US20060140777A1 - Control system for the movement of a piston - Google Patents

Control system for the movement of a piston Download PDF

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Publication number
US20060140777A1
US20060140777A1 US10/535,528 US53552805A US2006140777A1 US 20060140777 A1 US20060140777 A1 US 20060140777A1 US 53552805 A US53552805 A US 53552805A US 2006140777 A1 US2006140777 A1 US 2006140777A1
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United States
Prior art keywords
piston
capacitive element
voltage
control system
electronic device
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Abandoned
Application number
US10/535,528
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English (en)
Inventor
Egidio Berwanger
Julio Rodrigues
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Empresa Brasileira de Compressores SA
Original Assignee
Empresa Brasileira de Compressores SA
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
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Assigned to EMPRESA BRASILEIRA DE COMPRESSORES S.A. -EMBRACO reassignment EMPRESA BRASILEIRA DE COMPRESSORES S.A. -EMBRACO ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: BERWANGER, EGIDIO, RODRIGUES, JULIO CESAR
Publication of US20060140777A1 publication Critical patent/US20060140777A1/en
Abandoned legal-status Critical Current

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Classifications

    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02KDYNAMO-ELECTRIC MACHINES
    • H02K7/00Arrangements for handling mechanical energy structurally associated with dynamo-electric machines, e.g. structural association with mechanical driving motors or auxiliary dynamo-electric machines
    • H02K7/14Structural association with mechanical loads, e.g. with hand-held machine tools or fans
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04BPOSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS
    • F04B17/00Pumps characterised by combination with, or adaptation to, specific driving engines or motors
    • F04B17/03Pumps characterised by combination with, or adaptation to, specific driving engines or motors driven by electric motors
    • F04B17/04Pumps characterised by combination with, or adaptation to, specific driving engines or motors driven by electric motors using solenoids
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04BPOSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS
    • F04B35/00Piston pumps specially adapted for elastic fluids and characterised by the driving means to their working members, or by combination with, or adaptation to, specific driving engines or motors, not otherwise provided for
    • F04B35/04Piston pumps specially adapted for elastic fluids and characterised by the driving means to their working members, or by combination with, or adaptation to, specific driving engines or motors, not otherwise provided for the means being electric
    • F04B35/045Piston pumps specially adapted for elastic fluids and characterised by the driving means to their working members, or by combination with, or adaptation to, specific driving engines or motors, not otherwise provided for the means being electric using solenoids
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04BPOSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS
    • F04B49/00Control, e.g. of pump delivery, or pump pressure of, or safety measures for, machines, pumps, or pumping installations, not otherwise provided for, or of interest apart from, groups F04B1/00 - F04B47/00
    • F04B49/06Control using electricity
    • F04B49/065Control using electricity and making use of computers
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02KDYNAMO-ELECTRIC MACHINES
    • H02K33/00Motors with reciprocating, oscillating or vibrating magnet, armature or coil system
    • H02K33/02Motors with reciprocating, oscillating or vibrating magnet, armature or coil system with armatures moved one way by energisation of a single coil system and returned by mechanical force, e.g. by springs
    • H02K33/10Motors with reciprocating, oscillating or vibrating magnet, armature or coil system with armatures moved one way by energisation of a single coil system and returned by mechanical force, e.g. by springs wherein the alternate energisation and de-energisation of the single coil system is effected or controlled by movement of the armatures
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02KDYNAMO-ELECTRIC MACHINES
    • H02K33/00Motors with reciprocating, oscillating or vibrating magnet, armature or coil system
    • H02K33/16Motors with reciprocating, oscillating or vibrating magnet, armature or coil system with polarised armatures moving in alternate directions by reversal or energisation of a single coil system
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/032Reciprocating, oscillating or vibrating motors
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04BPOSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS
    • F04B2201/00Pump parameters
    • F04B2201/02Piston parameters
    • F04B2201/0201Position of the piston
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04BPOSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS
    • F04B2201/00Pump parameters
    • F04B2201/02Piston parameters
    • F04B2201/0206Length of piston stroke
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04BPOSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS
    • F04B2203/00Motor parameters
    • F04B2203/04Motor parameters of linear electric motors
    • F04B2203/0401Current
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04BPOSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS
    • F04B2203/00Motor parameters
    • F04B2203/04Motor parameters of linear electric motors
    • F04B2203/0402Voltage
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02KDYNAMO-ELECTRIC MACHINES
    • H02K11/00Structural association of dynamo-electric machines with electric components or with devices for shielding, monitoring or protection

