CN117419063A - Test device and performance test method for centrifugal compressor of auxiliary power device - Google Patents
Test device and performance test method for centrifugal compressor of auxiliary power device Download PDFInfo
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- CN117419063A CN117419063A CN202310748791.5A CN202310748791A CN117419063A CN 117419063 A CN117419063 A CN 117419063A CN 202310748791 A CN202310748791 A CN 202310748791A CN 117419063 A CN117419063 A CN 117419063A
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- 238000012360 testing method Methods 0.000 title claims abstract description 26
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- 230000001105 regulatory effect Effects 0.000 claims abstract description 19
- 230000000087 stabilizing effect Effects 0.000 claims abstract description 13
- 230000000903 blocking effect Effects 0.000 claims abstract description 12
- 208000006673 asthma Diseases 0.000 claims abstract 2
- 238000001228 spectrum Methods 0.000 claims description 6
- 238000004088 simulation Methods 0.000 claims description 4
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- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 claims description 3
- 238000004458 analytical method Methods 0.000 claims description 3
- 238000012545 processing Methods 0.000 claims description 3
- 230000004044 response Effects 0.000 claims description 3
- 238000007789 sealing Methods 0.000 claims description 3
- 239000000741 silica gel Substances 0.000 claims description 3
- 229910002027 silica gel Inorganic materials 0.000 claims description 3
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Classifications
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
- F04D—NON-POSITIVE-DISPLACEMENT PUMPS
- F04D27/00—Control, e.g. regulation, of pumps, pumping installations or pumping systems specially adapted for elastic fluids
- F04D27/001—Testing thereof; Determination or simulation of flow characteristics; Stall or surge detection, e.g. condition monitoring
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
- F04D—NON-POSITIVE-DISPLACEMENT PUMPS
- F04D17/00—Radial-flow pumps, e.g. centrifugal pumps; Helico-centrifugal pumps
- F04D17/08—Centrifugal pumps
- F04D17/10—Centrifugal pumps for compressing or evacuating
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Abstract
The invention discloses a test device and a performance test method of a centrifugal compressor of an auxiliary power device, which belong to the field of auxiliary power devices, and comprise a tested pressure air machine, a pressure stabilizing box, a dynamic pressure sensor, a total temperature probe, a total pressure probe, a volute, an exhaust switching section, a variable frequency motor, an exhaust main valve, an exhaust auxiliary valve, a de-asthma valve, an air inlet regulating valve, a gear box and a torsion meter, wherein the performance test method comprises the following steps: firstly, powering up a frequency motor to drive a tested centrifugal compressor to rotate, and obtaining a blocking point of the centrifugal compressor; gradually closing the main exhaust valve, and continuously collecting the pneumatic characteristics of the centrifugal compressor; dynamic pressure values at different positions on the casing are monitored through dynamic pressure sensors, and the flow instability boundary is accurately captured. The invention can collect the blocking point and the flow instability boundary of the centrifugal compressor at different folding rotational speeds, can rapidly and accurately obtain the stable working range and the pneumatic performance of the centrifugal compressor at the full rotational speed, and reduces the development cost and the risk of the centrifugal compressor of the auxiliary power device.
Description
Technical Field
The invention belongs to the technical field of auxiliary power, and particularly relates to a test device and a performance test method of a centrifugal compressor of an auxiliary power device.
Background
The auxiliary power unit (APU, auxil iary Power Unit) is used as one of the components of the second power system of the aircraft, and is widely applied to military and civil aircraft, such as military fighters, military transport aircraft, civil large airliners, civil public service aircraft, and the like. The APU has the characteristics of small volume, light weight, long service life, high reliability, capability of simultaneously outputting power and compressed air and the like, plays an important role in improving the safety, the guarantee and the comfort of an airplane and the comprehensive utilization rate of energy sources, has more than hundreds of products, and has become essential key airborne equipment of the airplane from tens of kilowatts to thousands of kilowatts in power.
