CN102854902A - Chamber pressure adjusting method - Google Patents

Abstract

The invention discloses a chamber pressure adjusting method which is used for performing reduced-pressure control on a pressure adjusting bin, wherein the pressure adjusting bin is provided with one or more pressure reducing valves; and one or more pressure reducing bins output gas from the pressure adjusting bin through corresponding pressure reducing valves to reduce the pressure of the pressure adjusting bin. The method comprises the following steps of: inputting the target pressure of the pressure adjusting bin and the time required for reducing the pressure to the target pressure; measuring the current actual pressure of the pressure adjusting bin; and automatically adjusting the opening of the pressure reducing valve according to the target pressure and the actual pressure of the pressure adjusting bin so that the actual pressure of the pressure adjusting bin reaches the target pressure within the required time. Through the invention, the reduced-pressure control on the pressure adjusting bin can be accurately, safely and quickly realized.

Description

A chamber pressure regulation method

technical field

The invention relates to the technical field of air pressure control, in particular to a method for adjusting chamber pressure.

Background technique

With the development of aviation technology, the decompression control of the chamber has become increasingly important. For example, by controlling the decompression of a chamber, it is possible to simulate the air pressure state of aerospace personnel training at an altitude of tens of thousands of meters. It is also necessary to apply decompression technology in the field of medical research, such as: in a decompression system, animals are placed in a low-pressure chamber, so as to observe the changes of physiological parameters of animals under low-pressure conditions. Through the study of changes in the above physiological parameters, it is possible to better understand, treat and protect humans or other animals under extreme conditions.

Referring to FIG. 1 , the decompression system in the prior art includes: a decompression chamber 20 and a pressure regulation chamber 10 . Wherein, the decompression chamber 20 outputs gas from the decompression chamber 10 through the decompression valve 11 of the decompression chamber 10 to reduce the pressure in the decompression chamber 10 . The pressure of the decompression chamber 20 is much lower than the pressure value that the decompression chamber 10 needs to achieve. The surge chamber 10 may include: a pressure sensor 13 and a parameter measuring device 12, and the parameter measuring device 12 is used to acquire physiological parameter information of experimental animals under different pressure conditions. The pressure sensor 13 is used to obtain the real-time pressure value of the pressure regulating chamber 10 . When adjusting the pressure of the pressure regulating cabin 10, the staff obtains the current pressure of the pressure regulating cabin 10 through the pressure sensor 13, and artificially adjusts the opening degree of the pressure reducing valve 11 according to the difference between the current pressure and the target pressure, so that the pressure regulation The pressure of the chamber 10 is reduced to the target pressure.

In order to be more realistic, it is necessary to depressurize the pressure in the surge chamber 10 to the target pressure in a relatively short period of time. However, the time requirement cannot be met through artificial adjustment, and the adjustment is not accurate, which is prone to large deviations, which will eventually affect the experimental results.

Similarly, in other pressure regulating systems, the same problem exists.

Therefore, how to quickly and accurately realize the low pressure of the chamber has become an urgent problem to be solved by those skilled in the art.

Contents of the invention

The problem to be solved by the present invention is to provide a chamber pressure regulation method to obtain the target air pressure accurately and quickly.

In order to solve the above problems, the present invention provides a method for regulating chamber pressure, which is used for decompression control of a pressure regulating chamber, the pressure regulating chamber is provided with one or more pressure reducing valves, one or more decompression chambers Exporting gas from the surge chamber through a corresponding pressure reducing valve to reduce the pressure of the surge chamber, the method comprising:

Enter the target pressure of the surge chamber and the time required to drop to the target pressure;

Measure the current actual pressure of the surge tank;

According to the target pressure and actual pressure of the pressure regulating chamber, the opening degree of the pressure reducing valve is automatically adjusted, so that the actual pressure of the pressure regulating chamber reaches the target pressure within the required time.

Optionally, while measuring the current actual pressure of the surge chamber, one or more of the following information is measured: temperature information of the surge chamber, humidity information of the surge chamber, concentration information of oxygen in the surge chamber, The concentration information of carbon dioxide in the surge chamber, the pressure information of the decompression chamber, and the temperature information of the decompression chamber.

Optionally, the chamber pressure regulation method further includes: placing experimental animals in the surge chamber, and measuring physiological parameter information of the experimental animals while measuring the current actual pressure of the surge chamber.

