# An Introduction to Noise, Vibration and Electric Machines

This article introduces noise and vibration in electric machines, discussing the sources of vibration and where it can be found. It will also characterize noise vibration and harshness in electric machines, identifying what some of the features to look for are and why this is important.

There will also be discussion regarding the reason behind testing both noise and vibration together. There are many reasons why it is important to test these together and why communication is key. Workers in these areas need to have knowledge of both of them.

There will also be an overview of the HBK eDrive solution.

## Introduction to Vibration in Electric Machines

### A Simple Measurement Chain – Electric and Mechanical Vibration

Figure 1. Simple Measurement Chain – Electric and mechanical measurements. Image Credit: HBM

Figure 1 depicts an overview of the electric powertrain. There is a battery with DC electric current that goes into an inverter. This inverter switches on and off tens of thousands of times per second – it is a pulse with modulation signal (PWM). This DC energy is being converted using pulse-width modulation to AC with a high frequency content.

This high frequency voltage and current then goes into a motor and creates high-frequency magnetics. These high frequency magnetics are creating high frequency torque. A lot of this gets averaged out to form DC, but if it is analyzed in detail, there is noise created by these high frequency magnetics and voltage. The chain is DC voltage to AC voltage, to magnetics, to torque and speed.

This torque and speed also has a rotational element that has torque ripple and order effect resonances that have their own excited noise and vibration. These resonances can go into an output, like a propeller or a transmission, which have their own series of effects.

One of the reasons to care about this is driver experience. People do not want to hear terrible high-pitched whining at a certain speed. From a durability and fatigue issue, vibrations or noises are indicators that things are going wrong. Parts failing early needs to be avoided.

In this circuit what is in the inverter is going to end up in the mechanical output. Therefore noise in the output might be being caused by the inverter. Root cause analysis is necessary to understand why things are happening.

### Motor Construction – Sources of Vibration

Figure 2. Single motor pole for a PM machine highlighting iron slots and windings. Image Credit: HBM

Motor construction is a source of vibration. Figure 2 depicts a piece of a motor stator and rotor. The stator is in gray and the rotor is in green and brown. The colored dashes are the windings which have three-phase AC current going through them.

There are two sources of noise and vibration within motor construction, rotational speed and inverter switching. There is a low order noise and vibration caused by rotation and a higher order noise and vibration caused by the switching effects.

Inverter Switching

The intention is to obtain rotational forces, and so torque needs to be produced in the rotational direction. But when exciting the current radially, there is an equal and opposite force that goes out into the stator. If the inverter is being turned on and off at tens of kilohertz, there is an excitation force going out into the stator at tens of kilohertz.

If this structure, the stator, has a natural frequency or any resonances, the housing is going to be excited. This is a source of both noise and vibration.

Rotational Speed

Another source, rotational speed, is due to the physical construction of the machine. The permanent magnets highlighted in the brown want to stick to the gray iron. If the shaft of a motor was grabbed and spun, there would be a ptum, ptum, ptum sound. This is the sound of the magnets trying to stick to the slot teeth.

At a static position or during rotation, the magnets want to stick to these teeth. This creates something called torque ripple. Torque ripple is a function of the number of magnets and the number of slots. Essentially, vibratory effects are created from the speed of rotation.

### Inverter Operation

Figure 3. PWM to synthesize sinusoidal output. Image Credit: HBM

Figure 3 is a PWM signal, a pulse with modulated inverter command, where the inverter is being turned on and off at variable pulse widths. If this is filtered out, a smooth sine wave can be obtained.

Each one of these pulses is a voltage which becomes current and then torque. The individual pulses are going to create a noise and vibration effect at that high frequency switching. Unequally timed pulses result in multiple frequencies of noise and vibration.

Figure 4. Voltage, current and torque, highlighting the correlation between the 3 values. Image Credit: HBM

There are other control techniques, such as a six step, which is featured in the graph in Figure 4. The voltage is in blue, where there are six discrete steps in voltage. This translates to the current which has the shape of a sine wave, but with pronounced, jagged peaks. These jagged peaks are harmonics.

