Tension Profile

TENSION PROFILE –DYNAMIC TENSION CLAMPS Marco Wishart Engineering Manager Rockwell Automation Drive Systems 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 on this 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 tension limits 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 DT 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 maximum slip and horsepower capabilities of bridle 5. These capabilities are dependent on bridle 5 entry tension which is exit 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. Line Overview PAYOFF REEL losses B1E BRIDLE 1 Entry (payoff) tension zone B1X Entry looper tension zone B2E BRIDLE 2 B2X B3E BRIDLE 3 Leveler tension zone B3X B4E BRIDLE 4 Pickle tank tension zone Independent Zone B4X Exit looper tension zone B5E BRIDLE 5 TENSION REEL Exit (tension reel) tension zone Drawing 1 If the tension references are correct and the operator does not change the tension references, the dynamic tension clamping will not have any effect on the zone tensions. The only purpose of dynamic tension clamping is to 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 line example. Bridle 1 . 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 maximum tension so a reduced entry tension may be used in this situation. The lower tension reference limit is the bridle 1 slip/hp regenerating limit minus entry losses. The payoff is typically current/tension regulated. Many times. The entry losses are subtracted because they are seen at the entry side of the bridle but are not produced by the payoff reel.TENSION PROFILE . are in and out of the passline. The entry loss value may change if equipment like levelers. The upper tension reference limit is bridle 1 slip/horsepower motoring limit minus the entry losses (remember. the speed regulator output should . Since bridle 1 is a speed regulator. The payoff tension may also limited if the entry looper (strip accumulator) tension is not on. If the entry looper tension is off.drawing 2 Payoff Reel The payoff (or unwind) reel will always have zero entry tension (since no strip is coming into the reel).entry side Bridle 1 is the pacer for the entry end. the tension reference to the bridle is only used as a current regulator feedforward signal. The entry side tension reference for the bridle is entry tension reference plus entry losses. The limits for the payoff are dependent on the exit tension of bridle 1. This may necessitate changing the loss value as the losses change. If the feedforward signal contains all the correct tensions and losses for the bridle.DYNAMIC TENSION CLAMPS ENTRY TENSION DYNAMIC CLAMPING motoring (slip) multiplication factor from calculations x B1X tension (entry side of bridle) Minimum Select + motoring HP maximum delta tension value from calculation entry losses Maximum entry tension (from mill builder) Reference Select entry tension reference Thread tension To Exit Side of Payoff Reel and Entry Side of Bridle 1 Tension Reference Stall tension Looper tension not on tension * Minimum entry tension (from mill builder) B1X tension (entry side of bridle) regenerating (slip) multiplication factor from calculations - Maximum Select regenerating HP maximum delta tension value from calculation entry losses Entry Tension Zone Entry Tension Ref from level 2 entry losses B1X * Entry tension is limited to fixed value if looper tension is Off to prevent bridle 1 slippage Bridle 1 Drawing 2 Entry Tension Zone . the tension at the exit side of bridle 1 is zero. pinch rolls. etc. losses always add in the direction of strip travel). It has a speed regulator with an outer position loop to regulate tower position. drawing 3 Bridle 1 .exit side Bridle 1 exit side tension reference is looper tension minus half of all bending losses. The DT 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. It is assumed in this example that the looper tension in the middle strand is the tension desired.TENSION PROFILE . ENTRY LOOPER ZONE DYNAMIC CLAMPING motoring (slip) multiplication factor from calculations x B2X tension (exit side of bridle) Minimum Select + motoring HP maximum delta tension value from calculation - bending losses Maximum entry looper tension (from mill builder) Reference Select entry looper tension reference Entry Side of Entry looper and Entry Side of Bridle 2 Tension Reference and Exit Side of Bridle 1 Tension Reference Thread tension Stall tension Minimum entry looper tension (from mill builder) B2X tension (exit side of bridle) regenerating (slip) multiplication factor from calculations regenerating HP maximum delta tension value from calculation Maximum Select - bending losses Entry Tension Zone Entry Looper Tension Ref. Examining the output of the speed regulator can indicate if there are additional losses not accounted for. 