Modeling wind-turbine gearboxes

Modeling wind-turbine gearboxes

Why do these efficient, highly-engineered mechanisms often fail sooner than expected?

Gearboxes in general are a result of over 80 years of accumulated engineering knowledge. So why do gearboxes for wind turbines sometimes fail after seven to 11 years — way less than the anticipated 20-year design life of the entire turbine structure? This is a complex question with many variables to consider and no easy answer. For example, it was once thought there was an incomplete understanding of the loading conditions the gearbox sees as it suffers high torques from blades subjected to gusty winds. Also, gearboxes turn at low rpms and therefore generate a thin lubricant-film thickness, which makes them prone to micropitting and wearing of the gears and bearings. In addition, the units see a large range in operational temperatures and high vibrations at the nacelle.

To try and get a handle on the causes of early gearbox failure, the National Renewable Energy Laboratory's (NREL) Gearbox Reliability Collaborative (GRC) about four years ago began collecting data from two custom-built planetary gearboxes instrumented with over 200 strain gages, proximity probes, accelerometers, and acoustic emission sensors. One of the units is in the field; the other resides on a dynamometer in a lab. The gearboxes are big and heavy enough to require positioning via cranes.

The goals of the GRC are to reveal the causes and loading conditions that result in the premature failure of wind turbine gearboxes and recommend improvements for the industry.

In these endeavors, the GRC is performing gearbox modeling as well as dynamometer and field testing. “The dynamometer tests let us validate computer model predictions under a controlled setting with increasing levels of complexity,” says Jeroen van Dam, a senior engineer at NREL and the GRC project lead “The field tests, of course, provide us the real-world data that the models ultimately must predict accurately. The field-test data can also be used to design a better dynamometer test for new gearbox designs. Our efforts also include condition monitoring as well as populating a gearbox-failure database. Condition monitoring should help us develop a better operation- and-maintenance strategy and reduce gearbox downtime. The failure database stores the hard data we collect on gearbox problems. This data is intended to help us understand the root cause of gearbox failure,” he says.

From a software point-of-view, the project's complexity necessitates the use of many different products. They include specialized packages intended specifically for gear design and in-house codes for studying gear micro geometries. Also seeing use are high-end commercial FEA software for predicting how the entire gearbox will react with the turbine structure.

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Designing the gears

At the start of the project, NREL retained Ed Hahlbeck, owner of Powertrain Engineers Inc., Pewaukee, Wis., as the gear designer. “The two gearboxes are nearly identical in design and were intended to be representative, ‘generic’ versions of a classic wind-turbine gearbox,” he says. “Some of the gearing was reconditioned and the rest comprised a new design. For example, we changed the sun pinion, originally fixed on bearings, to a floating style, which let the gear find its own position and divide the load equally among the planets.”

Also, the original spherical bearings had since gone out of favor because of a poor track record, says Hahlbeck. “Spherical bearings have pure rolling in only two places across the roller,” he says. “Elsewhere, there is a slight speed differential, which may have led to uneven wear and thus have been one of reasons gearboxes failed. Roller bearings, on the other hand, have pure rolling across the contact line and have generally done better historically in wind-turbine gearboxes.”

The program of choice at the early stages of gear design came from KISSsoft software, which specifically targets gears, bearings, and shafts. “We started with a clean sheet of paper, so to speak,” says Hahlbeck. “Given are general requirements such as loads, ratios, and life targets. It is necessary to decide how much the torque splits at each point, the size of the gears, how they interact, and then do a layout. This is an iterative process. Basically, we develop the system into a configuration and, from that, start designing the components. KISSsoft let us perform thousands of what-ifs in a short time to do the gear sizing and help zero-in on the optimal gearbox configuration.”

Part of the problem with wind-turbine gearbox design in general comes from lack of a common standard, an issue the software helps address, says Hahlbeck. “The American Gear Manufacturer's Association (AGMA) has had a gear-rating system used for many years and guys like me who have been doing gear design for 50 years were accustomed to that method. Germany developed DIN standards, later incorporated into today's ISO standard. The software, with the click of a button, gives users gear ratings with either method. But the approaches are different. Worse yet, they are not consistently different. Some applications yield two quite close results, while others diverge enough to cause concern.”

