Vibration Analysis for beginners 5 (Rules for evaluating machine vibration, Signal path from sensor)

Summary

本视频是《振动分析入门》系列的第五部分，主要介绍了模拟信号通过模数转换器(A/D)转换为数字信号的过程。强调了采样和量化的重要性，并解释了混叠现象及其预防方法。通过傅里叶变换(FFT)将信号转换到频域，分析振动信号的频率成分。视频还介绍了机器故障和轴承分析的基础知识，包括不平衡、不对中、松动等故障的检测方法以及共振和轴承故障频率的识别。

Takeaways

• ⏲️ 振动传感器的模拟信号需要通过模数转换器（A/D转换器）转换为数字信号才能进行分析。
• 🔄 数字化信号是对输入信号的描述，但并不完全等同于原始信号，重建的模拟信号与原始信号相似但存在差异。
• 📈 采样是将信号的时间轴分成均匀的段，并从每个段中取样，以防止混叠现象。
• 🔍 为了防止混叠，使用低通滤波器确保高于采样频率一半的频率不会进入转换器。
• 🎞️ 混叠现象的一个常见例子是快速旋转物体的电影拍摄，如飞机螺旋桨看起来旋转速度异常慢或反向旋转。
• 📊 通过给定的最大频率（fmax）和测量样本数，可以计算测量持续时间。
• 🔢 量化是将采样值在垂直轴上调整以适应处理数字信号的设备有限的精度。
• 📊 频谱分析揭示了组成振动信号的频率，通过快速傅里叶变换（FFT）计算。
• 🛠️ 振动分析可分为机械故障分析和轴承分析，包括不平衡、不对中和机械松动等基本机械故障。
• 🔧 轴承故障发生在高频范围，通过信号解调来识别特定的轴承故障频率。

Q & A

为什么振动传感器的信号需要通过模数转换器转换成数字形式？

振动传感器的信号是模拟形式的，为了在分析器中使用，必须转换成数字形式，因为数字信号可以被计算机和其他设备处理。

模数转换过程中的采样是什么？

采样是将信号的时间轴分割成均匀的小段，并从每一段中取样，这样可以得到一组离散的点，这些点的间隔对应于采样频率。

什么是混叠现象，它如何影响信号的转换？

混叠现象是指当原始连续信号包含高于采样频率一半的频率时，信号在转换过程中会被扭曲。为了防止混叠，使用低通滤波器确保高于采样频率一半的频率不会进入转换器。

为什么在进行振动测量时，采样频率要高于最高捕获频率的2.56倍？

这是基于快速傅里叶变换（FFT）的工作原理，采样频率是最高捕获频率的2倍可以提供抗混叠保护，而2.56倍则是一个标准，可以更有效地防止混叠。

量化在数字信号处理中起什么作用？

量化是因为计算机和其他处理数字信号的设备只能以有限的精度表达数字，所以必须在垂直轴上调整采样值，将采样值分配到特定的容差带内。

什么是时间域和频率域，它们在振动分析中有什么作用？

时间域是信号的时波形表示，而频率域是通过FFT计算得到的信号的频谱。频谱可以揭示组成振动信号的频率，提供比时间域更丰富的信息。

什么是泄漏现象，它是如何影响FFT计算的？

泄漏现象是指当信号非周期性时，能量会“逃逸”或“泄漏”到几个接近实际频率的谱线上，导致谱线在多个线上扩散。为了减轻泄漏，可以使用窗函数使信号人为地变得周期性。

机器机械故障分析和轴承分析在振动分析中有什么区别？

机器机械故障分析主要关注低频范围内的不平衡、不对中和机械松动等问题，而轴承分析则关注高频范围内的轴承故障，这些故障通常由球的冲击引起。

如何通过振动测量来检测机器的不平衡故障？

如果频谱中显示速度频率处有单一的高线，这通常表示不平衡故障。例如，如果频谱中只有25Hz处有一条高线，计算25Hz乘以60得到1500RPM，如果机器的实际速度确实是1500RPM，则故障为不平衡。

轴承故障频率是如何确定的，它与轴承的振动频率有什么关系？

轴承故障频率是由轴承的球冲击引起的振动冲击（轴承音调）的重复频率确定的。轴承故障频率不会出现在轴承的频谱中，只有球冲击产生的振动频率（轴承音调）是可见的。

信号解调在轴承故障分析中起什么作用？

信号解调用于识别故障频率。它包括去除低于500Hz的频率（高通滤波器），并使用包络检测人为地向信号添加能量，然后使用FFT处理信号以创建频谱。

Outlines

00:00

😀 振动分析基础：模拟信号数字化

本段介绍了振动分析的基础知识，包括模拟信号通过A/D转换器转换为数字信号的过程。强调了采样和量化的重要性，以及如何通过采样频率避免混叠现象。同时，解释了测量时长的计算方法，以及量化过程中精度的限制。最后，介绍了快速傅里叶变换（FFT）如何将复杂信号分解为不同频率的组合。

