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# Torsional Vibration: What is it?

Siemens Experimenter

Question: Look at this RPM curve: what is unusual about it?

Figure 1: RPM vs time curve of a 4 cylinder engine run-up.

Answer: While the overall rpm increases from 1000 RPM to 3500 RPM, it does not increase steadily. There is a variation (i.e. fluctuation) in the rotational speed within each rotational cycle (see zoomed in plot below):

Figure 2: There is a 100 RPM fluctuation in rotational speed!

Torsional vibration is the fluctuation in the rotational velocity of a rotating component. These fluctuations are superimposed on the steady running speed.

Why does torsional vibration matter?

Just about every rotating machinery system has fluctuations in speed (engines, electric motors, hydraulic pumps, etc.). Some examples include:

• Electric motors have distinct poles that cause small variations in speed
• Engines have combustion events that cause the crankshaft to slightly speed up and down
• Hydraulic pumps have distinct chambers in which liquid flows in and out. As liquid is forced into and out of discharge ports at different rates during the rotation cycle, there are slight variations in speed

These unsteady fluctuating speed changes are called torsional vibration.

Torsional vibration can cause a variety of problems:

• Durability problems: flexible coupling wear, gear ware, etc.
• Vibration comfort: vibrations traveling to the steering wheel, seats, pedals, etc.
• Noise problems: gear whine, clutch chatter
• Synchronization problems: reduced performance, reduced fuel economy

How to measure torsional vibration?

Measuring torsional vibration requires measuring the RPM of a shaft with a high number of pulses per revolution (PPR) (i.e. taking many samples per rotation as the shaft is rotating). To capture the torsional vibration, a high PPR must be used as the speed is changing within each single revolution of the shaft.

Below is an example of the same RPM run-up (as Figure 2) being measured with two different PPR rates. The red curve was measured with 120 PPR and the black curve was measured with 1 PPR.

Figure 3: The lower PPR rate (black) did not capture the torsional vibration. The high PPR (red) captured the fluctuation of rotational speed within the rotation cycle.

Real life example: When accelerating in your vehicle, the speedometer shows the needle smoothly moving up in speed. In reality, there are minor fluctuations as the RPM increases. See the video below.

(view in My Videos)

The RPM appears to increase smoothly because the gauge is only sampling about once per revolution of the crankshaft. If the gauge sampled faster, the fluctuation in speed (torsional vibration) would become more apparent. Cars may even be returned to the dealership because users would believe the engine was running unsteadily!

Which sensor to use?

There are many sensor options to measure torsional vibration (accelerometers, strain gauges, optical sensors, magnetic pickups, incremental encoders, etc.).

Two common sensors used to measure torsional vibration are magnetic pickups or optical encoders (in conjunction with zebra tape / zebra disks).

Magnetic pickups are a popular tool as they are robust, relatively inexpensive, and have low sensitivity to ambient dust. However, the pulses per revolution of the magnetic pickup is limited to the number of teeth on the gear being measured. Each time a tooth passes the sensor counts one pulse (Figure 4).

Figure 4: A magnetic pickup sensing the teeth passing on a gear.

The other type of sensor is an optical sensor used in conjunction with zebra tape (Figure 5) or a zebra disk (Figure 6). This allows the user to get a very high pulse per revolution number. Each white line on the zebra tape/disk is detected as one pulse: therefore different PPR rates can be set according to how densely striped the tape/disk is.

Figure 5: An optical sensor detecting the pulses on a shaft wrapped in zebra tape.

Caution should be used with zebra tape.  As the tape wraps around the shaft, the overlap at the ends can create a butt joint.  This butt joint may create what appears to be large fluctuations in the rpm which are not really present in the shaft rotation.   A correction algorithm can be applied to remove the butt joint effect.

Figure 6: Zebra disk: one disk with 40 divisions and one disk with 100 divisions. The disk would be put on the butt end of a shaft if it was difficult to wrap in zebra tape (see right).

When sampling for torsional orders, the PPR rate must be at minimum twice the order of interest! So, to measure a 60th torsional order, at least 120 PPR should be used (often a safety factor of 10 is applied as a PPR has no aliasing protection). See Figure 7.

