PDH Course E246. DC Dynamic Braking. Carlo DeLuca, PE, MBA. PDH Center Dakota Lakes Drive Herndon, VA

Transcription

1 PDH Course E246 DC Dynamic Braking Carlo DeLuca, PE, MBA 2007 PDH Cener 2410 Dakoa Lakes Drive Herndon, VA Phone: Fax: An Approved Coninuing Educaion Provider

2 Definiion DC Dynamic Braking Carlo DeLuca, PE, MBA Dynamic Braking is a mehod used o elecrically sop movemen of a mechanical device. This mehod generally precludes use of oher mechanical braking devices. Elecrical energy is used o hal movemen and defea ineria of he moving device afer he power used o creae and mainain movemen is removed. The key word here is energy. Energy refers o force a a disance a a prescribed period of ime. Horsepower is commonly used o express mechanical power. However, i acually is a classical erm for energy. Horsepower is defined as 550 f. lbs. sec. Thus, if we were o lif 275 pounds for 2 fee for 1 second, we would exer one horsepower (275 lbs. imes 2 f. for 1 sec. would equal 550 f. lbs. sec.). A frequenly used erm for elecrical power is was. For direc curren applicaions, was is generally he produc of volage imes amperage. However, classical erms for elecrical energy is coulombs or joules. One joule is equal o one wa second. When we pay our elecric bill, we are paying for energy in he form of kilowa hours (or housands of was per hour). The conversion of elecrical energy o mechanical energy is 746 wa sec. o one horsepower. The dimension of power and ime is crucial o Dynamic Braking. No only mus we specify he ask of sopping device movemen, bu we mus also specify he ime frame in which he movemen mus sop. The advanages in using elecrical Dynamic Braking raher han mechanical braking devices can be readily recognized. Response o braking commands can be immediae; he braking acion can be easily auomaed; componens are generally less expensive; and he braking device requires less mainenance. Perhaps he main disadvanage is ha he elecrical energy required o sop he device wihin he required ime may no be convenienly available. Consideraions for Circui Developmen We will concenrae on Dynamic Braking of devices employing direc curren moors. While circuis can be devised o perform dynamic braking on Alernaing Curren moors, he principles of moor operaion are differen. Direc curren moor roaion can be easily reversed by simply reversing he polariy of he volage (or curren). AC moors someimes require changes o he inernal circui or wiring hookup. Thus, simply reversing he curren flow effecs braking acion on a DC moor. Our firs concern in circui developmen is o define he ask and parameers of performance. Wha mus be done? How reliable and accurae mus performance be? How much energy can be used and how much is available? Oher associaed consideraions are cos of produc, cos and ime o develop and ease of manufacure. Once he ask and parameers are defined, we consider he componens necessary o complee he ask. This can range from high-ech devices such as cusom compuers o commonly available resisors, capaciors ec. Carlo DeLuca Page 2of 11

3 When considering he ask, he applicaion of he device mus be aken ino accoun. An applicaion I have experienced involved a remoely conrolled, long range, opical zoom lens which required insan sopping while focusing. On a larger scale, Dynamic Braking is used o supplemen brakes on rains. This course will deal wih a model airplane DC moor used o drive a propellor. I was chosen for an essenial reason, he componens were readily available. Defining he Task and Parameers Our ask will be o sop roaion of he propellor as quickly as possible o preven injury o people or objecs ha migh be near he propellor blades when i is on he ground. Also, sopping roaion quickly upon landing will assis in shorening he landing roll. An aracive feaure would be o acually reverse propellor roaion upon landing o effec reverse hrus braking of he airplane and furher shorening he landing run. The circui mus employ only componens ha are ligh in weigh o keep aircraf weigh o a minimum. The funcion mus be conrolled by a simple swich which can be operaed wih a remoe conrolled device for maneuvering he airplane. The device is limied o minimal use of he energy ha is provided for he operaion of he airplane moor. Any addiional energy sources mus be minimal in weigh. The power source o be used for moor operaion is a 6 vol baery capable of delivering 30 amperes for abou 15 minues. Upon bench esing, he moor wih he propellor insalled used approximaely 29 amperes upon iniial applicaion of power wih amperage decreasing o seady sae condiion a approximaely 22 amperes wihin abou ½ second. Upon removal of power, he propellor sopped roaing in 3 o 4 seconds, indicaing ha fricion was minimal. These ess were done wih lile or no exernal air movemen. I is sressed ha his daa is approximae. More precise measuremens would require high qualiy insrumenaion. The accuracy for collecing daa was accommodaed wih a digial mulimeer and imer. Keeping his in mind, he daa is adequae for calculaion of parameers. In order o sop he propellor, i will be necessary o apply a leas he same amoun of energy in opposiion o he movemen ha was used o accelerae he propellor o seady sae velociy. The energy, herefore, o accelerae he device o seady sae rae of revoluion (revoluions per minue or RPM) can be approximaely deermined by calculaing he wa-secs. or joules expended a sarup (6 vols from 29 o 22 amperes for ½ second). Because overcoming ineria from a sopped posiion was necessary, he amperage naurally varied before achieving seady sae condiion. Alhough he rae of amperage change may no have been linear, we will assume i was for he accuracy we require. Thus, we can use average amperage, given volage and esimaed ime o deermine he wa-secs. (or joules) required o accelerae he moor and propellor. The following calculaions depic he iniial amperage as i o and he seady sae amperage as i ss. The average amperage is shown as i av. Carlo DeLuca Page 3of 11

