MODAL SPACE - IN OUR OWN LITTLE WORLD

模态空间–在我们自己的小世界中   

Pete Avitabile 著  KINGSCI INSTRUMENTS-KSI科尚仪器 组织 westrongmc 译

Should I always use a hard tip for impact testing . . .

so the input spectrum is flat over all frequencies?

Well . . . too hard a tip may cause problems.

难道我总要用硬锤头进行锤击试验…

以使得所有频率上的输入谱是平坦的吗？

嗯…锤头太硬会有问题。

For some reason, everyone thinks that the input spectrum should be flat over the whole frequency range of interest when performing an impact test. But what do we mean by "flat" anyway. Well, it would be better to say that the input spectrum should be "reasonably flat" over all frequencies with "no significant drop-outs or zeros" in the frequency spectrum. So what does that mean?

出于某些原因，人皆认为进行锤击试验时，在感兴趣的整个频率范围内，输入谱应该是平坦的。但是我们所说的“平坦”到底是什么。嗯，更恰当的说法是，输入谱在所有频率上应该是“还算平坦”，并且频谱上“没有明显的漏点或零点”。那么这是什么意思？

Basically, we want the input spectrum to have sufficient, fairly even excitation over the frequency range of concern. If the input spectrum were to completely drop off to zero, then the structure would not be excited at that frequency which is not desirable. I use the words "reasonably flat" to allow for some engineering judgment as to what is acceptable.

总的说来，我们想要输入谱在关心的频率范围内具有足够的、相当平坦的激励。假设输入谱完全衰减到零，则在这个频率上激不起结构，这是我们所不希望的。我用“还算平坦”这个词以允许对于什么是我们可以接受的作出某种工程判断。

Of course, many times people don't like engineers to use judgment, so they identify specific criteria or limits to force the situation to be controlled. At times, specifications have been written with specific criteria such as "the input spectrum should roll-off no more than 3 dB over the FFT analysis frequency range". This is a very specific requirement which does not allow the engineer to think. It just forces him to follow a rule without thinking. A criterion like this one may force a poor measurement to be made. But if we don't have to think (or are not allowed to think) then inappropriate measurements could be acquired.

当然，大多数情况下，人们不喜欢工程师使用判断力。所以他们确定了具体的标准或限值以强制情况可控。有时，发布了带有具体标准的技术规范，诸如“在FFT分析频率范围内，输入谱衰减不得超过3dB”。这是一个非常具体的要求，不允许工程师进行思考。它只会使工程师不得不遵守规则，而无需思考。一个类似这样的标准可能会使得糟糕的测量结果一定发生。如果我们不要思考（或不允许去思考），那么就可能采集不到恰当的测量结果。

Now you asked about using a hard tip for all your impact tests. I'll answer that in a minute but first let's discuss some basics about the selection of hammer tips for an impact test. First of all, let's remember that the input force spectrum exerted on the structure is a combination of the stiffness of the hammer tip as well as the stiffness of the structure. Basically the input power spectrum is controlled by the length of time of the impact pulse. A long pulse in the time domain, results in a short or narrow frequency spectrum. A short pulse in the time domain, results in a wide frequency spectrum.

刚才，你问过，对于所有的锤击试验使用硬锤头。这个问题我稍后解答，让我们还是先讨论一些关于锤击试验的锤头选择的基本知识。首先我们记得，施加到结构上的输入力谱是锤头硬度以及结构硬度综合作用的结果。总的说来，输入功率谱是由冲击脉冲的时间长度控制的。时域内的长脉冲产生短或窄频谱。时域内的短脉冲产生宽频谱。

Let's look at some cases and see what this means from a measurement standpoint. (In all the following figures, black is the FRF, blue is the input spectrum and red is the coherence).

让我们来看一些实例，并从测量的角度来理解这是什么意思。（下面所有图中，黑色为频响FRF，绿色为输入谱，而红色为相干）。

Now let's use a very soft tip to excite a structure over an 800 Hz frequency range. As shown in Figure 1, we see that the input power spectrum (blue) has some significant roll-off of the spectrum past 400 Hz. We also notice that the coherence (red) starts to drop off significantly after 400 Hz and the FRF (black) does not look particularly good past 400 Hz. The problem here is that there is not enough excitation at higher frequencies to cause the structure to respond. If there is not much input, then there is not much output. Then none of the measured output is due to the measured input and the FRF as well as the coherence are not acceptable.

现在，我们使用一个非常软件的锤头来激励一个结构，频率范围为800Hz。如图1所示，我们看到，过了400Hz，输入功率谱（蓝色）有较明显的衰减。也注意到，400Hz之后，相干（红色）开始明显衰减，而且过了400H，频响FRF（黑色）看上去也不是特别好。此处症结在于，高频部分没有足够的激励来引起结构响应。没有输入就没有输出。因为测得的输入、频响、以及相干不可接受，则不必妄谈测得的输出。

Now let's use a very hard tip to excite a structure over a 200 Hz frequency range. As shown in Figure 2, we see that the input power spectrum (blue) is extremely flat over all frequencies of interest. We also notice that the coherence (red) is not particularly good for this measurement. The problem here is that there is too much excitation at higher frequencies causing all the modes of the structure to respond.  (We'll discuss this further in a moment.)

