicClamps

DynamicClamps

DynamicClamps

Drawing 8

The values going to the E and the X into each block actually will go to each drive. The drive will thendetermine its portion of the load in the bridle. The losses are also added or subtracted as needed in the diagram togive each drive its final entry and exit tension reference.

As an example, bridle 1 has the entry losses added to the entry tension reference. This is because the tensionseen at the entry side of bridle 1 will be equal to the tension that the payoff reel is providing (entry tension

reference)plus entry losses (pinch rolls, leveler, etc.). If these losses were not included, the entry tension wouldstill be correct, but the speed regulator in bridle 1 would have to account for the losses since they wouldnt be fed

forward.

The data shown in the tension reference grid (page 10) identifies the source of references to each drive. The

speed regulated and independent zone regulators get the tension reference plus (or minus) additional losses.Losses due to undriven looper roll inertia for bridles bordering a looper are not shown in the grid.


11/25


Payoff

Reel

Always 0 Payoff reel

(entry)tension

reference

same as exit

side tensionreference

same as

reference

B1X slip/hp

motoring limit- entry losses

B1X slip/hp

regeneratinglimit - entry

losses --- ---

Bridle 1 Same asExit Side

tension

reference inpayoff reel

Entry looper

tension

reference

Entry - Exit

--- ---

Entry tension

reference +

entry losses

Looper

tension ref -

1/2 looper

bendinglosses

Entry

Looper

Entry

loopertension

reference

Always 0 same as

entry tensionreference

same as

reference

B2X - 1/2

looperbending

losses

B2X slip/hp

regeneratinglimit -

1/2 bendinglosses

--- ---

Bridle 2 Same asentry looper

tension

reference

Leveler

tensionreference

Entry -Exit Determined

by loaddistribution

and any

speed reg.

error

B3X slip/hp

motoring limit- leveler

losses

(B3E- B2X)

B3X slip/hp

regeneratinglimit - leveler

losses

Entry tension

reference +1/2 looper

bending

losses

Exit tension

reference

Bridle 3 Levelertension

reference

Tank tension

reference

Upstream -

downstream

--- ---

Entry tension

reference +leveler

losses

Exit tension

reference

Bridle 4 Tank(proccess)

tension

reference

Exit loopertension

reference

Upstream -downstream

13200 lbsfrom mill

builder spec

700 lbsfrom mill

builder spec

Entry tensionreference +

pickle tank

losses

Exit tensionreference

- 1/2 looper

bendinglosses

Exit

Looper

Exit loopertension

reference

Always 0 Same as exitlooper

tension

reference

Same as exitlooper

tension

reference

B4E slip/hpmotoring limit

+ 1/2 exit

looper

bending

losses

B4E slip/hpregenerating

limit + 1/2

exit looper

bending

losses

--- ---

Bridle 5 Exit looper

tensionreference

Tension reel

tensionreference

Upstream -

downstream

--- ---

Entry tension

reference +1/2 exit

looperbending loss

Exit tension

reference

Tension

ReelTension reel

tension

reference

Always 0 Tension reeltension

reference +

bendinglosses

Same astension reel

tension

reference

B5E slip/hpmotoring limit

B5E slip/hpregenerating

limit

--- ---

Tension

Speed

Tension

Tension/

Elongation (speed)

*

Speed

Tension

Tension

Speed

Tension

Entry side

Tension

Reference

Exit Side

tension

reference

Tension

reference

T

Tensionfeedback

Upper tensionlimit

Lowertension limit

Entry tensionref from drive

Exit tensionref from drive

Determined

by load

distribution

and anyspeed reg.

error

Determined

by loaddistribution

and anyspeed reg.

error

Determinedby load

distribution

and anyspeed reg.

error

Determined

by loaddistribution

and anyspeed reg.

error

Notes:

* Bridle 2 is tension when weld passes or operator selects tension mode or elongations. If eleongation is selected, the speed reference is a % less than bri dle 3 speed reference.

