Loads on wind turbine gearboxes are difficult to imagine and more so to quantify. Experience and software can provide some insight and solutions to designing better replacement gears.
By: N.K. Chinnusamy, President of Excel Gear Inc.
Gearboxes designed to acceptable and proven industrial standards can fail in wind turbine applications for reasons not fully understood. One reason could be the automated stopping and re-starting of the generator, which results in torque that far exceeds the levels of maximum rated power.
Wind-turbine applications require developing experimental and analytical tools along with instrumentation to fully understand the machine’s operational characteristics. Recent generations of wind turbines use condition-monitoring systems capable of measuring input and transient peak torques, along with the radial and axial movement of bearings and shafts to detect the onset of in-service failures before they occur.
Generating gear loads
Wind turbine gearboxes connect a relatively low-speed rotor to a high-speed generator. Synchronous generators must run at synchronous speed, while induction generators run slightly above that (e.g. 105% of synchronous speed but that depends on load). For 60-Hz power, synchronous speed is found by dividing 3,600 by half the number of electrical poles in the generator. Synchronous speeds can be 3,600, 1,800, 1,200 rpm and so on. Rotor speed depends upon its diameter, typically 10 to 20 rpm. This combination requires a large speed-up ratio. Gear boxes for 60-cycle power with large speed-up ratios are complex in design and require epicyclic (planetary) gear sets. Planetary gear boxes have multiple meshes, speeds, and a complex power flow.
A varying wind speed and turbulence place loads on the input shaft in addition to the torque that all prime movers exert. The blades are long compared to the length of input shaft. In addition, they operate in the boundary layer so wind speed is higher at the top of the rotor sweep compared to the bottom. And then each blade tip generates a vortex which increases turbulence for downwind units.
The design of the rotor, hub, and main shaft is of utmost importance for the stability of the rotor. Varying wind speeds and turbulence produce moments on the end of the input shaft which cause shaft deflection and loads on bearings. If these effects can be isolated from the gearbox input shaft, then they do not impact the gearbox design. When the effects are not isolated, care must be taken so gear meshes are not misaligned.
Load equalization in planetary gears must be addressed for long gear life. The planet carrier must accommodate the centering force of the planet gears. Mesh frequencies must be set to prevent exciting resonant frequencies.
To make matters worse, wind-turbine gear boxes must work in extreme cold or hot temperatures. This requirement makes it difficult to find an ideal lubricant. Lubrication of bearings and gears is somewhat difficult in epicyclic gear boxes and care must be taken to assure that all bearings and gears are adequately lubricated under all temperature conditions. Cleanliness and the proper amount of lubrication are critical for the life of the components. During run-in on a test rig, cleanliness of lubrication must be checked periodically and proper lubricant flow must be established at low-speed running. Only then should final tests be run at full load and speed.
Most gear failures will be the result of fatigue, which can be either surface or bending fatigue. However, tooth breakage can occur due to misalignment or deflection under load. Gears may fail due to defective material or heat treatment, cracks in hardening, gear grinding, or any combination of these. Pitting or scoring may also cause gear failure. Premature bearing failure accelerates the gear failure even when gears are correctly designed and manufactured.
Because gearboxes are located in nacelles 60 to 100 m off the ground, maintenance and repairs are difficult and expensive. Even routine maintenance is time-consuming. This means there is a high premium on long life and reliability.
The growth of the wind-turbine industry is creating technological developments focused on the manufacturing larger, more precise, and optimized gearing. The need for better performance, quieter operation, and higher efficiency means the primary goal is to limit losses and control other factors that reduce efficiency.
Because of the number of units that will be manufactured and installed, there is need for longer life and higher efficiency. One way to achieve longer life and higher efficiency is to develop new technology and computer tools that optimize gear geometry. Examples of technological development are improved finish with REM technology and electro-polishing. These technologies, which are used in automobile racing, are having significant, positive impacts in gearing.
In building a wind-turbine gearbox, it is also important to establish the correct bearing clearances, preloads, and proper gearbox operating temperatures critical to long life. Sophisticated measuring techniques with bearing-inspection gauges are necessary to ensure these results. Verification of gearbox performance through computerized analysis and testing is a crucial step to ensuring long life. The critical factor here, as with all similar power transmission applications, is that the gears are properly designed and manufactured. Other mechanical components that make up the assembly, along with the gearing, must be applied and designed so the overall system performance does not suffer shortcomings that could affect the unit’s performance and life.