The centrifugal compressor is used as one of the core components of the APU, plays an important role in improving the circulation parameters and the power-weight ratio of the core machine of the APU, meeting the air-entraining requirements of an aircraft engine under the conditions of starting, ground maintenance, cabin environment control and the like, realizes the deep fusion of the secondary power and the environmental control system through the air sharing of the components, improves the comprehensive and integrated degree of the system, and is the foundation for developing the APU core machine. How to accurately evaluate the stable working range of the centrifugal compressor, realize the measurement of the available stability margin of the compressor, avoid the flow instability of the compressor and become a hot spot problem which is always concerned in recent years at home and abroad. However, since the numerical simulation cannot rapidly and accurately predict the stable working range of the centrifugal compressor, the reliability is insufficient, and in the aspects of a centrifugal compressor test device and a performance test method, a large-flow axial flow compressor test method is mostly used, the incoming flow angles of different inlets are less to measure, the blocking boundary is possibly not tested, and the test cost is high; and whether the centrifugal compressor is in a stable working range is judged through sound, the reliability is low, and the method is not suitable for modern advanced small-size centrifugal compressors.
Disclosure of Invention
The technical problems to be solved by the invention are as follows:
in order to overcome at least one defect of the prior art and improve the accuracy of a performance test method of a centrifugal compressor, the invention discloses a test device and a performance test method of an auxiliary power device centrifugal compressor, and solves the test difficulty of a modern small-size high-pressure ratio centrifugal compressor.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the test device of the centrifugal compressor of the auxiliary power device comprises a tested centrifugal compressor and is characterized by further comprising a pressure stabilizing box, a dynamic pressure sensor, a total temperature probe, a total pressure probe, a volute, an exhaust switching section, a variable frequency motor, an exhaust main valve, an exhaust auxiliary valve and an anti-asthma valve; the air enters the pressure stabilizing box, the pressure stabilizing box is connected with the tested centrifugal compressor, the volute is arranged behind the tested centrifugal compressor, the exhaust auxiliary valve and the relief valve are arranged on the exhaust switching section of the downstream of the volute in parallel, the exhaust main valve is arranged behind the exhaust switching section, the total temperature probe, the total pressure probe and the dynamic pressure sensor are all arranged in the flow channel of the tested centrifugal compressor, and the variable frequency motor is connected with the tested centrifugal compressor to drive the tested centrifugal compressor to rotate.
Preferably, the device also comprises an air inlet regulating valve and a gear box, wherein the air inlet regulating valve is arranged on an inlet pipeline of the pressure stabilizing box, and the front end of the air inlet regulating valve is provided with a flow measuring device; the variable frequency motor drives the tested centrifugal compressor to rotate through the gear box.
Preferably, the device further comprises a torsion meter, wherein the torsion meter is arranged on an output shaft of the variable frequency motor and is used for measuring the torque of the tested centrifugal compressor and the output shaft of the variable frequency motor.
Preferably, the tested centrifugal compressor comprises a flow passage formed by a hub and a casing, and an inlet variable camber guide vane, a centrifugal impeller, a diffuser and a volute are arranged in the flow passage according to the direction from front to back of air flow.
Preferably, the rotatable angle of the inlet variable camber guide vane is-30 degrees, so that the inlet variable camber guide vane is used for simulating the distribution of inlet air flow angles, multi-station measurement is realized, the implementation difficulty is low, and the test cost is reduced; the downstream exhaust switching section of the volute is provided with a bleed port with a certain area, and the bleed port can be used for increasing the flow of the inlet of the flow passage to ensure that the blocking boundary of the tested centrifugal compressor is collected.
Preferably, the dynamic pressure sensors are uniformly distributed along the circumferential direction of the inner wall of the centrifugal impeller casing, the number of the dynamic pressure sensors is 3-8, and the axial positions are from the front edge of the centrifugal impeller to the tail edge of the centrifugal impeller to +10% of the chord length, and from the diffuser to +10% of the chord length to +90% of the chord length; the total temperature probes and the total pressure probes are respectively and circumferentially distributed along the inner wall of the centrifugal impeller casing, the number of the total temperature probes and the total pressure probes is 3-8, and the axial positions of the total temperature probes and the total pressure probes are respectively from-250% chord length to-50% chord length of the front edge of the centrifugal impeller and from +50% chord length to +250% chord length of the tail edge of the centrifugal impeller.