Optionally, the chamber pressure regulation method further includes: during the decompression control process, at least outputting the opening degree of the decompression valve and the real-time pressure of the pressure regulation chamber at a fixed time.

Optionally, the output is one or any combination of voice output, display output or print output.

Optionally, the chamber pressure regulation method further includes: during the decompression control process, at least regularly storing the opening degree of the decompression valve and the real-time pressure of the pressure regulation chamber.

Optionally, the chamber pressure regulating method further includes: at least when the opening degree of the decompression valve or the actual pressure of the pressure regulating chamber is greater than a threshold, issuing a sound, light or displaying an alarm.

Optionally, the opening degree of the pressure relief valve is adjusted in the following manner:

Set the pressure of the surge chamber to satisfy P _t = P ₀ ×K × t, wherein, P ₀ is the pressure before the pressure of the pressure control cabin, P _t is the pressure of the pressure control cabin after the decompression time t, and t is the decompression time , K is the rate ratio of decompression;

According to the pressure difference of the pressure regulating chamber before and after decompression, the opening degree of the decompression valve is adjusted.

Optionally, the value of K is greater than -1 and less than 0.

Optionally, adjusting the opening degree of the decompression valve according to the pressure difference of the pressure regulating chamber before and after decompression includes:

Obtain the opening degree of the pressure reducing valve before decompression;

According to F _k = F _ka + ΔPa + F _kb × ΔPa ² , calculate the opening degree of the pressure reducing valve after decompression, where F _k is the opening degree of the pressure reducing valve after decompression, and F _ka is the decompression before decompression The opening degree of the valve, ΔPa is the reduced pressure, F _kb is the proportional coefficient;

Adjust the opening degree of the pressure reducing valve from F _ka to F _k .

Compared with the prior art, the present invention has the following advantages: the decompression chamber outputs gas from the decompression chamber through the decompression valve to reduce the pressure of the decompression chamber, and when the decompression control is performed on the decompression chamber, the input pressure regulation The target pressure of the pressure regulating chamber and the time required to reach the target pressure are measured, and the current actual pressure of the pressure regulating chamber is measured, and then according to the target pressure and actual pressure of the pressure regulating chamber, the opening degree of the pressure reducing valve is automatically adjusted to make the actual pressure of the pressure regulating chamber The pressure reaches the target pressure at the desired time. By converting manual adjustment to automatic adjustment, high speed, accuracy and safety of decompression control can be guaranteed.

Description of drawings

Fig. 1 is the structural representation of decompression system in the prior art;

2 is a schematic flow diagram of a chamber pressure regulating method according to an embodiment of the present invention;

Fig. 3 is the structural representation of decompression system in the embodiment of the present invention;

FIG. 4 is a schematic structural diagram of the detection device in FIG. 3 .

Detailed ways

In order to make the above objects, features and advantages of the present invention more comprehensible, specific implementations of the present invention will be described in detail below in conjunction with the accompanying drawings.

In the following description, many specific details are set forth in order to fully understand the present invention, but the present invention can also be implemented in other ways than those described here, so the present invention is not limited by the specific embodiments disclosed below.

As mentioned in the background technology section, in the prior art, the opening degree of the pressure-relief valve of the pressure-regulating cabin is artificially adjusted. Since it takes a period of time for the staff to obtain the actual pressure of the pressure-regulating cabin and calculate the adjustment value of the pressure-reducing valve, the It will take some time for the pressure reducing valve to be adjusted to an appropriate opening degree, which cannot meet the requirement of rapid decompression. In addition, in the process of manually adjusting the opening degree of the decompression valve, hand shaking is likely to cause errors, so that the actual pressure of the decompression chamber is inconsistent with the target pressure. In addition, there are potential safety problems in the way of artificially adjusting the opening degree of the pressure reducing valve of the pressure regulating chamber.

In view of the above-mentioned defects, the present invention provides a method for adjusting chamber pressure, which is used for depressurizing control of the pressure regulating chamber. The pressure regulating chamber is provided with one or more pressure reducing valves, and one or more decompression chambers pass through The corresponding decompression valve outputs gas from the surge chamber to reduce the pressure of the surge chamber, specifically including: inputting the target pressure of the surge chamber and the time required to drop to the target pressure; measuring the current actual pressure of the surge chamber; According to the target pressure and actual pressure of the pressure regulating chamber, the opening degree of the pressure reducing valve is automatically adjusted, so that the actual pressure of the pressure regulating chamber reaches the target pressure within the required time.

