EP3234373A1

EP3234373A1 - Actuating drive for a control valve, in particular a steam turbine control valve, and method for operating same

Info

Publication number: EP3234373A1
Application number: EP15785149.4A
Authority: EP
Inventors: Hubert Schaber
Original assignee: Voith Patent GmbH
Current assignee: Voith Patent GmbH
Priority date: 2014-12-19
Filing date: 2015-10-28
Publication date: 2017-10-25
Also published as: CN107002716A; WO2016096221A1; CN107002716B; US20180274567A1; US10400799B2; DE102014226666B3

Abstract

The invention relates to an actuating drive for a control valve, in particular a steam turbine control valve, comprising a working cylinder, which has a piston and a piston rod, which is connected to the piston and which forms an actuator for the control valve, wherein the piston bounds a first pressure chamber of the working cylinder and the first pressure chamber has a first pressure connection for introducing a pressurized working medium in order to move the piston together with the piston rod against the force of a spring associated with the working cylinder by the application of pressure; comprising an external working-medium circuit, to which the working cylinder is connected in order to selectively introduce the working medium into or lead the working medium out of the first pressure chamber; wherein the external working-medium circuit has a working-medium pump driven by a motor; and the working-medium pump is connected to the first pressure connection of the first pressure chamber by means of a pressure line connected to a pressure side of the working-medium pump, wherein a check valve or stop valve that opens in the direction of the first pressure connection is provided in the pressure line. The actuating drive according to the invention is characterized in that a short-circuit line branches off from the pressure line before the check valve or stop valve in the flow direction of the working medium, which short-circuit line connects the pressure line to a suction side of the working-medium pump, the working cylinder thus being bypassed, and a short-circuit valve is arranged in the short-circuit line, by means of which short-circuit valve the short-circuit line can be selectively blocked so as to prevent flow of the working medium to the suction side.

Description

Actuator for a control valve, in particular steam turbine control valve

and method of operating the same

The present invention relates to an actuator for a control valve, in particular for a steam turbine control valve, according to the preamble of claim 1 and a method for operating the same.

In steam power plants, the steam generated by means of a steam generator is supplied to the steam turbine via at least one, usually two to four steam turbine control valves, in which it is expanded to produce mechanical work and subsequently supplied to a condenser for condensation. The steam turbine control valves are positioned in parallel steam supply lines of the steam turbine in order to be able to distribute the enormous steam volume flows to the various steam turbine control valves. Despite the distribution, the vapor flow rates per valve are still so large that the valves usually weigh several tons and corresponding to the valve body has a high weight, which must be moved by a correspondingly strong actuator. To drive the control valves therefore predominantly hydraulic or optionally also pneumatic actuators are usually used, which have a working cylinder with a piston connected to a piston rod as an actuator for the valve body of the respective control valve, by retracting the piston rod in and extending the piston rod the working cylinder to actuate the valve body, so that this, for example, in said steam power plant, more or less closes the flow cross-section of the steam turbine control valve.

To displace the piston with the piston rod in the working cylinder, the piston defines at least one pressure chamber into which a pressurized working medium, either a hydraulic working medium, for example oil, or a pneumatic working fluid, such as air, may be introduced to displace the piston against the force of a spring. The pressure of the working medium is established via a working medium pump in the external working medium circuit to which the working cylinder is connected with at least one corresponding pressure port of the pressure chamber. Since the external working medium circuit, as in one embodiment of the present invention, is generally designed as a closed circuit, this usually also has a tank line in addition to a pressure line, via which the pressurized working fluid from the working medium pump is introduced into the first pressure chamber , the working fluid via a second pressure port of a second pressure chamber from the second pressure chamber, which is positioned on the side facing away from the first pressure chamber side of the piston and separated from the first pressure chamber via the piston, and for example, the suction side of the working medium pump supplies. As a result, a double-acting cylinder for extending and retracting the piston can be created.