Preferably, the dynamic pressure sensor is fixed on the sensor base in a threaded connection or organic silica gel sealing mode, so that the acquisition of dynamic pressure signals is realized.
Preferably, the air inlet regulating valve, the air exhaust main valve and the air exhaust auxiliary valve are pneumatic film sleeve regulating valves so as to realize high flow precision regulation; the surge relief valve adopts an electromagnetic regulating valve to increase the flow of the tested centrifugal compressor, quickly exit the unstable flow working condition and ensure the safety of equipment.
The performance test method of the test device comprises the following steps:
(1) The variable frequency motor is electrified, the tested centrifugal compressor is driven to rotate through the gear box, the exhaust main valve and the exhaust auxiliary valve are all opened, the relief valve is in a closed state, the blocking point of the tested centrifugal compressor is obtained through the flow measuring device, and the pneumatic performance data of the tested centrifugal compressor are collected through the total temperature probe and the total pressure probe;
(2) Gradually closing the main exhaust valve to increase the back pressure of the outlet of the centrifugal compressor to be tested and reduce the flow, and continuously collecting the pneumatic performance data of the centrifugal compressor to be tested through the total temperature probe and the total pressure probe;
(3) The dynamic pressure sensor monitors the high-frequency response dynamic pressure p (T) of the tip surface of the tested centrifugal impeller and the tip surface of the diffuser in real time, selects the time T of one circle of rotation of the compressor as one micro-element time consumption, calculates the variation characteristic value of the pressure p (T) along with the time T, and acquires the power spectrum maximum amplitude S of the pressure signal through Fourier transformation max The following formula is shown:
wherein p is t (f) P (t) is a dynamic pressure signal, e is a mathematical natural constant, and the value of p (t) is about 2.718281;
if S max Less than the critical value S crit Judging that the centrifugal compressor is in a stable working state, and continuously collecting pneumatic performance data; if S max Greater than S crit Judging that the centrifugal compressor enters a flowing unstable working condition, wherein the last stable working point is regarded as a stable boundary under the current reduced rotating speed;
(4) When the centrifugal compressor enters a flowing instability working condition, the number, the propagation speed and the frequency information of stall groups are obtained by processing the collected real-time pressure p (t) through a polar coordinate signal analysis method;
(5) Changing the folding rotational speed of the air compressor, and repeating the steps (1) to (4), so as to finally obtain the blocking point and the flow instability boundary of the tested centrifugal air compressor under different folding rotational speeds, and obtain the pneumatic performance of the tested centrifugal air compressor in the full rotational speed.
Preferably, the maximum amplitude threshold S of the power spectrum is described in step 3 crit According to the numerical simulation pressure ratio pi under different folding rotational speeds of centrifugal compressor t Determining that its value is 5 pi t ～15π t dB。
Compared with the prior art, the invention has the beneficial effects that:
the invention can rapidly and accurately obtain the stable working range and the pneumatic performance of the centrifugal compressor under the full-rotation-speed working condition, and reduces the development cost and risk of the centrifugal compressor of the auxiliary power device.
Drawings
Fig. 1 is a schematic diagram of a test apparatus for a centrifugal compressor of an auxiliary power unit.
Fig. 2 is a schematic diagram of aerodynamic performance of the auxiliary power unit in the full speed range of the centrifugal compressor.
Fig. 3 is a flow chart of a method for testing the performance of a centrifugal compressor of an auxiliary power unit.
FIG. 4 is a schematic diagram of a centrifugal compressor tested with an auxiliary power unit
FIG. 5 is a schematic view of an exhaust transition section downstream of the volute
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention become more apparent, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are intended to be illustrative of the invention and should not be construed as limiting the invention in any way. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a test device and a performance test method of a centrifugal compressor of an auxiliary power device, and aims to rapidly and accurately obtain a stable working range and pneumatic performance of the centrifugal compressor under the full-rotation-speed working condition, and reduce the development cost and risk of the centrifugal compressor of the auxiliary power device.