Tension Reference Grid

Entry - Exit

Entry - Exit

Entry - Exit


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PREDICTIVE TENSION CONTROL REGULATORS (PTC)

The regulators in the drive can use the tension information to determine there torque requirements in an openloop fashion by feeding forward all tension, losses, and inertia comps directly to the current/tension loop,bypassing the speed regulator.

PI

speed

losses

dv

dt

PI

-

+

x

x

0

Speed

Regulator

Current

Regulator

Master Tension or

Follower Regulator

Speed

Reference

Windage/Friction Losses

Inertia comp

Entry Tension

Reference

Exit Tension

Reference

T of Bridle

Motoring Load

Percentage

Regenerating

Load Percentage

Load Distribution

Additional Losses (if any)

Speed

Feedback

Current/

Tension

Feedback

To Firing

Circuit

Total feedforward tension reference

PI

Process Trim Trim Limit

Drawing 10

Drawing 10 shows a simplified tension /follower regulator. The speed reference is used to determine inertiacomps and windage/friction losses. The entry and exit tension values are subtracted from each other to calculate

the T for the bridle. This value is then analyzed to determine if the bridle is motoring or regenerating. This

value is then multiplied by the appropriate load distribution value. All these values are summed up and fedforward into the current/torque regulator as the reference. An outer loop (process trim) also gets this value as areference. The current/torque feedback is also used by the outer loop. Any error between these values isintegrated and added/subtracted from the speed reference up to a set percentage (trim limit) to modify or droopthe speed reference. This allows the speed regulator to stay out of the way for the set percentage, but become

active if something goes wrong (like a strip break) and prevent a runaway situation.


13/25


PI

speed

losses

dv

dt

PI

-

+

x

x

0

Speed

Regulator

Current

Regulator

Master Speed Regulator

Speed

Reference

Windage and Friction

Losses

Inertia comp

Entry Tension

Reference

Exit Tension

Reference

T ofBridle

Motoring

Load

Percentage

Regenerating

Load

Percentage

Load Distribution

Additional Losses

(if any)

Speed

Feedback

Current/Tension

Feedback

To Firing

Circuit

Load

Balance

signal to

followers

filter

If all compensations are correct, the output of the speed

regulator should always be zero (or very low). This signal

can be montitored to determine if unknown mechanicallosses are occuring.

Total feedforward

tension reference

Drawing 11

Drawing 11 shows a simplified speed master. It is similar to the tension/follower except it does not have aprocess trim regulator. The tension reference, losses, etc. are still fed forward to the current/tension regulator. Ifthese values are accurately calculated, the output of the speed regulator should be minimal. The output of the

speed regulator can be monitored after commissioning to determine if some unknown losses are occurring in theprocess. The output of the speed regulator can also be fed to the followers in a bridle to aid in load sharing, sincethe follower would not be aware of additional load that is not fed forward from the reference.

DYNAMIC TENSION CONTROL AND LOAD DISTRIBUTION VALUE CALCULATIONS

The values needed for dynamic tension control clamps and bridle load distribution are shown in an examplebelow.

There are two limiting factors in any bridle, slip and horsepower. For example, if the bridle has amultiplication factor of 2 and there is 10 lbs on the entry side and 21 lbs on the exit side, the bridle will slip. Itcan only handle two times the input tension or 20 lbs in this case. This is the slip limitation of the bridle. The

only way to increase the multiplication of this bridle would be to increase the angle of wrap or the coefficient offriction between the strip and the roll or add a pinch/snubber roll on one of the bridle rolls. On the other hand if

the input tension was 1,000,000 lbs the theoretical output tension could be 2,000,000 lbs, but if the the bridlehorsepower is too low, the bridle cannot perform this amplification. This is the horsepower limitation of the

bridle.


14/25


Example

Using the example given in drawing 1, entry bridle of a three zone pickle line. The mill builder has given thefollowing information about the bridle. We will ignore bending losses is this example, but they should be addedto horsepower values if the strip is heavy or the rolls are have small diameters.

The following horsepowers were selected for the motors by the mechanical contractor:

Roll 1 = 250 HPRoll 2 = 200 HPRoll 3 = 150 HP

Roll 4 = 200 HP

If maximum tension in = 17820 lbs then minimum tension out will not be less than 7326 lbs

If maximum tension out = 13200 lbs then minimum tension in will not be less than 2200 lbs

Top strip speed = 1065 fpm

Roll 1 has a 220angle of wrap.




