CN104977119B - A kind of single-piston damp type optical fiber differential pressure pickup - Google Patents

Abstract

The invention provides a single-piston damping optical fiber differential pressure sensor. A piston is slidably arranged in the casing, springs are respectively arranged at both ends of the piston, end caps are fixed at both ends of the casing, and the other ends of the spring are respectively fixed on the corresponding On the end cover, there are probe sockets penetrating through the end cover at the relative positions on the end cover. The probe socket is sealed with a light-transmitting sheet, and the probe socket is located on the outside of the light-transmitting sheet. An optical fiber pointing to the piston is provided. The probe, the two ends of the piston are respectively fixed with reflective sheets at the positions opposite to the optical fiber probe, the side walls at both ends of the housing are provided with fluid through holes communicating with the inner cavity of the housing, and the output ends of the receiving optical fibers in the two optical fiber probes are respectively connected to the photosensitive The components are connected, and each photosensitive component is correspondingly connected with a signal processing module. In order to solve the problems that the existing differential pressure sensor is not suitable for many occasions, has poor practicability, insufficient measurement accuracy, and cannot meet the requirements of actual differential pressure measurement. The invention belongs to the field of differential pressure detection.

Description

A single-piston damping optical fiber differential pressure sensor

technical field

The invention relates to a sensor and belongs to the technical field of optical fiber sensing.

Background technique

Differential pressure sensors are widely used in industry and are mainly used to measure the pressure difference of equipment, components or fluids at different positions. They are widely used in detection fields such as tail pressure difference, gas flow, liquid level, and clean room monitoring. Nowadays, differential pressure sensors using different principles have appeared, such as resistive, capacitive, inductive, throttle, magnetic liquid, MEMS, etc. Among them, resistive and capacitive are more common, and other types are not practical due to Strong, limited or still in the concept stage, and has not been promoted, but resistive and capacitive differential pressure sensors also have their own shortcomings, and cannot be well competent in many occasions.

Contents of the invention

The purpose of the present invention is to provide a single-piston damping optical fiber differential pressure sensor to solve the problems that the existing differential pressure sensor is not suitable for many occasions, its practicability is not strong, the measurement accuracy is not enough, and it cannot meet the actual pressure differential measurement requirements. .

The solution of the present invention is as follows: a single-piston damping optical fiber differential pressure sensor includes a probe structure, a photosensitive element and a signal processing module. , the two ends of the piston are respectively provided with a spring, one end of the two springs is fixed on the piston, the two ends of the housing are respectively sealed and fixed with end caps, and the other ends of the two springs are respectively fixed on the corresponding end caps, The two end caps are respectively provided with a probe jack through the end cap at the opposite position, and the two probe jacks are respectively sealed with a light-transmitting sheet, and the two probe jacks are respectively arranged on the outside of the light-transmitting sheet. There is an optical fiber probe pointing to the piston, the optical fiber probes are perpendicular to the end face of the piston, reflectors are respectively fixed at the positions opposite to the optical fiber probe at both ends of the piston, and a The fluid through hole communicated with the inner cavity of the housing, and the outgoing ends of the receiving optical fibers in the two optical fiber probes are respectively connected to a photosensitive element, and each photosensitive element is correspondingly connected to a signal processing module.

Preferably, the optical fiber bundle in the fiber optic probe includes an incident optical fiber and an outgoing optical fiber, the incident optical fiber and the receiving optical fiber are arranged in parallel to each other in the fiber optic probe, there is one incident optical fiber, and the single receiving optical fiber has a size parameter of 50 ± 3 The receiving fiber is closely arranged to form a circular fiber bundle structure with the incident fiber as the center, and the boundary distance between the incident fiber and the receiving fiber is 130-140 ;

Preferably, the structures and specifications of the two springs are the same. When the fluid through holes are connected to the outside atmosphere, the piston is located in the center of the housing, and the two springs are in a natural state, that is, the springs have no tension and compression set;

Preferably, the two probe sockets are set at the exact center of the end cap, the two probe sockets and the piston are coaxial, and in the natural state, the distance between one of the optical fiber probes and the reflective sheet corresponding to the optical fiber probe is The distance from another fiber optic probe to another reflector is the same;

Preferably, the light-transmitting sheet is a glass sheet, and the light-transmitting sheets are all arranged at the port where the probe socket is located on the inner side of the end cover;