By translating from the jagged peaks and harmonics to look at torque signature, it is clear that when the inverter is switched on, there is a resulting spike in torque. When it is switched off, there is a dip in torque. This torque is directly correlated to that voltage and current.

This torque excites the shaft and downstream components. There are a lot of control techniques and any time we are pulsing current or voltage, we are pulsing torque and creating forces outward.

## Characterizing NVH for Electric Machines

### Inverter Voltage Influence on Mechanical Torque

Figure 5. Voltage, current and torque for a control change in a 3-phase machine highlighting the dependence of torque on excitation. Image Credit: HBM

By looking at inverter effects on frequency, it can be found that torque has a frequency component due to AC excitation and slotting effects.

Figure 5 shows the same example from before. The voltage on the left-hand shows a smooth PWM with modulated-type voltage. This results in a sinusoidal current, which results in a torque that has some ripple due to excitation effects but is relatively stable.

When switching that control technique and operating the inverter in a different method, what is called a six step can be obtained (the right side of the diagram in Figure 5). Here there are significantly fewer switches per second.

On the left-hand side there are 13 kilohertz and on the right side there are 500 hertz. There is high harmonic content in the current and there are wild torque swings that are going to result in noise and vibration downstream. This inverter controlled voltage and current is going to create a torque ripple later in the path. Inverter controlled torque ripple is used for sound design.

### Voltage, Current and Torque Frequency Content

Figure 6. Frequency spectrum comparing current and torque during PWM and 6 step operation. Image Credit: HBM

The best way to analyze all this is through frequency. In Figure 6, there is current on the left and torque on the right. The PWM is highlighted in blue, and the six step is highlighted in red. In the current FFT plot, there is a big peak at the fundamental in both, which is expected. Fundamental and rotational current and torque are similar.

However, there is almost no fifth harmonic for the PWM, but a huge one for the six step. This shows that there can be additional losses, additional torque ripple, and additional issues.

There is a big spike in torque at 200 Hertz. This is a function of the number of poles because it is a four-pole machine. There is a spike around the fundamental, as well as a very large spike at the fifth harmonic for both the six step and torque.

Another harmonic is present at 600 Hertz which is a function of the switching. The switching content of the torque can be seen. This frequency content is what is going to result in noise and vibration. A vibration spectrum will probably show spikes at 600 Hertz and at 250 Hertz, resulting from that electrical current.

### Current Causes Vibration

Figure 7. Frequency spectrum comparing current and vibration for a steady state machine operation. Image Credit: HBM

Along that same note, by taking take current and vibration rotational effects, shown in black in Figure 7, it can be seen that vibration and current correlate very closely to one another. The peaks are at the same frequency, they are just at different amplitudes, which is a transfer function. Thus, some machine vibrations are caused by the current.

By looking at inverter switching, shown in Figure 7 in green, it can be seen that there are also peaks at the same frequencies. Again, there is the possibility of this being the root cause behind noise being transferred out to the housing or to the driver of the vehicle.

Lastly, this specific converter had another field switching, where again this 20-kilohertz carrier frequency is being translated into the vibratory function. Thus, current and vibration or current and noise can be very closely correlated.

Torque sensors often have a bandwidth limit of up to six kilohertz, and so an accelerometer or a vibration measurement can be used as an indicator of torque ripple beyond a given frequency.

The underlying conclusion of this is that current goes to torque, which goes to vibration. The factors are all linked.

Figure 8. Frequency spectrum comparing current and vibration for a steady state machine operation at 3 loading points. Image Credit: HBM

As you increase current loading by putting in more current and torque into a machine, the level of vibration increases. Figure 8 shows a test ran at three different load states: 0, 13 and 26 newton-meters. The resulting vibration spectrum shows that as our torque increases, the amount of vibration increases as well.

These are directly correlated phenomena. There is going to be a drastic increase in gear mesh orders as loading increases. There might be certain circumstances or resonant modes or given operation points where torque ripple is higher and potentially gear measure orders are higher. Looking at these things, the current and vibration can indicate what is happening downstream in the gearbox and the transmission.