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.DYNAMIC TENSION CLAMPS be zero or near zero. from level 2 B2X Bridle 1 Bridle 2 Drawing 3 Entry Looper Tension Zone . Half of all the losses are subtracted from this tension before the 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. tension in front of the roll is higher than tension past the roll. In elongation. a inertia comp value for the bridles can be determined. always add in the direction of strip travel. T1 entry T2 exit T3 accel + decel entry exit + + - T4 tension change * = no change T1 T2 T3 T4 * * * * * * * * Bridle 2 . The entry side tension reference is looper tension reference plus half of looper bending losses (plus any undriven looper roll inertia compensation if needed). The bridle following the looper has half the bending losses added to the entry side of the bridle tension (also looper tension reference). See drawing below. By taking the derivative of the strip speed on both sides of the looper and adding them together and multiplying that value by the total tower tension change. tension after the roll is higher than tension in front of the roll. Bridle 2 and bridle 3 make up the tension leveler zone in this example.TENSION PROFILE . .A certain amount of energy is required to make the strip conform the roll in a looper.e. The roll acts like a motoring motor during deceleration i.e. either bending or friction. 2. this bridle reverts to a speed regulating scheme. Losses. Success has been achieved by splitting half the bending losses to the bridle before the looper and half to the bridle after. it will regulate to the tension reference sent. An undriven roll acts like a regenerating motor on acceleration i. Any speed change on either side of the looper must be accounted for.entry side Bridle 2 in this example is either a tension or elongation regulator. Inertia compensation for undriven looper (accumulator) rolls . When the leveler is in tension mode. Bending losses . The bridle before the looper has half of the bending losses subtracted from the exit side tension of the bridle (which is the looper tension reference).DYNAMIC TENSION CLAMPS 1.The rolls in the loopers are typically undriven. The tension reference for the entry side is leveler tension reference plus leveler losses. from level 2 Bridle 2 Bridle 3 Drawing 4 Leveler Tension Zone . Bridle 3 .DYNAMIC TENSION CLAMPS LEVELER ZONE DYNAMIC CLAMPING motoring (slip) multiplication factor from calculations x T3 tension (exit side of bridle) Minimum Select + - motoring HP maximum delta tension value from calculation leveler losses Maximum leveler tension (from mill builder) Reference Select - B3E leveler tension reference B2X Thread tension Entry Side of Bridle 3 Tension Reference and Exit Side of Bridle 2 Tension Reference Stall tension Minimum leveler tension (from mill builder) T3 tension (exit side of bridle) regenerating (slip) multiplication factor from calculations regenerating HP maximum delta tension value from calculation Maximum Select leveler losses Leveler Tension Zone Leveler Tension Ref.TENSION PROFILE .entry side Bridle 3 is the process section speed pacer.exit side Bridle 2 exit side tension reference is leveler tension reference limited by bridle 3 exit side slip/hp limits minus leveler losses.drawing 4 Bridle 2 . . Tank tension controls the height of the catenary in the tank.DYNAMIC TENSION CLAMPS TANK ZONE DYNAMIC CLAMPING Maximum tank tension (from mill builder) Reference Select leveler tension reference Entry Side of Bridle 4 Tension Reference and Exit Side of Bridle 3 Tension Reference Thread tension Stall tension Minimum tank tension (from mill builder) Tank (Process) Tension Zone Tank Tension Ref.TENSION PROFILE . An outer tension loop is also employed based on a load cell that measures tank tension. Bridle 4 . from level 2 Bridle 3 Bridle 4 Drawing 5 Pickle Tank (Process) Tension Zone . The tension reference calculation is based on gauge and width to keep a desired catenary height.exit side The tension reference for the exit side of bridle 3 is pickle tank tension reference.drawing 5 Bridle 3 .entry side Bridle 4 is responsible for tension in the tank (the independent tension zone). . It is interesting to note that without true tension feedback. The upper and lower limits for this bridle are only the mill builder set limits. The only thing a bridle is good at regulating is DT across the bridle. The reference to the entry side of bridle 4 is the calculated tension references plus tank losses. a bridle is not a good tension regulator. The tension in front of the bridle is determined by the tension after the bridle and DT of the bridle. TENSION PROFILE . Bridle 5 . An accumulator or looper may have some losses that need to be accounted for by the bridles that border the loop tower or car.DYNAMIC TENSION CLAMPS EXIT LOOPER ZONE DYNAMIC CLAMPING motoring (slip) multiplication factor from