Definitions

  • the present invention relates to fluid-pumping devices such as, for example, linear compressors and, particularly, to a system and a method for controlling this kind of device, being driven by a linear electric motor.
  • a linear motor is an ancient idea, but it was carried out only recently with maturation in the field of control and actuation of electric machines.
  • a linear motor replaces rotary electric motors with many advantages, among which the economy of electric energy, since it used a more direct conversion of electric energy with less loss.
  • Especially the use of linear compressors in present-day cooling cycles has been scarce due to the technologic difficulties usually encountered.
  • a linear motor and of a linear compressor may vary; the latter may be of simple or double effect, while the motor may comprise a work coil and a magnet; and this magnet may be either moveable or static.
  • Linear-type compressors are known from the prior art and are constituted by a mechanism in which the piston makes an oscillatory movement, and in most cases there is an elastic means interconnecting the cylinder and the piston, which imparts a resonant characteristic to this movement the energy being supplied by a linear-displacement motor.
  • Equivalents such as piston-actuated water pumps or any fluid-pumping device can benefit from the object of the present invention.
  • the mechanism is provided with a discharge valve constructed in such a way, that, if the piston exceeds the maximum displacement course expected in its oscillatory movement, for instance when the voltage imposed on the motor is excessive, there will be contact of the piston with this discharge valve, and this valve will allow the piston to advance a little, thus preventing an impact against the plate of the valve head.
  • the design of the mechanism does not allow the piston to advance past a determined point; otherwise, the piston would collide with the valve plate. Due to the search for a more optimized design, as far as efficiency is concerned, the ratio between the course of displacement of the piston and the diameter of the piston is not great, which makes the performance of the compressor more dependent upon the variations in the course of displacement of the piston. As an example, the gas-discharge process gives a very small option of the course, namely about 5% of the total.
  • a monitoring system is foreseen for monitoring the times the piston passes by a determined reference point within the compressor. In this way, when the residence time of said piston beyond the reference point exceeds a pre-established value, the voltage level is momentarily reduced during the respective movement, thus avoiding a collision with the valve plate.
  • the movement of the piston is controlled by counting discrete points thereof along the cylinder of the compressor. In case the piston moves excessively, the value of the average voltage applied to the respective motor is reduced so as to decrease the movement amplitude of said piston.
  • Another way adopted to provide re-feeding to this voltage controller is to observe whether the piston collides with the valve plate. Such a collision is detected by means of a microphone or accelerometer, which generates a command for reducing the voltage applied to the motor and consequently the course of displacement of the piston.
  • the objective of the invention is to control stroke course of displacement of the piston of a linear compressor or of any fluid-pumping device, such as piston-actuated water pumps, allowing the piston to advance as far as the end of its mechanical course of displacement, even In extreme load conditions, without allowing the piston to collide with the valve system.
  • Another objective of the present invention is to provide control over the course of displacement of the piston of a linear compressor or any other fluid-pumping device, without the need for information about the displacement of the middle point of oscillation of the piston.
  • a further objective is to provide control over the amplitude of the course of oscillation of a linear compressor or any fluid-pumping device, allowing control over the cooling capacity developed by the compressor.
  • objectives of the present invention are to obtain a control system that meets the objectives of the present invention, that is easy to implement on an industrial scale and that has a low unit cost of manufacture and replacement, and to obtain a system that is self-fed, dispensing with the use of an additional external source, and that still has a low consumption of electric energy.
  • a control system foreseen for controlling the movement of a piston In a fluid-pumping device, the piston being displaceable in a block of the fluid-pumping device and being driven by a motor fed by a voltage.
  • the system comprises a semiconductor electronic device having an outlet and an Inlet, the semiconductor electric device cyclically applying the voltage to the motor for driving the piston, a resistive element, a capacitive element, a piston-position sensor for indicating the passage of the piston by a point at the block of the fluid-pumping device, the capacitive element being electrically connected to the semiconductor device between and re-feeding the outlet and the inlet, the capacitive element triggering the semiconductor electronic device to apply the voltage to the motor; the capacitive element being charged by means of the resistive element at each cycle of application of voltage to the motor, the capacitive element being discharged at least partly when the piston passes by said point.