It's an ongoing issue because the global wind industry needs a single accepted standard, says Hahlbeck. “AGMA has been doing a lot of work to converge standards, but there are differences in the general philosophy on rating, especially on strength,” he says.

Currently, to obtain the Germanischer Lloyd WindEnergie GmbH rating that insurance companies require to commission a turbine, manufacturers in America, Europe, and Asia all use ISO 6336 for gear rating. Germanischer Lloyd is a hundreds-years-old international organization originally conceived to ensure that ships were correctly built.

“KISSsoft is also expanding the capability to model micro geometry, which will let us dispense of poorly-supported code such as the German code LVR,” says Hahlbeck. “In gear-speak, micro geometry is a term used to talk about modifications to the gear teeth to accommodate distortions and loading in service,” he says. “The classic example is when a pinion transmits torque, the teeth twist, distorting load distribution across the face. The designer must adjust the angle across the tooth ever so slightly, in the range of microns. The tooth also bends like a little cantilever beam, which distorts the involute and necessitates further adjustment.” These adjustments are known as 3D mesh analysis.

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Another advantage of toolbox-type software is users need not spend a lot of time and effort setting up an FEA model when they can get faster and just-as-exact results using equations and iterations in what's known as a closed solution, says Hahlbeck. “KISSsoft does not require meshing the component. But when a bearing is loaded, the program goes into enough detail to tell how much load is on each roller and what the stress is in each contact across the face of the roller. In early design stages, it doesn't make sense to use standard FEA for gears and bearings because it is too computationally intensive. Also, Germanischer Lloyd does not support the rating of gears with FEA unless supported with extensive test data.”

Although gear-tooth calculations themselves might not be as perfect as with a properly executed FEA model, says Hahlbeck, they are grounded in historical application. “To be useful, FEA must correlate with real-world test results,” he says. In fact, the GRC project is intended to close the loop between design and design tools, measurement and testing, and field experience. Included are KISSsoft, Caylx, bearing-design programs like Romax, code that General Electric is using, and a micro geometry program called LDP, which was developed at Ohio State University under Don Houser, founder of its Gear Lab.

“A further area of interest is micropitting,” says Hahlbeck. “Currently, a proposal for a micropitting standard is ‘on the street,’ as they say. It's actually a technical paper to be used for a while to see how it conforms to experience. KISSsoft has also included this rating method in its software.”

Dan Kondritz of Switzerland-based KISSsoft explains further. “We took the Pro/Engineer drawings from the proposed gearbox as the data source for setting-up models inside of the software,” he says. “The GRC gearboxes were proprietary planetary gearsets. Turned out, the tilt on one of the original gears was off, so the software found a problem early-on, before a chip was cut.”

Interestingly, during GRC presentations, it became evident that different tools often gave different results; for instance, in calculating gear contact, says Kondritz. “And inconsistencies in the interpretation of data cropped up, even among PhDs. A simple example is whether a unit is in pounds per square inch or pounds per square millimeter. Other units of force and reaction were also misunderstood. And a common problem not necessarily specific to the project is manufacturing to the wrong engineering drawing revision. That's why the complex designs require an extraordinary attention to detail.”

Early GRC results have indicated there probably needs to be a new service factor established for wind turbines, says Kondritz. “What that will be is yet to be determined. Also established was the need for a new set of design recommendations for bearings.”

Modeling the entire gearbox

Once the gearbox design was fairly complete, FEA came in handy to predict how the whole mechanism will react to the external loading, continues Hahlbeck. Software from Ansol Inc., Hilliard, Ohio, lets users model as little or as much of the machine as they want, including all of the housing, support structure, and gear and bearing contacts.

