Graded alarm method and system adaptive to fan resonance

Abstract

The invention discloses a grading alarm method and system adaptive to fan resonance, and relates to the technical field of wind power. Comprising the following steps: carrying out a fan frequency knocking test, and calculating average inherent frequency of all blades and fan inherent frequency; calculating the rotation frequency at the rated rotation speed according to the rated operation rotation speed, and calculating the rotation frequency and the passing frequency at different operation rotation speeds; the rotation frequency and the passing frequency at different operation rotation speeds and the inherent frequency of the fan are compared, and resonance interference rotation is determined; establishing a scoring system, and calculating the score of the current operation state; and determining an alarm level according to the score of the current operation state, and triggering an alarm. According to the invention, comprehensive judgment is carried out from the global characteristics of the system, the vibration condition generated by resonance is warned, subsequent expansion can be continued to be compatible with an automatic adjustment means, and integrated automatic control of alarm and avoidance is realized.

Description

Technical Field

[0001] The present invention relates to the field of wind power technology, and in particular to a hierarchical alarm method and system adapted for wind turbine resonance. Background Art

[0002] In the current power industry, speed regulation of rotating machinery is widely used, not only in large fans, but also in high-power water pumps. However, after the speed regulation of the rotating machine, its inherent frequency will inevitably resonate with the rotation frequency and the passing frequency. When the resonance is excited, it will cause great harm to the equipment itself. In recent years, the frequent impeller breakage, main shaft breakage, and bearing damage accidents of power plant fans are mostly caused by resonance, which seriously affects the safety and economic benefits of power companies, and also causes great obstacles to the people's livelihood and industrial development.

[0003] With the current technology, it is almost impossible to eliminate the resonance phenomenon of equipment. For equipment whose resonance frequency has been figured out, it can be circumvented through adjustment. Even so, as the equipment runs, wear, dust accumulation, etc. will cause changes in its inherent frequency, so it is necessary to make regular adjustments based on the actual situation of the equipment, which has great limitations. Summary of the invention

[0004] In view of the existing problem that when resonance is excited, great harm will be caused to the device itself, the present invention is proposed.

[0005] Therefore, the problem to be solved by the present invention is how to make an alarm strategy with comprehensive evaluation by analyzing the natural frequency and considering the difficulty of exciting resonance and the intensity of hazard when the natural frequency of the equipment is known.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0007] In the first aspect, an embodiment of the present invention provides a graded alarm method adapted for fan resonance, which includes performing a fan frequency knocking test to calculate the average natural frequency of all blades and the natural frequency of the fan; calculating the rotation frequency at the rated speed according to the rated operating speed, and calculating the rotation frequency and the pass frequency at different operating speeds; comparing the rotation frequency and the pass frequency at different operating speeds and the natural frequency of the fan to determine the resonance interference speed; establishing a scoring system and calculating the score of the current operating status; determining the alarm level according to the score of the current operating status, and triggering an alarm and recording.

[0008] As a preferred scheme of the graded alarm method adapted to fan resonance described in the present invention, the calculation of the average natural frequency of all blades includes the following steps: selecting m0 test points on the fan blades; performing a tapping test using an eddy current sensor at each test point; recording the 1st to nth order natural frequencies of each test point, averaging the square of the data from the m0 test points, and calculating the average natural frequency of the blade; wherein m0 is a constant.

[0009] As a preferred solution of the hierarchical alarm method adapted to fan resonance of the present invention, the natural frequency of the fan is calculated by arithmetically squaring the natural frequencies of all blades.