  • the objectives are achieved by a method of controlling the movement of a piston in a fluid-pumping device, the piston being displaceable in a fluid-pumping device and being driven by a motor fed by a voltage.
  • This method comprises the steps of: charging a capacitive element by means of a resistive element; monitoring the movement of the piston by means of a position sensor; maintaining the charge level of the capacitive element until the position sensor has detected the passage of the piston by a predetermined point at the compressor block; and discharging the capacitive element at least partly.
  • a fluid-pumping device comprising a piston displaceable in a block, the piston being driven by a motor fed by a voltage.
  • This device comprises a circuit having a semiconductor electronic device, a resistive element, a capacitive element, a piston-position sensor for indicating the passage of the piston by a point at the compressor block.
  • the resistive element and the capacitive element are electrically connected to the semiconductor electronic device, re-feeding an outlet and an inlet of the latter, the capacitive element being charged by means of the resistive element and being discharged at least partly when the piston passes by said point.
  • FIG. 1 shows a linear compressor schematically
  • FIG. 2 illustrates the curves of piston displacement and the voltage on the linear motor provided with the control system of the present invention
  • FIG. 3 illustrates a control system for controlling the position of the piston of a linear compressor according to a first embodiment of the present invention
  • FIG. 4 illustrates a control system for controlling the position of the piston of a linear compressor according to a second embodiment of the present invention
  • FIG. 5 illustrates the behavior of the signals generated by the bidirectional start switch and the time relationship of these signals with the voltage of the circuit branch that contains the capacitor Cy.
  • a linear compressor 1 basically comprises a piston 10 that is displaced in oscillatory motion within the block 5 , so as to compress a gas that is charged and discharged through a valve plate 11 , which comprises a charge valve 13 and a discharge valve 12 .
  • an elastic means such as a spring 4 is associated with the piston 10 , so that the latter can have a resonant movement within the block 5 of the compressor 1 .
  • the movement of the piston 10 is induced by a linear-type motor 2 , which in turn is driven by an electric voltage V, which should be controlled in order to prevent the piston 10 from colliding with the plate 11 .
  • the object of the present invention is applicable to any fluid-pumping device 1 , as for example a water pump.
  • any fluid-pumping device 1 as for example a water pump.
  • the methods of controlling the movement of the piston 10 employed in earlier techniques include monitoring motion times of the piston by means of microcontrolled circuits.
  • the times to be monitored include: (I) residence time “t 0 ” of the piston 10 beyond a point R that is physically defined in its course of displacement, and this point is close to the end of the maximum course of displacement M possible to the piston 10 , (ii) the time “t c ” of duration of the complete cycle, (iii) the time “t om ” corresponding to the maximum course of displacement M possible to the piston 10 .
  • the average voltage V m applied to the motor 2 is incremented, if the time “t 0 ” is shorter than the desired time “t od ”, and vice-versa.
  • the desired displacement “P” is maintained for supplying a determined cooling capacity (see FIG. 2 ).
  • the point M Is very close to the valve plate 11 , being typically at a distance of some dozens of micrometers, while the point R is located close to the valve plate 11 , being typically at a distance of from 1 to 2 millimeters, a distance sufficient to avoid collision of the piston 10 with said plate 11 .
  • a re-feed (or self-fed) electronic circuit 30 , 40 that alters the amplitude of the course of displacement of the piston 10 , with the same approach employed in other systems that are controlled by microcontrollers, but without the need for monitoring the cited times.
  • the detection of the passage of the piston by the defined physical point R may be effected by some type of physical sensor S installed inside the compressor 1 , be it of the contact, optical or inductive or any other type (see FIG. 3 , in this case).
  • this detection may also be effected by adding a magnetic disturbance to the voltage present in the terminals of the motor 2 , this disturbance being created, for example, by a constructive detail of the magnetic circuit of the motor. This is the case of the construction of the circuit 40 , FIG. 4 .
  • the position sensor S may comprise the circuits 30 , 40 illustrated In FIGS. 3 and 4 , which include a position sensor S p by direct contact and a position sensor L s by inductive sensor, respectively, and which can effect the control automatically, without the need to employ a microcontrolled circuit
  • the control system and method are carried out by means of a tiristor semiconductor device or bidirectional power switch T, which cyclically applies an electric voltage V to the motor L.
