JP3054352B2 - How to operate pumps connected in parallel - Google Patents

How to operate pumps connected in parallel

Info

Publication number
JP3054352B2
JP3054352B2 JP7339969A JP33996995A JP3054352B2 JP 3054352 B2 JP3054352 B2 JP 3054352B2 JP 7339969 A JP7339969 A JP 7339969A JP 33996995 A JP33996995 A JP 33996995A JP 3054352 B2 JP3054352 B2 JP 3054352B2
Authority
JP
Japan
Prior art keywords
pump
flow rate
pressure
supply
flow
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.)
Expired - Lifetime
Application number
JP7339969A
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Japanese (ja)
Other versions
JPH09151858A (en
Inventor
久雄 井土
養一 山東
豊充 金井
昌治 小林
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.)
Chiyoda Corp
Original Assignee
Chiyoda Corp
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Filing date
Publication date
Application filed by Chiyoda Corp filed Critical Chiyoda Corp
Priority to JP7339969A priority Critical patent/JP3054352B2/en
Publication of JPH09151858A publication Critical patent/JPH09151858A/en
Application granted granted Critical
Publication of JP3054352B2 publication Critical patent/JP3054352B2/en
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Description

【発明の詳細な説明】DETAILED DESCRIPTION OF THE INVENTION

【0001】[0001]

【発明の属する技術分野】本発明は、インバータ制御さ
れる可変速モータにて駆動される複数のポンプの運転方
法に関するものである。
BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of operating a plurality of pumps driven by an inverter-controlled variable speed motor.

【0002】[0002]

【従来の技術】インバータ制御される可変速モータにて
駆動される複数のポンプによって供給圧力または供給流
量を制御する流体供給装置に於いて、2台目以降のポン
プを起動(または停止)する時には、ポンプの流量(ま
たは吐出圧)に応じてインバータの周波数の変化率を2
段階に変化させることにより、被運転ポンプの増減時の
圧力変動を抑制するようにした技術を本出願人は既に提
案している(特開平4−358781号公報参照)。
2. Description of the Related Art In a fluid supply apparatus in which a supply pressure or a supply flow rate is controlled by a plurality of pumps driven by a variable speed motor controlled by an inverter, when a second or subsequent pump is started (or stopped). , The rate of change of the inverter frequency according to the pump flow rate (or discharge pressure) is 2
The present applicant has already proposed a technique in which the pressure fluctuation at the time of increase and decrease of the operated pump is suppressed by changing the operation in stages (see Japanese Patent Application Laid-Open No. 4-358787).

【0003】[0003]

【発明が解決しようとする課題】しかしながら、この方
法によると、2台目以降のポンプ起動時の圧力上昇を抑
制するためには、新たに起動したポンプの流量が正とな
った後の、インバータ周波数の2段目の変化率を低く設
定する必要がある。そのため、図5に示したように、需
要の増加率が比較的低い場合は問題が無いが、需要の増
加率がある程度以上高い場合には、新たな起動ポンプの
流量増加速度が追従できず、供給圧力の回復が遅れ気味
となっていた。
However, according to this method, in order to suppress a pressure increase at the time of starting the second and subsequent pumps, the inverter after the flow rate of the newly started pump becomes positive is reduced. It is necessary to set the rate of change of the second stage of the frequency low. Therefore, as shown in FIG. 5, there is no problem when the rate of increase in demand is relatively low, but when the rate of increase in demand is higher than a certain level, the flow rate increase rate of the new starting pump cannot follow, The recovery of the supply pressure had been delayed.

【0004】本発明は、このような従来技術の欠点を解
消し、需要の増加率にあまり影響されずに、新たなポン
プ起動時の圧力上昇を低く抑え、かつポンプ速度を速や
かに上昇させて供給圧力を短時間で回復させることので
きる並列接続されたポンプの運転方法を提供することを
目的に案出されたものである。
The present invention solves the above-mentioned drawbacks of the prior art, suppresses the pressure rise at the time of starting a new pump low, and increases the pump speed quickly without being greatly affected by the rate of increase in demand. The present invention has been devised for the purpose of providing a method of operating a pump connected in parallel which can recover a supply pressure in a short time.