[0010] As a preferred solution of the hierarchical alarm method adapted to fan resonance of the present invention, wherein: the rotation frequency is calculated according to the rated operating speed: according to the rated operating speed n e Calculate the rotation frequency (Hz):

[0011] υ r =n e / 60

[0012] Combined with the number of fan blades M, calculate the passing frequency of the fan at rated speed:

[0013] υ t =υ r ×M

[0014] Calculation of the rotation frequency and passing frequency at different operating speeds includes: According to the ratio relationship, the fan N times the rated speed is obtained. t and r ; When the fan speed increases from 0 to the rated speed n e , then there will be (0,1,2...,n e ) rotation frequency and passing frequency, denoted as υ t，N and r，N .

[0015] As a preferred solution of the graded alarm method adapted for wind turbine resonance described in the present invention, the scoring system includes a vibration monitoring condition score POV, a resonance excitation score PORE and a resonance speed deviation score DORE; the scoring system is calculated using a scoring method of (PORE×DORE+POV).

[0016] As a preferred solution of the hierarchical alarm method adapted to fan resonance of the present invention, when the scoring system is implemented, the fan operation has the following conditions: if the fan speed is at the core position where the resonance occurs, that is, And the vibration exceeds the alarm value; if the fan speed is at the core position where resonance occurs, that is However, the vibration does not exceed the alarm value; if the fan speed is at a higher position where resonance occurs, that is, But the vibration exceeds the alarm value; if the fan speed is at a higher position where resonance occurs But the vibration does not exceed the alarm value; if the fan speed is in a safe position But the vibration exceeds the alarm value; different scores are output according to different fan operating conditions.

[0017] As a preferred solution of the hierarchical alarm method adapted to fan resonance described in the present invention, the alarm includes: setting a multi-color alarm, displaying an alarm button on the DCS screen, and performing cumulative statistics of the alarm time in the background.

[0018] In the second aspect, an embodiment of the present invention provides a graded alarm system adapted to fan resonance, which includes: a frequency knocking test module, used to perform a fan frequency knocking test, calculate the average natural frequency of all blades, and obtain the natural frequency of the fan; a rotation frequency calculation module, which calculates the rotation frequency at the rated speed according to the rated operating speed, and calculates the rotation frequency and pass frequency at different operating speeds; a frequency matching and resonance detection module, which compares the rotation frequency and pass frequency at different operating speeds and the natural frequency of the fan to determine the resonance interference speed; a subsystem module, which is used to establish a scoring system and calculate the score of the current operating status; an alarm triggering and recording module, which is used to determine the alarm level according to the score of the current operating status and trigger an alarm.

[0019] In a third aspect, an embodiment of the present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, wherein: when the computer program instructions are executed by the processor, the steps of the graded alarm method adapted to wind turbine resonance as described in the first aspect of the present invention are implemented.

[0020] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program instructions are executed by a processor, the steps of the graded alarm method adapted to wind turbine resonance as described in the first aspect of the present invention are implemented.

[0021] The beneficial effects of the present invention are as follows: the present invention uses a comprehensive scoring mechanism to issue an alarm based on the known resonance frequency, combined with a certain avoidance rate and real-time vibration monitoring data of the fan, to give the operator an equipment operation warning, and to judge the current vibration jump generated according to the same current and historical operating state of the equipment, and issue a warning, and collect information in the comprehensive scoring mechanism for alarm. It can be seen that the present invention makes a comprehensive judgment based on the overall characteristics of the system, issues a warning for the vibration caused by resonance, and can continue to expand compatibility with automatic adjustment means in the future to achieve integrated automatic control of alarm + avoidance. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0023] Figure 1 This is a hierarchical alarm configuration diagram adapted for fan resonance.

[0024] Figure 2 Schematic diagram of the blower blade impact points. DETAILED DESCRIPTION

[0025] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the accompanying drawings.

[0026] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0027] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0028] Example 1

[0029] Reference Figure 1-2 , which is the first embodiment of the present invention, provides a hierarchical alarm method adapted to fan resonance, comprising:

[0030] S1: Perform a frequency tapping test on the fan to calculate the average natural frequency of all blades and the natural frequency of the fan.