  • the trigger circuit G (gate or inlet G) of this switch T is actuated by means of the position sensor Sp, Ls, which sends a signal that generates the angle of triggering said switch T, this signal causing a retardation time proportional to the discharge level of the capacitor Cy.
  • the gate circuit G connected to the capacitor Cy sends a voltage signal to the linear motor 2 for a longer or shorter time, for the purpose of adjusting the cooling capacity of said linear compressor 1 .
  • FIG. 5 illustrates the wave shape of the voltage V applied to the motor 2 and the stretches where the semiconductor device T does not conduct, as well as the wave shape of the current I.
  • the capacitor Cy is associated to the semiconductor device T, so that it will be associated between—and re-fed—the outlet S G and the inlet G of the latter, and also in association with the switch S, which indicates the passage of the piston by the point R.
  • FIG. 5 illustrates how this solution interferes with the voltage level V of the inlet of the motor L m .
  • Raising the voltage in the branch of the capacitor Cy is a function of the capacitance values of the Cy and Cx and of the resistance R B .
  • it is possible to adjust the circuit 30 , 40 to varied constructions of the compressor 1 so that the semiconductor electronic device T can be adequately triggered (see stretch A′ in FIG. 5 , where the semiconductor T conducts).
  • the discharge velocity of the capacitor Cy is a function of the capacitance values of Cy, Cx and of the resistance values of R, R T (see stretch B of the curve in FIG. 5 ), which should be designed in an adequate way, so that the triggering of the electronic device T will occur in an adequate way.
  • a first preferred embodiment of the movement-control system includes the circuit 30 , which comprises a position sensor Sp constituted by an electromechanical switch that is directly driven by the piston 10 when the latter passes by the point R, resulting in alteration of operation of the semiconductor electronic device T.
  • the capacitor Cy in the next semicycle, will cause the semiconductor electronic device T to enter with some delay, as may be inferred from the deformation of the voltage curve V at the point 23 , illustrated in FIG. 2 (see also FIG. 3 ).
  • the residence time at zero level (or a sufficiently low level in the winding Lm of the motor 2 , so that the latter will not operate) of voltage V will depend upon the time during which the contact of the position sensor Sp has remained closed and upon the value of Ri+Rt (for example, a thermostat).
  • the values Ri+Rt should be such, that when Rt is at the condition of maximum resistance and the piston 10 reaches the point M, the capacitor Cy will be discharged at such a level, that the semiconductor electronic device T will not be triggered in the next semicycle.
  • the senor S is carried out by means of a sensor or inductive element L i .
  • the circuits 30 , 40 are self-fed and, therefore, they dispense with the use of an external feed source, which reduces the costs of manufacture and maintenance.
  • the transistor T 1 closes the circuit in the two embodiments, so as to trigger the electronic device T, actuating as a bidirectional switch: now charging the capacitor Cy, now discharging it.
  • the present invention brings about, as an advantage, the possibility of dispensing with the use of an external feed source, in addition to resulting in a low consumption of electricity (in the milliamperes range) and in addition to enabling the replacement thereof in the event of a failure.
  • the present invention also foresees a method for controlling the movement of a piston 10 in a linear compressor 1 or any other fluid-pumping device 1 .
  • This method comprises the steps of:
  • the capacitive element Cy is again charged, as may be seen in FIG. 5 .
  • the system and method of the present invention enable one to estimate, at each cycle, the oscillation amplitude of the piston 10 much more precisely, enabling the electronic control to react for compensating the variations in the cooling capacity (in the case of application in compressors), which are slow variations, maintaining the average amplitude of the course of oscillation of the piston 10 at the desired value and equal to P.
  • This system and method also enables rapid reactions of the electronic control for compensating shape variations in the operation conditions caused by fluctuations in the feed voltage, and these corrections should be imposed at each oscillation cycle, so as to correct the amplitude of the stroke of the piston 10 in the final portion of its path, after passing by the physical reference point R.
  • the system and method of the present invention result in the advantage of a rapid reaction, with corrections at each cycle, without the need for estimates based on the voltage and current imposed on the motor 2 , and without mistakes due to secondary variables such as temperature, the construction of the motor 2 and the displacement of the middle point of oscillation of the piston due to the average difference in pressure between the faces 8 , 9 of the piston 10 .
  • the present invention enables one to implement an effective control over the course of displacement of the piston 10 , independently of the required cooling capacity, whereby one can prevent the piston 10 from bumping against the valve plate 11 , even in the presence of rapid disturbances caused by the natural fluctuation of the voltage in the commercial network of electric energy.