【0005】[0005]

【課題を解決するための手段】このような目的を果たす
ために、本発明に於いては、インバータ制御の可変速モ
ータで個々に駆動される複数のポンプを並列接続し、被
駆動ポンプ数の増減によって所要の供給圧力または供給
流量を得るようにしたポンプの運転方法に於いて、新た
な起動ポンプの流量が正となる以前、または新たな起動
ポンプの吐出圧が既運転ポンプの吐出圧と等しくなる以
前の領域は、インバータの周波数を許容最大速度で増加
させ、新たな起動ポンプの流量が正となった後、または
新たな起動ポンプの吐出圧が既運転ポンプの吐出圧と等
しくなった後の領域は、既運転ポンプの流量または回転
数を目標値として新たな起動ポンプをフィードバック制
御するように構成した。またこの場合は、新たな起動ポ
ンプの流量または回転数を制御量とするコントローラの
応答性を、供給圧力または供給流量に応じて変化させる
ものとした。
In order to achieve such an object, in the present invention, a plurality of pumps individually driven by an inverter-controlled variable speed motor are connected in parallel, and the number of driven pumps is reduced. in pump operating method that to obtain the required supply pressure or supply rate by increasing or decreasing, new
Before or after a new start pump flow is positive
The reason why the discharge pressure of the pump becomes equal to the discharge pressure of the running pump
The previous region increases the inverter frequency at the maximum allowable speed
After the new startup pump has a positive flow, or
The discharge pressure of the newly started pump is equal to the discharge pressure of the already operated pump
After the recovery, the area of the pump that has already been operated
Feedback system for a new start-up pump with the target number
It was configured to control. In this case, the responsiveness of the controller that uses the flow rate or the rotation speed of the new starting pump as a control amount is changed according to the supply pressure or the supply flow rate.

【0006】[0006]

【発明の実施の形態】以下に添付の図面を参照して本発
明の構成を詳細に説明する。
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The configuration of the present invention will be described below in detail with reference to the accompanying drawings.

【0007】図1は、本発明が適用された流体供給装置
を示している。図1に於いて、複数のポンプ1の吸入口
は、共通の吸入管路2を介して流体タンク3に接続され
ている。そしてこれらのポンプ1の各吐出口は、それぞ
れ逆止弁4及びオリフィス5を介して共通の供給管路6
に接続されている。この供給管路6の末端は、流体ユー
ザ7に接続されている。
FIG. 1 shows a fluid supply device to which the present invention is applied. In FIG. 1, the suction ports of a plurality of pumps 1 are connected to a fluid tank 3 via a common suction line 2. Each discharge port of these pumps 1 is connected to a common supply line 6 through a check valve 4 and an orifice 5, respectively.
It is connected to the. The end of this supply line 6 is connected to a fluid user 7.

【0008】各ポンプ1の吐出口に設けられたオリフィ
ス5には、流量を検出するための流量伝送器8がそれぞ
れ設けられている。また共通の供給管路6には、供給圧
力を検出するための圧力伝送器9が設けられている。そ
して各流量伝送器8により検出された流量が流量指示調
節計10を介して、また圧力伝送器9により検出された
供給圧力が圧力指示調節計11を介して、各ポンプ1に
対応して設けられた演算器12にそれぞれ入力される。
各演算器12は、これらの入力に基づいて制御信号を生
成し、その出力を対応するインバータ13に供給する。
これにより、各ポンプ1のモータが可変速制御される。
The orifice 5 provided at the discharge port of each pump 1 is provided with a flow transmitter 8 for detecting a flow rate. The common supply line 6 is provided with a pressure transmitter 9 for detecting a supply pressure. The flow rate detected by each flow transmitter 8 is provided for each pump 1 via the flow rate indicating controller 10 and the supply pressure detected by the pressure transmitter 9 is provided via the pressure indicating controller 11. Are input to the calculated arithmetic units 12, respectively.
Each computing unit 12 generates a control signal based on these inputs, and supplies the output to a corresponding inverter 13.
Thereby, the motor of each pump 1 is controlled at a variable speed.