The test device for the centrifugal compressor of the auxiliary power device comprises the centrifugal compressor to be tested and is characterized by further comprising a pressure stabilizing box, a dynamic pressure sensor, a total temperature probe, a total pressure probe, a volute, an exhaust switching section, a variable frequency motor, an exhaust main valve, an exhaust auxiliary valve and an anti-surge valve; the air enters the pressure stabilizing box, the pressure stabilizing box is connected with the tested centrifugal compressor, the volute is arranged behind the tested centrifugal compressor, the exhaust auxiliary valve and the relief valve are arranged on the exhaust switching section of the downstream of the volute in parallel, the exhaust main valve is arranged behind the exhaust switching section, the total temperature probe, the total pressure probe and the dynamic pressure sensor are all arranged in the flow channel of the tested centrifugal compressor, and the variable frequency motor is connected with the tested centrifugal compressor to drive the tested centrifugal compressor to rotate.
Preferably, the device also comprises an air inlet regulating valve and a gear box, wherein the air inlet regulating valve is arranged on an inlet pipeline of the pressure stabilizing box, and the front end of the air inlet regulating valve is provided with a flow measuring device; the variable frequency motor drives the tested centrifugal compressor to rotate through the gear box.
Preferably, the device further comprises a torsion meter, wherein the torsion meter is arranged on an output shaft of the variable frequency motor and is used for measuring the torque of the tested centrifugal compressor and the output shaft of the variable frequency motor.
Preferably, the tested centrifugal compressor comprises a flow passage formed by a hub and a casing, and an inlet variable camber guide vane 1, a centrifugal impeller 2, a diffuser 3 and a volute are arranged in the flow passage according to the direction of airflow from front to back.
Preferably, the rotatable angle of the inlet variable camber guide vane 1 is-30 degrees, so that the inlet variable camber guide vane is used for simulating the distribution of inlet air flow angles, multi-station measurement is realized, the implementation difficulty is low, and the test cost is reduced; the volute downstream exhaust switching section 4 is provided with a bleed hole with a certain area, and the bleed hole can be used for increasing the flow of the inlet of the flow passage through bleed gas, so that the blocking boundary of the tested centrifugal compressor is ensured to be collected.
Preferably, the dynamic pressure sensors are uniformly distributed along the circumferential direction of the inner wall of the casing of the centrifugal impeller 2, the number of the dynamic pressure sensors is 3-8, and the axial positions are from the front edge of the centrifugal impeller to 10% chord length to the tail edge of the centrifugal impeller to +10% chord length, and from the diffuser to +10% chord length to +90% chord length; the total temperature probes and the total pressure probes are respectively and circumferentially distributed along the inner wall of the centrifugal impeller casing, the number of the total temperature probes and the total pressure probes is 3-8, and the axial positions of the total temperature probes and the total pressure probes are respectively from-250% chord length to-50% chord length of the front edge of the centrifugal impeller and from +50% chord length to +250% chord length of the tail edge of the centrifugal impeller.
Preferably, the dynamic pressure sensor is fixed on the sensor base in a threaded connection or organic silica gel sealing mode, so that the acquisition of dynamic pressure signals is realized.
Preferably, the air inlet regulating valve, the air exhaust main valve and the air exhaust auxiliary valve are pneumatic film sleeve regulating valves so as to realize high flow precision regulation; the surge relief valve adopts an electromagnetic regulating valve to increase the flow of the tested centrifugal compressor, quickly exit the unstable flow working condition and ensure the safety of equipment.