Preferably, the probe socket is provided with an internal thread, and the fiber optic probes are respectively screwed and fixed in the probe socket;

Preferably, the middle part of the end cover is provided with a protruding part extending into the housing, a sealing ring is provided between the protruding part and the inner wall of the housing, and a spring positioning groove is opened on the protruding part along the length direction of the housing, and the spring positioning The groove is an annular groove, and the inner diameter of the spring positioning groove is less than or equal to the inner diameter of the spring, the outer diameter of the spring positioning groove is greater than or equal to the outer diameter of the spring, and one end of the spring is extended and fixed in the spring positioning groove;

Preferably, the protrusion is a cylindrical structure matching the inner diameter of the housing;

Preferably, two fluid through holes are respectively opened on the side walls at both ends of the housing, each fluid through hole corresponds to the raised portion on the end cover at the end, and the position of the raised portion corresponding to the fluid through hole is opened There is a through hole connected with the spring positioning groove, and the fluid flows into the chamber inside the housing through the fluid through hole and the through hole in turn;

Preferably, a sealing ring is provided between the piston and the inner wall of the housing, and a sealing ring is also provided between the end cover and the inner wall of the housing;

Preferably, the piston is made of hard alloy;

The working principle of the sensor is: the other end of the incident optical fiber is connected to the light source to couple the incident light, the output end of the receiving optical fiber is connected to the photosensitive element, and the output light intensity signal is passed into two fluids to be measured through the two fluid through holes respectively. When the fluid pressures in the detection chambers on the left and right sides are equal, the piston is in the middle equilibrium position, the axial resultant force on the piston is zero, and the piston does not produce axial displacement; when there is a pressure difference in the fluid in the detection chambers on the left and right sides of the piston, the piston Loss of balance, sliding to the side with lower pressure, thereby compressing the damping spring on this side, the damping spring on the other side is stretched, and the piston moves to a new equilibrium position where the resultant axial force is zero. When the piston is in the middle balance position, the optical fiber bundles with the same structure on both sides of the sensor and the reflective sheet on the piston end face are at the same distance, so that the output optical signal intensity of the two optical fiber bundles receiving the optical fiber is equal, and the photosensitive element converts the optical signal into an electrical signal. Signal processing module amplification, rectification, filtering and other processing links, and with the corresponding algorithm calculation, can get the fluid pressure difference between the two detection positions, the output value is 1 after photoelectric conversion and signal processing calculation; after the piston slides to the low pressure side , the distance between the optical fiber bundle on the low-voltage side and the reflective sheet on the end face of the piston decreases, and the output optical signal intensity of the receiving optical fiber weakens, while the distance between the optical fiber bundle on the high-voltage side and the reflective sheet on the end face of the piston increases, and the output optical signal intensity of the receiving optical fiber increases. After signal processing and calculation, the output value will change exponentially, thereby improving the detection sensitivity. Through the change of the final output value, the pressure difference between the fluids in the two detection chambers of the sensor can be judged, so as to realize the detection of the pressure difference at different positions.

1. The sensor intensity compensation principle

Referring to Fig. 3, the light source in this method The emitted light is divided into two equal paths through the Y -type coupler, and one path enters the probe side, reaching the photodetector after reflection , the other way into the probe side, reaching the photodetector after reflection . Then the output signals of the two photodetectors are:

In the formula: is the optical power output by the light source; is the transmittance of the incident fiber; is the transmittance of the receiving fiber; , is the sensitivity of the photodetector; is the coupling ratio.

right , Divide to get:

According to the above formula, it can be concluded that the calculated and processed output signal eliminates the power fluctuation of the light source and the error of the coupler. At the same time, the symmetrical design is adopted in the design, which can also eliminate the error caused by the fiber loss. Select a stable photoelectric detection element to avoid errors introduced by the photoelectric detection element.