【0009】図2に示された流体供給装置は、図1に示
されたものと概ね同様であるが、この場合、供給管路6
が網の目のように分岐されて複数の流体ユーザ7に接続
されている。この供給管路6の圧力は、複数のポイント
でそれぞれ別々の圧力伝送器9により検出され、それら
の検出信号が、圧力演算器14によって平均化されて圧
力指示調節計11に供給される。それ以外の点に関し
て、図2の実施例は、図1の実施例と概ね同様である。
The fluid supply device shown in FIG. 2 is generally similar to that shown in FIG. 1, but in this case the supply line 6
Are branched like a mesh and connected to a plurality of fluid users 7. The pressure in the supply line 6 is detected at a plurality of points by separate pressure transmitters 9, and their detection signals are averaged by a pressure calculator 14 and supplied to a pressure indicating controller 11. Otherwise, the embodiment of FIG. 2 is generally similar to the embodiment of FIG.

【0010】このような流体供給装置は、上下水道用の
ポンプ装置、化学プラント等に於ける材料供給装置、或
いは空港などに於ける燃料供給設備などに広く適用可能
である。
Such a fluid supply device can be widely applied to a pump device for water supply and sewerage, a material supply device in a chemical plant or the like, or a fuel supply facility in an airport or the like.

【0011】各ポンプ1の吐出口にある流量伝送器8に
て流量を常時計測し、新たなポンプを起動する場合、新
たな起動ポンプからの流量が零である領域、換言すれば
新たな起動ポンプの流量が正となる以前、または新たな
起動ポンプの吐出圧が既運転ポンプの吐出圧と等しくな
る以前の領域は、許容最大速度でインバータ13の周波
数を増加させてモータを起動し、流量が正となった後
または新たな起動ポンプの吐出圧が既運転ポンプの吐出
圧と等しくなった後の領域は、既に運転されているポン
プの流量(または回転数)を目標値に置いて新たな起動
ポンプの流量(または回転数)をフィードバック制御
し、新たな起動ポンプの流量(または回転数)が既運転
ポンプの流量(または回転数)と等しくなった後は、こ
れら2台のポンプを同期運転させる。
When the flow rate is constantly measured by the flow rate transmitter 8 at the discharge port of each pump 1 and a new pump is started, a region where the flow rate from the newly started pump is zero, in other words,
Before the new start pump flow becomes positive, or
When the discharge pressure of the starting pump is
Before starting, the motor is started by increasing the frequency of the inverter 13 at the maximum allowable speed, and after the flow rate becomes positive ,
Or the discharge pressure of the newly started pump is
In the area after the pressure becomes equal to the pressure, the flow rate (or rotation speed) of the already started pump is set to the target value, and the flow rate (or rotation speed) of the new startup pump is feedback-controlled. After the flow rate (or the number of revolutions) becomes equal to the flow rate (or the number of revolutions) of the already operated pumps, these two pumps are operated synchronously.

【0012】より詳しく説明すると、既に運転されてい
るポンプに対して新たなポンプを追加起動する場合、新
たな起動ポンプの吐出圧が既運転ポンプの吐出圧に達す
るまでは、そのポンプの流量は零である。従って、イン
バータの周波数の上昇速度を最大限に大きくしても、
時点の供給圧力および供給流量に影響を与えずに新たな
起動ポンプの回転数を急速に上昇させることができる。
More specifically, when a new pump is additionally started with respect to an already operated pump, the flow rate of the newly started pump is not changed until the discharge pressure of the already operated pump reaches the discharge pressure of the already operated pump. It is zero. Therefore, increasing the maximum increase rate of the frequency of the inverter, the current
The speed of the new start-up pump can be rapidly increased without affecting the current supply pressure and supply flow rate.