Figure 7: The dark blue range shows no order information because the PPR rate is not high enough. Here, the sampling rate was 120 PPR and past the 60th order there are no more orders showing.

The Simcenter SCADAS front end features two high-performance tacho inputs, including direct current or ICP power supply for the input sensors. Simcenter SCADAS RV4 input modules allow to up to four tacho pulse streams at a high pulse rate either offline or in real time. Making measuring torsional vibration easy!

Torsional Orders

Torsional orders aid in diagnosing which component is contributing to the torsional vibration.

After generating a colormap from the RPM vs time data of the 4 cylinder engine run-up (from Figure 1) it is clear that 2nd order (and its harmonics) are the dominant orders (Figure 8, left).

Figure 8: Left: The colormap generated from the RPM run-up data from a 4 cylinder engine. A harmonic cursor was added showing that 2nd order and its harmonics are the dominant orders. Right: The x-axis represents the overall RPM level during the engine run-up (1000 RPM - 3500 RPM). The y-axis represents the fluctuation in RPM (torsional vibration) at each overall RPM value. The torsional vibration decreases as the RPM increases except at crankshaft resonance (around 2600 RPM).

The 2nd order is the firing order of this 4 cylinder engine. The firing order is usually the dominant order for torsional vibration in engines.

The crankshaft is driven by cylinders that fire within each rotation of the crankshaft. Each time the cylinder fires, the crankshaft speeds up a little. However, due to the inertia properties of the crankshaft, it slows down between each combustion event. This non-constant rotational speed is the torsional vibration.

Higher torsional vibration at lower RPM:

The slower the engine is firing, the longer the time between combustion events, and the more the crankshaft slows between combustion events. Therefore, the lower the RPM, the greater the torsional vibration (see the right side of Figure 8: the torsional vibration increases as the RPM decreases).

Also, the less cylinders an engine has, the less combustion events per revolution of the crankshaft, and the longer the time between combustion events. Therefore less cylinders can lead to greater torsional vibration.

Torsional resonance:

In the Figure 8 (above) order cut, there is clearly crankshaft resonance around 2600 RPM (the peak in torsional vibration).

Below (Figure 9) is an example of how the crankshaft may be moving at resonance.

Figure 9: The peak in torsional vibration is due to crankshaft resonance. The animation shows how the crankshaft may be moving at resonance.

This twisting motion of the crankshaft amplifies the amount of torsional vibration seen in the system.

How are torsional orders used in NVH analysis?

Torsional orders aid in determining whether or not torsional vibration greatly contributes to the noise and vibration level in the product.

Imagine taking data at the driver’s right ear (DRE) with a microphone. The second order data is displayed below in Figure 10. This shows the decibel level at the DRE corresponding to a certain RPM.

Figure 10: 2nd order noise data taken at the driver’s right ear.

Notice there is a large peak around 2600 RPM. An engineer may wonder what is causing that peak. After overlaying the 2nd torsional order on the graph, it is clear that the peak in dB is caused by the crankshaft’s torsional resonance (Figure 11).

Figure 11: The peak in decibel level around 2600 at the driver’s right ear is caused by the crankshaft resonance.

The peaks align showing that the crankshaft resonance is what is contributing the most to the second order peak at the driver’s right ear.

Torsional orders are a great tool to determine whether the torsional vibration is driving the level of noise or vibration of a product!

Enjoy exploring torsional vibration!

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Siemens Experimenter

This is a nice post, Jacklyn..  I think it will help a lot of people..

Theorist

Hi guys!

I've confused respect of the white paper about torsional vibration.

In the chapter "Processing and Analysis" from the white paper, in the part of "torsional Resonances", coments that is possible to develop Experimental Modal Analysis at the rotating shaft to find torsional damping too. I've search some bibliography about that process, e.g. how to do it or which modal analysis technique (maybe PolyMAX, EFDD, SSI, etc.) can I use for that but I don't find information about that. Can you suggest me some bibliography abut that?.

Jair

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