The performance test method of the test device comprises the following steps:
(1) The variable frequency motor is electrified, the tested centrifugal compressor is driven to rotate through the gear box, the exhaust main valve and the exhaust auxiliary valve are all opened, the relief valve is in a closed state, the blocking point of the tested centrifugal compressor is obtained through the flow measuring device, and the pneumatic performance data of the tested centrifugal compressor are collected through the total temperature probe and the total pressure probe;
(2) Gradually closing the main exhaust valve to increase the back pressure of the outlet of the centrifugal compressor to be tested and reduce the flow, and continuously collecting the pneumatic performance data of the centrifugal compressor to be tested through the total temperature probe and the total pressure probe;
(3) The dynamic pressure sensor monitors the high-frequency response dynamic pressure p (T) on the tip surface of the tested centrifugal impeller 2 and the tip surface of the diffuser 3 in real time, selects the time T of one circle of rotation of the compressor as one micro-element time consumption, calculates the variation characteristic value of the pressure p (T) along with the time T, and acquires the power spectrum maximum amplitude S of the pressure signal through Fourier transformation max The following formula is shown:
wherein p is t (f) P (t) is a dynamic pressure signal, e is a mathematical natural constant, and the value of p (t) is about 2.718281;
if S max Less than the critical value S crit Judging that the centrifugal compressor is in a stable working state, and continuously collecting pneumatic performance data; if S max Greater than S crit Judging that the centrifugal compressor enters a flowing unstable working condition, wherein the last stable working point is regarded as a stable boundary under the current reduced rotating speed;
(4) When the centrifugal compressor enters a flowing instability working condition, the number, the propagation speed and the frequency information of stall groups are obtained by processing the collected real-time pressure p (t) through a polar coordinate signal analysis method;
(5) Changing the folding rotational speed of the air compressor, and repeating the steps (1) to (4), so as to finally obtain the blocking point and the flow instability boundary of the tested centrifugal air compressor under different folding rotational speeds, and obtain the pneumatic performance of the tested centrifugal air compressor in the full rotational speed.
Preferably, the maximum amplitude threshold S of the power spectrum is described in step 3 crit According to the numerical simulation pressure ratio pi under different folding rotational speeds of centrifugal compressor t Determining that its value is 5 pi t ～15π t dB。
The object of the present invention is fully effectively achieved by the above-described embodiments. Those skilled in the art will appreciate that the present invention includes, but is not limited to, those illustrated in the drawings and described in the foregoing detailed description. While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims.
Claims (10)
1. The test device of the centrifugal compressor of the auxiliary power device comprises a tested centrifugal compressor and is characterized by further comprising a pressure stabilizing box, a dynamic pressure sensor, a total temperature probe, a total pressure probe, a volute, an exhaust switching section, a variable frequency motor, an exhaust main valve, an exhaust auxiliary valve and an anti-asthma valve; the air enters the pressure stabilizing box, the pressure stabilizing box is connected with the tested centrifugal compressor, and the volute is arranged behind the tested centrifugal compressor; the exhaust auxiliary valve and the de-asthmatic valve are arranged on the exhaust switching section at the downstream of the volute in parallel, the exhaust main valve is arranged at the rear of the exhaust switching section, the total temperature probe, the total pressure probe and the dynamic pressure sensor are all arranged in the flow passage of the tested centrifugal compressor, and the variable frequency motor is connected with the tested centrifugal compressor to drive the tested centrifugal compressor to rotate.
2. The test device of the centrifugal compressor of the auxiliary power device according to claim 1, further comprising an air inlet regulating valve and a gear box, wherein the air inlet regulating valve is arranged on an inlet pipeline of the pressure stabilizing box, and the front end of the air inlet regulating valve is provided with a flow measuring device; the variable frequency motor drives the tested centrifugal compressor to rotate through the gear box.
3. The test device for the centrifugal compressor of the auxiliary power device according to claim 2, further comprising a torsion meter, wherein the torsion meter is arranged on an output shaft of the variable frequency motor and is used for measuring the torque of the tested centrifugal compressor and the output shaft of the variable frequency motor.
4. The test device of the centrifugal compressor of the auxiliary power device according to claim 1, wherein the tested centrifugal compressor comprises a flow passage formed by a hub and a casing, and an inlet variable camber guide vane, a centrifugal impeller, a diffuser and a volute are arranged in the flow passage according to the front-to-back direction of air flow.