4 i i o ss 29a 22a iav ( io + iss) 2 ( ) a joules vols amperes@ 1sec joules @ 0.sec wa sec. The minimum energy required o insanly sop roaion of he propellor is 76.5 joules. More energy will no only sop he device bu, if he energy remains in opposiion o he movemen, i will acually reverse he roaion. Anoher consideraion is he ime required o deliver he proper amoun of energy. In order o calculae he ime required o deliver he energy, we mus consider he effecive resisance of he moor. When operaing a DC moor, he apparen resisance varies beween he sarup of he moor o he ime i reaches consan speed. The original apparen resisance deermines wha is known as locked roor resisance. This can be deermined by prevening he moor from roaing, applying a known volage and measuring he amperage hrough he moor. We have deermined his value from our amperage daa upon sarup of he moor and have ermed i as i o or i a ime zero. As he moor achieves roaional velociy, i creaes an opposing elecromoive force (back EMF) which limis he amperage o ha necessary o mainain energy o drive he load, in his case he propellor. We have ermed his amperage as i ss, or i a seady sae. However, when power is removed from he moor, he back EMF no longer is presen. Thus, in order o deermine effecive resisance, we can apply locked roor amperage o he commonly known equaion for DC resisance. R v i ohms We are now ready o explore opions for circuiry. The condiions saed ha any addiional energy or power sources be minimal or, preferably, no used. While some famous scienis saed ha energy can neiher be creaed nor desroyed, we do know ha energy can be sored. A common elecrical energy sorage device is he capacior. Applicaion of capaciors o AC circuis is differen in some respecs o DC circuis. This is illusraed in PDH course E219- Single o Three Phase Conversion Circui. Applying capaciors o DC circuis concenraes on heir capabiliy o sore energy. As we know, capaciors consis of wo plaes of conducive maerial placed in very close proximiy o each oher wih a hin layer of elecrical insulaion beween hem. When one plae is conneced o receive a posiive charge and he oher conneced o he negaive, he plaes will hold ha charge unil he plaes are hen elecrically conneced o dissipae he charge. The ime required o dissipae he charge is relaed o he resisance in he connecion ha dissipaes he charge. We can charge he capacior wih he power source used o run he moor. A he proper ime, power can be removed and a calculaed charge can be applied o he moor in opposie polariy o provide sopping. A greaer amoun of our calculaed energy can be applied if reversal of he moor is desired. Circui 1" shows a basic circui o accomplish his. Carlo DeLuca Page 4of 11