2. Sensor Mathematical Model

2.1 Mathematical model of intensity modulation

The detection principle of the detection cavity on each side of the present invention is the same as that of the reflective intensity modulation optical fiber sensor. As shown in Figure 4, the light emitted by the outgoing optical fiber TF in the optical fiber bundle is irradiated on the reflective sheet, and after being reflected by the reflective sheet, it is transmitted to the receiving fiber RF endface in the fiber bundle. The reflected light can be received by the receiving optical fiber only when there is an overlapping area between the end face of the reflected light cone and the end face of the receiving optical fiber. When the distance d between the optical fiber bundle and the reflective sheet changes, according to the reflection theorem, as d continues to increase, the bottom of the light cone becomes larger from small to large, from not entering the end face of the receiving fiber, to gradually entering the end face of the receiving fiber, and then to complete coverage , as d further increases, the reflected light and its coverage area will no longer change, but the intensity will continue to decrease due to distance. The quantitative analysis of this process is as follows:

Let the light intensity modulation function of the sensor be M , which is the ratio of the luminous flux received by RF to the luminous flux sent by TF , which reflects the intensity modulation characteristics of the reflective intensity modulation fiber sensor. Here, for the simplification of the mathematical model and the convenience of calculation, without affecting the distribution of the intensity modulation characteristic curve, the intensity distribution of the optical fiber output light field and the intensity distribution of the reflected light field are ignored. It may be assumed that the output light intensity is along the The radial direction is evenly distributed, then the illuminance on the end surface of the reflected light cone is:

(1)

In the formula is the optical power loss coefficient of the incident light; is the luminous flux coupled from the light source to the emitting fiber; R is the radius of the end face of the reflected light cone.

It is also considered that the illuminance of the end surface of the reflected light cone is uniformly distributed, then the input luminous flux of the receiving optical fiber is:

(2)

In the formula is the loss coefficient of the receiving fiber, and S is the overlapping area of the end face of the reflected light cone and the end of the receiving fiber.

Then the light intensity modulation function M is:

(3)

Because the optical power loss coefficient is a fixed value for the already determined sensor system, the value of M is mainly determined by the ^ratio of S and R2 .

(3) In the formula, the radius R of the end surface of the reflected light cone can be calculated by the following formula:

(4)

In the formula: is the radius of the launching fiber, NA is the numerical aperture of the fiber, and d is the distance between the fiber probe and the reflective sheet.

(3) In the formula, the overlapping area S of the reflected light cone end face and the receiving fiber end can be calculated by the following formula:

; (5)

In the formula: L is the center distance between the transmitting fiber and the receiving fiber, is the receiving fiber radius, , is the central angle formed by the intersection of the bottom end of the light cone and the end face of the receiving fiber, , .

In order to make the sensor designed by the present invention have good linearity and sensitivity, the initial state of the sensor is designed to work near the middle position of the front slope curve section of the above-mentioned strong modulation function M. At this time, the corresponding reflected light cone end face and receiving fiber end The overlapping area S is the second formula in formula (5), then the unilateral intensity modulation model of the sensor of the present invention is:

( ) (6)

2.2 Sensor Mathematical Model

The following analyzes the relationship between the sensor intensity modulation model and the pressure difference. It is known that the pressures of the fluids at both ends are respectively , , then the fluid pressure on both sides of the sensor piston is:

; (7)

In the formula: the cross-sectional area on both sides of the sensor piston is equal, namely ;

The force analysis on the two measurements of the piston is as follows:

(8)

In the formula: is the initial deformation of the spring, is the piston displacement, , is the spring stiffness coefficient on both sides, and the springs on both sides are the same, so .

Then formula (8) can be simplified as: (9)

Simultaneously (7), (9) formula has: (10)

Since the size of the sensor and the damping spring have been determined in the design stage, the above formula (10) and is a constant, then the piston displacement Proportional to the pressure difference across the sensor.

Also set is the initial distance between the optical fiber bundles on both sides of the sensor and the reflector; , After the deformation of the inner spring of the sensor, the distance between the optical fiber bundles on both sides and the reflective sheet, where for the high voltage side, for the low pressure side. Then there are:

; (11)

Simultaneously (10), (11) formula has: (12)

(13)

Substituting equations (12) and (13) into equation (6), the intensity modulation function of the detection chambers on both sides of the sensor can be obtained when there is a pressure difference between the detection chambers on both sides , . it's easy to see , for about unary function of , because , The other parameters in are determined in the sensor design stage, so they are all constants. In order to eliminate the error caused by the intensity fluctuation of the light source to the sensor, the output value of the sensor is , The ratio of , so as to compensate the intensity of the sensor. Therefore, the sensor mathematical model can be expressed as:

(14)

Through the above mathematical model, the pressure difference on both sides of the sensor can be obtained The relationship with the size of the output optical signal.