5. The test device of the centrifugal compressor of the auxiliary power device according to claim 4, wherein the inlet variable camber guide vane has a rotatable angle of-30 to 30 degrees and is used for simulating the distribution of inlet air flow angles; the downstream exhaust switching section of the volute is provided with a bleed port with a certain area, and the bleed port can be used for increasing the flow of the inlet of the flow passage to ensure that the blocking boundary of the tested centrifugal compressor is collected.
6. The test device of the centrifugal compressor of the auxiliary power device according to claim 4, wherein the dynamic pressure sensors are uniformly distributed along the circumferential direction of the inner wall of the centrifugal impeller casing, the number of the dynamic pressure sensors is 3-8, and the axial positions are from the front edge of the centrifugal impeller to 10% chord length to the tail edge of the centrifugal impeller to +10% chord length, and from the diffuser to +10% chord length to +90% chord length; the total temperature probes and the total pressure probes are respectively and circumferentially distributed along the inner wall of the centrifugal impeller casing, the number of the total temperature probes and the total pressure probes is 3-8, and the axial positions of the total temperature probes and the total pressure probes are respectively from-250% chord length to-50% chord length of the front edge of the centrifugal impeller and from +50% chord length to +250% chord length of the tail edge of the centrifugal impeller.
7. The test device for the centrifugal compressor of the auxiliary power device according to claim 6, wherein the dynamic pressure sensor is fixed on the sensor base in a threaded connection or an organic silica gel sealing manner, so as to collect dynamic pressure signals.
8. The test device for the centrifugal compressor of the auxiliary power device according to claim 1, wherein the air inlet regulating valve, the air exhaust main valve and the air exhaust auxiliary valve are pneumatic film sleeve regulating valves; the relief valve is an electromagnetic regulating valve.
9. A method of testing the performance of a test apparatus according to any one of claims 1 to 8, comprising the steps of:
(1) The variable frequency motor is electrified, the tested centrifugal compressor is driven to rotate through the gear box, the exhaust main valve and the exhaust auxiliary valve are all opened, the relief valve is in a closed state, the blocking point of the tested centrifugal compressor is obtained through the flow measuring device, and the pneumatic performance data of the tested centrifugal compressor are collected through the total temperature probe and the total pressure probe;
(2) Gradually closing the main exhaust valve to increase the back pressure of the outlet of the centrifugal compressor to be tested and reduce the flow, and continuously collecting the pneumatic performance data of the centrifugal compressor to be tested through the total temperature probe and the total pressure probe;
(3) The dynamic pressure sensor monitors the high-frequency response dynamic pressure p (T) of the tip surface of the tested centrifugal impeller and the tip surface of the diffuser in real time, selects the time T of one circle of rotation of the compressor as one micro-element time consumption, calculates the variation characteristic value of the pressure p (T) along with the time T, and acquires the power spectrum maximum amplitude S of the pressure signal through Fourier transformation max The following formula is shown:
wherein p is t (f) The frequency domain value obtained by Fourier transformation of the dynamic pressure signal is p (t) which is the dynamic pressure signal, and e is a mathematical natural constant which is 2.718281;
if S max Less than the critical value S crit Judging that the centrifugal compressor is in a stable working state, and continuously collecting pneumatic performance data; if S max Greater than S crit Judging centrifugal compressed airThe machine enters a flowing unstable working condition, and the last stable working point is regarded as a stable boundary under the current reduced rotating speed;
(4) When the centrifugal compressor enters a flowing instability working condition, the number, the propagation speed and the frequency information of stall groups are obtained by processing the collected real-time pressure p (t) through a polar coordinate signal analysis method;
(5) Changing the folding rotational speed of the air compressor, and repeating the steps (1) to (4), so as to finally obtain the blocking point and the flow instability boundary of the tested centrifugal air compressor under different folding rotational speeds, and obtain the pneumatic performance of the tested centrifugal air compressor in the full rotational speed.
10. The method of claim 9, wherein in step 3 the power spectrum maximum amplitude threshold S crit According to the numerical simulation pressure ratio pi under different folding rotational speeds of centrifugal compressor t Determining that its value is 5 pi t ～15π t dB。
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