Q&A with Bill Mark

Penn State University


What is your position at Penn State?

I’m with the applied research laboratory and graduate program in acoustics, and I’ve been here about 20 years. I’m also on the faculty of the acoustics program, and I’ve sponsored and guided graduate students, usually one per semester. Over the years, I’ve had five masters’ students, a few in mechanical engineering, and two PHD students.

In the applied research laboratory, I specialize in gear noise, gear vibrations, gear metrology, and gear health monitoring—and, by extension, how these elements are tied together.

How would you tie them together?

In gear metrology, we measure deviations of the teeth from conjugate surfaces, from equally spaced conjugate surfaces. These tooth deviations cause vibration excitation. This ties the metrology to the vibration excitation. Whether the deviations are caused by manufacturing errors or by damage to the teeth due to wear or fracture, they affect the vibration excitation. Therefore, the vibration responds in very much the same way.

The physics of all of this is really the same, relative to gear health monitoring. If you can detect and analyze the vibration response caused by a deviation—whether it’s tooth damage or manufacturing error—it all affects the vibration excitation.

Which ties it to noise analysis …

Yes. In fact, it was originally the noise caused by gears that got me interested in this area. It’s a challenging area—engineers like to be challenged.

How are you growing?

Before coming to Penn State, I spent 25 years at a consulting firm in Cambridge, Massachusetts (Bolt, Beranek and Newman) in the noise control group there. One of our projects involved gear noise. I saw there was potential to do some new things. At that time, gear noise wasn’t well understood at all. There was an opportunity to do some original work. I grabbed on and ran with it, and it’s been a wonderful career. I feel very fortunate to be paid to do what’s my hobby.

After all these years, are you still learning?

Of course! I’m a permanent student. It’s mathematically challenging. People regard gearing as an old technology, which, in a sense, it is. But it’s also amenable to mathematical analysis.

It’s been challenging, but we’ve been studying the relationship between any kind of errors on the teeth and the vibration caused by these errors. Considering the design of the gears, especially helical gears, it turns out the axial and transverse contact ratios play an important role in how the design of gears affects the vibration excitation.

I’m sure the landscape has changed for your profession since you came to Penn State.

It’s utterly amazing what is possible with CNC gear metrology equipment today. To give you an example, we measured gears and developed the vibration excitation accurately for errors on the gears that are a tenth of a micron, or 4 micro inches. That’s one fifth of the wavelength of the visible spectrum of light.

It’s utterly amazing that the equipment is capable of measuring errors that small, consistently. We have one here at PSU and it’s remarkable what’s possible. Sometimes I wonder if the people who make these machines truly understand how good their machines really are.

You recently published a book. Can you tell our readers about it? What was the inspiration behind it?

Some very small gear manufacturing errors cause unacceptable vibration excitations and noise. The book shows how to efficiently measure any manufacturing deviations of parallel-axis involute gears, compute the vibration excitation (transmission error) caused by such deviations, and compute the specific manufacturing deviation causing any user-identified transmission-error tone caused by the deviation, such as a ghost tone or a sideband tone. It also shows how to provide a precise measurement and display of the average three-dimensional modification of the tooth working surfaces. Its practical use by at least one major gear manufacturing firm provided motivation for me to document the technology in a book. The relatively recent availability of CNC dedicated gear metrology machines makes such implementations practical.

What was your experience like writing the book?

I attempted to make the developments as accessible as possible, while including in a later chapter the full mathematical derivation of the results. A summary chapter explains how to measure a gear and implement all of the results in software.

Who would find this information most relevant?

Anyone interested in understanding how gear manufacturing errors (and tooth damage) cause transmission-error vibration excitations and noise. I welcome comments and feedback about the book.

MORE INFORMATION: Dr. Mark’s book can be purchased on Amazon.com. He can be reached at (814) 865-3922 or via email at wdm6@psu.edu.