05:06

🔍 振动信号的频谱分析与机器故障诊断

第二段深入讲解了振动信号的频谱分析，包括FFT的限制、泄漏现象及其解决方法。讨论了机械故障分析，如不平衡、不对中和机械松动等低频故障的检测方法。介绍了振动测量的单位（mm/s）以及如何通过频谱分析识别故障类型。此外，还提到了共振现象的识别方法，以及轴承分析的基础知识，包括轴承故障频率的识别。

10:08

🛠️ 轴承故障分析与信号解调技术

最后一段专注于轴承故障分析，解释了轴承故障频率的计算方法和信号解调技术。说明了如何通过高通滤波和包络检测来识别轴承的故障频率，并通过FFT分析得到故障频率的频谱。强调了在轴承分析中忽略人工失真产生的谐波频率，专注于识别实际的故障频率。

Keywords

💡模拟信号

模拟信号是指连续变化的信号，如视频中提到的振动传感器产生的信号。在视频分析中，模拟信号需要通过A/D转换器转换成数字信号才能进行处理。模拟信号的特点是连续的，但无法直接由数字设备处理，因此必须经过采样和量化的过程。

💡数字信号

数字信号是由离散的值组成的信号，与模拟信号相对。在视频中，通过A/D转换器将模拟信号转换成数字信号，以便进行分析和处理。数字信号易于存储和处理，是现代电子设备中常用的信号形式。

💡A/D转换器

A/D转换器是将模拟信号转换为数字信号的设备。在视频中，A/D转换器通过采样和量化两个阶段来实现转换。采样是将时间轴分割成均匀的段并取样，而量化则是将采样值调整到有限的精度。A/D转换器在振动分析中至关重要，因为它允许分析软件处理和分析信号。

💡采样

采样是将连续的模拟信号转换成离散的数字信号的过程。在视频中，采样涉及到在时间轴上均匀地取样，以获得一组离散的点。采样频率决定了这些点的间隔，如果采样频率过低，可能会导致信号失真，即所谓的混叠现象。

💡混叠

混叠是当采样频率低于信号中最高频率的两倍时发生的现象，会导致信号失真。在视频中，为了防止混叠，使用低通滤波器来确保高于采样频率一半的频率不会进入转换器。混叠是信号处理中需要避免的问题，因为它会引入错误的频率成分。

💡低通滤波器

低通滤波器是一种允许低频信号通过而阻止高频信号的设备。在视频中，低通滤波器用于防止混叠现象，确保只有低于采样频率一半的频率进入A/D转换器。这是确保数字信号质量的重要步骤。

💡量化

量化是将采样值调整到有限精度的过程。在视频中，由于数字设备只能以有限的精度表达数字，因此需要对采样值进行量化。量化过程中，信号的垂直轴被划分为容差带，每个采样值根据其落在哪个容差带内而被赋予特定的值。

💡傅里叶变换

傅里叶变换是一种数学工具，可以将复杂信号分解为不同频率的组合。在视频中，通过傅里叶变换可以将振动信号分解为组成其的各个频率，从而得到信号的频谱。频谱类似于音乐符号，告诉人们需要按下哪些钢琴键以及用多大的力度来重现原始声音。

💡FFT（快速傅里叶变换）

FFT是傅里叶变换的一种算法，用于计算信号的频谱。在视频中，FFT用于分析振动信号，揭示组成振动信号的频率。FFT是振动分析中的关键技术，因为它允许分析者识别和量化信号中的频率成分。

💡窗函数

窗函数是一种用于信号处理的技术，通过在信号的开始和结束处施加某种形状的波形来减少信号的不连续性。在视频中，窗函数用于使信号在进行FFT分析时变得周期性，从而减少频谱泄漏现象。不同的窗函数（如矩形窗、汉宁窗和平坦窗）具有不同的特性，适用于不同的分析需求。

💡轴承分析

轴承分析是振动分析的一个分支，专注于分析轴承的故障。在视频中，轴承故障通常发生在高频范围内，并且通过轴承振动（由球体冲击引起的音调）来表示。轴承分析通过识别特定的故障频率来确定轴承的状况，这对于预防设备故障和计划维护至关重要。