[0031] S1.1: Select m0 test points on the fan blade, wherein m0 in the present invention is 4 (TAP POINT 1-4).

[0032] Among them, the test point is located at 1 / 2 of the blade tip width w, and the four test points are located at 1 / 5h, 2 / 5h, 3 / 5h and 4 / 5h of the blade height h respectively.

[0033] S1.2: Perform a tap test using an eddy-current sensor at each test point.

[0034] like Figure 2 As shown in the figure, the eddy current sensor is attached to each TAP POINT position, and the blade is struck to stimulate the natural frequency (υ g，1x ~υ g，nx ), where υ g，1x Expressed as the first-order natural frequency of the blade, υ g，nx Expressed as the nth order natural frequency of the blade.

[0035] S1.3: Record and calculate the natural frequency of each blade.

[0036] Record the 1st to nth order natural frequencies (υ g，1x，1 ~υ g，nx，1 , g，1x，2 ~υ g，nx，2 , g，1x，3 ~υ g，nx，3, , g，1x，4 ~υ g，nx，4 The data of the four test points are squared and averaged to obtain the average natural frequency (υ g，1x，avg ~υ g，nx，avg ).

[0037] S1.4: Calculate the average natural frequency of all blades to obtain the natural frequency of the fan.

[0038] The natural frequency of all blades is squared to obtain the natural frequency of the fan. g,f，1x ~υ g, f ，nx .

[0039] S2: Calculate the rotation frequency at the rated speed according to the rated operating speed, and calculate the rotation frequency and passing frequency at different operating speeds.

[0040] Preferably, according to the rated operating speed n e Calculate the rotation frequency: υ r =n e / 60, the unit is Hz (Hertz), and combined with the number of fan blades M, the passing frequency of the fan at rated speed is calculated:

[0041] υ t =υ r ×M

[0042] At the same time, according to the ratio relationship, the fan N times υ at rated speed can be obtained. t and r ;

[0043] Similarly, when the fan speed increases from 0 to the rated speed n e, then there will be (0,1,2...,n e ) rotation frequency and passing frequency, denoted as υ t，N and r，N .

[0044] S3: Compare the rotation frequency and passing frequency at different operating speeds and the natural frequency of the fan to determine the resonant interference frequency.

[0045] Compare the calculated rotation frequency υ t，N , through frequency υ r，N When the frequency multiples and the natural frequency of the fan are close to or even equal to the natural frequency of a certain order of the fan, the rotation frequency v is considered r，N and the passing frequency υ t，N The corresponding fan speed is the resonance interference speed.

[0046] S4: Establish a scoring system and calculate the score of the current operating status.

[0047] Depend on Figure 1 It can be seen that the configuration of the present invention mainly consists of three parts, including: POV is the vibration monitoring condition scoring, which evaluates the vibration output monitored by the system in real time and outputs the evaluation results;

[0048] PORE is the resonance excitation score, which is evaluated by correctly selecting the monitoring speed and converting the function to evaluate the output when the monitoring speed reaches res1x~res4x and the speed gear.

[0049] DORE is the resonant speed deviation score, which evaluates the deviation between the selected resonant speed range and the actual speed and finally draws an evaluation.

[0050] Considering the intensity of resonance, the general principle is that no matter what the cause of the resonance phenomenon is, it should be avoided. The lower the order of the natural frequency of the equipment, the easier it is to excite resonance, and the higher the order, the more difficult it is to excite the resonance phenomenon. Therefore, the resonance phenomenon caused by the natural frequency of the equipment should be rated from level one to level four according to the difficulty of being excited. That is, the resonance caused by interference with the first-order natural frequency is level one, and so on, the resonance caused by interference with the fourth-order natural frequency is level four.

[0051] The 1st to 4th order natural frequencies of the equipment are defined as Res 1X ~Res 4X , then the corresponding excitation Res 1X ~Res 4X The resonance-causing ratings are defined as Lvr1 to Lvr4.