Coefficient of friction is .135 (strip is oily)

If the mill builder does not provide minimum tension values, calculate maximum T and subtract this value from

the maximum values to get the minimum values.

Calculate the motoring horsepower required to get maximum work out of the rolls in the bridle - slip dependenthorsepower.

1) Find amplification factor T2= T1 efa

whereeis the Naperian constant

fis the coefficient of friction (usually .15 to .18 for steel rolls)a is angle of wraps in radians

R is the amplification factor for each roll:

R1 = e

pi/180 * 220 * 0.135

= 1.679

R2 = epi/180 * 220 * 0.135 = 1.679

R3 = epi/180 * 230 * 0.135

= 1.719

R4 = epi/180 * 220 * 0.135

= 1.679

1 4

32

PAYOFF LOOPERT5

T4

T3

T2

T1

MOTORING


15/25


2) Find the T for motoringmaximum tension. T is the tension change across the bridle. It can be broken

down to tension change across the individual rolls in the bridle. Remember the bridle will motor when the

incoming tension is higher than the outgoing tension.

T5 = 17820 lbs maximum tension on incoming side of bridle per mill builder

T5 - T4 = TROLL1= 17820 lbs - (17820 lbs/1.679) = 7206 lbs

This value can be used to determine needed for this roll for maximum motoring tension.

Roll 1 calculations:HP = tension (lbs) * strip speed (fpm) / 33000

7206 lbs *1065fpm / 33000 = 232 HP

Roll 2 calculations:T4 = 17820 lbs - 7206 lbs = 10614 lbs

T4 - T3 = TROLL2= 10614 lbs - (10614 lbs /1.679) = 4292 lbs

4292 lbs*1065fpm / 33000 = 138.5 HP

Roll 3 calculations:

T3 = 10614 lbs - 4292 lbs = 6322 lbs

T3 - T2 = TROLL3= 6322 lbs - (6322 lbs) /1.719) = 2644 lbs

2644 lbs*1065fpm / 33000 = 85 HP


T2 = 6322 lbs - 2644 lbs = 3678 lbs


2644 lbs*1065fpm / 33000 = 48 HP

The total bridle horsepower used is 503.5 HP. In this example, T1 tension is greater than the minimum tension

calculated above. T1 tension = 3678 lbs - 1487 lbs = 2191 lbs which is less than the 2500 lbs out the mill builderhas specified. Using the above HP ratings, we can determine the percentage each roll must pull to achieve thedesired results.

Roll 1 - 232HP / 503.5HP = 0.461 or 46.1% of the bridle load

Roll 2 - 138.5HP / 503.5HP = 0.275 or 27.5% of the bridle load



16/25



This splitting of loads among rolls can be considered the natural distribution of loads. Since our mill builderhas specified that T1 tension will never be less than 7326 lbs and T5 tension will never be greater than 17820,

Tbridle= lbs.

The total horsepower needed for motoring the bridle at worst case is:HP = 10494 lbs * 1065 fpm / 33000 = 338.7 HP

Based on the ratios for each roll and multiplying by the total HP....

Roll 1 = 156 HPRoll 2 = 93 HP

Roll 3 = 57 HP

Roll 4 = 32 HP

This is the horsepower required for Tbridle= 10494 lbs.

Now do the same calculations for regeneratingbridle, T1 < T5.

1 4

32

PAYOFF LOOPERT1

T2

T3

T4

T5

REGENERATING

The amplification factor for the rolls is the same.

R1 = epi/180 * 220 * 0.135 = 1.679

R2 = epi/180 * 220 * 0.135

= 1.679

R3 = epi/180 * 230 * 0.135

= 1.719

R4 = epi/180 * 220 * 0.135 = 1.679

3) Find the T for regenerating maximum tension. Remember the bridle will regenerate when the incomingtension is lower than the outgoing tension.