EP 0 055 351 A1 describes a corresponding electrohydraulic actuator, with a two-sided working cylinder connected to an external working medium circuit, wherein in the external working medium circuit a working medium pump delivers working fluid from a working fluid reservoir via a check valve into either a first pressure chamber or a second pressure chamber of the working cylinder Extend piston rod with the same effect as the force of a compression spring or retract against the force of the compression spring. About the position of the piston or the piston rod, the degree of opening of a turbine control valve is determined. For coarse positioning of the piston in the working cylinder, a binary flow switch is provided as a four-way slide valve with three switch positions, the two control lines are connected to the pressure chambers on both sides of the piston in the cylinder and further via a pressure line to the pressure side of the pump and a Tank line is connected to the working medium supply. For fine positioning of the piston, an electro-hydraulic converter in the form of a pilot-operated servo valve is provided. A disadvantage of the actuator according to EP 0 055 351 A1 is that the efficiency is limited by the throttle losses at the control edges of the throttling directional control valves, which are designed as a continuous valves. Furthermore, high demands are placed on a constant supply pressure in order to be able to precisely regulate the position of the piston in the working cylinder.

DE 40 30 107 A1 describes a corresponding actuator in which throttle losses are largely avoided by continuous valves. According to this actuator, which also has a cylinder with two pressure chambers, which are connected to an external working medium circuit with a working medium pump is working with the working medium pump, which is designed as a fixed displacement pump and is driven by a variable speed motor, working fluid via an open in the direction of flow check valve pumped a first pressure chamber of the working cylinder, so that the piston with the piston rod against the force of a compression spring retracts. The disadvantage is that the extension of the piston rod is effected solely by the force of the compression spring, whereby the dynamic control behavior is determined asymmetrically and in the direction of the spring force by only the hydraulic-mechanical design of the flow resistance and can not be affected by electrical control signals. In addition, the working medium pump must be able to approach across all speed ranges against the pressure prevailing in the pressure chamber of the working cylinder pressure.

Also in the actuator according to EP 2 620 655 A1 throttling losses in continuous valves are largely avoided and also provided by a servomotor driven working fluid pump in the external working medium circuit is variable in speed and working fluid from a first Pressure chamber of the working cylinder in a second pressure chamber of the working cylinder and can pump vice versa, thereby quickly adjust the desired position of the piston and thus the piston rod. However, this also has the disadvantage that the working medium pump must be able to work across all speed ranges against the working medium pressure in the two pressure chambers of the working cylinder and a relatively expensive synchronous servomotor is necessary for dynamic and precise control. In addition, the working medium pump must be able to apply a holding pressure against the spring, with which the piston is pressurized, in the stationary state of the piston. The torque required for the holding pressure at low speed is a thermally unfavorable operating case for the motor of the working medium pump. The working medium pump tends to overheat at high pressures and low flow rate, which is required for fine positioning of the piston.

The present invention has for its object to provide an actuator for a control valve, in particular steam turbine control valve of the type described above, and a method for operating such an actuator, with which throttling losses in the external working medium circuit are advantageously avoided, the actuator has low manufacturing costs and advantageous Avoiding thermally unfavorable operating conditions of the working medium pump and a motor driving this works.

The object of the invention is achieved by an actuator and a method for operating the same according to the independent claims. In the dependent claims advantageous and particularly expedient embodiments of the invention are given.

An actuator according to the invention for a control valve, in particular a steam turbine control valve, has a working cylinder with an external working medium circuit connected thereto. The working cylinder comprises a piston with a piston rod connected thereto, which forms an actuator for the control valve. The piston rod is accordingly extendable from the working cylinder and retractable in this, thereby determining the opening cross section of the control valve, for example by direct or indirect connection of the piston rod to a valve body of the control valve, so that the valve body a flow cross-section of the control valve in dependence on the position of the piston rod more or less opens. The piston of the working cylinder limits at least a first pressure chamber of the working cylinder and the first pressure chamber has a first pressure port for introducing a pressurized working medium in the first pressure chamber to the piston with the piston rod against a force of a spring, in particular compression spring which is associated with the working cylinder to move by pressurization. For example, the piston rod moves increasingly with increasing pressure in the first pressure chamber in the working cylinder and with decreasing pressure in the first pressure chamber from the working cylinder. Advantageously, a second pressure chamber provided on the side of the piston remote from the first pressure chamber is increasingly exposed to working medium pressure at the same time as a decreasing pressurization in the first pressure chamber, as will be explained below.

