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CN115594044B - A method for measuring elevator balance coefficient with improved inspection accuracy - Google Patents

A method for measuring elevator balance coefficient with improved inspection accuracy Download PDF

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Publication number
CN115594044B
CN115594044B CN202211120800.8A CN202211120800A CN115594044B CN 115594044 B CN115594044 B CN 115594044B CN 202211120800 A CN202211120800 A CN 202211120800A CN 115594044 B CN115594044 B CN 115594044B
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elevator
frequency
balance coefficient
amplitude
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CN115594044A (en
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方杰
董琪琪
张杰梁
张煌辉
林晓
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Fujian Metrology Institute
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Fujian Metrology Institute
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B66HOISTING; LIFTING; HAULING
    • B66BELEVATORS; ESCALATORS OR MOVING WALKWAYS
    • B66B5/00Applications of checking, fault-correcting, or safety devices in elevators
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R19/00Arrangements for measuring currents or voltages or for indicating presence or sign thereof
    • G01R19/0092Arrangements for measuring currents or voltages or for indicating presence or sign thereof measuring current only

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Maintenance And Inspection Apparatuses For Elevators (AREA)

Abstract

A measuring method for elevator balance coefficient to increase inspection accuracy includes carrying out signal extraction from elevator inspection site to determine bandwidth, frequency, distortion rate and sensing characteristic current signal characteristics of signal, carrying out current signal processing to make up and down whole course operation of elevator car with no-load and rated load capacity of 25%, 40%, 50%, 75%, 100% and 110% respectively, measuring current value of motor when elevator car and counterweight are operated to same horizontal position, carrying out current signal processing to original sampled data of measured current value including one or more of sliding average algorithm, quasi-synchronous sampling method or amplitude phase frequency dynamic compensation method, recording current value after current signal processing, drawing current-load curve, and load rate corresponding to intersection point of up and down operation curve is balance coefficient of elevator. The invention can accurately measure the current and improve the balance coefficient test accuracy.

Description

Measurement method for elevator balance coefficient for improving inspection accuracy
Technical Field
The invention belongs to the technical field of measuring methods, and particularly relates to a measuring method for an elevator balance coefficient, which improves inspection accuracy.
Background
With the increasing number of high-rise buildings, the application requirements of traction elevators are expanding. The requirements of people on riding comfort and safety performance of the elevator are also continuously improved. Wherein the elevator balance factor is an important performance index of the elevator, related to the economy, comfort and safety of elevator operation. The balance coefficient is bigger or smaller, which brings a certain potential safety hazard and is easy to cause the car to punch the top or squat. In addition, the improper design of the balance coefficient can cause the change of the tension of the steel wire ropes at the two sides of the traction sheave, accelerate the abrasion between the traction sheave and the steel wire ropes, influence the accurate action of the speed limiter-safety tongs, and aggravate the burden of an electric drive control system and the like. Therefore, the balance coefficient items need to be checked during elevator installation, modification, and major maintenance. The method for measuring the current involved in the elevator balance coefficient test mainly comprises a loading current method, an idle power method and a frequency converter method. The current loading method is widely used because of the simple method for measuring the balance coefficient.
The quick detection method for the balance coefficient of the T/CASEIT elevator is provided with the steps of respectively measuring the running currents of the elevator in the upper and lower running process when the load is 40% and 50% of rated load, solving the balance coefficient of the elevator based on the relation between the load and the current, and recording the current under the condition that the elevator car and the counterweight run to the same horizontal position. The elevator balance coefficient test method specified in TSG-T7001-2009 elevator supervision test and periodic test rule-traction and forced drive elevator is that the elevator cars with no-load and loading rated load capacity are respectively operated in the whole course up and down, when the elevator cars and the counterweight are operated to the same horizontal position, the current value of the motor is recorded, the current-load curve is drawn, and the load rate corresponding to the intersection point of the up-and-down operation curve is the balance coefficient of the elevator.