【0013】新たな起動ポンプの吐出圧が既運転ポンプ
の吐出圧と等しくなり、新たな起動ポンプの流量が正と
なった後は、既運転ポンプの流量(または回転数)を目
標値として、新たな起動ポンプの流量(または回転数)
フィードバック制御する。すると、新たな起動ポンプ
の流量(または回転数)と既運転ポンプの流量(または
回転数)との偏差が大きい領域は、新たな起動ポンプの
流量(または回転数)が急速に増加し、新たな起動ポン
プの流量(または回転数)と既運転ポンプの流量(また
は回転数)との偏差が減少するに連れて、新たな起動ポ
ンプの流量(または回転数)の増加率が緩やかになる。
[0013] The discharge pressure of the newly started pump is an already operated pump
After the discharge pressure becomes equal to the discharge pressure of the new startup pump and the flow rate of the new startup pump becomes positive, the flow rate (or rotation speed) of the new startup pump is set using the flow rate (or rotation speed) of the already operated pump as a target value.
Feedback control. Then, in a region where the deviation between the flow rate (or rotation speed) of the new startup pump and the flow rate (or rotation speed) of the already operated pump is large, the flow rate (or rotation speed) of the new startup pump rapidly increases, As the deviation between the flow rate (or rotation speed) of the new startup pump and the flow rate (or rotation speed) of the already operated pump decreases, the rate of increase in the flow rate (or rotation speed) of the new startup pump becomes slower.

【0014】この作用により、ポンプを急速に起動さ
せ、かつポンプ起動後の供給圧力の上昇率を低く抑える
ことが可能となる。また、新たな起動ポンプの流量(ま
たは回転数)制御の目標値となる既運転ポンプの流量
(または回転数)は、需要の増加に応じて増加するの
で、需要の増加率が高い場合は、目標値が大きくなり、
つまり目標値と実値との偏差が大きくなるので新たな起
動ポンプの流量(または回転数)上昇速度が高められ、
需要の増加率が低い場合は、目標値が小さくなり、つま
り目標値と実値との偏差が小さくなるので新たな起動ポ
ンプの流量(または回転数)上昇速度が緩やかになる。
これにより、需要変動に影響されずに、ポンプ起動後の
供給圧力の上昇を小さく抑え、かつ2台目以降のポンプ
を速やかに起動することが可能となる。
By this operation, it is possible to start the pump quickly and to suppress the rate of increase of the supply pressure after the pump is started to a low level. In addition, the flow rate (or rotation speed) of the already operated pump, which is the target value of the flow rate (or rotation speed) control of the new startup pump, increases in accordance with the increase in demand. Ri target value the name large,
That than the difference between the target value and the actual value is ing large new startup pump flow (or speed) increase rate is increased,
If the rate of increase in demand is low, Ri target value is small, knob
Ri target value and than the deviation between the actual value may turn small new start pump flow (or speed) rate of increase becomes moderate.
This makes it possible to suppress a rise in supply pressure after starting the pump to a small extent and to quickly start the second and subsequent pumps without being affected by fluctuations in demand.

【0015】また、供給圧力(または供給流量)が低い
場合は、起動ポンプの流量(または回転数)制御を行う
コントローラの感度を高く設定することにより、ポンプ
を急速に起動し、供給圧力が高くなるに従ってコントロ
ーラの感度を低く設定することにより、ポンプをさらに
速やかに起動し、かつ供給圧力の上昇を小さく抑えるこ
とが可能となる。
When the supply pressure (or supply flow rate) is low, the pump is started quickly and the supply pressure is increased by setting the sensitivity of the controller for controlling the flow rate (or rotation speed) of the starting pump high. By setting the sensitivity of the controller as low as possible, it is possible to start the pump more quickly and to suppress the rise in the supply pressure to a small value.

【0016】なお、上述した制御条件から、新たな起動
ポンプの流量が零、または新たな起動ポンプの吐出圧が
既運転ポンプの吐出圧より低い領域での制御条件を除外
し、新たな起動ポンプの流量が零の時から既運転ポンプ
の流量を目標値としてフィードバック制御することも可
能である。そしてこれによれば、制御のロジックをより
簡略な構成にできるという利点が得られる。
From the above control conditions, the control conditions in the region where the flow rate of the new start-up pump is zero or the discharge pressure of the new start-up pump is lower than the discharge pressure of the already operated pump are excluded, and the new start-up pump is excluded. It is also possible to perform feedback control from the time when the flow rate is zero to the flow rate of the operated pump as a target value. According to this, there is an advantage that the control logic can be simplified.