About the external working medium circuit, which has a driven by a motor, such as electric motor (electric motor) working medium pump, pressurized working fluid can be pumped into the first pressure chamber. Furthermore, the working medium can be discharged from the first pressure chamber via the external working medium circuit. The working medium pump is for this purpose with a connected to a pressure side of the working medium pump pressure line to the first Pressure connection of the first pressure chamber connected, wherein in the pressure line in the direction of the first pressure port and thus the first pressure chamber opening check valve or a shut-off valve is provided. According to the invention branches from the pressure line in the direction of flow of the working fluid upstream of the check valve or shut-off valve, based on the flow direction of the working medium from the working medium pump in the first pressure chamber, a short circuit line which connects the pressure line, bypassing the working cylinder with a suction side of the working medium pump, wherein in the Shorting a short-circuit valve is arranged, by means of which the short-circuit line is optionally shut off. Shut-off here means any state of the short-circuit valve which prevents a flow of the working medium from the pressure line via the short-circuit line to the suction side of the working medium pump.

On the suction side of the working medium pump, for example, a working fluid supply, also called tank, may be provided, from which the working fluid pump pumps working fluid and / or used to compensate for volume fluctuations in the external working fluid circuit, for example due to the displacement of the piston in the working cylinder.

According to an advantageous embodiment of the invention, the short-circuit valve is designed as an uncontrolled open-close valve having only two switching positions, namely a first switching position in which it blocks a flow cross-section of the short-circuit line, and a second switching position in which it the flow direction of the short-circuit line releases or opens. To lock up the previously performed for the shutdown applies. Particularly advantageously, the working cylinder on a second pressure chamber with a second pressure port, wherein not under the term pressure port It is imperative to understand that the second pressure chamber is subjected to an overpressure from the outside.

The piston of the working cylinder separates the first pressure chamber from the second pressure chamber. Advantageously, a reversing line is provided in the external working medium circuit, via which the first pressure port of the first pressure chamber with the second pressure port of the second pressure chamber is connected working medium, wherein in the reversing a reversing valve is provided by means of which the reversing is optionally shut off. Thus, pressurized working fluid from the first pressure chamber via the reversing line can be passed into the second pressure chamber to move the piston with the piston rod with reduction of the first pressure chamber and enlargement of the second pressure chamber, for example, extend.

The reversing valve is advantageously designed as an uncontrolled open-close valve, which has only two switching positions, namely a first switching position in which it blocks the flow cross section of the reversing line, and a second switching position in which it releases or opens the flow cross section of the reversing line. Again, the same applies to the previous shut-off analog.

According to a particularly advantageous embodiment of the invention, a throttle is also provided in the reversing line, which either has a constant cross section or limits a variable flow cross section in the case of a variably adjustable throttle. Thus, the stroke speed of the piston can be set or adjusted variably.

According to an advantageous embodiment, a quick-closing line is provided in parallel to the reversing line in the external working medium circuit, in which a quick-acting valve is arranged. The quick-closing line connects the first pressure port of the first pressure chamber working medium conducting with the second pressure port of the second pressure chamber, when the quick-closing valve is opened. This makes it possible to quickly reach a fail-safe position to drive the piston or the piston rod in the appropriate position, for example, retracted into the cylinder by the force of the spring or extended from the cylinder by the force of the spring.

The quick-acting valve is advantageously designed as an uncontrolled open-close valve, which has only two switching positions, namely a first switching position in which it blocks the flow cross-section of the quick-closing line, and a second switching position in which it opens or opens the flow cross-section of the quick-closing line.

At the second pressure port of the second pressure chamber, a tank line may be connected, which is connected working medium conducting with the suction side of the working medium pump, in particular free of an intermediate valve or a throttle device. The tank line is referred to herein as a tank line due to their connection to the suction side of the working medium pump, which does not necessarily mean that a separate working medium tank or working fluid supply is provided. Advantageously, however, the working fluid supply is connected to this tank line, so that the working medium pump can promote working fluid from the working fluid supply. However, the working medium supply can also serve exclusively to compensate for volume fluctuations in the external working medium circuit and does not have to be designed as a throughflow of working medium.

The reversing line and / or the quick-closing line advantageously branches in the flow direction of the working medium behind the check valve or shut-off valve, again seen in the flow direction of the working medium of the Arbeitsmediunnpunnpe to the first pressure port or the first pressure chamber, from the pressure line and opens into the tank line.