### Ramps and Spectrum Plots

Figure 9. Spectrum graph showing vibration bands and current bands for the rotational frequency of a ramp test. Image Credit: HBM

A common plot used for understanding rotational machinery is a spectral plot, where a machine is taken, a loading point fixed, and a sweep from zero to a certain speed is done. This is a plot of amplitude (z) versus frequency content (x) versus rotational speed (y). These plots are an easy way to graphically see the influence of speed on current and vibration.

When looking at both current and vibration in one of these plots, the darker lines at the angle are indicating harmonics or orders. The bright yellow line on the right, is the fundamental in the current. Subsequent orders or harmonics come off that. The red line indicates the fifth harmonic from the previous example. This fifth harmonic can also be followed in the vibration spectrum.

When doing a noise and vibration test, a way to understand the root cause of your vibration is to bring in a current and gain cohesive understanding this way. This graph was made in BK Connect, an HBK product.

## Why Measure Both?

### Benefits of Combined Testing

Since there is so much carryover between current and vibration, it is beneficial to look at a single test for both measurements. This reduces capital costs, which is especially advantageous for startups or new groups.

When making a change to an electric machine to increase efficiency, noise and vibration might be negatively affected, which comes into vehicle experience. On the other hand, by making a change in noise and vibration to increase the experience it can hurt the efficiency, and right now efficiency is paramount.

Communication between groups needs to be increased to optimize the system. An enjoyable vehicle experience needs to be mixed with a vehicle that can go as far as it needs to. Increasing communication speeds up development and ensures that vehicles get to the market more quickly.

In this era communication of vehicle simulation is important. This way the voltage state, current state, torque state and vibratory state can be shared in order to provide a full data set to understand the vehicle.

Communication is also very important to sound design.  There is an increase in the number of people trying to design sound into the machines. Anytime you are going to introduce noise, there is a chance of reducing efficiency. Solving these problems comes back to communication, speeding up development, and optimizing the end product.

Communication also helps with fatigue characterization. If a vibration or a resonance is causing fatigue and gear failure, it could be caused by magnetics. Increasing communication lines helps the vehicle team to get to root causes sooner.

Figure 10. Propeller motor start up with load and vibration measurements. Image Credit: HBM

Figure 10 shows a graph of voltage and current as a test is sped up. Voltage and current are increasing and vibration is going up and down with loading. This example was a lift fan for an electric aircraft – all these issues and solutions apply to aerospace as well as automotive.

## HBK eDrive Solution

### High Accuracy Power Measurements and Simplified Data Collection of Electromechanical Signals

All the tests shown in this article were carried out with eDrive test equipment. The HBK eDrive solution system is a power analyzer that gives very accurate power and efficiency measurements. Simplified data collection of electromechanical signals allows measurement of accelerometers, many torques and speeds, and many voltages and currents. There is a wide variety of sensors all with one system.

### Future-Proofing

The eDrive enables future-proofing of testing capabilities. The chassis has seven card slots. In these seven slots, up to seven cards can be added for voltage and current, or torque and speed, or vibration. This enables test customization. For example, if a customer buys when they do not have noise and vibration needs, they could add them in the future if required.

### Auditable Tests

The eDrive tests are auditable. All the data is recorded so that customers can go back through the data and understand what happened to the test and why. Furthermore, everything is time aligned so that things can be correlated very closely. This is especially useful when applying unusual control techniques such as pulsing currents that might be causing asynchronous vibrations.

### Full Data Streaming / Raw Data Collection

Full data streaming means that customers know where their results came from. For everything measured, the raw data is also measured. Calculations can be fed back to an automation system.

### Simplified Measurement Chain

Sensors → Acquisition → Software

HBM torque sensors aim is to simplify the measurement chain. HBM makes sensors and pair them with acquisitions to measure the full bandwidth of the torque sensor, which allows measurement of the full bandwidth of an accelerometer.

HBM also provides analysis software, which enables analysis of electric machines, efficiency mapping and then production of spectrum graphs, rain flowcharts, and a lot of noise and vibration measurements.

This information has been sourced, reviewed and adapted from materials provided by Hottinger Baldwin Messtechnik GmbH (HBM).

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