【0017】図は、2台目のポンプ流量が正となった
後に1台目のポンプ流量を目標値として2台目のポンプ
流量を制御した場合の解析結果を、需要の増加率の違い
に対応させて示す。
FIG. 4 shows an analysis result when the second pump flow rate is controlled using the first pump flow rate as a target value after the second pump flow rate becomes positive, showing the difference in the rate of increase in demand. Are shown in correspondence with.

【0018】図は、2台目のポンプ流量が正となった
後に1台目のポンプ流量を目標値として2台目のポンプ
流量を制御し、その流量制御のコントローラの感度を供
給圧力の上昇に応じて低下させた場合の解析結果を、同
じく需要の増加率の違いに対応させて示す。
FIG. 3 shows that after the flow rate of the second pump becomes positive, the flow rate of the second pump is controlled by using the flow rate of the first pump as a target value, and the sensitivity of the controller of the flow control is determined by the supply pressure. The analysis results for a case where the demand is decreased in accordance with the rise are shown in correspondence with the difference in the rate of increase in demand.

【0019】図からは、需要の増加が大きい場合で
も、図5に示した従来法に比して短時間で供給圧力が回
復することが分かる。また図からは、ポンプ起動時の
流量制御のフィードバック応答性を供給圧力に応じて変
化させることにより、供給圧力の回復が一段と速くなる
ことが分かる。
FIG. 4 shows that even when the increase in demand is large, the supply pressure recovers in a shorter time than in the conventional method shown in FIG. FIG. 3 shows that the recovery of the supply pressure is further accelerated by changing the feedback responsiveness of the flow control at the time of starting the pump according to the supply pressure.

【0020】[0020]

【発明の効果】このように本発明によれば、インバータ
を利用した可変速モータにて駆動される複数のポンプに
より供給圧力(または供給流量)を制御する流体供給装
置において、2台目以降のポンプを速やかに起動し、か
つ供給圧力および供給流量の変動を小さく抑える上に大
きな効果を奏することができる。
As described above, according to the present invention, in a fluid supply device in which a supply pressure (or a supply flow rate) is controlled by a plurality of pumps driven by a variable speed motor using an inverter, This has a great effect on quickly starting the pump and suppressing a change in the supply pressure and the supply flow rate to be small.

【図面の簡単な説明】[Brief description of the drawings]

【図1】供給配管系が単一の場合の流体供給装置の概略
構成図。
FIG. 1 is a schematic configuration diagram of a fluid supply device when a single supply piping system is used.

【図2】供給配管系が複数の場合の流体供給装置の概略
構成図。
FIG. 2 is a schematic configuration diagram of a fluid supply device when there are a plurality of supply piping systems.

【図3】本発明によるポンプ運転方法を適用した場合の
供給圧力、ポンプ回転数、ポンプ流量の経時変化線図。
FIG. 3 is a graph showing changes over time in supply pressure, pump rotation speed, and pump flow rate when the pump operation method according to the present invention is applied.

【図4】本発明によるポンプ運転方法の別例を適用した
場合の供給圧力、ポンプ回転数、ポンプ流量の経時変化
線図。
FIG. 4 is a graph showing a change with time of a supply pressure, a pump rotation speed, and a pump flow rate when another example of the pump operation method according to the present invention is applied.

【図5】従来のポンプ運転方法を適用した場合の供給圧
力、ポンプ回転数、ポンプ流量の経時変化線図。
FIG. 5 is a graph showing changes over time in supply pressure, pump rotation speed, and pump flow rate when a conventional pump operation method is applied.

【符号の説明】[Explanation of symbols]

1 ポンプ 2 吸入管路 3 流体タンク 4 逆止弁 5 オリフィス 6 供給管路 7 流体ユーザ 8 流体伝送器 9 圧力伝送器 10 流体指示調節計 11 圧力指示調節計 12 演算器 13 インバータ 14 圧力演算器 Reference Signs List 1 pump 2 suction line 3 fluid tank 4 check valve 5 orifice 6 supply line 7 fluid user 8 fluid transmitter 9 pressure transmitter 10 fluid indicating controller 11 pressure indicating controller 12 computing unit 13 inverter 14 pressure computing unit