The measuring method is widely applied, but still has the following defects that (1) the judgment that the car and the counterweight are positioned at the same horizontal position is difficult, the requirement on operators is high, and the personnel reading error is large. (2) During the whole running stage of the elevator in the ascending or descending direction, the current is a fluctuating process, and a large random error exists for instantaneous fluctuating current sampling. (3) The waveforms of the current signals are greatly different between the front end and the rear end of the frequency converter. (4) The open clamp ammeter or clamp transformer is used as current collecting equipment, and the indexes of signal bandwidth, transformation ratio, phase shift and the like of the selected current measuring instrument directly determine the measuring accuracy.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for measuring the balance coefficient of the elevator, which improves the inspection accuracy, realizes accurate measurement of current and achieves the aim of improving the inspection accuracy of the balance coefficient.
The invention is realized in the following way:
The elevator balance coefficient measuring method for improving the inspection accuracy comprises the following steps:
step S1, accurately identifying current signal characteristics:
the method comprises the steps of performing signal extraction work from an elevator inspection site, collecting operation current of an elevator by using a broadband digitizer, a broadband fluxgate sensor or a broadband shunt, and determining bandwidth, frequency, distortion rate and sensing characteristic current signal characteristics of the signal;
step S2, current signal processing:
The method comprises the steps of respectively carrying out full-course operation up and down on a lift car with no load and 25%, 40%, 50%, 75%, 100% and 110% of rated load capacity, and measuring the current value of a motor when the lift car and a counterweight are operated to the same horizontal position;
the method comprises the steps of carrying out current signal processing on the original sampled data of the measured current value to ensure the accuracy of a data analysis process, wherein the current signal processing comprises one or more of a moving average algorithm, a quasi-synchronous sampling method or an amplitude/phase frequency dynamic compensation method;
And S3, recording the current value after the current signal processing, drawing a current-load curve, and obtaining the load rate corresponding to the intersection point of the uplink and downlink running curves as the balance coefficient of the elevator.
Further, the quasi-synchronous sampling method specifically refers to:
and (3) filtering the frequency characteristic of the original sampling data, taking the filtered signal as a synchronous signal, resampling the original sampling sequence to achieve full-period transformation, and further eliminating errors caused by asynchronous sampling.
Further, the sliding average algorithm specifically refers to:
the width of the queue for the moving average is formed by extending the time width of 5% left and right by taking the moment that the car and the counterweight are at the same horizontal position as the center, and the average value of the queue is calculated according to the formula (1):
Wherein:
-an arithmetic mean value, a, of N current sample values in the queue;
i j, namely the value of the jth current in the queue, A;
n-the number of current samples in the queue.
Further, the amplitude/phase frequency dynamic compensation method specifically refers to:
Under laboratory conditions, the amplitude index is subjected to sweep frequency measurement by using a standard signal source, the frequency response of the angle difference is analyzed by using a known angle difference or a shunt with a negligible angle difference as a comparison reference, and then a mathematical correction model of amplitude frequency and phase frequency is established according to the measurement result.
Further, between the step S1 and the step S2, the method further includes:
And performing model selection configuration on the current measuring instrument, namely simulating a plurality of typical electrical signals which are commonly used under the conditions of abstract complexity and dynamic change under laboratory conditions, checking bandwidth, amplitude and phase frequency characteristic indexes, and selecting the current measuring instrument with the error meeting the requirement.
The invention has the advantages that:
1. And the original sampling data is subjected to frequency characteristic filtering treatment by adopting a quasi-synchronous sampling method, the filtered signal is used as a synchronous signal, and the original sampling sequence is resampled to achieve full-period transformation, so that errors caused by asynchronous sampling are eliminated, and the accuracy of the data analysis process is ensured.
2. The current value is calculated by utilizing a moving average algorithm, so that the problems of large field reading error of workers and large random error of sampling instantaneous fluctuation current are solved, and the working efficiency and the measuring accuracy are greatly improved.
3. When the current is measured, the amplitude and the phase are dynamically compensated according to the frequency analysis result, so that the accuracy of measuring the current signal by the clamp ammeter or the clamp transformer is ensured.
4. The current signal characteristics of bandwidth, frequency, distortion rate and sensing characteristics are identified, and typical electrical signals which are commonly used under abstract complex and dynamic change working conditions are simulated under laboratory conditions to perform type selection configuration of a current measuring instrument, so that the problems of large current waveform difference between the front end and the rear end of a frequency converter and the like caused by introducing a variable-current frequency conversion module are solved, the current signal characteristics are more suitable for the actual running condition of an elevator, and the current measuring instrument is high in pertinence, practicability and accuracy.