calculations x B4E tension (exit side of bridle) Minimum Select + motoring HP maximum delta tension value from calculation +- bending losses Maximum exit looper tension (from mill builder) Reference Select exit looper tension reference Entry side of Exit Looper and Bridle 5 Tension Reference and Exit Side of Bridle 4 Tension Reference Thread tension Stall tension Minimum exit looper tension (from mill builder) B4E tension (entry side of bridle) regenerating (slip) multiplication factor from calculations regenerating HP maximum delta tension value from calculation Maximum Select +- bending losses Exit Looper Tension Zone Exit Looper Tension Ref.entry side Bridle 5 entry side tension reference is exit looper tension limited by bridle 4 slip/hp limits plus half of the exit looper bending losses.exit side Bridle 4 exit side tension reference is looper tension minus half of all exit looper bending losses.drawing 6 Bridle 4 . from level 2 B4E Bridle 4 Bridle 5 Drawing 6 Exit Looper Tension Zone . Exit Looper The exit looper tension reference is the looper tension reference value limited by bridle 4 entry tension slip/hp limits 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. Inertia compensation for undriven tower rolls is also added to the reference if needed. from level 2 B5E * Exit tension is limited to fixed value if looper tension is Off to prevent bridle 6 slippage Bridle 5 Drawing 7 Exit Tension Zone . The bending losses are added because they are seen by the tension reel but do not add to strip tension. The exit side tension reference for the bridle is exit tension reference. Since bridle 5 is a speed regulator. Tension Reel . The lower tension reference limit is the bridle 5 slip/hp regenerating limit plus bending losses. The tension reel is typically current/tension regulated. the tension reference to the bridle is only used as a current regulator feedforward.drawing 7 Bridle 5 .DYNAMIC TENSION CLAMPS EXIT TENSION DYNAMIC CLAMPING motoring (slip) multiplication factor from calculations x B5E tension (exit side of bridle) Minimum Select + motoring HP maximum delta tension value from calculation Maximum exit tension (from mill builder) Reference Select exit tension reference Thread tension To Entry Side of Tension Reel and Exit Side of Bridle 5 Tension Reference Stall tension Looper tension not on tension * Minimum exit tension (from mill builder) B5E tension (exit side of bridle) regenerating (slip) multiplication factor from calculations - Maximum Select regenerating HP maximum delta tension value from calculation Exit Tension Zone Exit Tension Ref. It has a speed regulator with an outer position loop to regulate tower position.TENSION PROFILE . The limits for the tension reel are dependent on the entry tension of bridle 5.entry side The tension (or rewind) reel will always have zero exit tension (since no strip is coming out of the reel).exit side Bridle 5 is the speed pacer for the exit end. 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 drive will then determine its portion of the load in the bridle. The dynamic tension clamps shown below the dotted line in the drawing 8 are also shown in drawings 2 through 7. If these losses were not included. Dynamic Clamps Dynamic Clamps Dynamic Clamps Independent zone Dynamic Clamps Dynamic Clamps min Payoff Tension Reference Entry Looper Tension Reference Leveler Tension Reference Tank (process) Tension Reference DYNAMIC TENSION CLAMPING OVERVIEW Exit Looper Tension Reference Tension Reel Tension Reference E = Entry Side Tension Reference X = Exit Side Tension Reference Drawing 8 The values going to the E and the X into each block actually will go to each drive. the entry tension would still be correct. but the speed regulator in bridle 1 would have to account for the losses since they wouldn’t be fed forward. leveler. bridle 1 has the entry losses added to the entry tension reference. The data shown in the tension reference grid (page 10) identifies the source of references to each drive.). As an example. etc. This is because the tension seen 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. Payoff Reel E Entry Looper Bridle 1 X E T X E T Bridle 2 X E T Bridle 3 E X T X E + E X T T + + Tension Reel Bridle 5 E X T Tank losses 0 0 Exit Looper Bridle 4 X E X T T 0 + + (-) + + 0 (-) + PI Entry losses Leveler roll losses Bending losses 1/2 of total looper bending losses load cell 1/2 of total looper bending losses max.TENSION PROFILE . The losses are also added or subtracted as needed in the diagram to give each drive its final entry and exit tension reference. . The speed regulated and independent zone regulators get the tension reference plus (or minus) additional losses. The tension reference grid give reference information for the whole line. Losses due to undriven looper roll inertia for bridles bordering a looper are not shown