Most gear failures will be the result of fatigue, a condition dependent on the force on the tooth and the number of tooth-load cycles. If a tooth has more than one load cycle per revolution, this must be taken into account when calculating life. Although life is usually stated in hours, it is the number of load cycles that is important. For example, if a pinion drives two gears, its life will be one half that of the pinion driving one gear (assuming the same torque on both gears).
Preliminary planetary design
Recent software can assist with gearbox design and analyses. One such program, Excel-lent, includes a table of commonly used gear materials with values from AGMA standards. If a special material is used, it can be added to the table. Also, if a higher-grade material is used, material values can be changed to reflect the new material.
Planetary gearboxes have multiple meshes and speeds, and complex power flows. This requires determining the number of stress cycles and torque for each gear. Planetary design can be evaluated using, for example, calculations from (gear researchers) Merritt chapter 11 or Buckingham page 129. The software mentioned calculates life based on a mesh of a single pair of gears. The software converts between life and stress cycles with:
Cs = 60Lω
where Cs = Stress cycles; L = life, hours; ω and ω = speed, rpm.
If a sun gear has three planets, the load input to the mesh calculation is 1/3 the total load. The actual life is also one-third the calculated life. For example, if the total power to a simple three-planet stage is 90-kW, the mesh power is about 30 kW. If the calculation shows a 300,000-hour life for the sun gear, the true sun gear life is 100,000 hr.
The reduction in load on the teeth in the mesh has a larger effect than the increased number of gear tooth load cycles. Consequently, the result of having three planets is much longer life.
For example, consider a simple planetary system consisting of a fixed internal gear with 72 teeth and an input shaft carrying three planet gears with 27 teeth driving a sun gear with 18 teeth. Following the calculations in Buckingham’s text, we get values in the table below.
The equivalent speed for calculating life is obtained by dividing the pitch-line velocity by the gear pitch circumference. The life obtained is for the given input speed. Using these values will give the life for an input speed of 100 rpm.
Notice that the power in the two planet gear meshes (PA and PS in the table) are less than the transmitted power, PT. Power in planetary meshes can be lower, as shown here, or much higher. When the power is higher, it referred to as circulating power.
A planetary box will ordinarily have three planets. In this case the table would be reflected in Value that change for a gearbox.
With the speeds and loads determined, we proceed to the gear design. The planet gears are reverse loaded on every cycle. This means that 70% of the bending-fatigue strength should be used in the calculations. The easiest way to do this is with a new material. For example, if we plan to use 4140, add a new material with a name such as “4140 70% Bending”. Only the bending-fatigue value is changed for reverse loaded gears. All other values remain the same. Inputs to the design program would then be as they appear in the input screen.
The design program uses approximate methods so there is only one material specification for both gears. Note that the safety factor selected is “Wind Turbine and Critical Apps”. This uses a safety factor of 1.56 in calculation instead of the standard 1.0.
Data is then transferred to the analysis section, also part of the design software. The analysis program allows selecting different materials for the two gears. Note that the special material titled “4140 70% Bending” has been selected for the planet gear. Also, the Profile shifts have been set to zero. Profile shifts may be used in planetary gearboxes but they must be picked considering all three gears – sun, planet, and ring. For preliminary designs, using a zero value is best.
Examining the data in the analysis section reveals a power capacity slightly low for sun-gear surface fatigue. This can be changed by increasing the face width to 90-mm or by changing the material to one with a higher surface-fatigue value. Ease in making such changes allows for checking many combinations.
Designing an epicyclic gear train, especially a compound one with an overall ratio of about 80:1, is typically a complex task. Many kinematically correct solutions will not work because of excess circulating power. Using software such as Excel-lent for load and life calculations can take a large amount of time off the task because non-feasible solutions are eliminated early.
When a designer selects three planets, care must be taken so that the sun and internal gears are coaxial. The three planets have a strong centering effect. If the sun and internal gears are not coaxial, a large load may be transferred to the bearings. In that case, both the bearings and the gears may fail prematurely.
A third software section provides design and manufacturing data. The software mentioned, for example, includes an option for calculating correction factors for balancing beam strength or specific sliding, a requirement for wind-turbine gear boxes.
Gearbox design is a complex, iterative process. The three programs in the Excel-lent software package can greatly reduce the time needed to process repetitive calculations. WPE
Filed Under: Featured, Gearboxes