“Even today, trying to properly analyze a global model using just raw computing power would take too long to solve,” says Hahlbeck. “Sandeep Vijayakar, a Houser protégé and the founder of Ansol, figured out a way to look at things like contacts, which are nonlinear, identify their location in the mesh, and replace them with equations — and do so automatically with iterations. Problems are thus reduced to a manageable size, but it still takes about a month to set up a global FEA model of a whole wind-turbine gearbox.”

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Ansol has provided customized gear analysis as well as analysis software since 1989. “Our Calyx software fits in after engineers have done a few passes with a design and they then want to dive deep into the gearbox and do a realistic simulation,” says Vijayakar. “It's almost impossible to realistically model a wind-turbine gearbox with general-purpose FE code such as Nastran, which is designed to do everything. We used general tools a long time ago, but were not able to analyze more than a couple of gears at a time. So we started building software specifically for gearbox analysis.”

General-purpose FEA runs into trouble with gears because they are high-precision pieces with precise surfaces. “Because Calyx finite elements were designed with gears in mind, models can have precise surface definitions and high resolutions in the contacts,” says Vijayakar. “The software performs accurate contact-pressure calculations, also important for gears. Gearbox deflections are on the micron level, so general-purpose FEA would require multitudes of tiny finite elements, which would take forever to run. Thus, what was needed was a specialized FE method that can perform accurate calculations without using tiny elements. Basically, we changed the mathematical formulation that defines the element. In a computer program, there are formulas that describe how the shape and deformation of the element is controlled. Our formulation is different and it produces much more accurate curvatures. Curvature is really important in modeling gear tooth or bearing roller contacts because contact pressure depends strongly on curvature.”

Ansol also exploited the fact that gears operate in the linear-elasticity regime, says Vijayakar. “General-purpose contact solvers are full nonlinear codes and they iterate on the solution. This means they guess what the contact pressure is going to be and then keep improving that guess, a process that could go on forever. In contrast, the Calyx solver finishes in a fixed number of steps.”

For illustration purposes, consider a wiper blade touching the windshield of a car, an example of a nonlinear problem, says Vijayakar. “General-purpose FEA operates just fine in similar regimes,” he says. “But we target gearboxes and thus can use a much faster contact solver.”

Vijayakar says that Houser and his students have been doing a lot of the heavy analysis lifting on the GRC project. “They have modeled the entire gearbox with inputs including the basic design, all the gear surface modifications, relief angles, and material properties,” he says. “Also included is a detailed bearing description with the roller geometry and the load on the bearings, as well as the shaft geometry and the housing model, including housing flexibility. Additional load factors include the weight of the blades, how much weight is hanging off of the nacelle, and wind loads or how much bending moment is being caused by the wind. Last, gravitational loading is included because the gearbox deforms under its own weight, which pushes the contacts around.”

According to Vijayakar, gear designs done in CAD do not carry enough precision in the gear data-sets. “So collecting all the needed data and putting it into the gear-design program takes a lot of time,” he says. “Designers must talk to all the engineers and make sure there are no mistakes. They must read all the drawings carefully and then input the data into the code. The GRC project has been valuable to the wind turbine industry and software providers alike because it has given developers a chance to improve their codes for wind-turbine problems.”

Analyzing micropitting

Don Houser of the Ohio State Gear Lab says he and his students have been involved with GRC for about a year. “It is a worthwhile endeavor because getting test data in this economy is tough,” he says. “One such place that material durability is being studied to a large extent is at the University of Munich in Germany. It has around 50 FZG back-to-back gear testing machines for this purpose. At Ohio State, we have three such machines and very few others are running in this country.”

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One aim of the GRC project is to understand more of what happens in the gearbox and then reproduce those conditions in the lab rig for a more-controlled test setting, says Houser. “I'm sure it's an expensive endeavor that only the government could afford. We are looking forward to getting some of that data to check out our Calyx model and also what our in-house LDP program can do to predict deflections at the micro scale.”

No matter the application, a major problem is that gears always seem to play second fiddle, says Houser. “With airplanes and helicopters, for instance, gears are looked at as a commodity or just something to be purchased. University centers dealing with helicopters all focus on the blades even though the gearbox supports the whole helicopter. A wind turbine is just a helicopter inverted.”