5 Circui 1 Circui 1 depics an elecrical schemaic designed o apply power o a moor. This is done using a swich (SW1). The swich is a double pole, single hrow swich (DPST) wih an on and an off posiion. The schemaics show hree circui condiions, ON ; OFF ; and BRAKE. The red lines indicae he par of he circui ha is conneced o a posiive side of he power and he green lines indicae he negaive side. SW1 connecs o a second swich (SW2) which is conneced o a capacior. This swich is a double pole, double hrow swich wih a momenary posiion for one posiion. A hird swich (labeled Reverse Swich ) is shown, bu is an opion. I is no used on his applicaion, bu can be used o reverse direcion for a posiioning device (such as a zoom lens). This will be considered o remain in he posiion shown for our discussion. When he circui is in he ON posiion (lef diagram) SW1 connecs he power source direcly o he moor. The moor posiive connecion is shown wih a plus sign. While he moor is being normally powered, SW2 is in a normal posiion and has conneced he power negaive side o he capacior hrough pin 1. The posiive side of he power is conneced hrough a diode o he oher capacior connecion. The diode is shown as an arrow figure. This is an elecrical check valve and will only allow curren flow in he direcion of he arrow. Thus, while he moor is running, he capacior is charged o he sysem volage. Noe ha he lines in red show posiive charge and in green show negaive charge when a circui is compleed. Carlo DeLuca Page 5of 11

6 When he circui is in he OFF posiion (middle diagram), SW1 is urned o he off posiion and SW2 is lef in he normal posiion. Power is now disconneced o he moor and he capacior erminals are no conneced. Alhough he negaive erminal of he capacior is sill conneced o he moor, curren canno flow o he moor from he posiive side because he diode prevens curren flow in ha direcion. Noe ha here is no complee circui, and par of he wiring conains neiher red nor green lines. Also noe ha no connecion exiss beween he posiive and negaive erminals of he capacior, hus he capacior remains charged. In his case, he moor will coas o a sop. When he circui is in he BRAKE posiion, Dynamic Braking is acuaed. To effec braking, SW2 is swiched o he momenary posiion. This can only remain while he swich is held in his posiion. When he swich is released, i is spring loaded o reurn o he normal posiion. In he momenary or BRAKE posiion, he negaive erminal of he capacior is conneced hrough pin 2 of SW2 o he side of he moor ha was previously conneced o he posiive power source. The posiive side of he capacior is conneced hrough pin 4 of SW2 o he side of he moor ha was conneced o he negaive power source. Noe ha he posiive (red line) is direced o he opposie side of he moor as shown in he ON diagram. The sored energy in he capacior will coninue delivering power in he opposie direcion, providing dynamic braking unil is energy is depleed or unil he swich is released. The device is now prepared o be run again upon urning power on hrough SW1. In he applicaion for a model airplane, boh swiches can be operaed remoely wih remoe conrol devices, or SW2 can be replaced wih a relay operaed auomaically from SW1. For immediae braking acion, SW2 mus be swiched immediaely afer SW1 swiches off he power. If immediae braking is no swiched on, he propellor will be allowed o deplee is kineic energy in coasing o a sop or slowing roaion. Thus, if dynamic braking is applied laer, he energy in he capacior will be greaer han required o sop and he excess energy in he capacior will end o reverse moor roaion. The nex ask is o deermine he specificaions for he componens. The swich SW1 mus be able o swich and carry a leas 30 amperes seady sae. The swich SW2 (or relay if used) mus be able o carry a 30 amperes surge for a very shor ime. The diode mus be able o susain a surge amperage caused by a 6 vol poenial for a fracion of a second, probably no more han 30 amperes. The energy required was previously deermined o be 76.5 wa-secs. o sop he propellor. The equaion for deermining he value of a capacior o sore energy is W=(½) Ce 2. W represens joules in wa-secs., C represens he value for capaciance in farads and E represens he value of volage used o charge he capacior. However, he equaion represens energy available provided he capacior charge is compleely dissipaed. Thus, we will be concerned wih a capaciance value larger han ha indicaed in order o effec soppage wihin a reasonable ime span. W C Ce 2W 2x e farads Carlo DeLuca Page 6of 11

7 To effec sopping in reasonable ime, we shall increase his value by 50% and calculae he ime o sop movemen. Thus, 150% of 4.25 farads is 6.38 farads. The ime and rae of power dissipaion can be deermined by volage and amperage decrease in discharging a capacior. Volage increase and decrease in charging and discharging a capacior is exponenial in naure. I is relaed o he mahemaical naural number e (2.713~~~). Because we will be using e for ha number, we will depar from use of ha leer in he nex few calculaions o signify volage and will use lower case v insead. v o = volage a ime zero or charged volage i o = amperage a ime zero or iniial amperage v = volage a specified ime i = amperage a specified ime v i voe ioe Joules vi v ie v v 2 R e 2 vr e o o o o o 2 2 To calculae he amoun of energy impared wihin a given ime, we inegrae he equaion. V Joules R ax 1 e dx a e Simplified : ax Joules Vo 2 C e 0 2 [ 1 e ] 2 Using he appropriae values for he elemens in his equaion:: V o = 6 Vols; C = 6.38 Farads; R = 0.21 ohms; and Joules = 76.5 wa-secs We will solve for. = seconds. Carlo DeLuca Page 7of 11

