PAE-TILOGY Linear Motors 70 Mill orest d. Webster, TX 77598 (8) 6-7750 ax (8) 6-7760 www.trilogysystems.om E-mail emn_support_trilogy@parker.om Motor Sizing Appliation Note By Jak Marsh Introdution Linear motor sizing is relatively straightorward when the proper mathematial relationships are used. Given a moving mass and motion proile, the equations o motion and a ew motor parameters an be used to alulate a motor s temperature rise. In the irst step, the ore required by the moving mass and motion proile is alulated. In the next step, a model o the motor s thermal perormane is used to alulate the inal temperature o the motor windings. The and ontinuous urrent and power and the voltage required an also be alulated or sizing the ampliier and power supply Parker-Trilogy s WebTIPS sizing sotware uses this approah to alulate motor temperature rises that have been veriied by experimental results and thousands o appliations over many years. This Appliation Note will give a simpliied overview o the equations and algorithms used by the sotware and provide an example spreadsheet to use when the sotware pakage is not appliable. Motion Proile igure. Typial Motion Proile Motor sizing usually begins by deining the motion proile and total moving mass, M. It is important to inlude the masses o the motor, user payload, and all other moving items in M. A typial motion proile is shown in igure. The ore required or eah portion o the motion proile an be alulated as ollows, () = M a + ri = ri = M ( a) + ri = 0 05/06/005
where a is the aeleration rate (V / t ) and ri is the ore required to overome rition. The and ores or the proile are given by () = Max( =,,, ) + t + t + + t + t + The motion proile shown in igure is just an example. More ompliated proiles will require dierent approahes to alulate the and ontinuous ores required. Unusual motion proiles, suh as amollowers or exponential aelerations, an almost always be desribed by equations or tabular data. Basi alulus and physis an be used to determine aeleration vs. time rom this data. The relationship or ore vs. time an then be determined by using =ma and inorporating ritional ores, external ores, gravitational ores, et. An alulation an be perormed on this data to determine the ontinuous ore required. The and ontinuous urrents or a given motor an be alulated by using the motor s ore onstant,. The ore onstant is the amount o ore that will be generated by the motor at a given urrent level. () = / I This an be rearranged to alulate the urrents required, () I I = = / / Power Calulations One the urrent required is known, the thermal power that is generated in the motor an be alulated by using (5) P g = I where is the motor s resistane. However, resistane is a untion o temperature so the value o P g will inrease as the motor heats up during use and its resistane inreases. Sine the motor s resistane is usually given at a speii temperature, its value at the inal temperature must be determined. The resistane o opper inreases 0.9% per degree C o temperature rise. The ollowing equation an be used to alulate resistane values, 0.9( T T = + 00 ) (6) The motor will ontinue to heat up until the amount o power generated in the windings equals the amount o power being dissipated by the surroundings. The ollowing equation desribes the power being dissipated by the motor s surroundings, (7) P = T T T ) D (
where T is the system s thermal dissipation onstant in Watts/deg C, T is the motor temperature, and T is the ient temperature o the surroundings. The system s thermal dissipation onstant is an experimentally measured value. It is also the reiproal o the motor s thermal resistane, T, usually given in deg C/Watt. inal Temperature Calulations Sine power-in must equal power-out at steady-state, setting P g equal to P D and simpliying will yield the equation or the motor s steady-state temperature, P D = P T ( T T ( T g T T ) = I 0.9( T T ) = + 00 ) (8) T = + T T 0.9 00 This shows that given a motor s ore onstant, ient resistane, and thermal dissipation onstant, the steady-state temperature o the windings an be alulated or a given ore output. One T is known, an be determined using (6). The atual thermal power generated by the motor windings an be alulated by using the motor s inal resistane value and (5), P P = = I I Sine (8) is omplex, it is probably best to build it into a spreadsheet or sotware pakage to minimize errors due to hand alulation. An example o suh a spreadsheet is shown in Table. The parameters used are or a Parker-Trilogy 0-S oil. The rms input value an be hanged to determine the eet on T,, and P. (Ohms) 8.6 (N/A) 7. T(W/deg C).6 T (deg C) 5 rms (N) 57 T (deg C) 9.5 (Ohms) 9. Irms (A). Prms (W) Table. Sizing Spreadsheet Example using 0-S Motor