T5 = 13200 lbs maximum tension on outgoing side of bridle per mill builder

T5 - T4 = TROLL4= 13200 lbs - (13200 lbs/1.679) = 5338 lbs

This value can be used to determine needed for this roll for max. motoring tension.

Roll 4 calculations:HP = tension (lbs) * strip speed (fpm) / 33000

5338 lbs *1065fpm / 33000 = 172 HP



17/25


T4 = 13200 lbs - 5338 lbs = 7862 lbs

T4 - T3 = TROLL3= 7862 lbs - (7862 lbs /1.719) = 3288 lbs

3288 lbs*1065fpm / 33000 = 106 HP



1850 lbs*1065fpm / 33000 = 60 HP



1101 lbs*1065fpm / 33000 = 35.5 HP

This can be considered the natural distribution of load for the the regenerating bridle. The total bridlehorsepower used is 373.5 HP. But this examples T1 tension is greater than the minimum tension calculated

above. T1 tension = 2724 lbs - 1101 lbs = 1623 lbs which is less than the 2200 lbs out the mill builder hasspecified. Using the above HP ratings, we can determine the percentage each roll must pull to achieve the desired

results.

Roll 1 - 35.5HP / 373.5HP = 0.095 or 9.5% of the bridle load

Roll 2 - 60HP / 373.5HP = 0.16 or 16% of the bridle load


Roll 4 - 172HP / 373.5HP = 0.46 or 46% of the bridle load

Since our mill builder has specified that T1 tension will never be less than 2200 lbs and T5 tension will never be

greater than 13200, Tbridle= 11000 lbs.

The total horsepower needed for motoring the bridle at worst case is:HP = 11000lbs * 1065 fpm / 33000 = 355 HP

Based on the ratios for each roll and multiplying by the total HP....

Roll 1 = 33.7 HPRoll 2 = 56.8 HP

Roll 3 = 100.4 HP

Roll 4 = 163.3 HP


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This is the horsepower needed for Tbridle= 11000 lbs.

The horsepower ranges for the bridle are as follows:

Bridle Motoring HP Regenerating HP

1 156 33.72 93 56.83 57 100.4

4 32 163.3

The following horsepowers were selected for the motors by the mechanical contractor:

Roll 1 = 250 HP

Roll 2 = 200 HPRoll 3 = 150 HPRoll 4 = 200 HP

The calculated horsepower values fit into the horsepower given by the mill builder for the desired tensionscalculated above.

SLIP / HORSEPOWER AND LOAD SHARING CALCULATIONS

If it were possible to buy motors that had the horsepowers calculated above, the natural load distributionvalues could be used by the regulator for motoring and regenerating load percentages. Unfortunately, we see that

the horsepowers needed do not directly correlate to available motor sizes and different horsepowers are needed formotoring and regenerating. The load distribution numbers must be determined to maximize the amplification and

horsepower abilities of the bridle.

Determine the maximum T for each roll in the bridle based on the given motor horsepowers.

Roll 1 T = 250HP * 33000 / 1065fpm = 7746 lbs

Roll 2 T = 200HP * 33000 / 1065fpm = 6197 lbs

Roll 3 T = 150HP * 33000 / 1065fpm = 4648 lbs

Roll 4 T = 200HP * 33000 / 1065fpm = 6197 lbs

Now that the maximumT for each roll has been determined, find out what initial or T1 tension is needed forthat maximum T across each roll. For motoring operation, the following equations apply:

1 4

32

PAYOFF LOOPERT5

T4

T3

T2

T1

MOTORING

T1 = x


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T2 = 1.679x roll 4 amplification

T3 = 2.886x roll 3 and 4 amplification

T4 = 4.846x roll 2,3, and 4 amplificationT5 = 8.136x amplification from all rolls

Now find the value for x in each of the maximum T across each roll.

