Interpreting Colormaps

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A colormap (sometimes called a spectrogram or Campbell plot) can give insight into the causes of high levels of noise and/or vibration that rotating machinery is experiencing. Products from cars to washers to airplanes can be diagnosed using a colormap analysis.

 

To create a colormap, several Fourier Transforms are performed at multiple rpms or instances in time while the rotating machinery is operating.  These Fourier Transforms are assembled into a plot with three dimensions:

  • Frequency
  • RPM or Time
  • Amplitude

For details on how to create a colormap in Simcenter Testlab, see the ‘Throughput Processing’ knowledge base article.

 

In this article, several different colormap examples will be shown to illustrate the following issues:

  1. Orders
  2. Resonances
  3. Modulated Orders
  4. Transients
  5. Electric Switching

 

Using this article as a reference, the hope is that the reader will be able to identify issues of their product using similar analysis.

 

Order

 

Figure 1 below is a colormap of the sound at driver’s ear produced in a vehicle with a four cylinder engine.  The second order is producing the highest amplitude sound at the driver’s ear. There are two regions of high amplitude in second order:

  • 3000 to 3500 rpm
  • 4800 rpm and above  

These regions are denoted in red in the colormap.

 

colormap_order.pngFigure 1: Second order is the largest amplitude sound in this recording of a vehicle with a four stroke, four cylinder internal combustion engine.

An order is a vibration or sound that changes frequency proportionally to the operating speed (in rpm) of a product. To produce a second order, an event occurs in the rotating system twice per revolution.  In this case, the combustion event occurs twice per revolution of the engine crankshaft.

 

See knowledge base article “What is an order?” to learn about the relationship between orders, events, frequencies, and more.

 

Why is there a strong 2nd order in this example?

 

The high second order is caused by combustion events in the engine.  Combustion is the most “violent” event in an engine, causing it to vibrate and, in turn, create noise. In a four cylinder engine, there are two combustion events with each revolution of the engine crankshaft as shown in Figure 2.

 

engine.pngFigure 2: In a four cylinder engine, there are two combustion events (red explosions) per revolution of the crankshaft.

Not all four cylinders fire with each revolution, because it is a four stroke engine.  The piston must travel up and down the cylinder twice to create a complete engine cycle, as shown in Figure 3.

 

engine_cycle.pngFigure 3: In a four stroke engine, two revolutions of the crankshaft are required for one combustion cycle. The piston position is indicated by the black rectangle.

Here is what happens during an engine cycle:

  • Intake - The air fuel mixture enters the cylinder.
  • Compression – Air fuel mixture is compressed by the piston traveling up the cylinder.
  • Power – Air fuel mixture is ignited, throwing the piston down causing the crankshaft to rotate.
  • Exhaust – Air fuel mixture is vented out of cylinder.

To keep the engine running, half of the combustion events occur during one revolution, the other half in the next revolution.

 

What can be done?

 

With a vibration or sound source like an engine, there are a few options that can be employed to reduce the vibration or sound it produces:

  • Combustion Timing – The timing of the combustion events can be adjusted to try and reduce vibration. For example, igniting the air fuel mixture slightly before the piston is at top dead center of the cylinder.  This could make the pressure buildup in the cylinder more gradual and decrease vibration. 
  • Dampers - It is common practice to have a damper between the engine and the rest of the propulsion system. This could be a simple inertial mass flywheel damper, that once spinning, helps smooth the impulses from each combustion event. More sophisticated damper designs include dual-mass flywheels.
  • Absorbers - Centrifugal pendulum absorbers can be used on engines to reduce the vibration of specific orders.

If neither the engine nor its control strategy can be modified, the vehicle can be modified instead.  To reduce the amount of vibration or sound experienced by the driver, the following could be changed:

  • Mounting/Isolation – The motor can be isolated from the support structuring using elastomeric bushings.
  • Acoustic Treatment – The dashboard and interior of the car can be sealed with acoustic treatment to reduce the amount of sound that reaches the driver ear.

 

Resonance

 

In Figure 4, the colormap shows high vibration levels measured on a piece of machinery.  The high levels occur at two different frequency bands: 450 Hertz and 750 Hertz.

 

This high vibration is caused by resonances in the machinery fixturing that are excited by the operating frequencies of the equipment. When the operating frequencies line up with the resonant frequencies, higher levels of vibration or sound are created. 

 

colormap_resonance.pngFigure 4: Colormap shows resonances at 450 Hertz and 750 Hertz.

These resonances manifest themselves as horizontal lines in the colormap. The resonances of the fixturing are constant frequency, because they do not change with the rpm of the operating inputs.  The natural frequencies, or resonances, are inherent properties of the fixturing.

 

The colormaps in this article have rpm on the bottom axis, frequency on the vertical axis, and amplitude shown in color.  Depending on user preference, the bottom rpm axis and vertical frequency axis can be swapped.  This would make the resonances show as vertical lines, rather than horizontal lines.