Drawings
The invention will be further described with reference to the accompanying drawings, in conjunction with examples.
FIG. 1 is a schematic flow chart of the method of the present invention.
Fig. 2 is a three-phase current waveform at the power supply end of an elevator according to an embodiment of the invention.
Fig. 3 is a phase a current spectrum in fig. 2.
Fig. 4 is a schematic diagram of a current signal feature recognition method according to the present invention.
FIG. 5 is a diagram illustrating queue time width selection in the moving average algorithm of the present invention.
Fig. 6 is a schematic diagram of a moving average calculation in the moving average algorithm of the present invention.
Fig. 7 is a diagram of a resampling synchronization signal in the quasi-synchronous sampling method of the present invention.
Fig. 8 is a graph showing amplitude frequency characteristics in the amplitude/phase frequency dynamic compensation method of the present invention.
Fig. 9 is a graph showing phase frequency characteristics in the amplitude/phase frequency dynamic compensation method of the present invention.
Fig. 10 is a schematic of a phase trigger signal simulated under laboratory conditions in accordance with the present invention.
Fig. 11 is a schematic representation of a square wave signal simulated under laboratory conditions according to the present invention.
Fig. 12 is a schematic representation of a half-wave rectified signal simulated under laboratory conditions according to the present invention.
Fig. 13 is a graph of amplitude error obtained for a clamp ammeter and a clamp transformer of the present invention using a composite of analog signals to develop performance signals.
Fig. 14 is a graph of phase error resulting from the present invention using a composite of analog signals to develop performance signals for a clamp ammeter and a clamp transformer.
Detailed Description
As shown in fig. 1, an elevator balance coefficient measuring method for improving inspection accuracy includes the steps of:
step S1, accurately identifying the current signal characteristics, as shown in FIG. 4:
The basis of accurate measurement of signals is the identification of signal characteristics, namely the definition of the actual physical meaning of the measured signals, such as the bandwidth, frequency, distortion rate, sensing characteristics and the like. In order to find out the current signal characteristics in the operation of the elevator, the embodiment carries out signal extraction work from an elevator inspection site, and acquires the operation current of the elevator by using a broadband digitizer and a broadband fluxgate sensor (a broadband shunt can also be adopted). Fig. 2 shows three-phase current waveforms at the power supply end, and it can be seen that the current distortion at the power supply end is serious, the frequency is power frequency, and the current from the power supply to the frequency converter can be measured in one direction only. The harmonic transformer is needed to accurately measure the severely distorted current, meanwhile, the characteristics of the current signal need to be grasped, and the signal analysis is carried out on the collected current signal by taking the phase A current as an example, and the spectrum of the phase A current is shown in fig. 3, wherein the figure mainly contains odd harmonics. The analysis results of the three-phase current characteristic parameters are shown in tables 1 and 2.
TABLE 1 three-phase current analysis results
Parameters (parameters) Phase A Phase B Phase C
Frequency of 50.010 49.988 50.009
Total harmonic distortion rate/(%) 128.3 133.78 130.75
Fundamental effective value/(A) 11.422 10.65 9.6886
Total effective value/(A) 18.576 17.79 15.949
TABLE 2 harmonic content of three-phase currents
As can be seen from the analysis result of the signal characteristic parameters, the harmonic content after 25 times is smaller, and the current measuring element needs to meet the correct conduction of a 1.25kHz signal, so that a basis is provided for the model selection of the current measuring instrument for inspection. In addition, when the elevator is lightly loaded or unloaded, if the elevator is only provided with uplink power by the counterweight in the uplink, the loop current of the power supply end is very small or not, and at the moment, because the background current is very small, the noise is large, the signal to noise ratio is low, the measurement error of the current is large, and the current signal needs to be processed in advance.