3. Results and Analysis

According to the above theoretical basis and formula, select the initial value , , , , Change from 0mm to 0.3mm, which is the transmission distance at both ends From 0.866mm to 1.166mm, From 0.866mm to 0.566mm, the output result of the sensor. After the simulation experiment, the change of luminous flux on the side corresponding to the increased displacement (high voltage side) is shown in Figure 5; the change of luminous flux on the side corresponding to the decreased displacement (low voltage side) is shown in Figure 6;

According to Fig. 5, it is not difficult to see that the luminous flux on the high-voltage side increases with the distance from the piston, and has a good linearity. This is because the initial state of the sensor works near the middle position of the front slope curve section of the strong modulation function M , that is, the end face of the reflected light cone and the end face of the receiving fiber are in the intersecting state. At this time, as the distance d increases, the light coupled into the receiving fiber The intensity increases, so the luminous flux on the high-voltage side shows an increasing trend, while maintaining good linearity.

According to Figure 6, it is not difficult to see that the luminous flux on the low pressure side shows a decreasing trend as the piston moves away, and it also has a good linearity. The same as the high-voltage side, at this time, as the distance d decreases, the light intensity coupled into the receiving fiber will decrease, so the luminous flux on the low-voltage side shows an increasing trend while maintaining good linearity.

The change curve of luminous flux ratio with displacement is shown in Figure 7. It is not difficult to see that the output result in the form of ratio increases gradually from a constant value of 1. When the output value is 1, it means that the sensor has no pressure difference, the piston is in the middle balance position without sliding, and the output light intensity on both sides is equal. When there is a fluid pressure difference in the sensor, the balance is broken, the output light intensity on one side increases, and the other side decreases, and its output value rapidly increases exponentially. Therefore, after the ratio processing, the output value of the sensor is greatly amplified, thereby effectively improving the sensitivity of the sensor; at the same time, the output value of the sensor still maintains a good linearity.

Compared with the prior art, the present invention has the following main advantages: through structural design, theoretical research and experimental analysis, it can be seen that the sensor has a smaller structure, higher accuracy and reliability, better adaptability and interchangeability And other advantages, strong practicability, the output signal will be multiplied after the output signal is calculated by photoelectric conversion and signal processing, thereby improving the detection sensitivity, the sensor can be applied to multiple pressure difference detection occasions.

At the same time, the differential pressure sensor adopts a piston structure as a pressure detection device. When encountering fluid pressure, the piston moves in translation, and the fluid pressure difference can be calculated only according to the translation amount of the piston, which has lower requirements for optical fiber sensing. , the calculation and measurement are simpler, and the piston structure is more stable, less susceptible to external interference, less prone to damage, and longer service life, which greatly improves the reliability, adaptability and interchangeability of the sensor, and is suitable for use as The measurement of fluid differential pressure; the sensor's strength compensation principle is simpler and more practical.

Description of drawings

Fig. 1 is a structural representation of the present invention;

Fig. 2 is the cross-sectional schematic diagram of probe structure in the present invention, and wherein, 101 represents light source, 102 represents to-be-measured fluid;

Fig. 3 is a schematic diagram of the sensor intensity compensation method;

Fig. 4 is a positional relationship diagram between the reflected light cone and the receiving optical fiber;

Among them: 103 refers to the reflective surface, 104 refers to the emission spot, 105 refers to the end face of the reflected light cone, 106 refers to the end face of the receiving fiber, 107 refers to the tangent between the end face of the reflected light cone and RF, 108 refers to the end face of the reflected light cone and RF Compatibility, 109 means that the end face of the reflected light cone intersects with RF;

Fig. 5 is a curve diagram of luminous flux change on the high voltage side;

Fig. 6 is a curve diagram of luminous flux variation on the low-voltage side;

Fig. 7 is a curve of luminous flux ratio changing with displacement.

detailed description

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be described in further detail below with reference to the accompanying drawings,

Example:

Referring to Figures 1 and 2, this embodiment provides a single-piston damping optical fiber differential pressure sensor, including a probe structure 1, a photosensitive element 2 and a signal processing module 3,

