Modeling the Dynamics of an Ice Tank Carriage

Transcription

1 Modeling he Dynamics of an Ice Tank Carriage The challenge: To model he dynamics of an Ice Tank Carriage and idenify a mechanism o alleviae he backlash inheren in he design of he gearbox. Maplesof, a division of Waerloo Maple Inc., 28 Execuive Summary Inroducion Problem Saemen 1. Model Descripion of Ice Tank Carriage 2. Verifying Model Accuracy 3. Improving Model Dynamics Resuls ** This applicaion was developed using Maple and MapleSim Page 1 of 9

2 Execuive Summary Tradiional ships due o heir design can no be used o sail hrough ice-covered waers such as hose presen in he Arcic. Maneuvering hrough ice-covered waers requires a special design of ship commonly known as an icebreaker. An icebreaker has hree disinguishing feaures ha enable i o crush he ice beneah i. These are: 1) a srenghened hull, 2) an ice-clearing shape, and 3) a powerful engine. Before an icebreaker is consruced, he design of each of hese hree feaures is rigorously esed and opimized in an ice ank. An ice ank is a refrigeraed waer ank in which a scale model of he ship's hull is pulled by a ganry carriage hrough a layer of formed ice. The ganry carriage is driven by an elecric moor hrough a gearbox ha is elecronically conrolled o obain he required orque and speed performance for he scale model. Tha said, problems inheren in he design of he ice ank could poenially disor he inegriy of any es resuls ha are obained. This was he case, when i was noed ha he speed of he model ship became unsable when he ganry carriage was operaing a low speeds. Invesigaion ino his problem led o he source of he error; i was found ha he force generaed by he ship s hull when breaking ice would creae backlash beween he gear eeh driving he ganry carriage. The conroller, in an aemp o correc for he backlash, would cause he speed of he model ship o overshoo and hen undershoo, gradually increasing in magniude o a poin ha would cause evenual damage o he equipmen. To recify he error, a high-fideliy mahemaical model of he ice ank sysem was creaed using MapleSim and Maple. The model was simulaed using wo differen parameer ses; he firs parameer se simulaed he model wihou perurbaions from breaking he ice, while he second se included he effecs of breaking he ice. This was done o ensure ha he model accuraely capured he vehicle dynamics refleced in he real sysem. To alleviae he backlash in he gearbox, differen soluions were esed on he model. Re-calibraing he PID conroller reduced he backlash presen in he sysem, however i was no able o remove i o a level ha was deemed saisfacory by he eam. As an alernaive, a orque preload componen was added o he oupu shaf of he gearbox as a means o preven he gear eeh from slipping. Using he Opimizaion Templae in MapleSim, i was found ha applying a orque preload of -3.5 Nm was sufficien o sabilize he speed of he ganry carriage and hus he model ship. Inroducion An icebreaker is used o sail hrough ice-covered waers because is design enables i o break and clear ice along is pah. An icebreaker, which ypically moves a speeds ranging from.2 m/s o 4. m/s, is able o crush he ice beneah i by driving is bow up ono he ice and using is massive weigh o break he ice. Before consrucion of an icebreaker begins, i is rigorously esed in an ice ank. An ice ank consiss of a refrigeraed waer basin, which provides a physical modeling environmen o measure he vehicle dynamics of ship's hull as i is pulled hrough a layer of ice. The scale model of he ship's hull is pulled along he ice ank via a suspended ganry mechanism, which is driven by an elecric moor and gearbox assembly. The composiion of he formed ice is modified o reflec he ice/waer condiions of he environmen where he icebreaker will operae. The ice ank presen in our faciliy measures 9m by 12m by 3m. To ge accurae ice ank simulaion resuls, i is of umos imporance ha any problems inheren in he design of he ice ank be correced. Tha said, wihou an accurae model of he ice ank mechanism, disinguishing he source of error beween he ice ank or he ship's design can become very difficul. As a resul, i is Page 2 of 9

3 common pracice in indusry o develop a mahemaical model of he ice ank which, when simulaed accuraely predics he performance seen in he ice ank basin. Problem Saemen This documen presens he seps involved in developing an accurae model of he ice ank carriage. In addiion, i illusraes he approach ha was aken o eliminae chaer in he gearbox, due o backlash beween he gear eeh. 1. Model Descripion of Ice Tank Carriage 1.1 Free-Body Diagram The free-body diagram shown in Figure 1 is a simplified represenaion of a model ship in an ice ank. As shown, he force of he waer F waer and he force from he impac of breaking he ice F ice are opposing he force driving he ganry carriage F drive. Alhough i is no depiced, i is imporan o noe ha he moor/drive conains a gearbox. The gearbox ranslaes he moor orque ino a linear force ha pulls he ganry carriage. In he acual physical sysem, he rail is locaed along he op of he ice ank basin (ha is, he inerface beween he ice and he model ship). In his diagram, he rail is locaed below he Moor/Drive componen for he purposes of illusraing he ineracion of he forces in he sysem. Figure 1: Free-Body diagram of Ice Tank Mechanism Page 3 of 9

4 Physical Model Represenaion The free body diagram in Figure 1 can be easily convered ino physical model represenaion using MapleSim. The MapleSim diagram depiced in Figure 2 is a physical model represenaion of he sysem. The orque sep componen in his represenaion was added o eliminae backlash in he gear during ice breaking. The reason for adding he orque sep componen is discussed in he nex secion. As can be seen in he diagram, he physical model is made up of a plan and conroller submodels. The conroller submodel adjuss he volage level driving he moor in response o changes (or errors) in he speed of he model ship. These changes are relayed back o he PID conroller hrough a speed sensor ha is conneced beween he ganry carriage and model ship submodels. Page 4 of 9