The invention can ensure the high speed, accuracy and safety of decompression control by converting manual adjustment into automatic adjustment.

A detailed description will be given below in conjunction with the accompanying drawings.

Referring to Fig. 2, the present embodiment provides a method for regulating chamber pressure, which is used for depressurizing control of a pressure regulating chamber, wherein the pressure regulating chamber is provided with one or more pressure reducing valves, one or more pressure reducing valves The ballast chamber outputs gas from the surge chamber through the corresponding pressure reducing valve to reduce the pressure of the surge chamber, including the following steps:

Step S1, inputting the target pressure of the surge chamber and the time required to reach the target pressure;

Step S2, measuring the current actual pressure of the surge chamber;

Step S3, according to the target pressure and the actual pressure of the pressure regulating chamber, automatically adjust the opening degree of the pressure reducing valve, so that the actual pressure of the pressure regulating chamber reaches the target pressure within the required time.

Referring to FIG. 3 , the above method can be realized by using the decompression system shown in FIG. 3 . The pressure relief system includes:

The pressure regulating cabin 100 is provided with one or more pressure reducing valves;

One or more decompression chambers, output gas from the decompression chamber 100 through corresponding decompression valves to reduce the pressure of the decompression chamber;

The detection device at least includes a pressure sensor 810 arranged in the pressure regulating cabin, for obtaining the actual pressure of the pressure regulating cabin 100;

The input device 400 is used to input the target pressure of the surge chamber 100 and the time required to reach the target pressure;

The controller 300 is connected with the detection device, the input device 400 and the pressure reducing valve, and automatically adjusts the opening degree of the pressure reducing valve according to the target pressure and the actual pressure of the pressure regulating cabin 100, so that the actual pressure of the pressure regulating cabin 100 is within the required range. time to reach target pressure.

In this embodiment, the decompression system obtains the actual pressure of the pressure regulating chamber 100 through the pressure sensor 810, and inputs the target pressure of the pressure regulating chamber 100 and the time required to reach the target pressure through the input device 400, and then the controller 300 according to the pressure of the pressure regulating chamber 100 The target pressure and the actual pressure are adjusted, and the opening degree of the decompression valve is adjusted, so that the actual pressure of the pressure regulating chamber 100 reaches the target pressure within the required time, ensuring the high speed, accuracy and safety of decompression.

The surge chamber 100 is a chamber whose pressure is to be adjusted. In this embodiment, the experimental animals are placed in the surge chamber 100 to simulate the pressure of the experimental animals in high altitude.

Referring to FIG. 3 , the decompression system in this embodiment includes two decompression chambers, namely: a first decompression chamber 910 and a second decompression chamber 920 . Correspondingly, the pressure regulating chamber 100 includes two pressure reducing valves, namely: a first pressure reducing valve 140 and a second pressure reducing valve 150 . The first decompression chamber 910 outputs the gas in the decompression chamber 100 through the first decompression valve 140 to reduce the pressure of the decompression chamber 100, and the second decompression chamber 920 is output from the decompression chamber 100 through the second decompression valve 150 gas to reduce the pressure of the surge chamber 100.

The decompression valve may be provided with an electronic switch for receiving control information to control the opening degree of the decompression valve. The opening degree of the pressure reducing valve refers to the opening degree of the pressure reducing valve, and its value is greater than or equal to 0 and less than or equal to 1.

The pressure of each decompression chamber is much lower than the target pressure of the decompression chamber, for example, the pressure of the first decompression chamber 910 can be 0.1 MPa, and the actual pressure of the decompression chamber 100 is 1.5 MPa.

In the process of the decompression chamber inputting gas to the pressure regulation chamber 100 through the pressure relief valve, the larger the opening degree of the pressure relief valve is, the more gas the decompression chamber outputs from the pressure regulation chamber 100, so that the pressure of the pressure regulation chamber 100 The faster the descent. The opening degree of each decompression valve in this embodiment may be the same or different.