8 Checking our calculaions, we use = secs. and solve for he Joules in he equaion. We arrive a a soluion. Joules = 76.6 wa-secs close enough! Now we shall evaluae he soluion. We have discovered ha he soluion will hal movemen wihin abou 3/4 second from removing power o he moor. However, we have specified a capacior which sores 150% of he required energy in order o enable soppage wihin a reasonable ime. This means ha abou 38 wa-secs of energy will coninue o be applied o he moor. The moor will be reversed for a shor period of ime unless he energy is disconneced from he moor. This requires furher circuiry. Also, we saed ha he componens mus be ligh in weigh. A capacior of over 6 farads will be oo heavy for insallaion in a model airplane. While his soluion can funcion in some applicaions, i is no feasible for his applicaion. Insead of an energy sorage device, perhaps we can use he exising moor power source o provide he braking energy. We will require reversing he polariy of he moor power for only a few enhs of a second. Remoe swiching can be easily done wih a relay. These devices are ligh in weigh, acuaed by low currens and can swich high currens. In order o conrol ime duraion, we can use he volage decrease feaure of a charged capacior o operae only he relay. The energy required o do his is far less han needed o sop he moor and can be done wih a much smaller and ligher capacior. Circui 2" shows such a circui. Circui 2 Carlo DeLuca Page 8of 11

9 Again, he red lines indicae posiive polariy and green represens negaive polariy. The Reverse Swich shown is also an opion and will be considered o remain in his posiion for our discussion. I can be used in alernae applicaions. Noe ha only one swich is used in his circui (SW1). I is a double pole, double hrow (DPDT) swich. I conains wo common erminals. Each swiches wo poles in wo posiions. The commons are mechanically joined. The circui also employs a relay wih he same swich configuraion (DPDT). The schemaics show hree circui condiions, RUN, BRAKE and OFF. The relay is acuaed by a coil which is powered by a capacior while in he BRAKE posiion. Conneced across he coil of he relay is a variable resisor (poeniomeer) which is adjusable from 0 o 25 ohms. The RUN circui condiion shows SW1 in he on posiion. Power is delivered o he moor hrough he swich and he relay. The relay is no acuaed and connecs he power o he posiive side of he moor hrough erminal 3, and he swich SW1 connecs he negaive o he opposie side of he moor. The moor now urns in he inended direcion. The capacior is conneced o he negaive polariy of he power source and is conneced o he posiive polariy hrough he on posiion of he second pole of SW1. When he swich is in his posiion he capacior is charged o he power source volage. The BRAKE circui condiion shows SW1 moved o urn power off o he moor. SW1 now divers he negaive polariy of he moor power source o one coil erminal (5) of he relay. The posiive side of charged capacior is conneced hrough he second pole of SW1 o he opposie coil erminal (6). The relay now acuaes while he capacior is discharging and assumes he condiion shown in he BRAKE circui. I is imporan o noe ha he poeniomeer is conneced in parallel o he coil. When he relay acuaes, negaive power from he moor power source is applied o he side of he moor ha was formerly conneced o he posiive hrough erminal 2, and posiive power from he moor power source is applied o he side ha was negaive hrough erminal 4. The power polariy has been effecively reversed and reverse power is afforded o he moor and propellor unil he capacior is discharged. If he capacior discharges oo quickly, full braking will no occur. If he capacior is sill discharging afer sopping he moor, reversal of direcion will occur. As earlier indicaed, resisance and capaciance have a relaionship o ime of discharge, hus he poeniomeer is designed o adjus his. This feaure will be discussed laer. The OFF circui condiion simply shows he circuiry ha exiss once he capacior is discharged and he relay reurns o he normal off posiion. Noe ha SW1 is in he same posiion as in he BRAKE condiion. The relay swiches are in he same posiion as in he RUN circui. Alhough a par of he circui is sill conneced o negaive power, nohing is conneced o posiive power, and no curren is flowing. The capacior is discharged and ready o receive he RUN circui when SW1 is urned on. Selecion of componens for his circui used he same parameer requiremens for curren and volage for SW1 and he relay swiches, namely 30 amperes a 6 vols DC. The ask was now o selec he value of he capacior. When deermining he ime o discharge a capacior, elecrical engineers have a favorie ool. I is he ime ool. When he capaciance value is muliplied by he resisance value in a simple circui, i represens he ime (in seconds) he capacior discharges o approximaely 37% of he original volage. Carlo DeLuca Page 9of 11