 

At 450 Hertz, the machinery fixturing has fore/aft resonance on the right side as shown in Figure 5.

 

res2a.gifFigure 5: Mode shape of machinery being tested in 450 Hertz range.

 

At 750 Hertz, the machinery fixturing bends on both the left and right side as shown in Figure 6.

 

resonance.gifFigure 6: Mode shape of system being tested in 750 Hertz range.These fixturing resonances amplify the rotating machinery vibrations.

 

What to do about resonance issues?

 

Ideally, to reduce vibration or noise, the natural frequencies (or resonances) of the equipment and operating orders should not intersect. This could be done by changing the resonant frequency or modifying the operating speeds of the equipment:

  • Shift the Frequency of Resonance - Move the resonance higher, out of operating excitation frequency range, so it is no longer excited. This can be done by either increasing the stiffness or decreasing the mass of the structure.
  • Operating Speeds – If this equipment will operate at a fixed speed, the rpm could be selected where the least vibration occurs, far away from a resonance. In this example, perhaps it could run at 600 rpm. Or the upper operating rpm could be limited. For example, the equipment could be governed so it does not run above 2200 rpm.

 

If the operating frequencies and resonances cannot be shifted or changed, then the following can be considered:

  • Damping - Increase the damping in the structure, so it responds to the operating inputs with less amplitude.
  • Tuned Absorber – A tuned absorber could be added to the structure to reduce vibration at key speeds.

 

For more information on resonances, performing modal modifications, and tuned absorbers, see the Natural Frequency/Resonance article and Modification Prediction article.

 

Modulated Order - Sidebands

 

In the colormap of Figure 7, a modulated 62nd order can be seen. In this example, there is a 62 teeth gear that is being modulated twice per revolution. This modulation creates “sideband” orders that are two orders off of the 62nd order.

 

colormap_modulated.pngFigure 7: A modulated order has “sideband” orders. In this example, 62nd order is modulated twice per revolution, creating a 60th and 64th order.

When an order has sidebands, or is modulated, this can indicate a specific problem in the rotating machinery system. An example of how an eccentric gear can create modulated orders is explained next.

 

How does a 62nd gear order get modulated twice per revolution?

 

Looking a Figure 8, there are two gears (Note: Need to use some imagination, they are drawn without teeth). One of the gears is perfectly round (Gear 1), the other is not round (Gear 2). Instead, Gear 2 is oblong or eccentric. This could occur if the geometric properties are not well controlled during manufacturing, particularly in the hobbing process where the gear is formed.

 

eccentric_gear.pngFigure 8: A gear pair (drawn without showing gear teeth) with one perfectly round gear (Gear 1) and one eccentric or oblong shaped gear (Gear 2).

Gear 2 is pushed and pulled away from Gear 1 twice per rotation as shown in Figure 9. This causes a twice per revolution change in the gear teeth contact.

 

gear_position.pngFigure 9: Due to the eccentricity of Gear 2, the gears are pushed together and pulled apart twice per revolution.

If Gear 2 was perfectly round, the green curve would be flat, and no modulation would occur.

 

In Figure 10, the effect of modulation can be seen in both the revolution and order domains.  If the gear had 62 teeth, and the gears were both perfectly round, there would be a gear mesh order of only 62nd gear (top graph). With the eccentric gear, the two times per revolution push-pull modulates the gear mesh order creating sidebands (bottom graph).

 

modulation.pngFigure 10: Top – Revolution and order domain of single, unmodulated order. Bottom – Revolution and order domain of modulated order.

Because there are two modulations per revolution, there are sidebands two orders below and two orders above the main order.

 

What to do about gear eccentricity issues?

 

Making the eccentric gear perfectly round seems like a logical answer.  But from a noise or vibration point of view, this may not be the best way to reduce it.  When all the energy of the gear pair mesh is in a single order, the vibration and/or sound produced is higher in amplitude than the modulated sidebands. 

 

The eccentric gear distributes the energy over a broad frequency range, which makes the sound or vibration less, as shown in Figure 11.

 

sidebands.pngFigure 11: Top – Revolution and order domain of single, unmodulated order. Bottom – Revolution and order domain of modulated order.

Gear manufacturers can control the eccentricity, just for this purpose.

 

Note that it is not possible to associate physical features with the sideband orders.  For the 62nd order in the example used, there are 62 physical teeth on the gear.  However, for the 60th and 64th side band orders, there is no corresponding physical part with the same number of features as the side band orders, e.g., there is no 60 tooth or 64 tooth gear in the system.

 

Many different physical phenomenon can cause modulation, not just eccentric geometries.  For example, an off center rotation of a gear not centered on its shaft would cause a once per rotation modulation.

 

Transients

 

In the colormap of Figure 12, there is an increased amplitude band of sound in the frequency range of 1000 to 3000 Hertz.

 

colormap_transients.pngFigure 12: Impacts create a series of broad frequency responses.