The relationship between the opening degree of the pressure reducing valve and the reduced pressure can be:

F _k = F _ka + ΔPa + F _kb × ΔPa ² ,

Among them, F _k is the opening degree of the pressure reducing valve after decompression, F _ka is the opening degree of the pressure reducing valve before decompression, ΔPa is the reduced pressure, and F _kb is the proportional coefficient.

Due to the inclusion of multiple decompression chambers in this embodiment, the decompression process can be achieved more quickly than in the case of only one decompression chamber. Specifically, in order to achieve more precise control, the two decompression valves in this embodiment can be DN32 (that is, the diameter of the decompression valve is 32 mm) and DN40 (that is, the diameter of the decompression valve is 40 mm), so that Decompression at different rates and in different combinations. It should be noted that, in other embodiments, at least some of the pressure reducing valves may have the same diameter.

It should be noted that, in other embodiments of the present invention, under the premise of keeping the same number of decompression chambers and decompression valves, the number of decompression chambers or decompression valves can also be one, three or three more than one, which are all within the protection scope of the present invention.

In this embodiment, while measuring the current actual pressure of the surge chamber, one or more of the following information can also be measured: the temperature information of the surge chamber, the humidity information of the surge chamber, and the concentration information of oxygen in the surge chamber , the concentration information of carbon dioxide in the surge chamber, the pressure information of the decompression chamber, and the temperature information of the decompression chamber. Correspondingly, referring to FIG. 4, the detection device in this embodiment may also include one or more of the following devices:

The temperature sensor 820 arranged in the surge chamber 100 is used to obtain the temperature information of the surge chamber 100;

The humidity sensor 830 arranged in the pressure regulation cabin 100 is used to obtain the humidity information of the pressure regulation cabin 100;

The oxygen concentration sensor 850 arranged in the surge chamber 100 is used to obtain the oxygen concentration information in the surge chamber 100;

The carbon dioxide concentration sensor 860 arranged in the surge chamber 100 is used to obtain the concentration information of carbon dioxide in the surge chamber 100;

The pressure sensor 891 arranged in the decompression chamber is used to obtain the pressure information of the decompression chamber;

The temperature sensor 892 arranged in the decompression chamber is used to obtain the temperature information of the decompression chamber.

In addition, in this embodiment, experimental animals (such as: mice) can also be placed in the surge chamber 100, so that the physiological parameter information of the experimental animals can be measured while measuring the current actual pressure of the surge chamber 100 . Specifically, referring again to FIG. 4 , the detection device may further include: a physiological parameter measuring device 840 disposed in the surge chamber 100 for acquiring physiological parameter information of animals in the surge chamber 100 .

In this embodiment, pressure sensors 891 and/or temperature sensors 892 may be provided in only some decompression chambers, or pressure sensors 891 and/or temperature sensors 892 may be provided in each decompression chamber.

The pressure sensor 810 or the pressure sensor 891 can be a Honeywell high-pressure pressure sensor, which has automatic temperature compensation and correction inside, and has a fast response speed and high safety.

The temperature sensor 820 and the humidity sensor 830 can be integrated into one body. Specifically, the Swiss Shengshi Ruien HT1 series digital temperature and humidity transmitter can be used, so that the temperature and humidity signals can be digitally output, with high detection accuracy and fast response speed.

The physiological parameter measuring device 840 can be any physiological parameter monitoring instrument in the prior art, which is used to measure the electrocardiogram, blood pressure, pulse rate, blood oxygen saturation, respiration rate, body temperature and other physiological parameters of the experimental animals in the surge chamber. parameter.

In this embodiment, after acquiring the measurement information, the detection device sends the measurement information to the controller 300 .

The input device 400 is used to obtain the target pressure of the surge chamber 100 and the time relationship, such as: the pressure in the surge chamber 100 decreases linearly with time. Further, the pressure in the pressure regulating chamber 100 can also be kept constant for a period of time, such as: after the pressure regulating chamber 100 is depressurized for a period of time, it is still for a period of time, and then continues to reduce the pressure and maintain it.