The probe structure 1 includes a housing 11, the housing 11 is a cylindrical structure, a piston 12 is slidingly arranged in the housing 11, the material of the piston 12 is hard alloy, and a sealing ring 18 is arranged between the piston 12 and the inner wall of the housing 11 , the two ends of the piston 12 are respectively provided with a spring 14, one end of the two springs 14 is fixed on the piston 12, and the piston 12 is coaxial with the two springs 14, and the two ends of the housing 11 are respectively sealed and fixed with end caps 13 , the other ends of the two springs 14 are respectively fixed on the corresponding end caps 13. The structures and specifications of the two springs 14 are the same. When the fluid through holes 17 are connected to the external atmosphere, the piston 12 is located in the housing 11, the two springs 14 are in a natural state, that is, the springs 14 have no stretching and compression deformation, and the opposite positions of the two end caps 13 are respectively provided with a probe jack 131 through the end caps 13 where they are located. The ports inside the two probe jacks 131 located inside the end cap 13 are respectively sealed with light-transmitting sheets 15, the light-transmitting sheets 15 are made of transparent glass sheets, and the two probe jacks 131 are respectively arranged on the outside of the light-transmitting sheets 15 There is an optical fiber probe 19 pointing to the piston 12, the optical fiber probe 19 is perpendicular to the end face of the piston 12, an internal thread is arranged in the probe jack 131, the optical fiber probe 19 is screwed and fixed in the probe jack 131 respectively, and the two ends of the piston 12 are connected to the probe jack 131. Reflectors 16 are respectively fixed at the relative positions of the fiber optic probes 19, and the two probe jacks 131 are set at the very center of the end cap 13 where they are located. The two probe jacks 131 and the piston 12 are coaxial, and one of the fiber optic probes 19 to the distance of the optical fiber probe 19 corresponding to the reflective sheet 16 and another optical fiber probe 19 to the same distance to another reflective sheet 16;

The fiber optic bundle in the fiber optic probe 19 includes an incident optical fiber 191 and an outgoing optical fiber 192. The incident optical fiber 191 and the receiving optical fiber 192 are arranged parallel to each other in the optical fiber probe 19. There is one incident optical fiber 191, and the receiving optical fiber 192 is a single size parameter of 50 ± 3 The receiving optical fiber 192 is closely arranged to form a circular fiber bundle structure with the incident optical fiber 191 as the center, and the boundary distance between the incident optical fiber 191 and the receiving optical fiber 192 is 130-140 , the outgoing ends of the receiving optical fibers 192 in the two optical fiber probes 19 are respectively connected to a photosensitive element 2, and each photosensitive element 2 is correspondingly connected to a signal processing module 3;

The middle part of the end cover 13 is provided with a protruding part extending into the housing 11, the protruding part is a cylindrical structure matching the inner diameter of the housing 11, and a sealing ring 18 is arranged between the protruding part and the inner wall of the housing 11. The protrusion is provided with a spring positioning groove 132 along the length direction of the housing 11. The spring positioning groove 132 is an annular groove, and the inner diameter of the spring positioning groove 132 is less than or equal to the inner diameter of the spring 14, and the outer diameter of the spring positioning groove 132 is greater than or equal to that of the spring 14. Outer diameter, one end of the spring 14 extends and is fixed in the spring positioning groove 132, and a fluid through hole 17 communicating with the inner cavity of the housing 11 is respectively opened on the side walls at both ends of the housing 11, and each fluid through hole 17 is connected with the inner cavity of the housing 11. The protrusion on the end cover 13 at this end corresponds to the position of the protrusion corresponding to the fluid through hole 17. There is a through hole 133 communicating with the spring positioning groove 132. The fluid passes through the fluid through hole 17 and the through hole in turn. 133 flows into the cavity inside the housing 11.