According to one embodiment branches off in the flow direction of the working fluid in front of the check valve or shut-off valve, a pressure relief line with a pressure relief valve from the pressure line and flows into the tank line. Also, the pressure relief valve may be designed as uncontrolled open-close valve, that is, only two switching positions, namely a first switching position in which it blocks the flow cross-section of the pressure relief line, and a second switching position in which it releases the flow cross section of the pressure relief line. With the pressure relief line and the pressure relief valve unwanted pressure in the pressure line or on the pressure side of the pump can be avoided. The embodiment of the invention makes it possible that the motor, with which the working medium pump is driven, is designed as an electric asynchronous motor, which need not be able to run up against the working medium pressure in the first pressure chamber. Rather, the switched off especially in the stationary state of the working valve working medium pump, usually when the engine is de-energized when now the piston of the working valve can be moved with the piston rod, are first raised without pressure, without the engine a significant load torque must be absorbed.

An inventive method for operating an actuator therefore provides that for moving the piston and thus the piston rod to actuate the control valve, first the working medium pump is open with open short-circuit valve and closed check valve or shut-off valve with the engine at nominal speed and only then the Short-circuit valve is closed and working fluid with the working medium pump through the open check valve, which then automatically due to the pressure build-up after closing the short-circuit valve opens, or the shut-off valve, which can be opened in particular actively activated, is pumped into the first pressure chamber to move the piston rod against the force of the spring, for example, to retract into the working cylinder.

The invention has the advantage that an electric asynchronous motor is much cheaper than a servomotor, which can ramp up lastmomentbeaufschlagt. Furthermore, simple (unregulated) switching valves instead of control valves can be used, which avoids throttle losses. It is also possible to control the actuator with digital signals, that is, on-off signals, instead of control signals. Thus, for example, by clocked switching the short-circuit valve, the position of the piston in the working cylinder and thus the position of the piston rod can be adjusted. When the desired position has been reached, the engine can continue running with low energy consumption when the short-circuit valve is open, because it operates almost without load, or it can be switched off.

By opening the reversing valve, the spring force of the working cylinder can be used to change the position of the piston and thus the piston rod by pressure is discharged from the first pressure chamber, in the second pressure chamber and / or the working medium supply. If a variable throttle is provided in series with the reversing valve in the reversing line, the stroke speed of the working cylinder can be adjusted while reducing the volume of the first pressure chamber, despite the use of an open-close valve as a reversing valve.

Additionally or alternatively, it is possible to adjust the lifting speed in the case mentioned by clocked driving of the reversing valve. Although a preferred area of application of the actuator is the drive of a steam turbine control valve, the actuator can also drive other Control valves are used for example by gas turbines or other aggregates.

The invention will be described below by way of example with reference to an embodiment and the figure.

1 shows an embodiment of an inventively designed actuator is shown. The actuator controls, for example, the position of the valve body 100 relative to a valve seat 101 of a steam turbine control valve 102 shown here only schematically in the steam supply 103 of a steam turbine 104.

The actuator has a working cylinder 1 with a piston 2 and a piston rod 3 connected thereto, the piston rod 3 representing the actuator for the steam turbine control valve 102.

The piston 2 is biased by a spring 4 in the sense of closing the control valve, here steam turbine control valve 102. In the direction of the spring force, the piston rod 3 moves in the embodiment shown from the working cylinder 2, wherein in another embodiment, a retraction of the piston rod 3 could cause a closing of the control valve and correspondingly the piston would have to be biased in the other direction by the spring force. Of course, applications are conceivable in which the spring causes an opening of the control valve.

The working cylinder 1 has a first pressure chamber 5 with a first pressure port 6. By introducing pressurized working fluid into the first pressure chamber 5 and increasing the volume of the first pressure chamber 5, the piston rod 3 is retracted into the working cylinder 1 counter to the force of the spring 4 and the valve body 100 lifted from the valve seat 101, or in general open the control valve. This is a second Pressure chamber 7 on the side facing away from the first pressure chamber 5 of the piston 2 in the working cylinder reduced in volume and the working fluid from the second pressure chamber 7 is displaced via the second pressure port 8 into the tank line 9 of the external working medium circuit 10. The tank line 9, for example, substantially unpressurized and connected to the working medium supply 1 1, which compensates for the difference in volume of the working cylinder 1 between extended and retracted position of the piston rod 3. However, there are also external working medium circuits 10 with pressurized tank line 9 into consideration.