Roll 1 T5 - T48.136x - 4.846x = 7746 lbs

x = 2354 lbs

Roll 2 T4 - T34.846x - 2.886x = 6197 lbs

x = 3161 lbs

Roll 3 T3 - T22.886x - 1.679x = 4648 lbsx = 3850 lbs

Roll 4 T2 - T11.679x - x = 6197 lbsx = 9126 lbs

These 4 x values represent the 4 initial (T1) tensions that would be necessary to achieve maximum T across the

respective rolls based on the horsepower limitations of the motors. Now four separate calculations must be doneto determine which slip/HP ratio that is most appealing for this application. The ratio is a compromise of

maximum T (horsepower limited) and maximum bridle amplification (slip limited). Ideally, the ratio would bedynamic so at low initial tensions, we could utilize the maximum amplification and at high initial tensions,

maximum T could be utilized.


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Case 1

Starting with minimum x value - (T5 - T4)max.= 2354 lbs

T1 = 2354 lbsT2 = 2354 * 1.679 = 3952 lbs (T1 * roll 4 multiplication factor)T3 = 3952* 1.719 = 6794 lbs (T2 * roll 3 multiplication factor)

T4 = 6794 * 1.679 = 11407 lbs (T3 * roll 2 multiplication factor)T5 = 11407 * 1.679 = 19152 lbs (T4 * roll 1 multiplication factor)

This case yields Tbridle= 16789 lbs and amplification factor = 8.13. This case yields the best amplification factor(maximum bridle capacity based on wrap angle and coefficient of friction) but falls short of maximumhorsepower capacity of 24788 lbs. This example has every roll in the bridle limited by slip, not horsepower.

Case 2x value - (T4 -T3)max.= 3161 lbs

T1 = 3161 lbs

T2 = 3161 * 1.679 = 5307 lbs (T1 * roll 4 multiplication factor)T3 = 5307 * 1.719 = 9123 lbs (T2 * roll 3 multiplication factor)T4 = 9123 * 1.679 = 15317 lbs (T3 * roll 2 multiplication factor)

T5 = 15317 + 7746 = 23603 lbs (T4 + maximum T across roll 1)

Amplification factor = 23603 lbs / 3161 lbs = 7.3

This case yields Tbridle= 19902 lbs and amplification factor = 7.3. This example has three rolls limited by slip

and roll 1 horsepower limited.


T1 = 3850 lbsT2 = 3850 * 1.679 = 6464 lbs (T1 * roll 4 multiplication factor)

T3 = 6464 * 1.719 = 11111 lbs (T2 * roll 3 multiplication factor)




This case yields Tbridle= 21204 lbs and amplification factor = 6.5. This example has roll 3 and roll 4 limited byslip and roll 1 and roll 2 horsepower limited.


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Case 4

x value - (T2 -T1)max.= 9126 lbs

T1 = 9126 lbsT2 = 9126 * 1.679 = 15322 lbs (T1 * roll 4 multiplication factor)





This case yields Tbridle= 24788 lbs and amplification factor = 3.7. This example has roll 2,3 and 4 limited by

slip and roll 1 horsepower limited. This example yields the highest Tbridle(use of horsepower) but the lowestbridle amplification factor.

The mill builder has specified that the maximum in/minimum out tension (for motoring) are17820 lbs / 7326 lbs respectively. These values would fit into the Case 2 was used since it provides a good

balance of amplification versus Tbridle..

Now the load distribution of tensions throughout the bridle must be calculated. For case 2, Tbridle= 19902 lbs.

The load distribution = Troll / Tbridle.

Roll 1 = (T5 - T4) / 19902 = 0.39 or 39% of the load on the bridle




These numbers should be used in the load distribution scheme for the bridle when motoring (see motoring load

percentage on drawings 10 and 11). The Tbridleshould be multiplied by these percentages and used for the drive

as tension reference for the individual motors.

For regeneratingoperation (drawing 2) the following equations apply:

1 432

PAYOFF LOOPERT1

T2

T3

T4

T5

REGENERATING

T1 = x initial tension

T2 = 1.679x roll 1 amplificationT3 = 2.819x roll 1 and 2 amplificationT4 = 4.846x roll 1,2, and 3 amplification

T5 = 8.136x amplification from all rolls

Now find the value for x in each of the maximum T across each roll.