Claims (10)

1. a kind of single-piston damp type optical fiber differential pressure pickup, it is characterised in that：Including sonde configuration（1）, light-sensitive element（2）With Signal processing module（3）, the sonde configuration（1）Including housing（11）, housing（11）It is tubular construction, housing（11）Interior slip It is provided with piston（12）, piston（12）Two ends be respectively arranged with a spring（14）, two springs（14）One end fix In piston（12）On, housing（11）Two ends seal be fixed with end cap respectively（13）, two springs（14）The other end it is solid respectively Due to corresponding end cap（13）On, two end caps（13）On relative position on offer end cap where insertion respectively （13）Probe insertion（131）, two probe insertions（131）Inside sealing is provided with light transmission piece respectively（15）, two probe insertions （131）It is interior positioned at light transmission piece（15）Outside be respectively arranged with sensing piston（12）Fibre-optical probe（19）, fibre-optical probe（19） And piston（12）End face it is perpendicular, piston（12）Two ends and fibre-optical probe（19）It is respectively fixed with relative position reflective Piece（16）, housing（11）On the side wall at two ends or two end caps（13）It is upper to offer one and housing respectively（11）Inner space Fluid through-hole（17）, two fibre-optical probes（19）It is middle receive optical fiber exit end respectively with a light-sensitive element（2）It is connected, each Light-sensitive element（2）Correspondence is connected with a signal processing module（3）.

2. a kind of single-piston damp type optical fiber differential pressure pickup according to claim 1, it is characterised in that：Fibre-optical probe（19） In fibre bundle include incident optical（191）And the output optical fiber（192）, incident optical（191）With reception optical fiber（192）In optical fiber Probe（19）It is interior arranged in parallel, incident optical（191）Totally one, receive optical fiber（192）It is that single dimensional parameters are 50 ± 3Multimode fibre, receive optical fiber（192）With incident optical（191）Centered on successively closely arrangement composition one circle optical fiber Binding structure, and incident optical（191）With reception optical fiber（192）Between frontier distance be 130-140。

3. a kind of single-piston damp type optical fiber differential pressure pickup according to claim 1, it is characterised in that：Two springs（14） Structure and specification all same, in fluid through-hole（17）In the state of being connected with outside atmosphere, piston（12）Positioned at housing （11）Centre position, two springs（14）It is in nature.

4. a kind of single-piston damp type optical fiber differential pressure pickup according to claim 1, it is characterised in that：Two probe insertions （131）End cap where being opened in（13）Center position, two probe insertions（131）, piston（12）Three is coaxial, natural Under state, one of fibre-optical probe（19）To the fibre-optical probe（19）Corresponding reflecting piece（16）Distance and another light Fibre probe（19）To another reflecting piece（16）Distance it is identical.

5. a kind of single-piston damp type optical fiber differential pressure pickup according to claim 1, it is characterised in that：Light transmission piece（15）For Sheet glass, light transmission piece（15）May be contained within probe insertion（131）Positioned at end cap（13）The port of inner side.

6. a kind of single-piston damp type optical fiber differential pressure pickup according to claim 1, it is characterised in that：Probe insertion （131）Inside it is provided with internal thread, fibre-optical probe（19）It is tightened respectively in probe insertion（131）It is interior.

7. a kind of single-piston damp type optical fiber differential pressure pickup according to claim 1, it is characterised in that：End cap（13）In Portion is provided with and stretches into housing（11）Sealing ring is provided between interior lug boss, lug boss and housing (11) inwall（18）, it is raised Along housing in portion（11）Length direction offer spring locating slot（132）, spring locating slot（132）It is annular groove, and spring Locating slot（132）Internal diameter be less than or equal to spring（14）Internal diameter, spring locating slot（132）External diameter is more than or equal to spring（14）It is outer Footpath, spring（14）One end stretch and be fixed on spring locating slot（132）It is interior.

8. a kind of single-piston damp type optical fiber differential pressure pickup according to claim 1, it is characterised in that：Lug boss is and shell Body（11）The cylindrical structural that internal diameter matches.

9. a kind of single-piston damp type optical fiber differential pressure pickup according to claim 1, it is characterised in that：Two fluid through-holes （17）Housing is opened in respectively（11）On the side wall at two ends, each fluid through-hole（17）With the end cap positioned at the end（13）On it is convex The portion of rising is corresponding, correspondence fluid through-hole on lug boss（17）Position at offer and spring locating slot（132）What is be connected is logical Hole（133）, fluid passes sequentially through fluid through-hole（17）And through hole（133）It is flowed into housing（11）In internal chamber.

10. a kind of single-piston damp type optical fiber differential pressure pickup according to claim 1, it is characterised in that：Piston（12）With Sealing ring is provided between the inwall of housing (11)（18）, end cap（13）With housing（11）Inwall between be also equipped with sealing ring （18）.