When the pressure in the surge chamber 100 decreases linearly with time, the following relationship is satisfied:

P _t =P ₀ ×K×t,

Wherein, P ₀ is the pressure before the decompression of the regulator cabin 100, P _t is the pressure of the regulator cabin 100 after the decompression t moment, t is the decompression time, and K is the rate ratio of decompression, that is, the speed of the decompression straight line constant. The value of K may be greater than -1 and less than 0, such as -1/3, -0.5 or -2/3, etc. At this time, the opening degree of the pressure reducing valve is adjusted in the following way:

Set the pressure of the surge chamber to satisfy P _t = P ₀ ×K × t, wherein, P ₀ is the pressure before the pressure of the pressure control cabin, P _t is the pressure of the pressure control cabin after the decompression time t, and t is the decompression time , K is the rate ratio of decompression;

According to the pressure difference of the pressure regulating chamber before and after decompression, the opening degree of the decompression valve is adjusted.

Among them, according to the pressure difference of the pressure regulating chamber before and after decompression, adjusting the opening degree of the pressure reducing valve includes:

Obtain the opening degree of the pressure reducing valve before decompression;

According to F _k = F _ka + ΔPa + F _kb × ΔPa ² , calculate the opening degree of the pressure reducing valve after decompression, where F _k is the opening degree of the pressure reducing valve after decompression, and F _ka is the decompression before decompression The opening degree of the valve, ΔPa is the reduced pressure, F _kb is the proportional coefficient;

Adjust the opening degree of the pressure reducing valve from F _ka to F _k .

It should be noted that, in the present invention, the pressure of the surge chamber 100 can have any relationship with time.

Specifically, the input device 400 may be a keyboard, a mouse, a voice input device, or a touch input device.

The controller 300 can be selected from an industrial-grade monitoring notebook, so that it can control the opening degree of the pressure reducing valve in a highly convenient and accurate manner. Specifically, the controller 300 obtains the target pressure of the pressure regulating chamber from the input device 400, obtains the actual pressure of the pressure regulating chamber from the pressure sensor 810, calculates the opening degree of the pressure reducing valve to be adjusted according to the target pressure and the actual pressure, and then The opening degree of the decompression valve is adjusted so that the actual pressure of the pressure regulating chamber 100 reaches the target pressure within a required time.

The controller 300 sends a control signal to the electronic switch on the decompression valve, and the opening degree of the decompression valve can be controlled by controlling the electronic switch. Specifically, the controller 300 can set the opening degree of some or all of the pressure reducing valves to 1 (that is, fully open), and can also make the opening degree of some of the pressure reducing valves to be 0 (that is, completely close), or make some or all of the pressure reducing valves The opening degree of the pressure reducing valve is greater than 0 and less than 1 (that is, the opening part).

Specifically, the detection-related programs can be written in the controller 300 in a high-level language to improve the running speed, and the assembly language can be used in the controller 300 to write the programs related to the calculation control to ensure accurate and safe control.

The chamber pressure regulating method in this embodiment may also include one or more of the following steps:

During the decompression control process, at least the opening degree of the decompression valve and the real-time pressure of the pressure regulating chamber are output regularly;

During the decompression control process, at least the opening degree of the decompression valve and the real-time pressure of the pressure regulating chamber are stored regularly;

At least when the opening degree of the pressure relief valve or the actual pressure of the surge chamber is greater than the threshold value, sound, light or display alarm.

Specifically, referring again to Figure 3, in order to achieve the above steps, the decompression system may also include one or any combination of the following devices:

The output device 500 is connected to the controller 300, and is used to at least regularly output the opening degree of the pressure reducing valve and the real-time pressure of the pressure regulating cabin 100 during the decompression process;

The storage device 600, connected to the controller 300, is used for timing storage of at least the opening degree of the pressure reducing valve and the real-time pressure of the pressure regulating cabin 100 during the decompression process;

The alarm device 700 is connected to the controller 300, and is used for at least when the opening degree of the pressure reducing valve or the actual pressure of the pressure regulating chamber 100 is greater than the threshold value, an alarm is issued by sound, light or display.

Specifically, the actual pressure of the surge chamber can be tested every 1 second, and then the opening degree of the pressure relief valve and the real-time pressure of the surge chamber can be output and/or stored every 1 second.

Because in this embodiment, the controller 300 can also obtain: temperature information, humidity information, physiological parameter information, oxygen concentration information, carbon dioxide concentration information of the decompression chamber 100, pressure information and temperature information of the decompression chamber through the detection device , so the output device 500 may also output one or more of the above information together.