[0052] At the same time, the speed that will excite the equipment resonance is defined as Rev. Generally, there may be more than one speed point that may excite resonance in a rotating machine. According to the number of speed points, it is defined as Rev1~Rev n1 , where n1 is the number of resonant speed points.

[0053] Furthermore, the resonance excitation condition score (PORE) is:

[0054] According to the difficulty of exciting the natural frequency, Rev n To Res 1X ~Res 4X The phenomenon of mutual interference between the levels is given 7-4 points respectively. Generally, Res 1X Most easily stimulated, with a score of 4, Res 4X The most difficult to be motivated, the score is 7.

[0055] The Deviation from Resonance Speed ​​Condition Rating (DORE) is:

[0056] According to the deviation of the resonant speed, when the deviation between the actual operating speed of the fan and the resonant speed is within 1%, it is scored as 5 points; when the deviation is within 3%, it is scored as 4 points; when the deviation is within 5%, it is scored as 3 points; other speed ranges are scored as 0 points.

[0057] Among them, the deviation degree is the speed of any one cycle of the fan n x , and the actual fan speed n s The ratio is expressed as:

[0058]

[0059] The vibration monitoring condition scores (POV) are:

[0060] According to the DCS monitoring vibration data, reaching the alarm value is 10 points, reaching 80% of the alarm value is 8 points, and so on.

[0061] Preferably, the calculation of the scoring system includes:

[0062] It is proposed to adopt the scoring method of (PORE×DORE+POV).

[0063] When the system is implemented, the operation of the fan will present the following situations:

[0064] a. If the fan speed is at the core position where resonance occurs, that is If the vibration exceeds the alarm value, the system score output is 45 points;

[0065] b. If the fan speed is at the core position where resonance occurs, that is However, if the vibration does not exceed the alarm value, the system score output is 40 points;

[0066] c. If the fan speed is at a higher position where resonance occurs, that is However, if the vibration exceeds the alarm value, the system score output is 34 points;

[0067] d. If the fan speed is at a higher position where resonance occurs However, if the vibration does not exceed the alarm value, the system score output is 29 points;

[0068] e. If the fan speed is in a safe position But if the vibration exceeds the alarm value, the system score output is: 10 points.

[0069] S5: Determine the alarm level according to the score of the current operating status, and trigger the alarm and record.

[0070] Specifically, if the score is greater than or equal to 40 points, it is a red alarm, which means that the wind turbine has entered the core point of resonance and has a significant impact on the operation of the wind turbine;

[0071] If the score is greater than or equal to 20 points and less than 40 points, it is an orange alarm, which means that the fan has entered an area with a high resonance impact and has a certain impact on the operation of the fan;

[0072] If the score is greater than 10 points and less than 20 points, it is a yellow alarm, indicating that the fan has just entered the resonance range, but the monitoring data may not necessarily reflect the abnormality of the fan's operating status.

[0073] If the score is less than or equal to 10 points, it is in green operating state, the fan is not operating in the resonance area, and the fan score only reflects the vibration impact caused by other factors of the fan.

[0074] For red, orange and yellow alarms, not only should the alarm button be displayed on the DCS screen, but the alarm time should also be accumulated and counted in the background.

[0075] Furthermore, this embodiment also provides a hierarchical alarm system adapted to fan resonance, comprising:

[0076] Frequency knock test module, used to perform fan frequency knock test, calculate the average natural frequency of all blades, and obtain the natural frequency of the fan;

[0077] A rotation frequency calculation module calculates the rotation frequency at the rated speed according to the rated operating speed, and calculates the rotation frequency and the passing frequency at different operating speeds;

[0078] The frequency matching and resonance detection module compares the rotation frequency and passing frequency at different operating speeds and the natural frequency of the fan to determine the resonance interference frequency.

[0079] The subsystem module is used to establish a scoring system and calculate the score of the current operating status;

[0080] The alarm triggering and recording module is used to determine the alarm level according to the score of the current operating state and trigger the alarm.