Step S2, current signal processing:
The method comprises the steps of respectively carrying out full-course operation up and down on a lift car with no load and 25%, 40%, 50%, 75%, 100% and 110% of rated load capacity, and measuring the current value of a motor when the lift car and a counterweight are operated to the same horizontal position;
the original sampling data of the measured current value is subjected to current signal processing, so that the accuracy of a data analysis process is ensured;
The current signal processing comprises one or more of a moving average algorithm, a quasi-synchronous sampling method or an amplitude/phase frequency dynamic compensation method;
sliding average algorithm:
In the elevator balance coefficient test, the accuracy and reliability of current reading cannot be ensured because the running current value of the elevator up/down or on-load/no-load is unstable. The embodiment adopts a sliding average algorithm to improve the accuracy of measurement. Referring specifically to fig. 5, the current samples are sliding averaged. The width of the queue for the moving average is formed by extending a time width of 5% about the time point when the car and the counterweight are at the same horizontal position. Fig. 5 and 6 illustrate the signal processing procedure of the moving average algorithm. In fig. 5, T is the unidirectional full-travel time of the elevator, if the current collection time interval is M, the width of the data queue is 10% T, the total number of data in the queue is n=10%t/M, and the value of N is rounded up. The average value of the queues is calculated according to the formula (1), and the sliding average value of the queues is read at the time T0 corresponding to T/2. The data queue constructed in fig. 6 is in accordance with FIFO principles.
Wherein:
-an arithmetic mean value, a, of N current sample values in the queue;
I j, namely the value of the jth current in the queue, A6;
n-the number of current samples in the queue.
Quasi-synchronous sampling method:
The frequency of the current signal can have certain fluctuation in the elevator operation process, and the sampling is asynchronous due to the fact that the sampler selects the fixed frequency, namely, the discrete data sequence to be analyzed cannot be truncated in a whole period, so that an analysis method error is caused. One common processing method is quasi-synchronous sampling, which filters the frequency characteristic of the original sampled data, takes the filtered signal as a synchronous signal, resamples the original sampled sequence to achieve full-period transformation, and further eliminates errors caused by asynchronous sampling. Fig. 7 shows the effect of quasi-synchronous sampling. And calculating fundamental frequency and zero crossing point information of the synchronous signal, taking the fundamental frequency and zero crossing point information as sampling trigger signals, and resampling the original signal.
Amplitude/phase frequency dynamic compensation method:
When the clamp ammeter or the clamp transformer measures a current signal, amplitude-frequency characteristics and phase-frequency characteristics are two important performance indexes, and are keys for correctly executing current measurement. In general, it is necessary to calibrate it by experimental means. The method comprises the steps of carrying out sweep frequency measurement on amplitude indexes by using a standard signal source under laboratory conditions, analyzing the frequency response of the angle difference by using a shunt with known angle difference (or negligible angle difference) as a comparison reference, and then establishing a mathematical correction model of amplitude frequency and phase frequency according to the measurement result. Fig. 8 and 9 show amplitude-frequency characteristics and phase-frequency characteristics of a certain type of sensor. When current measurement is performed, the amplitude and phase are dynamically compensated according to the frequency analysis result.
And S3, recording the current value after the current signal processing, and drawing a current-load curve, wherein the load rate corresponding to the intersection point of the uplink and downlink operation curves is the balance coefficient of the elevator.
In addition, the current measuring instrument model selection configuration can be performed after the accurate identification of the current signal characteristics is performed in the step S1:
the current signal in elevator operation has rich information, especially in the start-up and braking phases, and changes relatively smoothly in the intermediate constant speed phase, even though the frequency and amplitude of the signal also have time-varying characteristics. Because of the introduction of the variable-current frequency conversion module, the current waveforms at the front end and the rear end of the frequency converter have large difference, and as mentioned above, when serious distortion exists in the signal waveforms, in order to accurately acquire the numerical value of the current characteristic parameter, correct instrument type selection configuration is required, and the indexes mainly examined have bandwidth, amplitude/phase frequency characteristics. According to the rule of the gauge, the measurement error of the current by adopting the secondary loading current method needs to be controlled to be +/-2%, and the measurement error of the power by adopting the no-load power method needs to be controlled to be +/-1%. The literature presently disclosed is silent about the selection of current or power measuring devices. The current main practice is to send a "clamp ammeter" or "power tester" for inspection, and in general, the metering department adopts a standard signal source to perform performance verification, so that the actual performance of the sending inspection equipment in field application cannot be estimated. In order to better develop the performance evaluation of the equipment, the embodiment simulates typical electrical signals which are commonly used under the conditions of abstract complexity and dynamic change under the laboratory condition, and can realize better performance evaluation to a certain extent, thereby providing reference for correctly carrying out the model selection configuration of the instrument. Fig. 10 shows a "phase trigger signal", fig. 11 shows an "analog square wave signal", and fig. 12 shows a "half-wave rectified signal". The following series of synthesized signals are used to perform performance experiments on a certain clamp ammeter and a certain clamp transformer. The amplitude and phase measurement indexes are mainly checked. The results of some experiments are shown in Table 3, FIG. 13 and FIG. 14.