In the external working medium circuit 10, a driven by a motor 12 working fluid pump 13 is provided, which has a suction side 14 and a pressure side 15. On the suction side 14, the tank line 9 is connected to the pressure side 15, a pressure line 16 is connected.

The pressure line 16 is connected at its end facing away from the working medium pump 13 at the first pressure port 6 of the first pressure chamber 5, so that the working medium pump 13 can pump working fluid from the tank line 9 and / or from the working fluid supply 1 1 via the pressure line 16 into the first pressure chamber 5.

The working medium pump 13 is designed for example as a fixed displacement pump, which is designed in terms of their delivery volume to a single rated speed. The motor 12 is designed, for example, as an electric asynchronous motor.

In the pressure line 16, a check valve 17 is provided which opens in the direction of the first pressure port 6 and in the direction of the working medium pump 13 and the pressure side 15 of the same blocks. Thus, when the working fluid pump 13 is turned off in the pressurized state of the first pressure chamber 5, the working fluid is held in the first pressure chamber 5 when the check valve 17 is closed. Instead of the check valve 17 could be provided a shut-off valve that is driven, for example, externally, in particular together with the short-circuit valve 19 described below. Upstream of the check valve 17 branches off from the pressure line 16 from a short-circuit line 18, which opens into the tank line 9 and thus on the suction side 14 of the working medium pump 13. In the short-circuit line 18, a short-circuit valve 19 is provided which connects the pressure side 15 of the working medium pump 13, bypassing the working cylinder 1 with the suction side 14 and the working medium supply 1 1 via the short-circuit line 18 in the de-energized state. In the activated state, however, the short-circuit valve 19 prevents a flow of working fluid from the pressure side 15 via the short-circuit line 18 to the suction side 14, so that a pressure builds up on the pressure side 15 in the pressure line 16, which opens the check valve 17 against the spring force of the check valve 17 ,

As long as the short-circuit line 18 is open to connect the pressure side 15 to the suction side 14, the motor 12 can run up without load torque to the rated speed and bring the working fluid pump 13 to its rated speed. After reaching the rated speed can then by operating the short-circuit valve 19, the working medium pump 13 pumping working fluid via the check valve 17 into the first pressure chamber 5 and the piston rod 3 moves, as shown, against the force of the spring 4 in the working cylinder 1 a. By the timing of the operation of the short-circuit valve 19, the desired position of the piston 2 and the piston rod 3 and thus of the valve body 100 relative to the valve seat 101 can be achieved. The motor 12 can then continue to run with low energy requirements or it can be switched off completely. If the piston rod 3, however, be extended, the reversing valve 20 is actuated in the reversing line 21, which downstream of the Check valve 17 branches off from the pressure line 16 and opens into the tank line 9, and the spring force of the spring 4, the working fluid from the first pressure chamber 5 via the reversing 21 in the tank line 9 or the working fluid supply 1 1 displace. With the adjustable throttle 22 provided here in the reversing line 21, the lifting speed of the working cylinder 1 can be adjusted during extension of the piston rod 3 and at the same time the reversing valve 20 can be designed as an uncontrolled open-close valve. Parallel to the reversing line 21 branches from the pressure line 16 still the quick-closing line 23 and flows into the tank line 9 a. By opening the quick-closing valve 24, the steam turbine control valve 102 can be quickly brought into the fail-safe position, for which the piston rod 3 is extended from the working cylinder 1. Again, the lifting speed can be adjusted by means provided in the quick-closing line 23 throttle 25 and the quick-closing valve 24 can be designed as an uncontrolled open-close valve.

Finally, from the pressure line 16 upstream of the check valve 17, the excess pressure line 26 branches off, in which the pressure relief valve 27, also called pressure relief valve, is arranged. The overpressure line 26 also opens into the tank line 9. The pressure relief valve 27 limits the maximum pressure in the pressure line 16.

Claims

Claims Actuator for a control valve, in particular steam turbine control valve (102)

with a working cylinder (1) which has a piston (2) and a piston rod (3) connected thereto, which forms an actuator for the control valve, the piston (2) delimiting a first pressure chamber (5) of the working cylinder (1) and the first pressure chamber (5) has a first pressure connection (6) for introducing a pressurized working medium to the piston

(2) with the piston rod

(3) against the force of a spring assigned to the working cylinder (1).