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Control Of Positive-Displacement Pumps (AREA)
  • Compressors, Vaccum Pumps And Other Relevant Systems (AREA)
  • Reciprocating Pumps (AREA)
US10/535,528 2002-11-19 2002-11-19 Control system for the movement of a piston Abandoned US20060140777A1 (en)

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/BR2002/000158 WO2004046550A1 (en) 2002-11-19 2002-11-19 A control system for the movement of a piston

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US20060140777A1 true US20060140777A1 (en) 2006-06-29

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US (1) US20060140777A1 (de)
EP (1) EP1567769A1 (de)
JP (1) JP2006506571A (de)
CN (1) CN1735749A (de)
AU (1) AU2002349191A1 (de)
WO (1) WO2004046550A1 (de)

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US20040061478A1 (en) * 2000-08-18 2004-04-01 French Michael J. Fuel injector driver circuit with energy storage apparatus
US20080269724A1 (en) * 2007-04-27 2008-10-30 Medtronic, Inc. Implantable drug delivery device with programmable rate capacitor charge control
US20080314056A1 (en) * 2005-11-09 2008-12-25 Marcio Roberto Thiessen Linear-Compressor Control System, a Method of Controlling a Linear Compressor and a Linear Compressor
FR2919356A1 (fr) * 2007-07-26 2009-01-30 Suntec Ind France Soc Par Acti Pompe modulante a liquide
US20100196173A1 (en) * 2007-07-24 2010-08-05 BSH Bosch und Siemens Hausgeräte GmbH Linear compressor
FR2984422A1 (fr) * 2011-12-15 2013-06-21 Bosch Gmbh Robert Procede de determination de la fin du mouvement de l'induit d'une pompe a piston lineaire
WO2017072532A1 (en) * 2015-10-30 2017-05-04 Aspen Pumps Limited Solenoid pump driver
US10973965B2 (en) * 2014-12-22 2021-04-13 Smith & Nephew Plc Systems and methods of calibrating operating parameters of negative pressure wound therapy apparatuses

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DE102007037956A1 (de) * 2007-05-21 2008-11-27 Jöst GmbH + Co. KG Schwingantrieb
ITGE20080036A1 (it) * 2008-04-30 2009-11-01 Dott Ing Mario Cozzani Srl Metodo per il controllo della posizione di un attuatore elettromeccanico per valvole di compressori alternativi.
DE102009019450A1 (de) * 2009-04-29 2010-11-11 Webasto Ag Verfahren zum Betreiben und Vorrichtung mit einer Dosierpumpe
ITRM20090537A1 (it) * 2009-10-19 2011-04-20 Etatron D S Spa "dispositivo di controllo della corsa del pistone di una pompa dosatrice"
EP2755775A4 (de) * 2011-09-13 2015-04-01 Graco Minnesota Inc Verfahren zur verstopfungsverhinderung in einem pumpsystem
KR102237723B1 (ko) 2015-10-28 2021-04-08 엘지전자 주식회사 압축기 및 압축기의 제어 방법
KR20170049277A (ko) * 2015-10-28 2017-05-10 엘지전자 주식회사 압축기 및 압축기의 제어 방법
CN106388878A (zh) * 2016-08-30 2017-02-15 苏州品诺维新医疗科技有限公司 一种动力控制装置及其控制方法、手术操作***
CN106175888A (zh) * 2016-08-30 2016-12-07 苏州品诺维新医疗科技有限公司 一种手术器械的告警***、告警方法及控制***
CN110552861B (zh) * 2018-05-30 2021-11-26 青岛海尔智能技术研发有限公司 用于压缩机控制的方法及压缩机

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CN1735749A (zh) 2006-02-15

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