10 V 1 1 = e = e = V o when = The manufacurer of he relay specifies he resisance of he coil as 40 ohms requiring a minimum of 6 vols DC o acuae. We canno place an adjusable resisor in series wih he coil o adjus rae of discharge because we require a full 6 vols o be applied o acuae he coil. However, we can place he adjusable resisance in parallel wih he coil and adjus he effecive resisance wihou reducing he iniial volage on he relay. Now i becomes necessary o know he volage a which he relay will de-acuae. Unforunaely, he manufacurers are raher reicen a specifying his daa because variaions occur wih each relay. Also, we will wan he opion o adjus he duraion jus o provide braking or o provide braking plus reversal of roaion. When we design adjusmen, we consider adjusmens ha are minimally sensiive o posiioning. Thus, we use a poeniomeer ha gives us variaions of resisance wihin he confines we anicipae and wih reasonable movemen. A poeniomeer was chosen wih a oal value of 25 ohms. The adjusmen knob is roaed approximaely 270 degrees for resisances of zero o 25 ohms. The mos criical adjusmen is he ime for braking. We shall se his ime a 0.3 seconds; however we will allow sufficien adjusmen o increase or decrease his resisance. Thus, we shall assign a value on he poeniomeer of less han half he adjusmen range, 10 ohms, which will allow more adjusmen for longer duraion. Normally, a relay will de-acuae a abou 40 o 50% of he acuaing volage, so we can begin wih our rusy ool o deermine a capaciance value for 37%, knowing we have adjusmen available. The poeniomeer will be placed in parallel wih he coil. We will use 40 ohms for he coil and 12.5 ohms for he adjused poeniomeer. Time for de-acuaion will be 0.3 seconds. R c = coil= 40ohms R p = poeniomeer = 10ohms R = oal = = + = = Rc Rp R R R = 8ohms = 03. C = = = farads R 8 Carlo DeLuca Page 10of 11

11 This value is also ermed 38k uf, or 38 housand microfarads. The capacior in Circui 1 is 168 imes larger. This capacior weighs only a few ounces and is suiable for use in he model airplane. The capacior used is he closes value available, 39k uf. Now, he longes ime duraion for volage o achieve 37% can be calculaed by using he maximum resisance adjused on he poeniomeer (25 ohms). When R p is insered ino he equaion above, he R becomes 15.4 ohms and he ime becomes 15.4 X = 0.6 seconds. This indicaes ha any reverse hrus acion will be minimal afer braking. If more ime is desired, he poeniomeer can be replaced wih one of 50 ohms or greaer o provide greaer. However, his will make adjusmen for braking more difficul. I mus be recognized ha all componens come wih value olerances, paricularly capaciors. This device is one ha will saisfy he ask and parameers defined. Thus, prior o redesigning a circui once a workable circui is compleed, i mus be assembled and esed. Using componens described in Circui 2, he circui was assembled and esed. The device funcioned well. Adjusmen of he poeniomeer produced soppage of he propellor almos immediaely afer normal power was removed. The adjusmen was urned o zero ohms, and inadequae braking was afforded, which indicaed adjusmen could be afforded o compensae for componen olerance variaions. The adjusmen was hen se o maximum resisance (25 ohms). The moor sopped and was placed ino reverse for abou 1½ seconds. Upon furher esing, i was deermined ha he relay de-acuaed a abou 25% of volage. This variaion is o be expeced and suppors he decision no o change he value of he poeniomeer. This concep can be used wih oher elecrical propulsion devices, such as linear moors. Relay swiching can also be applied o AC moors. The poin is: define he ask; define parameers of performance; deermine componens available; confirm feasibiliy of design and componens; and explore oher circui opions. Carlo DeLuca Page 11of 11