This is caused by two parts constantly impacting each other for brief moments of time.  These impacts show as vertical lines in the colormap. Impacts frequently occur in mechanical systems with tight clearances.  Each brief impact of the two parts creates a broad frequency response as shown in Figure 13.

 

transient_time_and_freq.pngFigure 13: A short transient event in the time domain creates a broad frequency response.

What can create a brief impact? A piston traveling up and down a cylinder in an engine will often scrape momentarily against the cylinder wall at a certain angular position during each revolution of the engine (Figure 14). 

 

piston_scraped.pngFigure 14: Piston has wear from repeatedly scraping cylinder wall.

Another example of a transient impact issue is gear clatter (Figure 15). 

 

rattle4.gifFigure 15: Gear rattle is caused by torque fluctuations on unloaded gear pairs.

In a transmission, there are several gear pairs. Only one gear pair is engaged at a time, while the others are not.  Due to torsional fluctuations in the engine speed, the gear pairs in the transmission experience torque pulses.  The torque pulses often create impacts in the unloaded gears because they are floating, and move back and forth easily.  Each impact creates a broad band frequency rattle.

 

Somtimes, a wavelet analysis is used to generate a colormap analysis for transient events, rather than a series of Fourier transforms. A wavelet analysis usually has a finer time-frequency resolution.

 

What to do about transient issues?

 

For transient issues like piston clatter and gear rattle, the impact events have to be reduced or eliminated.  In the case of a piston in a cylinder, the position of piston on the rod can be offset slightly to prevent impacts from occurring.  For a gear pair, one gear might need a slight load applied to it so the gear pair is not floating freely. Alternatively, changes in the micro-geometry of the gear teeth shape can improve the contact between gears so rattle occurs less frequently.

 

Electric Switching

 

Ever see something that looks like an order, but never crosses zero in your colormap?  See the example in Figure 16 below.

 

colormap_switching.pngFigure 16: Electric motor order and switching frequencies. The harmonics of the switching frequency separate as the electric motor is commanded to increase in speed.

This is the switching frequencies of power electronics, used to command an electric motor.  The amplitude of the vibration or sound created by the power electronics can be as high as the electric motor itself.

 

These switching frequencies are created by a Pulse Width Modulated (PWM) signal used to convert DC Voltages into AC Voltages to drive an electric motor as shown in Figure 17.

 

power_electronics.pngFigure 17: DC Voltage being converted to AC Voltage.

The Pulse Width Modulated (PWM Signal) turns on and off in a specific sequence.  The PWM has a base switching frequency.  Common base PWM frequencies include 2500, 5000, or 10000 times a second (ie, Hertz).  In Figure 16, the base frequency is 5000 Hertz, hence the switching frequencies are centered around 5000 Hertz.

 

In Figure 18, a base PWM is shown (top graph) with equal on and off time.  In order to produce a sine wave (bottom graph) for the electric motor, the off time is varied (middle graph) relative to the on time.

 

pwm_and_sine.pngFigure 18: Top – Base PWM, Middle – PWM with variable duration pulse, Bottom – Sine Wave that PWM creates.

The sine wave pattern that is used in the Pulse Width Modulation (PWM) commands the electric motor, changing its speed as shown in Figure 19.

 

pwm_and_motor.pngFigure 19: The width of the pulses are changed to create a sine wave pattern that increases and decreases the speed of the electric motor.

Varying the turning off time creates harmonics around base 5000 Hertz frequency seen in Figure 16. As the motor is commanded to increase in rpm, the harmonics spread farther apart from the base frequency.

 

What to do about power electronic switching noise issues?

 

There are two different ways that switching frequencies can be altered:

  • Base Frequency – The base frequency of the switching scheme can be changed. For example, it could be increased from 2500 Hertz to 15,000 Hertz which would be less audible to humans.  This also impacts the efficiency of the motor.
  • Switching Scheme – Instead of a very discrete PWM pattern, the switching scheme can be altered. For example, a randomized PWM switching scheme can be used as shown in Figure 20.

 

switching_schemes.pngFigure 20: Changing the PWM switching scheme can reduce the amplitude of the switching frequencies. Left graphs shows a discrete switching scheme, right graph is of a randomized switching scheme.

When changing a switching scheme, notice that the electric motor frequencies remain unaltered as shown in the lower part of both the right and left graph in Figure 20.

 

For information on how to analyze PWM signals in Simcenter Testlab, check out the Forum post: Simcenter Testlab: Evaluating PWM Signals

 

Conclusion

 

Hope this article helps in identifying your noise and vibration issues!

 

Questions?  Email peter.schaldenbrand@siemens.com or contact Siemens PLM GTAC support.

 

More Rotating Machinery links:

Comments
Enthusiast
Enthusiast

Hello.

 

It is really helpful document to analzye the traction motor emitting sound.

Espeically, the motor sound attenuation method is very practical and  guides me in the right direction.

 

Many thanks.

 

Regards,

 

Jeongsoo