5 The plan model consiss of 5 submodels. These are: 1) DC Moor, 2) Gear, 3) Ganry Carriage, 4) Model Ship, and 5) Breaking Ice. The DC Moor submodel was modeled using a simplified model of a DC Moor as an equivalen elecric circui The Gear submodel was modeled wih he buil-in siffness, damping and dead-space necessary o represen he backlash in he gear eeh The Ganry submodel was represened as an ideal roaional o ranslaion gear The Model Ship was represened as a sliding mass of approximaely 8, kg, wih a resising force o he damping effec of waer The Breaking Ice submodel was included in he model as a means o measure he sysem response due o breaking ice. This submodel was modeled using a simple single saw-ooh cycle: a linearly increasing force ha releases o zero when he ice breaks. Each of hese submodels, and he componens ha were used o model hem can be seen in he.msim file. Page 5 of 9

6 2. Verifying Model Accuracy The model in Figure 2 (wihou he preload orque componen) was simulaed using wo differen parameer ses. This was done o es he validiy and accuracy of he model agains real-world resuls. The firs parameer se simulaed he ice ank model wihou any perurbaions due o breaking ice, whereas he second parameer se simulaed he ice ank model aking ino accoun he effecs of breaking ice. The resuls of hese wo simulaions are shown in he nex wo secions, respecively. Sysem response wihou ice breaking perurbaions As can be seen from he four plos below, when he sysem was no perurbed (ha is, no breaking ice), he speed of he ganry carriage followed a smooh rajecory. In addiion, he error beween he sep inpu and he velociy feedback signal quickly wen o zero. In fac, he only reason ha here is an error is because i akes he sysem approximaely 35s o reach seady sae Probe1.GearTorque Probe3.SignalError Probe2.GanrySpeed 'Moor::Probe4'.MoorVolage Noe: These plos were obained by simulaing he model wih he parameer se defined in "IniialParamSe_NoPerubaions.params" file. Page 6 of 9

7 Sysem response wih ice breaking perurbaions As expeced, when he sysem was ordered o break ice, he speed of he ganry carriage began o oscillae. The sysem response o breaking ice can be seen in he four plos below. Annoaions on he plo describe he sysem response a differen ime seps. Probe1.GearTorque 12 Torque due o resisance of ice K2 Sudden release when ice breaks Probe3.SignalError Probe2.GanrySpeed Induced oscillaions in speed 'Moor::Probe4'.MoorVolage Increasing error signal Noe: These plos were obained by simulaing he model wih he parameer se defined in "IniialParamSe_Perubaions.params" file. Page 7 of 9

8 3. Improving Model Dynamics Many differen approaches were considered o remove he induced speed oscillaions in he ganry carriage. One approach ha was aken involved increasing he proporional gain of he PID conroller. Unforunaely, alhough increasing he gain reduced he chaer beween he gear eeh, i also amplified he volage supplied o he DC moor o a level ha was significanly larger han he raing of he moor. A common pracice used in indusry o remove gear backlash is o apply a preload orque o he gearbox. This forces he gear eeh o remain in conac a all imes. We were able o model he effecs of a preload orque by adding an "applied orque" block o he physical model. Deermining he amoun of "applied orque" needed o sabilize he speed of he ganry carriage was accomplished using he Opimizaion emplae (please refer o he Opimizaion.mw file locaed in he Documen Folder for more informaion). A suiable speed response was obained by using a orque load of -3.5Nm. The sysem response o a preload orque is shown in he following plos. Clearly, we can see ha he gear orque no longer shows signs of chaer, and ha he speed of he ganry carriage sabilizes o a desired speed Probe2.GearTorque Same orque disurbance due o breaking of ice Probe1.GanrySpeed Speed disurbance due o breaking ice quickly sabilizes o desired speed Probe3.SignalError.2 'Moor::Probe4'.MoorVolage Error due o breaking of ice sabilizes o desired speed Noe: These plos were obained by simulaing he model wih he parameer se defined in "FinalParamSe.params" file. Page 8 of 9

9 Resuls This documen oulines he seps aken o develop a high-fideliy physical model of he ice ank carriage ha accuraely depics he behavior during esing. The model was validaed by simulaing i using wo differen parameer ses. The firs parameer se simulaed he model wihou perurbaions from breaking he ice, while he second se included he effecs of breaking he ice. As expeced, when he sysem was se o break ice, he speed of he ganry carriage, and hus he model carriage, began o oscillae. Invesigaion ino his problem led o he source of he error. I was found ha he force generaed by he ship s hull when breaking ice would creae backlash beween he gear eeh driving he ganry carriage. The conroller, in an aemp o correc for he backlash, would cause he speed of he model ship o overshoo and hen undershoo. The addiion of a orque preload componen was considered o alleviae he backlash presen in he gearbox. Modeling he orque preload componen was achieved by using a orque sep componen. Using he Opimizaion Templae in MapleSim, i was found ha applying a orque preload of -3.5Nm was sufficien o sabilize he speed of he ganry carriage and, as a resul, he model ship. Legal Noice: Maplesof, a division of Waerloo Maple Inc. 28. Maplesof, Maple, and MapleSim are rademarks of Waerloo Maple Inc. All oher rademarks are he propery of heir respecive owners. This applicaion may conain errors and Maplesof is no liable for any damages resuling from he use of his maerial. Page 9 of 9