Houser and the current Gear Lab director, Ahmet Kahraman, have another project supported by DoE funding from the American Recovery and Reinvestment Act to do roller testing and predict micropitting for both gears and bearings. Micropitting is a kind of contact fatigue due to high surface loads and heat generation that together reduce the lubricant film.

“To model micropitting, we use both Calyx and our LDP module, which differs from normal tribological modeling,” says Houser. “Normal modeling involves equations for lube-film thicknesses and flash temperatures that are all based on steady-state rolling to simulate bearings that roll at a constant velocity,” he says. “However, gear teeth are only in contact for maybe a millisecond. Also because micropitting requires sliding action, it is necessary to account for the time-varying sliding velocity and radius change that happens in gears. These may affect friction and heat generation. Our model tries to capture all these phenomena.”

Getting to the bottom of gearbox reliability

The Gearbox Reliability Collaborative project comprises more than 70 industry partners, including wind-turbine manufacturers, software developers, bearing manufacturers, gear builders, and university research arms. GRC systems engineer Francisco Oyague (who just moved to a new wind-turbine startup, Boulder Wind Power, Boulder, Colo.) has been heavily involved in the analysis side. The goals of the GRC include understanding the global loading wind turbines see, investigating methods to predict deflections and stresses, and detecting degradation in parts.

“The GRC gearboxes were redesigned to reflect the configuration of the MW-class gearbox, a configuration consistent with current industry standards,” says Oyague. “The redesign let NREL provide GRC participants with the design information to perform the analysis. This is important because, typically, it would be quite difficult to obtain manufacturing drawings, material properties, and solid models because of the proprietary nature of the information. Further, another GRC goal is to produce a reliable reference data-set that can be used for the validation of new analytical tools.”

The idea of instrumenting the gearboxes is to validate a large number of assumptions that are generally defined by analysts to obtain results, says Oyague. “For example, some of these assumptions are the boundary conditions, so one of the areas we are trying to validate is the roller-load distribution in the planetary stage,” he says. “Planets on wind turbines are characterized as being thin-rimmed to reduce the overall weight of the gearbox. However, the high loads generate deformations of the planets that previously were not accounted for.”

According to Oyague, the GRC currently is focusing on the planetary stage, the initial stage of the gearbox that sees the highest loads and where it seems most failures happen. “We placed strain gages at the roots of the gear teeth in several locations along the ring gear. This lets us see stresses and back-track how the gears are misaligned.”

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GRC is also trying to measure everything going into the drivetrain from the main shaft, both in the field and the dynamometer. This provides torsional and bending loads. Additionally, because the gearbox and generator are both sitting on rubber mounts with a flex coupling in between, the group aims to understand how the gearbox is moving with respect to the main frame and with respect to the generator, and how everything interacts as a full system.

Under the hood of the Calyx model

Aaron Thaler, a graduate student of Don Houser, has been doing extensive modeling of the GRC gearbox in Calyx. He says the gearbox consists of a planetary stage followed by two parallel stages. The gearbox's speed ratio allows a nominal input rotor speed of 22 rpm to be increased to an output speed of 1,800 rpm, which is required by the generator to supply synchronous power to the electric grid. The wind turbine can also operate at a second nominal input speed of 14 rpm (output speed of 1,200 rpm) by way of the generator actively switching the number of magnetic poles used to generate electricity. A 323-kNm input torque created by the wind on the rotor blades is required to operate the generator at full rated power and maximum speed.

The wind turbine gearbox has been modeled using a 3D finite-element-based contact analysis program called Transmission3D from Ansol. The software lets users model the entire gearbox including the housing, gears, bearings, shafts, and planet carrier. Transmission3D uses the Calyx contact-analysis program to solve the contacts in the gearbox. It does so by first computing the finite element deflections and forces, and then employs a semi-analytical approach to analyze the contacts at gear meshes, bearings, and splines.

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