Ampliier Sizing The voltage required or eah step o the motion proile an be alulated by using the motor s BEM onstant, e, and Ohm s law, (9) V = V V V = = = 0 e e e V + V + V + The maximum voltage required will be the largest o these values, (0) V = Max V, V, V, V ) max ( Now all the ritial parameters or motor and ampliier sizing are known. The inal motor temperature will veriy the suitability o a given motor or a speiied motion proile and payload. The and ontinuous urrents and maximum voltage required will determine the power required rom the ampliier and power supply and the suitability o the given motor winding. The urrent alulations used in the model assume ideal motion while the urrent requirements in a servo system are almost always higher than ideal beause o outside disturbanes, vibrations, et. It is a good idea to selet an ampliier that will provide adequate urrent margin. An additional 0-0% is usually sae. The voltage alulations are airly preise so additional margin is not usually required or voltage. The thermal model only onsiders thermal power. Mehanial power is aounted or by the maximum voltage alulation. As long as the seleted ampliier and power supply an supply the required urrent at the maximum voltage, the mehanial power requirements will be met. However, during deeleration this mehanial power is onverted bak into eletrial power and must be re-absorbed by the ampliier and power supply. This is known as regeneration. or high loads and high speeds, this eet an be signiiant and external regeneration resistors might be needed by the ampliier. Most ampliier manuaturers give the speiiations and relationships needed to perorm regeneration alulations or their equipment and it is a good idea to hek these requirements or high load, high speed appliations. Duty Cyle Considerations It is possible to model a motion proile that requires large urrents and relatively low ontinuous urrents i long dwells are onsidered. Sine the thermal alulations are based on ores and urrents, are must be taken to evaluate the requirements o the motion proile against the ratings o the reommended motor. I the required s are larger than the motor s ratings, a larger motor must be used!
Additional WebTIPS eatures The alulation engine or WebTIPS uses the approah detailed so ar, but it also inorporates the ollowing eatures, The ability to model more omplex motion proiles, suh as sinusoidal motion and S-urve aeleration. Canned motion proile generators to simpliy data entry. The ability to inorporate loads due to vertial operation and/or external ores ating on the motor. Simpliied data entry or multi-axis system sizing. Advaned algorithms or urrent alulations using non-linear ore onstants or iron-ore motors. An empirial database o thermal dissipation onstants to ensure aurate results. The ability to repeat the alulations so many dierent motors and systems an be onsidered at one. Stored motor and atuator masses or more aurate results when more than one possibility is onsidered. Advaned models or ritional ores. The ability to work in SI or Imperial units and to swith bak-and-orth at will. Graphial representations o ore, Aeleration, Veloity, and Position vs. Time to veriy auray o the motion proile. Automati heking o proile requirements against motor speiiations to ensure suitability. Advaned reporting eatures to ustomize the output. The ability to store and retrieve proiles to maintain historial reords. Summary Anytime linear motors move a mass or exert ore, urrent lows through their windings and heat is generated. How quikly this heat an be removed and the maximum temperature the windings an withstand are what limits motor perormane. I a partiular motor is applied in a manner that exeeds its design apabilities, permanent ailure will result. Thereore it is important to be able to know aurately the temperature rise o a partiular motor in a given appliation. The ollowing relationship an be used to determine a motor s steady-state temperature based on a required ore output and three basi motor parameters, 5
(8) T = + T T 0.9 00 This algorithm an be built into a spreadsheet or simpliied results. An example o suh a spreadsheet is given in Table. (Ohms) 8.6 (N/A) 7. T(W/deg C).6 T (deg C) 5 rms (N) 57 T (deg C) 9.5 (Ohms) 9. Irms (A). Prms (W) Table. Sizing Spreadsheet Example using 0-S Motor Pre-pakaged sotware that inorporates additional eatures suh as simpliied motion proile modeling, ampliier and power supply sizing, and stored databases o motor parameters an be reated. Parker-Trilogy s WebTIPS is one suh sotware pakage. 6