───────────────────────────────────────────────────── フロントページの続き (72)発明者 小林 昌治 神奈川県横浜市鶴見区鶴見中央2丁目12 番1号 千代田化工建設株式会社内 (56)参考文献 特開 平3−246394(JP,A) 特開 平4−358781(JP,A) 特開 昭64−25202(JP,A) (58)調査した分野(Int.Cl.7,DB名) F04B 49/00 - 51/00 F04B 23/04 ──────────────────────────────────────────────────続 き Continuation of the front page (72) Inventor Shoji Kobayashi 2-12-1 Tsurumichuo, Tsurumi-ku, Yokohama-shi, Kanagawa Prefecture Inside Chiyoda Kako Construction Co., Ltd. (56) References JP-A-3-246394 (JP, A) JP-A-4-358781 (JP, A) JP-A-64-25202 (JP, A) (58) Fields investigated (Int. Cl. 7 , DB name) F04B 49/00-51/00 F04B 23/04

Claims (2)

(57)【特許請求の範囲】(57) [Claims] 【請求項1】 インバータ制御の可変速モータで個々に
駆動される複数のポンプを並列接続し、被駆動ポンプ数
の増減によって所要の供給圧力または供給流量を得るよ
うにしたポンプの運転方法であって、新たな起動ポンプの流量が正となる以前、または新たな
起動ポンプの吐出圧が既運転ポンプの吐出圧と等しくな
る以前の領域は、インバータの周波数を許容最大速度で
増加させ、 新たな起動ポンプの流量が正となった後、または新たな
起動ポンプの吐出圧が既運転ポンプの吐出圧と等しくな
った後の領域は、 既運転ポンプの流量または回転数を目
標値として新たな起動ポンプをフィードバック制御する
ことを特徴とする並列接続されたポンプの運転方法。
1. A pump operating method in which a plurality of pumps individually driven by an inverter-controlled variable speed motor are connected in parallel, and a required supply pressure or supply flow is obtained by increasing or decreasing the number of driven pumps. Before the flow of the new start-up pump becomes positive, or
When the discharge pressure of the starting pump is
Area before the inverter frequency is
Increase the flow after the new start pump flow is positive or
When the discharge pressure of the starting pump is
The method for operating the pumps connected in parallel is characterized by performing feedback control of a new starting pump using the flow rate or the number of revolutions of the already operated pump as a target value.
【請求項2】 既運転ポンプの流量または回転数を目標
値として新たな起動ポンプの流量または回転数を制御量
とするコントローラの応答性を、供給圧力または供給流
量に応じて変化させることを特徴とする請求項1に記載
の並列接続されたポンプの運転方法。
2. The target of the flow rate or the number of revolutions of the already operated pump
Control flow rate or rotation speed of new startup pump as value
The responsiveness of the controller is determined by the supply pressure or
The method according to claim 1, wherein the pump is changed according to the amount .
JP7339969A 1995-12-04 1995-12-04 How to operate pumps connected in parallel Expired - Lifetime JP3054352B2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP7339969A JP3054352B2 (en) 1995-12-04 1995-12-04 How to operate pumps connected in parallel

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP7339969A JP3054352B2 (en) 1995-12-04 1995-12-04 How to operate pumps connected in parallel

Publications (2)

Publication Number Publication Date
JPH09151858A JPH09151858A (en) 1997-06-10
JP3054352B2 true JP3054352B2 (en) 2000-06-19

Family

ID=18332490

Family Applications (1)

Application Number Title Priority Date Filing Date
JP7339969A Expired - Lifetime JP3054352B2 (en) 1995-12-04 1995-12-04 How to operate pumps connected in parallel

Country Status (1)

Country Link
JP (1) JP3054352B2 (en)

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP5386210B2 (en) * 2009-03-26 2014-01-15 株式会社川本製作所 Water supply equipment
JP7179673B2 (en) * 2019-04-24 2022-11-29 株式会社日立産機システム COMPRESSED AIR PRODUCTION FACILITY, COMPRESSED AIR TARGET PRESSURE ADJUSTMENT METHOD, AND COMPRESSED AIR TARGET PRESSURE ADJUSTMENT PROGRAM
JP6977106B2 (en) * 2020-05-21 2021-12-08 株式会社川本製作所 Water supply device

Also Published As

Publication number Publication date
JPH09151858A (en) 1997-06-10

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