in the grid.DYNAMIC TENSION CLAMPS The overall dynamic tension clamping scheme is represented in drawing 8. Exit.TENSION PROFILE . error Tension Bridle 5 Entry -Exit Entry tension Looper reference + tension ref entry losses 1/2 looper bending losses --- --- Tension reel Same as B5E slip/hp B5E slip/hp tension tension reel motoring limit regenerating reference + tension limit bending reference losses --- --- Entry tension Exit tension reference + reference 1/2 exit looper bending loss --- --- 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.Determined 13200 lbs 700 lbs Entry tension Exit tension tension downstream by load from mill from mill reference + reference reference distribution builder spec builder spec pickle tank .DYNAMIC TENSION CLAMPS Tension Reference Grid Entry side Tension Reference Payoff Reel Always 0 Exit Side tension reference Tension reference T Payoff reel same as exit (entry) side tension tension reference reference Tension feedback Upper tension Lower Entry tension Exit tension limit tension limit ref from drive ref from drive same as B1X slip/hp B1X slip/hp reference motoring limit regenerating .B2X) losses error Tank tension Upstream Entry .entry losses limit .Exit.entry losses --- --- Tension Bridle 1 Speed Entry Looper Same as Entry looper Entry . error Entry looper tension reference Always 0 Same as entry looper tension reference Leveler tension reference same as entry tension reference same as reference --- --- B2X .leveler limit .1/2 looper and any losses bending speed reg. losses error Always 0 Same as exit Same as exit B4E slip/hp B4E slip/hp looper looper motoring limit regenerating tension tension + 1/2 exit limit + 1/2 reference reference looper exit looper bending bending losses losses Exit looper Tension reel Upstream Entry . .Determined tension tension downstream by load reference reference distribution and any speed reg.Exit.leveler 1/2 looper and any losses losses bending speed reg.Determined reference downstream by load distribution and any speed reg.1/2 looper bending losses B2X slip/hp regenerating limit 1/2 bending losses Tension Bridle 2 Tension/ Elongation (speed) * Bridle 3 Leveler tension reference Speed Bridle 4 Tank (proccess) tension reference Tension Exit Looper Exit looper tension reference Speed Tension Reel Tension --- --- --- Entry tension Exit tension reference + reference leveler losses Exit looper Upstream Entry . error Always 0 Tension reel tension reference --- Determined B3X slip/hp B3X slip/hp Entry tension Exit tension by load motoring limit regenerating reference + reference distribution .Exit Determined Exit Side tension by load tension reference distribution reference in and any payoff reel speed reg. (B3E. An outer loop (process trim) also gets this value as a reference. bypassing the speed regulator. Master Tension or Follower Regulator Process Trim Current/ Tension Feedback Trim Limit PI Speed Feedback Additional Losses (if any) PI PI Speed Regulator Current Regulator To Firing Circuit losses Windage/Friction Losses + Total feedforward tension reference speed Inertia comp dv dt Speed Reference Motoring Load Percentage Load Distribution Entry Tension Reference - T of Bridle x x Exit Tension Reference 0 Regenerating Load Percentage Drawing 10 Drawing 10 shows a simplified tension /follower regulator. . The speed reference is used to determine inertia comps and windage/friction losses. This value is then analyzed to determine if the bridle is motoring or regenerating. The current/torque feedback is also used by the outer loop. This value is then multiplied by the appropriate load distribution value.DYNAMIC TENSION CLAMPS PREDICTIVE TENSION CONTROL REGULATORS (PTC) The regulators in the drive can use the tension information to determine there torque requirements in an open loop fashion by feeding forward all tension. The entry and exit tension values are subtracted from each other to calculate the DT for the bridle. Any error between these values is integrated and added/subtracted from the speed reference up to a set percentage (trim limit) to modify or ‘droop’ the speed reference. but become active if something goes wrong (like a strip break) and prevent a runaway situation. All these values are summed up and fed forward into the current/torque regulator as the reference. losses. This allows the speed regulator to stay out of the way for the set percentage.TENSION PROFILE . and inertia comps directly to the current/tension loop. the bridle cannot perform this amplification. This is the slip limitation of the bridle. The output of the speed regulator can also be fed to the followers in a bridle to aid in load sharing. the output of the speed regulator should always be zero (or very low). This signal can be montitored to determine if unknown mechanical losses are occuring. losses. The only way to increase the multiplication of this bridle would be to increase the angle of wrap or the coefficient of friction between the strip and the roll or add a pinch/snubber roll on one of the bridle rolls. It can only handle two times the input tension or 20 lbs in this case. the output of the speed regulator should be minimal. 