现在，让我们使用一个非常硬的锤头来激励一个结构，频率范围为200Hz。如图2所示，我们看到，输入功率谱（蓝色）在感兴趣的整个频率范围内极其平坦。也注意到，对于此次测量结果，相干（红色）不是特别好。此处症结在于，高频部分激励过甚，引起了结构所有阶模态的响应。（这点我们稍后进一步讨论。）

Now let's use a medium hardness tip to excite a structure over a 200 Hz frequency range such that the input force spectrum does not drop off significantly by the end of the frequency range of interest. As shown in Figure 3, we see that the input power spectrum (blue) rolls off by 10 to 20 dB by 200 Hz.  We also notice that the coherence (red) looks especially good at all frequencies over the 200 Hz band with the exception of anti-resonances. The drop off of the coherence is fully acceptable at these frequencies since the structure is non-resonant (anti-resonant) at these frequencies. This means that there is no response to measure so the coherence is expected to drop here. This is a good measurement.

现在，让我们利用中等硬度的锤头来激励结构，频率范围为200Hz，这样一来，在感兴趣频率范围的尾部，输入力谱没有明显的衰减。如图3所示，我们看到，输入功率谱（蓝色）在200Hz的位置衰减了10～20dB。也注意到，除了反共振频率之外，相干（红色）在200Hz范围内的所有频率上看上去都特别好。在这些反共振频率上，相干的衰减完全可以接受，因为在这些频率上，结构不产生共振（反共振）。这意味着测量不到响应，相干预期会在此处减小。这是个不错的测量结果。

Notice that the input spectrum is not perfectly flat as you suggested it should be. In fact, when the input is almost perfectly flat as shown in Figure 2, the measurement is not as good. Let's explain why this happens. Consider the measurement shown in Figure 4. This measurement was taken over a 400 Hz bandwidth. The hammer tip used had approximately 20 dB roll-off over the 400 Hz band which is probably acceptable for this measurement.

注意到，输入谱并不是如你所建议的那样完全平坦。实际上，当输入几乎完全平坦时，如图2所示，测量结果并不好。那我们解释这是为什么？考虑如图4所示的测量结果。这个测量结果是在400H带宽范围内采集到的。对于这个测量结果，在400Hz带宽范围内，所用锤头大约具有20dB的衰减，这大体上可以接受。

Now let's say that I wanted to only measure to 128 Hz and that I wanted to impose a restriction that the input spectrum could not roll off more than 3 dB. Well look at Figure 4 with the 128 Hz bandwidth specified. The input force spectrum rolls off approximately 2 to 3 dB over this 128 frequency band.  So the measurement should be acceptable. But what you have to realize is that while the analysis frequency band is only 128 Hz, the response of the structure is based on the energy imparted to the structure. So the structure responds well past 128 Hz because the input force excites all of those modes - even though I might not be interested in those frequencies.

现在，比如说我只想要测量到128Hz，并且我想限定输入谱衰减不得超过3dB。观察图4，图中具体指出了128Hz带宽。在这个128Hz频率范围内，输入力谱衰减了大约2～3dB。因此这个测量结果应该可以接受。但是你必须意识到，尽管频率范围只有128Hz，但结构响应是基于施加到结构中的能量的。在128Hz之外，由于输入激振力激起了所有阶模态，因此结构响应较大 — 尽管我可能对哪些频率并不感兴趣。

The accelerometer, mounted on the structure, measures all that response and outputs a voltage which is input to the analyzer. Just doing a quick eyeball of the total area under the curve of the FRF, it appears that only one-third of the energy is associated with the bandwidth of interest. The rest of the energy is associated with something that I'm not interested in measuring. But the accelerometer senses that energy! The ADC on your analyzer may need to be setup such that an overload does not occur due to the total response of the structure.

安装到结构上的加速度计，测量所有的响应并且输出一个电压，电压输入到信号分析仪。只要快速浏览一下频响FRF曲线下面的整个区域，看上去好像只有1/3的能量与感兴趣的带宽相关。其它部分的能量与某些情况相关，对之我没有兴趣测度。但是加速度计却感知到这个能量！可能需要对信号分析仪的ADC进行设置，这样，不会因结构总体响应而导致过荷发生。

If the signal is not analog filtered before it reaches the analyzer, then the ADC may need to set excessively high to avoid a potential overload. Remember, most of the energy of the signal is probably outside the 128 Hz bandwidth of interest!!! This results in a quantization problem in the ADC. This can easily be corrected through the use of an impact tip that does not needlessly excite modes outside the bandwidth of interest.

如果信号在输入到分析仪之前，没有进行模拟滤波，则ADC量程可能需要设置的很高，以避免潜在的过荷。记住，信号的大部分能量可能超出感兴趣的128Hz带宽！！！这会导致ADC中的量化问题发生。利用锤头很容易解决这个问题，只要锤头没有激起感兴趣带宽之外的模态，也没有这个必要激起。

So now you can see why I don't like to use a hard tip all the time for impact testing. Sure it gives a good flat input force spectrum. The problem is that it excites more modes than desired and may cause a poor measurement. Think about it and if you have any more questions about modal analysis, just ask me.

好了，现在你能理解对于锤击试验，我为何不喜欢一直用硬锤头了。确信无疑，它可以产生一个相当平坦的输入谱。问题在于，跟预期的相比，它激起了更多的模态，这或许会产生糟糕的测量结果。好好考虑一下，如果你有关于模态分析的任何其他问题，尽管问我好了。