[0081] This embodiment also provides a computer device, which is suitable for the case of a graded alarm method adapted for fan resonance, including a memory and a processor; the memory is used to store computer executable instructions, and the processor is used to execute computer executable instructions to implement the graded alarm method adapted for fan resonance as proposed in the above embodiment.

[0082] The computer device may be a terminal, and the computer device includes a processor, a memory, a communication interface, a display screen and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, an operator network, NFC (near field communication) or other technologies. The display screen of the computer device may be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device may be a touch layer covering the display screen, or a key, trackball or touchpad provided on the housing of the computer device, or an external keyboard, touchpad or mouse, etc.

[0083] This embodiment further provides a storage medium on which a computer program is stored. When the program is executed by a processor, the hierarchical alarm method adapted to wind turbine resonance as proposed in the above embodiment is implemented.

[0084] In summary, the present invention uses a comprehensive scoring mechanism to issue an alarm based on the known resonance frequency, combined with a certain avoidance rate and the real-time vibration monitoring data of the fan, to give the operator an equipment operation warning, and to judge the current vibration jump according to the same current and historical operating state of the equipment, and issue a warning, and collect information in the comprehensive scoring mechanism for alarm. It can be seen that the present invention makes a comprehensive judgment based on the overall characteristics of the system, and issues a warning for the vibration caused by resonance. It can be further expanded to be compatible with automatic adjustment means in the future, so as to achieve integrated automatic control of alarm + avoidance.

[0085] Example 2

[0086] Reference Figure 1 and Figure 2, which is the second embodiment of the present invention, and this embodiment provides a hierarchical alarm method adapted to fan resonance. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through experiments.

[0087] In order to verify the effectiveness of the graded alarm method adapted to fan resonance, this test selected three fans of model FX3000 as test objects, named fan A, fan B and fan C. The test mainly verifies the resonance characteristics of the fan at different speeds by measuring and analyzing the natural frequency of the fan blades and the resonance point of the fan, and triggers the alarm through the scoring system.

[0088] First, use an eddy current sensor to perform a tap test on the fan blades. Each fan blade is equipped with four test points (TAP POINT 1-4), which are located at 1 / 5h, 2 / 5h, 3 / 5h and 4 / 5h of the blade height and 1 / 2 of the width w. After the natural frequency of each test point is calculated by exciting the natural frequency of the blade, the data is squared and averaged to obtain the average natural frequency of each blade. Then, the average natural frequency of all blades is arithmetic squared to obtain the natural frequency of the entire fan.

[0089] The rotation frequency υr and the passing frequency υt of the fan are calculated from the rated speed. At the same time, in the process of speed from 0 to rated speed, the change of resonance frequency at different speeds is recorded, and the key resonance interference speed area is marked.

[0090] By comparing the fan's rotation frequency, pass frequency and its multiples with the fan's natural frequency, the fan's speed in the resonance area is identified, and the fan's operating status is scored through a scoring system. The three scoring elements include the vibration monitoring condition score (POV), the resonance excitation score (PORE) and the resonance speed deviation score (DORE), which are evaluated according to different speeds and vibration conditions.

[0091] Finally, the scoring system triggers the corresponding alarm level and records the alarm time according to different scoring values. When the score exceeds 40 points, a red alarm is triggered, indicating that the fan is in a serious resonance state; when the score is 2040 points, an orange alarm is triggered, indicating that the fan is in a high resonance impact area; when the score is 1020 points, a yellow alarm is triggered; when the score is less than or equal to 10 points, the alarm is green, indicating that the fan is operating normally.