0 Regenerating Load Percentage Drawing 11 Drawing 11 shows a simplified speed master. This is the horsepower limitation of the bridle. etc. .000. DYNAMIC TENSION CONTROL AND LOAD DISTRIBUTION VALUE CALCULATIONS The values needed for dynamic tension control clamps and bridle load distribution are shown in an example below.000 lbs the theoretical output tension could be 2. On the other hand if the input tension was 1. The tension reference.DYNAMIC TENSION CLAMPS Master Speed Regulator Current/Tension Feedback Speed Feedback PI PI Speed Regulator Current Regulator Speed Reference Additional Losses (if any) To Firing Circuit losses Windage and Friction Losses + Total feedforward tension reference speed Inertia comp filter dv dt Load Balance signal to followers Motoring Load Percentage Entry Tension Reference - Load Distribution T of Bridle x x Exit Tension Reference If all compensations are correct. but if the the bridle horsepower is too low. are still fed forward to the current/tension regulator. For example. since the follower would not be aware of additional load that is not fed forward from the reference. The output of the speed regulator can be monitored after commissioning to determine if some unknown losses are occurring in the process.TENSION PROFILE . If these values are accurately calculated.000. if the bridle has a multiplication factor of 2 and there is 10 lbs on the entry side and 21 lbs on the exit side.000 lbs. slip and horsepower. the bridle will slip. There are two limiting factors in any bridle. It is similar to the tension/follower except it does not have a process trim regulator. 719 = 1. 1) Find amplification factor T2 = T1 efa where e is the Naperian constant f is the coefficient of friction (usually . The following horsepowers were selected for the motors by the mechanical contractor: Roll 1 = 250 HP Roll 2 = 200 HP Roll 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 220° angle of wrap. entry bridle of a three zone pickle line. Coefficient of friction is . calculate maximum DT and subtract this value from the maximum values to get the minimum values. We will ignore bending losses is this example.679 T5 PAYOFF T4 2 T1 1 4 T3 MOTORING LOOPER T2 3 .135 = epi/180 * 220 * 0. Roll 3 has a 230° angle of wrap.slip dependent horsepower.135 = 1. The mill builder has given the following information about the bridle.DYNAMIC TENSION CLAMPS Example Using the example given in drawing 1. Calculate the motoring horsepower required to get maximum work out of the rolls in the bridle .135 = epi/180 * 230 * 0. Roll 2 has a 220° angle of wrap.135 (strip is oily) If the mill builder does not provide minimum tension values.135 = epi/180 * 220 * 0.679 = 1. but they should be added to horsepower values if the strip is heavy or the rolls are have small diameters. Roll 4 has a 220° angle of wrap.15 to .18 for steel rolls) a is angle of wraps in radians R is the amplification factor for each roll: R1 R2 R3 R4 = epi/180 * 220 * 0.679 = 1.TENSION PROFILE . 5 HP.138.4292 lbs = 6322 lbs T3 . Roll 1 calculations: HP = tension (lbs) * strip speed (fpm) / 33000 7206 lbs *1065fpm / 33000 = 232 HP Roll 2 calculations: T4 = 17820 lbs .679) = 4292 lbs 4292 lbs*1065fpm / 33000 = 138.275 or 27.(6322 lbs) /1.5HP / 503.5 HP Roll 3 calculations: T3 = 10614 lbs .T3 = DTROLL2 = 10614 lbs .(10614 lbs /1.T1 = DTROLL4 = 3678 lbs . T1 tension is greater than the minimum tension calculated above.85HP / 503. Using the above HP ratings.(3678 lbs) /1.5HP = 0. we can determine the percentage each roll must pull to achieve the desired results.1% of the bridle load Roll 2 .DYNAMIC TENSION CLAMPS 2) Find the DT for motoring maximum tension.5HP = 0. DT is the tension change across the bridle.461 or 46. It can be broken down to tension change across the individual rolls in the bridle. T1 tension = 3678 lbs . Roll 1 .TENSION PROFILE .719) = 2644 lbs 2644 lbs*1065fpm / 33000 = 85 HP Roll 4 calculations: T2 = 6322 lbs . Remember the bridle will motor when the incoming tension is higher than the outgoing tension.2644 lbs = 3678 lbs T2 .(17820 lbs/1.232HP / 503.T4 = DTROLL1 = 17820 lbs .5HP = 0.679) = 1487 lbs 2644 lbs*1065fpm / 33000 = 48 HP The total bridle horsepower used is 503.169 or 16. T5 = 17820 lbs maximum tension on incoming side of bridle per mill builder T5 . In this example.7206 lbs = 10614 lbs T4 .1487 lbs = 2191 lbs which is less than the 2500 lbs out the mill builder has specified.5% of the bridle load Roll 3 .9% of the bridle load .679) = 7206 lbs This value can be used to determine needed for this roll for maximum motoring tension.T2 = DTROLL3 = 6322 lbs . 