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Roll 4 T5 - T4

8.136x - 4.846x = 6197 lbsx = 1883 lbs

Roll 3 T4 - T3

4.846x - 2.819x = 4648 lbsx = 2293 lbs

Roll 2 T3 - T22.819x - 1.679x = 6197 lbs

x = 5435 lbs

Roll 1 T2 - T1

1.679x - x = 7746 lbsx =11407 lbs

These 4 x values represent the 4 initial (T1) tensions that would be necessary to achieve maximum T across the

respective rolls based on the horsepower limitations of the motors. Now four separate calculations must be doneto determine which slip/HP ratio is most appealing for this application. The ratio is a compromise of maximum

T (horsepower limited) and maximum bridle amplification (slip limited). Ideally, the ratio would be dynamic so

at low initial tensions, we could utilize the maximum amplification and at high initial tensions, maximum Tcould be utilized.

Case 1

Starting with minimum x value - (T5 - T4)max.= 1883 lbs

T1 = 1883 lbs



This case yields Tbridle= 13437 lbs and amplification factor = 8.13.

This case yields the best amplification factor (maximum bridle capacity based on wrap angle and coefficient offriction) but falls short of maximum horsepower capacity of 24788 lbs. This example has every roll in the bridle

limited by slip, not horsepower.


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Case 2

x value - (T4 -T3)max.= 2293 lbs

T1 = 2293 lbsT2 = 2293 * 1.679 = 3849 lbs (T1 * roll 1 multiplication factor)T3 = 3849 * 1.679 = 6464 lbs (T2 * roll 2 multiplication factor)




This case yields Tbridle= 15016 lbs and amplification factor = 7.54. This example has three rolls limited by slipand roll 4 horsepower limited.


T1 = 5435 lbs





This case yields Tbridle= 20734 lbs and amplification factor = 4.82. This example has roll 1 and roll 2 limited byslip and roll 3 and roll 4 horsepower limited.


T1 = 11407 lbs






This case yields Tbridle= 24788 lbs and amplification factor = 3.17. This example has roll 1,2 and 3 limited by

slip and roll 3 horsepower limited. This example yields the highest Tbridle(use of horsepower) but the lowest

bridle amplification factor.

The mill builder has specified that the maximum out/minimum in tension (for regenerating) are13200 lbs / 2200 lbs respectively. These values would fit into the Case 1 was used since it provides a good

balance of amplification versus Tbridle..


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Now the load distribution of tensions throughout the bridle must be calculated. For case 1, Tbridle= 13437 lbs.

The load distribution = Troll / Tbridle.Roll 4 = (T5 - T4) / 13437 = 0.46 or 46% of the load on the bridle



Roll 1 = (T2 - T1) / 13437 = 0.095 or 9.5% of the load on the bridle

These numbers also match the natural regenerating load distribution since we are using maximum bridleamplification. These numbers should be used in the load distribution scheme for the bridle when regenerating

(see regenerating load percentage on drawings 10 and 11). The Tbridleshould be multiplied by these percentagesand used for the drive as tension reference for the individual motors.

For the sake of simplicity, we will ignore looper bending losses for this example.

If motoring values selected for bridle 1 are as follows:amplification 7.3

max Tbridle 19902 lbs.

If regenerating values for bridle 1 are as follows:amplification 8.13

max Tbridle 13437 lbs.

The reference limits from the lookup tables (or level 2)are:entry looper tension 1100 to 17000 lbs

For dynamic tension clamping, these values would be used in drawing 2. The entry tension is dependent onlooper tension.

If looper tension was set to 1100 lbs, the entry tension maximum (motoring) limit would be dynamically clamped

8030 lbs (the motoring clamps are the minimum of B1X tension * 7.3 or B1X + 19902). The bridle would be in aslip limited clamp. If the looper tension was set to 3000 lbs, the entry tension would be dynamically clamped to21900. The bridle would be in a horsepower limited clamp.

If the looper tension was set to 17000 lbs, the minimum entry tension would be clamped to 3563 lbs ( theregenerating clamps are the maximum of B1X divided by 8.13 or B1X - 13437). The bridle is again in thehorsepower limited clamp. If the looper tension was 14000 lbs, the entry tension would be dynamically clamped

to 1722 lbs. The bridle would be in a slip-limited clamp.


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Date post:	12-Feb-2018
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