(4) to displace by pressurization;

with an external working medium circuit (10), to which the working cylinder (1) is connected, in order to selectively introduce the working medium into or out of the first pressure chamber (5); wherein the external working medium circuit (10) has a working medium pump (13) driven by a motor (12); and

the working medium pump (13) is connected to the first pressure connection (6) of the first pressure chamber (5) with a pressure line (16) connected to a pressure side (15) of the working medium pump (13), with a pressure line (16) in the direction of the first pressure port (6) opening check valve (17) or shut-off valve is provided;

characterized in that

A short-circuit line (18) branches off from the pressure line (16) in the flow direction of the working medium in front of the check valve (17) or shut-off valve, which connects the pressure line (16) to a suction side (14) of the working medium pump (13), bypassing the working cylinder (1). , and a short-circuit valve (19) is arranged in the short-circuit line (18), by means of which the short-circuit line (18) can optionally be shut off against the flow of the working medium to the suction side (14). Actuator according to claim 1, characterized in that the short-circuit valve (19) is designed as an unregulated open-close valve, which exclusively has two switching positions, namely a first switching position, in which there is a flow cross section of the short-circuit line (18) against the flow of working medium Suction side (14) blocked, and a second switching position in which it releases the flow cross section of the short-circuit line (18).

Actuator according to one of sprays 1 or 2, characterized in that the working cylinder (1) has a second pressure chamber (7) with a second pressure connection (8), the piston (2) forming the first pressure chamber

(5) separates from the second pressure chamber (7), and in the external working medium circuit (10) a reversing line (21) is provided, via which the first pressure connection (6) is connected to the second pressure connection (8) in a working medium-conducting manner, and in which a reversing valve (20) is provided, by means of which the reversing line (21) can be selectively shut off.

Actuator according to claim 3, characterized in that the reversing valve (20) is designed as an uncontrolled open-close valve which exclusively has two switching positions, namely a first switching position in which it blocks a flow cross section of the reversing line (21), and a second Switching position in which it releases the flow cross section of the reversing line (21).

Actuator according to one of claims 3 or 4, characterized in that a throttle (22), in particular a variably adjustable throttle (22), is provided in the reversing line (21).

6. Actuator according to one of claims 3 to 5, characterized in that a quick-action line (23) with a quick-action valve (24) is provided parallel to the reversing line (21) in the external working medium circuit (10), via which the first pressure connection (6) conducts the working medium can be connected to the second pressure connection (8), the quick-closing valve (24) being designed in particular as an unregulated open-close valve which exclusively has two switching positions, namely a first switching position in which it blocks a flow cross section of the quick-closing line (23), and one second switching position, in which it releases the flow cross section of the quick-action line (23).

7. Actuator according to one of claims 3 to 6, characterized in that a tank line (9) is connected to the second pressure connection (8), which is connected to the suction side (14) of the working medium pump (13) in a working medium-conducting manner, in particular free of one intermediate valve or throttle device, and the reversing line (21) branches off from the pressure line (16) in the flow direction of the working medium behind the check valve (17) or shut-off valve and opens into the tank line (9).

8. Actuator according to claim 7, characterized in that in the flow direction of the working medium in front of the check valve (17) or shut-off valve, an overpressure line (26) with an overpressure valve (27) branches off from the pressure line (16) and opens into the tank line (9), wherein the pressure relief valve (27) is designed in particular as an unregulated on-off valve which exclusively has two switching positions, namely a first switching position in which it blocks a flow cross section of the pressure relief line (26), and a second switching position in which it blocks the flow cross section of the pressure relief line (26) releases.

9. Actuator according to one of claims 1 to 8, characterized in that the motor (12) is designed as an electric asynchronous motor.

10. A method for operating an actuator according to one of claims 1 to 9, characterized in that in order to move the piston (2) with the piston rod (3) in order to actuate the control valve, first the working medium pump (13) with the short-circuit valve (19 ) and closed check valve (17) or shut-off valve with the motor (12) is ramped up to nominal speed without pressure and then the short-circuit valve (19) is closed against flow of working medium to the suction side (14) and working medium with the working medium pump (13) via the open check valve (17) or shut-off valve is pumped into the first pressure chamber (5) in order to move the piston rod (3) against the force of the spring (4).