Highlights

振动传感器的模拟信号需要通过模数转换器(A/D转换器)转换为数字信号才能在分析仪中使用。

数字化的数据只是描述输入信号，并不是输入信号的完全相同。

重建的模拟信号与原始信号不完全相同，只是相似。

采样是将信号的时间轴分割成均匀的段，并从每个段中取样。

如果原始连续信号包含高于采样频率一半的频率，信号将因混叠现象而失真。

为了防止混叠，使用低通滤波器确保高于采样频率一半的频率不进入转换器。

混叠的一个常见例子是快速旋转物体的电影拍摄，例如飞机螺旋桨会因采样频率过低而显得旋转缓慢或反向旋转。

给定最高捕捉频率fmax和测量样本数，可以计算测量持续时间。

为了防混叠，使用比最高捕捉频率高2.56倍的采样频率作为标准。

量化是将采样值在垂直轴上调整，因为处理数字信号的计算机和其他设备只能以有限的精度表达数字。

在分析仪中，我们可以将数字信号以时域形式显示，即时间波形。

频域表示更具有信息量，频谱揭示了构成振动信号的频率。

傅里叶变换是一种数学工具，可以将复杂信号分解为不同频率的组合。

快速傅里叶变换(FFT)用于计算频谱，尽管不容易解释，但对于我们的目的来说不必要。

FFT的一个限制是所有信号成分必须是周期性的，非周期性成分会导致频谱计算错误。

为了减轻非周期性信号的频谱泄漏，使用窗函数使信号人为地变得周期性。

振动分析可以分为机械故障分析和轴承分析两大类。

基本的机械故障包括不平衡、不对中和机械松动，这些故障可以在低频(10 - 1000 Hz)检测到。

轴承故障发生在高频范围(500 Hz至16 kHz)，由球冲击引起的轴承振动(轴承音调)表示。

轴承故障频率是特定于轴承的，可以通过信号解调来识别。

Transcripts

Hello and welcome to the 5th video in our series: Vibration Analysis for Beginners.

As we've learned from the previous videos, the signal from a vibration sensor is in analogue

form.

In order to work with it in analysers, the signal must be converted to digital form.

This conversion is done by an A/D converter.

The digitalised data only describes the input signal; it is not identical to the input signal.

When the digitised signal is reconstructed back to the analogue form, the reconstructed

signal is not exactly the same, only similar.

A/D converters convert analogue (continuous) signals into digital (discrete) signals.

The conversion of an analogue signal into a discrete digital signal involves two phases:

Sampling is performed by dividing the horizontal axis of the signal (time axis) into uniform

segments and taking a sample from each segment.

- This results in a set of discrete points with intervals corresponding to the sampling

frequency used.

- If the original continuous signal contains frequencies higher than half the sampling

frequency, the signal will be distorted by the phenomenon known as aliasing.

- You can see the same digital signal, but converted from different analogue signals.

- To prevent aliasing, a low pass filter is used to ensure that frequencies higher than

half the sampling frequency do not enter the converter.

Of course, these high frequencies are missing in the digitalised signal, but we have prevented

the creation of new - unrealistic - frequencies.

A common example of aliasing is a film capture of a fast-rotating object.

For example, an aircraft propeller will appear to rotate unnaturally slowly or in the opposite

direction due to the low sampling frequency.

With our current knowledge, we can calculate the measurement duration given fmax (the frequency

we still want to capture) and the number of samples for the measurement., fmax = 100Hz,

samples = 2048.

As a protection against aliasing, a sampling frequency 2.56 times higher than the highest

captured frequency is used as a standard.

The choice of 2.56 multiples is based on the operating principle of the Fast Fourier Transform.

It is the fact that 2 times the sampling rate itself provides anti-aliasing protection.

For example, to detect 100Hz with 2048 samples: 100Hz x 2.56 = 256Hz is the required sampling

frequency.

1/256 represents the time between samples in seconds, and with 2048 samples, 1/256 * 2048

= 8 seconds is the measurement duration.

Quantization: - Because computers and other devices that

process digital signals can only express numbers with limited precision, the sampled values

must be adjusted on the vertical axis.

This is an example of integer quantization.

The space around is divided into tolerance bands.

Each sample (the black dots) that falls into the given tolerance band is assigned the given

value (the green dots) during quantization.

Now we have a digital signal in the analyser and we can work with it.

For example, we can display it in its time-domain form - the time waveform.

However, a more informative representation is the frequency domain.

As shown in the previous video, the spectrum reveals the frequencies that compose the vibration

signal.