7 HP Based on the ratios for each roll and multiplying by the total HP. T1 PAYOFF T2 T5 1 2 4 T3 LOOPER T4 3 REGENERATING The amplification factor for the rolls is the same.48HP / 503.DYNAMIC TENSION CLAMPS Roll 4 .135 = epi/180 * 220 * 0.TENSION PROFILE . Roll 1 = 156 HP Roll 2 = 93 HP Roll 3 = 57 HP Roll 4 = 32 HP This is the horsepower required for DTbridle = 10494 lbs. T5 = 13200 lbs maximum tension on outgoing side of bridle per mill builder T5 .135 = epi/180 * 220 * 0.095 or 9. R1 R2 R3 R4 = epi/180 * 220 * 0..719 = 1.679 = 1.135 = 1. motoring tension.679 3) Find the DT for regenerating maximum tension.(13200 lbs/1. Roll 4 calculations: HP = tension (lbs) * strip speed (fpm) / 33000 5338 lbs *1065fpm / 33000 = 172 HP Roll 3 calculations: .135 = epi/180 * 230 * 0.T4 = DTROLL4 = 13200 lbs . Remember the bridle will regenerate when the incoming tension is lower than the outgoing tension.679 = 1.. T1 < T5.5% of the bridle load This splitting of loads among rolls can be considered the “natural” distribution of loads.. The total horsepower needed for motoring the bridle at worst case is: HP = 10494 lbs * 1065 fpm / 33000 = 338. Since our mill builder has specified that T1 tension will never be less than 7326 lbs and T5 tension will never be greater than 17820. Now do the same calculations for regenerating bridle.5HP = 0.679) = 5338 lbs This value can be used to determine needed for this roll for max. DTbridle = lbs. 283 or 28.7 HP Roll 2 = 56. 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.679) = 1850 lbs 1850 lbs*1065fpm / 33000 = 60 HP Roll 1 calculations: T2 = 4574 lbs .5HP = 0.5HP / 373.3288 lbs = 4574 lbs T3 .8 HP Roll 3 = 100.60HP / 373.T1 = DTROLL1 = 2724 lbs .4 HP Roll 4 = 163.. T1 tension = 2724 lbs .5338 lbs = 7862 lbs T4 .T2 = DTROLL2 = 4574 lbs .16 or 16% of the bridle load Roll 3 .5HP = 0.679) = 1101 lbs 1101 lbs*1065fpm / 33000 = 35.5% of the bridle load Roll 2 ..5HP = 0..T3 = DTROLL3 = 7862 lbs . Roll 1 = 33.5 HP This can be considered the “natural” distribution of load for the the regenerating bridle. we can determine the percentage each roll must pull to achieve the desired results. DTbridle = 11000 lbs.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.(4574 lbs) /1.1850 lbs = 2724 lbs T2 .5HP = 0.719) = 3288 lbs 3288 lbs*1065fpm / 33000 = 106 HP Roll 2 calculations: T3 = 7862 lbs .172HP / 373.106HP / 373.DYNAMIC TENSION CLAMPS T4 = 13200 lbs .(2724 lbs) /1.35. The total bridle horsepower used is 373.(7862 lbs /1. Roll 1 .095 or 9.1101 lbs = 1623 lbs which is less than the 2200 lbs out the mill builder has specified. Using the above HP ratings.3% of the bridle load Roll 4 .3 HP . But this examples T1 tension is greater than the minimum tension calculated above.5 HP.TENSION PROFILE . 3 The following horsepowers were selected for the motors by the mechanical contractor: Roll 1 = 250 HP Roll 2 = 200 HP Roll 3 = 150 HP Roll 4 = 200 HP The calculated horsepower values fit into the horsepower given by the mill builder for the desired tensions calculated above. Roll 1 Roll 2 Roll 3 Roll 4 DT = 250HP * 33000 / 1065fpm = 7746 lbs DT = 200HP * 33000 / 1065fpm = 6197 lbs DT = 150HP * 33000 / 1065fpm = 4648 lbs DT = 200HP * 33000 / 1065fpm = 6197 lbs Now that the maximum DT for each roll has been determined. For motoring operation. the following equations apply: T5 PAYOFF T4 2 T1 1 4 T3 MOTORING T1 = x LOOPER T2 3 . find out what initial or T1 tension is needed for that maximum DT across each roll. Unfortunately.7 56.8 100.4 163. The load distribution numbers must be determined to maximize the amplification and horsepower abilities of the bridle.DYNAMIC TENSION CLAMPS This is the horsepower needed for DTbridle = 11000 lbs. The horsepower ranges for the bridle are as follows: Bridle 1 2 3 4 Motoring HP 156 93 57 32 Regenerating HP 33.TENSION PROFILE . SLIP / HORSEPOWER AND LOAD SHARING CALCULATIONS If it were possible to buy motors that had the horsepowers calculated above. Determine the maximum DT for each roll in the bridle based on the given motor horsepowers. we see that the horsepowers needed do not directly correlate to available motor sizes and different horsepowers are needed for motoring and regenerating. the “natural” load distribution values could be used by the regulator for motoring and regenerating load percentages. x = 6197 lbs x = 9126 lbs These 4 x values represent the 4 initial (T1) tensions that would be necessary to achieve maximum DT across the respective rolls based on the horsepower limitations of the motors. Ideally.136x roll 4 amplification roll 3 and 4 amplification roll 2.2.T4 8.846x T5 = 8. maximum DT could be utilized.886x = 6197 lbs x = 3161 lbs Roll 3 T3 . Roll 1 T5 .T2 2.886x T4 = 4.679x = 4648 lbs x = 3850 lbs Roll 4 T2 . the ratio would be dynamic so at low initial tensions.846x = 7746 lbs