TABLE 3 phase trigger signal amplitude/phase measurement
As can be seen from table 3, under distorted signal conditions, the amplitude error exceeds 2% when the harmonic frequency is higher than 750Hz, or up to 15 harmonics. Considering that the harmonic amplitude measurement error has small error proportion of the total effective value, the total effective value error experiment is also needed, the signal is adopted for verification, the experimental result is shown in table 4, and the result shows that the amplitude measurement error of the clamp ammeter meets the requirement and can be used as a measuring instrument of a secondary loading current method.
TABLE 4 Total effective value measurement error of certain pincerlike ammeter
The current signal characteristics are identified and selected by a current measuring instrument or a current signal processing method is summarized, ① current distortion of a power supply end is serious, frequency is power frequency, a harmonic transformer with good use performance can accurately measure current, ② current of a motor end is basically sine wave but contains certain noise, frequency is generally low-frequency (a down-conversion frequency converter is used), the current is difficult to accurately measure by the common power frequency transformer, an electromagnetic transformer is adopted, when the frequency of the current signal is low, the angle difference of the transformer is large, the measuring accuracy of power can be obviously affected, ③ current from a power supply end to the direction of the frequency converter can be measured in a single direction only, bidirectional current between the frequency converter and the motor can be measured at a motor end, when the elevator is light-loaded or idle, if the elevator is only provided with uplink power by a counterweight, loop current at the power supply end is small or not, the current at the frequency converter end is large and is inverted, the frequency of the frequency converter end is unstable, such as a moving average algorithm is adopted, and the amplitude and the phase frequency of the current at the motor end can be dynamically compensated.
In addition, in the elevator balance coefficient test, only the type selection configuration of the current measuring instrument is made, and the elevator balance coefficient test accuracy can be improved.
The invention improves the elevator balance coefficient checking accuracy by selecting a proper current signal processing method and/or a proper current measuring instrument, adopts a quasi-synchronous sampling method, carries out frequency characteristic filtering treatment on the original sampling data, takes the filtered signal as a synchronous signal, resamples the original sampling sequence to realize full period conversion, further eliminates errors caused by asynchronous sampling, and ensures the accuracy of the data analysis process. The current value is calculated by utilizing a moving average algorithm, so that the problems of large field reading error of workers and large random error of sampling instantaneous fluctuation current are solved, and the working efficiency and the measuring accuracy are greatly improved. When the current is measured, the amplitude and the phase are dynamically compensated according to the analysis frequency, so that the accuracy of measuring the current signal by the clamp ammeter or the clamp transformer is ensured. The method has the advantages that current signal characteristics such as bandwidth, frequency, distortion rate and sensing characteristics are identified, and typical electrical signals which are commonly used under abstract complex and dynamic change working conditions are simulated under laboratory conditions to perform type selection configuration of a current measuring instrument, so that the problems of large current waveform difference between the front end and the rear end of a frequency converter caused by introducing a variable-current frequency conversion module are solved, the method is more suitable for the actual running condition of an elevator, and the method is high in pertinence, practicability and accuracy.