To calculate the spectrum, we use the Fast Fourier Transform (FFT).

It's not easy to explain, but for our purposes it's not necessary.

Imagine a piano with keys.

When the pianist activates the hammers by pressing the piano keys, the hammers hit the

strings.

Each string is tuned to a specific tone, which corresponds to a frequency.

When a pianist plays a combination of keys at the same time, a complex harmony is created,

made up of the sounds and loudness of the individual strings.

The Fourier transform is a mathematical tool that can decompose this harmony back into

individual string tones and loudness.

Any complex signal, such as human speech, music or the output of a vibration sensor,

can be described as a sum of different frequencies thanks to Fourier Transformation.

This produces a spectrum of the signal, which is analogous to musical notation that tells

you which keys on a piano to press and with what force to reproduce the original sound.

However, the FFT has one limitation: all signal components must be periodic.

If a non-periodic component is present, the FFT will incorrectly calculate its spectrum.

We observe that when the signal is non-periodic, energy "escapes" or "leaks" into several spectral

lines close to the actual frequency, causing the spectrum to spread over several lines

- this phenomenon is called leakage.

To mitigate this, a trick is used: the signal is artificially stitched together using windows,

making it periodic.

Windows also have another function: they dampen the signal at the beginning and end to ensure

a clean periodic signal when stitched together.

Different window types such as rectangular, Hanning and flat top have different characteristics

and in a vibration analyser you can select a window type to suit your needs best.

Vibration analysis can be broadly divided into two categories: machine mechanical fault

analysis and bearing analysis.

Basic machine mechanical faults include unbalance, misalignment and mechanical looseness.

We can detect these faults at low frequencies (10 - 1000 Hz).

Vibration measurements are measured in velocity (mm/s).

If the velocity values are high, examination of the spectrum can be helpful.

If the spectrum shows a single high line at the speed frequency, the fault is unbalance.

For example, if there is only one high line at 25 Hz, calculating 25 x 60 gives 1500 RPM.

If the speed is indeed 1500 RPM, the fault is unbalance.

Unbalance can be mechanical, requiring balancing, or

electrical (in the case of motors).

To differentiate, observe the velocity value when the motor is switched off.

If the velocity value decreases as the speed decreases, the fault is mechanical unbalance.

A rapid drop to almost zero (power cut) indicates an electrical fault.

If the speed line and its multiples (harmonics) are present in the spectrum, the fault is

looseness or misalignment.

Axial velocity values significantly lower than the radial values (e.g. less than 30%

of the radial value) suggest looseness.

In this case, readings should be taken on all machine feet.

This can be done without pads because velocity measurements at low frequencies are less sensitive

than high frequency acceleration measurements.

Locate the foot with the highest value; it likely points to the looseness failure.

This is often due to a broken anchor bolt.

If the axial velocity value is similar to or higher than the radial value, the fault

is misalignment, which requires alignment.

A unique type of fault is resonance, which is mimicked as an unbalance with a single

speed line in the spectrum.

Balancing will have minimal effect, as the real problem is the natural frequency of the

machine foundation near the speed frequency.

To identify this, measure the velocity at the foundation.

If the values are low at the ends and high in the middle, resonance is the problem.

Strengthening of the foundation is usually required - this will change the natural frequency.

The other aspect of vibration analysis is bearing analysis.

Bearing faults occur in the high frequency range (500 Hz to 16 kHz) and are represented

by the bearing vibrations - a tone - caused by ball impacts.

Acceleration (g) is used to measure vibration.

An increase in vibrations in the high frequency spectrum indicates a worsening bearing condition.

Bearing analysis focuses on the fault frequencies that are specific to bearings.

What is a bearing fault frequency?

Imagine a pitting on the outer race.

Each ball hitting the pitting causes a vibration shock (the tone).

If there is a crack on the outer race, we calculate the time interval (T) between shocks

based on the speed frequency and ball count.

This time interval defines the repeating frequency of the shocks - the fault frequency.

In this example, it's the fault frequency of the outer race.

But bearing fault frequencies don't appear in the bearing's spectrum; only the vibration

frequency from the ball impact (bearing tone) is evident.

Such a ball impact can be seen in the time domain:

To identify fault frequencies, signal demodulation is used.

This involves removing frequencies below 500 Hz (high-pass filter):

and artificially adding energy to the signal using envelope detection.

The signal is then processed using FFT to create the spectrum.

Due to the artificial distortion, the spectrum contains many harmonic frequencies that we

ignore.

Our fault frequency in this case is 10 Hz.