x = 2354 lbs Roll 2 T4 .TENSION PROFILE .3. and 4 amplification amplification from all rolls Now find the value for x in each of the maximum DT across each roll.846x .886x .1.T3 4.T1 1. The ratio is a compromise of maximum DT (horsepower limited) and maximum bridle amplification (slip limited). Now four separate calculations must be done to determine which slip/HP ratio that is most appealing for this application.4.DYNAMIC TENSION CLAMPS T2 = 1. we could utilize the maximum amplification and at high initial tensions.136x .679x T3 = 2.679x . . .719 = 11111 lbs T4 = 11111 + 6197 = 17308 lbs T5 = 17308 + 7746 = 25054 lbs (T1 * roll 4 multiplication factor) (T2 * roll 3 multiplication factor) (T3 + maximum DT across roll 2) (T4 + maximum DT across roll 1) Amplification factor = 25054 lbs / 3850 lbs = 6.3. Case 3 x value . This example has three rolls limited by slip and roll 1 horsepower limited.679 = 19152 lbs (T1 * roll 4 multiplication factor) (T2 * roll 3 multiplication factor) (T3 * roll 2 multiplication factor) (T4 * roll 1 multiplication factor) This case yields DTbridle = 16789 lbs and amplification factor = 8.5.679 = 5307 lbs T3 = 5307 * 1.13. = 3161 lbs T1 = 3161 lbs T2 = 3161 * 1.5 This case yields DTbridle = 21204 lbs and amplification factor = 6. This example has roll 3 and roll 4 limited by slip and roll 1 and roll 2 horsepower limited. = 2354 lbs T1 = 2354 lbs T2 = 2354 * 1. not horsepower.(T3 -T2)max.3 This case yields DTbridle = 19902 lbs and amplification factor = 7. This case yields the best amplification factor (maximum bridle capacity based on wrap angle and coefficient of friction) but falls short of maximum horsepower capacity of 24788 lbs.(T5 .T4)max.679 = 15317 lbs T5 = 15317 + 7746 = 23603 lbs (T1 * roll 4 multiplication factor) (T2 * roll 3 multiplication factor) (T3 * roll 2 multiplication factor) (T4 + maximum DT across roll 1) Amplification factor = 23603 lbs / 3161 lbs = 7. = 3850 lbs T1 = 3850 lbs T2 = 3850 * 1.TENSION PROFILE .719 = 6794 lbs T4 = 6794 * 1.679 = 6464 lbs T3 = 6464 * 1.679 = 11407 lbs T5 = 11407 * 1.719 = 9123 lbs T4 = 9123 * 1.(T4 -T3)max. Case 2 x value . This example has every roll in the bridle limited by slip.DYNAMIC TENSION CLAMPS Case 1 Starting with minimum x value .679 = 3952 lbs T3 = 3952* 1. and 3 amplification amplification from all rolls Now find the value for x in each of the maximum DT across each roll.679 = 15322 lbs T3 = 15322 + 4648 = 19970 lbs T4 = 19970 + 6197 = 26167 lbs T5 = 26167 + 7746 = 33913 lbs (T1 * roll 4 multiplication factor) (T2 + maximum DT across roll 3) (T3 + maximum DT across roll 2) (T4 + maximum DT across roll 1) Amplification factor = 33913 lbs / 9126 lbs = 3. DTbridle = 19902 lbs.11 or 11% 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). These values would fit into the Case 2 was used since it provides a good balance of amplification versus DTbridle.T3) / 19902 = 0.DYNAMIC TENSION CLAMPS Case 4 x value . For regenerating operation (drawing 2) the following equations apply: T1 PAYOFF T2 T5 1 4 2 T3 REGENERATING T1 = x T2 = 1.(T2 -T1)max.T1) / 19902 = 0. The load distribution = DTroll / DTbridle..819x T4 = 4.679x T3 = 2. 3 . This example has roll 2.39 or 39% of the load on the bridle Roll 2 = (T4 . Roll 1 = (T5 .19 or 19% of the load on the bridle Roll 4 = (T2 . = 9126 lbs T1 = 9126 lbs T2 = 9126 * 1. For case 2.3 and 4 limited by slip and roll 1 horsepower limited.T4) / 19902 = 0. This example yields the highest DTbridle (use of horsepower) but the lowest bridle amplification factor.136x LOOPER T4 initial tension roll 1 amplification roll 1 and 2 amplification roll 1.7. The DTbridle should be multiplied by these percentages and used for the drive as tension reference for the individual motors. Now the load distribution of tensions throughout the bridle must be calculated.846x T5 = 8.2. The mill builder has specified that the maximum in/minimum out tension (for motoring) are 17820 lbs / 7326 lbs respectively.T2) / 19902 = 0.TENSION PROFILE .31 or 31% of the load on the bridle Roll 3 = (T3 .7 This case yields DTbridle = 24788 lbs and amplification factor = 3. 846x = 6197 lbs x = 1883 lbs Roll 3 T4 .13. maximum DT could be utilized.T4)max.846x . = 1883 lbs T1 = 1883 lbs T2 = 1883 * 1.T4 8. we could utilize the maximum amplification and at high initial tensions.679x = 6197 lbs x = 5435 lbs Roll 1 T2 .DYNAMIC TENSION CLAMPS Roll 4 T5 . This example has every roll in the bridle limited by slip.679 = 15320 lbs (T1 * roll 1 multiplication factor) (T2 * roll 2 multiplication factor) (T3 * roll 3 multiplication factor) (T4 * roll 4 multiplication factor) This case yields DTbridle = 13437 lbs and amplification factor = 8.4.679x .679 = 5308 lbs T4 = 5308 * 1.2.T3 4.