The foregoing is merely illustrative of the preferred embodiments of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1.一种提高检验准确度的电梯平衡系数的测量方法,其特征在于:包括如下步骤:1. A method for measuring the balance coefficient of an elevator with improved inspection accuracy, characterized in that it comprises the following steps: 步骤S1:电流信号特征的准确辨识:Step S1: Accurate identification of current signal characteristics: 从电梯检验现场开展信号提取工作,利用宽频带数字化仪、宽带磁通门传感器或宽频带分流器采集电梯的运行电流,明确信号的带宽、频率、畸变率和传感特性电流信号特征;Carry out signal extraction work at the elevator inspection site, use a wideband digitizer, wideband fluxgate sensor or wideband shunt to collect the elevator's operating current, and clarify the signal's bandwidth, frequency, distortion rate and sensing characteristic current signal characteristics; 进行电流测量仪器选型配置:在实验室条件下模拟一些常用于抽象复杂及动态变化工况下的典型电气信号,考核带宽、幅值和相位频率特性指标,选择误差满足要求的电流测量仪器;Select and configure current measuring instruments: simulate some typical electrical signals commonly used in abstract, complex and dynamically changing working conditions under laboratory conditions, examine the bandwidth, amplitude and phase-frequency characteristic indicators, and select current measuring instruments with errors that meet the requirements; 步骤S2:电流信号处理:Step S2: Current signal processing: 分别将空载、装载额定载重量的25%、40%、50%、75%、100%、110%的轿厢作上下全程运行,当轿厢和对重运行到同一水平位置时,测得电动机的电流值;The car is run up and down full distance with no load, 25%, 40%, 50%, 75%, 100% and 110% of rated load respectively. When the car and counterweight are at the same level, the current value of the motor is measured. 将测得的电流值的原始采样数据进行电流信号处理,确保数据分析过程的准确性;所述电流信号处理,包括:滑动平均算法、准同步采样法、或幅值/相位频率动态补偿法中的一种或多种;The original sampled data of the measured current value is subjected to current signal processing to ensure the accuracy of the data analysis process; the current signal processing includes: one or more of a sliding average algorithm, a quasi-synchronous sampling method, or an amplitude/phase frequency dynamic compensation method; 其中,所述滑动平均算法,具体是指:The sliding average algorithm specifically refers to: 以轿厢与对重处于同一水平位置的时刻为中心,左右延拓5%的时间宽度构成用于滑动平均的队列的宽度,队列的平均值按式(1)计算:The width of the queue used for sliding average is formed by extending the time width of 5% to the left and right, with the moment when the car and the counterweight are at the same horizontal position as the center. The average value of the queue is calculated according to formula (1): 式中:Where: —队列中N个电流取样值的算术平均值,A; —The arithmetic mean of the N current sampling values in the queue, A; Ij—队列中的第j个电流取值,A;I j —the jth current value in the queue, A; N—队列中电流取样值的个数;N—the number of current sampling values in the queue; 步骤S3:记录经过电流信号处理后的电流值,绘制电流-负荷曲线,上、下行运行曲线的交点所对应的载荷率即为电梯的平衡系数。Step S3: Record the current value after current signal processing, draw a current-load curve, and the load rate corresponding to the intersection of the up and down running curves is the balance coefficient of the elevator. 2.如权利要求1所述的一种提高检验准确度的电梯平衡系数的测量方法,其特征在于:所述准同步采样法,具体是指:2. A method for measuring the balance coefficient of an elevator with improved inspection accuracy as claimed in claim 1, characterized in that: the quasi-synchronous sampling method specifically refers to: 将原始采样数据进行频率特性滤波,以滤波后的信号作为同步信号,对原采样序列进行重采样使其达到整周期变换,进而消除采样不同步带来的误差。The original sampling data is frequency-filtered, and the filtered signal is used as the synchronization signal. The original sampling sequence is resampled to achieve a full-cycle transformation, thereby eliminating the error caused by asynchronous sampling. 3.如权利要求1所述的一种提高检验准确度的电梯平衡系数的测量方法,其特征在于:所述幅值/相位频率动态补偿法,具体是指:3. A method for measuring the balance coefficient of an elevator with improved inspection accuracy as claimed in claim 1, characterized in that: the amplitude/phase frequency dynamic compensation method specifically refers to: 在实验室条件下,用标准信号源对幅度指标进行扫频测量,用已知角差或角差可以忽略的分流器作为比较参考来分析角差的频率响应,然后依据测量结果建立幅频和相频的数学修正模型。Under laboratory conditions, the amplitude index is swept and measured with a standard signal source, and the frequency response of the angular difference is analyzed using a shunt with a known angular difference or a negligible angular difference as a comparative reference. Then, a mathematical correction model of the amplitude-frequency and phase-frequency is established based on the measurement results.
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