Specifically, the output device 500 may be one or any combination of voice output device, print output device or display output device, so that the output is one or any combination of voice output, display output or print output.

The storage device 600 can be any storage, such as: U disk, flash memory or hard disk. The storage device 600 can also store: temperature information, humidity information, physiological parameter information, oxygen concentration information, carbon dioxide concentration information of the pressure regulation chamber 100 of the pressure regulation chamber 100, oxygen concentration information, carbon dioxide concentration information, pressure information and temperature information.

The alarm device 700 can be a voice alarm device, a light alarm device or a display alarm device, etc., so that when any information obtained by the detection device does not meet the normal conditions, a corresponding alarm message can be issued to inform the staff in time, The safety of decompression is guaranteed.

This embodiment can realize the decompression of the pressure regulating chamber accurately, safely and quickly.

Although the present invention has been disclosed above with preferred embodiments, the present invention is not limited thereto. Any person skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, so the protection scope of the present invention should be based on the scope defined in the claims.

Claims (10)

1. chamber pressure control method, it is characterized in that be used for exchanging ballasting and carry out Decompression Controlling, described pressure regulation cabin is provided with one or more reduction valve, one or more decompression chambers are exported gas to reduce the pressure in pressure regulation cabin by the reduction valve of correspondence from the pressure regulation cabin, described method comprises:

The goal pressure in input pressure regulation cabin and being down to the required time of goal pressure;

Measure the current actual pressure in pressure regulation cabin;

According to goal pressure and the actual pressure in pressure regulation cabin, the open degree of automatically regulating reduction valve makes the actual pressure in pressure regulation cabin reach goal pressure in the required time.

2. chamber pressure control method as claimed in claim 1, it is characterized in that, when measuring the current actual pressure in pressure regulation cabin, measure in the following information one or more: the pressure information of the concentration information of carbon dioxide, decompression chamber, the temperature information of decompression chamber in the concentration information of oxygen, the pressure regulation cabin in the humidity information in the temperature information in pressure regulation cabin, pressure regulation cabin, the pressure regulation cabin.

3. chamber pressure control method as claimed in claim 1 or 2 is characterized in that, also comprises: put into animal used as test in described pressure regulation cabin, when measuring the current actual pressure in pressure regulation cabin, measure the physiological parameter information of described animal used as test.

4. chamber pressure control method as claimed in claim 1 is characterized in that, also comprises: in the Decompression Controlling process, carry out timing output to the open degree of major general's reduction valve and the real-time pressure in pressure regulation cabin.

5. chamber pressure control method as claimed in claim 4 is characterized in that, the described a kind of or combination in any that is output as in voice output, demonstration output or the printout.

6. chamber pressure control method as claimed in claim 1 is characterized in that, also comprises: in the Decompression Controlling process, carry out the timing storage to the real-time pressure in the open degree of major general's reduction valve and pressure regulation cabin.

7. chamber pressure control method as claimed in claim 1 is characterized in that, also comprises: when the actual pressure in the open degree of reduction valve or pressure regulation cabin during greater than threshold value, send voice, light or show alarm at least.

8. chamber pressure control method as claimed in claim 1 is characterized in that, the open degree of described reduction valve is regulated in the following manner:

The pressure that the pressure regulation cabin is set satisfies P _t=P ₀* K * t, wherein, P ₀The pressure before the decompression of pressure regulation cabin, P _tBe decompression t constantly after the pressure in pressure regulation cabin, t is decompression time, K is the speed ratio of decompression;

According to the pressure differential in pressure regulation cabin before and after the decompression, the open degree of regulating reduction valve.

9. chamber pressure control method as claimed in claim 8 is characterized in that, the value of described K is greater than-1 and less than 0.

10. chamber pressure control method as claimed in claim 8 is characterized in that, according to the pressure differential in pressure regulation cabin before and after the decompression, the open degree of regulating reduction valve comprises:

Obtain the open degree of the front reduction valve of decompression;

According to F _k=F _Ka+ Δ Pa+F _Kb* Δ Pa ², calculate the afterwards open degree of reduction valve of decompression, wherein, F _kThe open degree of reduction valve after the decompression, F _KaBe the open degree of reduction valve before the decompression, Δ Pa is the pressure that reduces, F _KbIt is scale-up factor;

With the open degree of reduction valve from F _KaTransfer to F _k

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