(T5 .819x .679 = 3161 lbs T3 = 3161 * 1. The ratio is a compromise of maximum DT (horsepower limited) and maximum bridle amplification (slip limited). the ratio would be dynamic so at low initial tensions. Now four separate calculations must be done to determine which slip/HP ratio is most appealing for this application.136x . .1.719 = 9124 lbs T5 = 9124 * 1. This case yields the best amplification factor (maximum bridle capacity based on wrap angle and coefficient of friction) but falls short of maximum horsepower capacity of 24788 lbs.T1 1. not horsepower. Case 1 Starting with minimum x value . Ideally.T2 2.x = 7746 lbs x =11407 lbs These 4 x values represent the 4 initial (T1) tensions that would be necessary to achieve maximum DT across the respective rolls based on the horsepower limitations of the motors.819x = 4648 lbs x = 2293 lbs Roll 2 T3 .TENSION PROFILE . 679 = 3849 lbs T3 = 3849 * 1.TENSION PROFILE .679 = 15324 lbs T4 = 15324 + 4648 = 19972 lbs T5 = 19972 + 6197 = 26169 lbs (T1 * roll 1 multiplication factor) (T2 * roll 2 multiplication factor) (T3 + maximum DT across roll 3) (T4 + maximum DT across roll 4) Amplification factor = 26169 lbs / 5435 lbs = 4. This example yields the highest DTbridle (use of horsepower) but the lowest bridle amplification factor.719 = 11111 lbs T5 = 11111 + 6197 = 17308 lbs (T1 * roll 1 multiplication factor) (T2 * roll 2 multiplication factor) (T3 * roll 3 multiplication factor) (T4 + maximum DT across roll 4) Amplification factor = 17308 lbs / 2293 lbs = 7.54 This case yields DTbridle = 15016 lbs and amplification factor = 7.(T3 -T2)max.54.(T2 -T1)max. This example has roll 1.82 This case yields DTbridle = 20734 lbs and amplification factor = 4. = 11407 lbs T1 = 11407 lbs T2 = 11407 * 1.DYNAMIC TENSION CLAMPS Case 2 x value .679 = 19152 lbs T3 = 15322 + 6197 = 25349 lbs T4 = 25349 + 4648 = 29997 lbs T5 = 29997 + 6197 = 36194 lbs (T1 * roll 1 multiplication factor) (T2 + maximum DT across roll 2) (T3 + maximum DT across roll 3) (T4 + maximum DT across roll 4) Amplification factor = 36194 lbs / 11407 lbs = 3. This example has roll 1 and roll 2 limited by slip and roll 3 and roll 4 horsepower limited. The mill builder has specified that the maximum out/minimum in tension (for regenerating) are 13200 lbs / 2200 lbs respectively. Case 4 x value .679 = 6464 lbs T4 = 6464 * 1.. Case 3 x value . . This example has three rolls limited by slip and roll 4 horsepower limited. = 5435 lbs T1 = 5435 lbs T2 = 5435 * 1. These values would fit into the Case 1 was used since it provides a good balance of amplification versus DTbridle.17.17 This case yields DTbridle = 24788 lbs and amplification factor = 3.2 and 3 limited by slip and roll 3 horsepower limited.82.(T4 -T3)max. = 2293 lbs T1 = 2293 lbs T2 = 2293 * 1.679 = 9126 lbs T3 = 9126 * 1. The DTbridle should be multiplied by these percentages and used for the drive as tension reference for the individual motors. If the looper tension was set to 17000 lbs. DTbridle = 13437 lbs.46 or 46% of the load on the bridle Roll 3 = (T4 .DYNAMIC TENSION CLAMPS Now the load distribution of tensions throughout the bridle must be calculated. The bridle would be in a horsepower limited clamp. The bridle would be in a slip limited clamp.13437).TENSION PROFILE . the entry tension would be dynamically clamped to 21900. we will ignore looper bending losses for this example.T1) / 13437 = 0. the entry tension would be dynamically clamped to 1722 lbs. If the looper tension was 14000 lbs.3 or B1X + 19902).28 or 28% of the load on the bridle Roll 2 = (T3 . These numbers should be used in the load distribution scheme for the bridle when regenerating (see regenerating load percentage on drawings 10 and 11).T4) / 13437 = 0. The bridle would be in a slip-limited clamp. the minimum entry tension would be clamped to 3563 lbs ( the regenerating clamps are the maximum of B1X divided by 8. If motoring values selected for bridle 1 are as follows: amplification 7. The entry tension is dependent on looper tension. If looper tension was set to 1100 lbs. For case 1. The reference limits from the lookup tables (or level 2)are: entry looper tension 1100 to 17000 lbs For dynamic tension clamping. the entry tension maximum (motoring) limit would be dynamically clamped 8030 lbs (the motoring clamps are the minimum of B1X tension * 7.13 or B1X . For the sake of simplicity.T3) / 13437 = 0. If the looper tension was set to 3000 lbs.3 max DTbridle 19902 lbs.095 or 9. . The load distribution = DTroll / DTbridle. If regenerating values for bridle 1 are as follows: amplification 8. Roll 4 = (T5 .13 max DTbridle 13437 lbs.T2) / 13437 = 0.15 or 15% of the load on the bridle Roll 1 = (T2 .5% of the load on the bridle These numbers also match the “natural” regenerating load distribution since we are using maximum bridle amplification. these values would be used in drawing 2. The bridle is again in the horsepower limited clamp. Copyright © 2002 Rockell Automation. . Printed in USA. Inc. All rights reserved.