[0092] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A hierarchical alarm method adapted to fan resonance, characterized in that: include, Conduct fan frequency knocking test to calculate the average natural frequency of all blades and the natural frequency of the fan; Calculate the rotation frequency at rated speed according to the rated operating speed, and calculate the rotation frequency and passing frequency at different operating speeds; Comparing the rotation frequency and the passing frequency at the different operating speeds and the natural frequency of the fan to determine the resonant interference rotation; Establish a scoring system and calculate the score of the current operating status; An alarm level is determined according to the score of the current operating status, and an alarm is triggered.

2. The hierarchical alarm method adapted to fan resonance according to claim 1, characterized in that: The calculation of the average natural frequency of all blades comprises the following steps: Select m0 test points on the fan blades; Tap testing was performed using eddy current sensors at each test point; The 1st to nth order natural frequencies of each test point are recorded, and the square average of the data of m0 test points is performed to calculate the average natural frequency of the blade; where m0 is a constant.

3. The hierarchical alarm method adapted to fan resonance according to claim 2, characterized in that: The fan natural frequency is calculated by squaring the natural frequencies of all blades.

4. The hierarchical alarm method adapted to fan resonance according to claim 3, characterized in that: The rotation frequency is calculated based on the rated operating speed: According to the rated operating speed n e Calculate the rotation frequency (Hz): u r =n e / 60 Combined with the number of fan blades M, calculate the passing frequency of the fan at rated speed: u t =υ r ×M Calculation of the rotational frequency and the passing frequency at different operating speeds includes: According to the ratio relationship, the fan N times υ at rated speed is obtained. t and r ; When the fan speed increases from 0 to the rated speed, e , then there will be (0,1,2...,n e ) rotation frequency and passing frequency, denoted as υ t，N and r，N .

5. The hierarchical alarm method adapted to fan resonance according to claim 4, characterized in that: The scoring system includes a vibration monitoring condition score POV, a resonance excitation score PORE and a resonance speed deviation score DORE; The scoring system is calculated using the scoring method of (PORE×DORE+POV).

6. The hierarchical alarm method adapted to fan resonance according to claim 5, characterized in that: When the rating system was implemented, the wind turbines operated in the following conditions: If the fan speed is at the core position where resonance occurs, that is, the deviation η≤3%, and the vibration exceeds the alarm value; If the fan speed is at the core position where resonance occurs, that is, the deviation η≤3%, but the vibration does not exceed the alarm value; If the fan speed is at a higher position where resonance occurs, that is, (3% < deviation η ≤ 5%), but the vibration exceeds the alarm value; If the fan speed is at a higher position where resonance occurs (3%<deviation η≤5%), but the vibration does not exceed the alarm value; If the fan speed is in a safe position (deviation η>5%), but the vibration exceeds the alarm value; Different scores are output according to different fan operating conditions.

7. The hierarchical alarm method adapted to fan resonance according to claim 6, characterized in that: The alarm includes: Set a three-color alarm, display the alarm button on the DCS screen, and perform cumulative statistics of the alarm time in the background to calculate the cumulative time the fan enters the resonance range, providing data basis for the interval of fan impeller inspection.

8. A hierarchical alarm system adapted to fan resonance, based on the hierarchical alarm method adapted to fan resonance according to any one of claims 1 to 7, characterized in that: Also includes, Frequency knock test module, used to perform fan frequency knock test, calculate the average natural frequency of all blades, and obtain the natural frequency of the fan; A rotation frequency calculation module calculates the rotation frequency at the rated speed according to the rated operating speed, and calculates the rotation frequency and the passing frequency at different operating speeds; The frequency matching and resonance detection module compares the rotation frequency and the passing frequency at different operating speeds and the natural frequency of the fan to determine the resonance interference frequency; The subsystem module is used to establish a scoring system and calculate the score of the current operating status; The alarm triggering and recording module is used to determine the alarm level according to the score of the current operating state and trigger the alarm.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the hierarchical alarm method adapted to wind turbine resonance as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the hierarchical alarm method adapted to wind turbine resonance as described in any one of claims 1 to 7 are implemented.

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