The gearbox is the vital link transferring rotor energy to the generator in the vast majority of wind turbines. With the power capacities of wind machines accelerating rapidly, designing ever larger gearboxes with optimal vibration characteristics and then testing these characteristics is crucial to ensure a long, and quiet, life. Ralf Dinter and his colleagues explains.
The rapid development of wind power in recent years has resulted in rated outputs for turbines of up to 6 MW. The overwhelming proportion of such systems contain a drive train made up of a number of major elements — the gear unit, coupling and a high-speed generator.
The development of the various power classes of wind turbines has given rise to different drive and gear unit concepts. These are essentially of two types, helical gear units and single- and double-stage planetary gear units. In addition to the more typical double-bearing rotor shaft, there are also solutions where the gear unit takes over the function of the second rotor bearing.
Figure 1, right, shows the major developmental stages of wind turbine gearboxes for several classes of turbine up to 5 MW.
For the development and design of gearbox units in response to the higher levels of torque found in larger machines, the relevant calculating methods are used, taking into consideration the special boundary conditions and loadings that are found in wind turbines. Owing to stringent noise requirements, particularly important are the noise generation chain, together with the trial of prototypes.
Gear unit concepts
The structure of a modern wind turbine and its main elements is shown in Figure 2, right. It can be seen that the rotor is connected directly to the gearbox via the rotor shaft, usually with a shrink disk.
Because of the gear meshing which takes place inside it, which inevitably becomes a source of excitation, the gear unit influences the noise generated.
Vibration is transmitted from the gear meshes through parts like shafts, bearings and housings, from the housing surface to the environment and via the connection of the gear unit to the main structural elements. The development of such systems to meet environmental and economic requirements, particularly with regard to sound characteristics, is possible only with the help of modern tools.
The layout of a typical helical planetary gear unit is shown in Figure 3, overleaf on page 142. The planet gear stage is driven, via the planet carrier, by a fixed ring gear. The connection to the helical gear is made by a sun gear designed to be elastic for an even load distribution to the planets. The gear units are constructed with labyrinth seals which limit the maximum oil level in the gearbox. The gears are lubricated with a combined splash-circulation system.
The main stage of the two-stage planetary gear units shown in Figure 3 is constructed with planet gears similar to those found in a single-stage helical planetary gear unit. However, in this case, there are normally four planet gears used instead of the more typical three. This is in order to achieve a higher power density. In the second planetary gear stage, three planet gears are sufficient, however.
As in all branches of engineering, testing designs is vital and at the Winergy facilities, for example, various test rigs with an output of up to 14 MW are available for trialling prototypes and serial testing gear units. These test rigs are designed to generate the mechanical loads. Right now Winergy is planning a new generation of test benches, the system test bench, in which a complete drive train of a wind turbine can be tested with its main components such as the gearbox, coupling, generator, frequency converter, grid access, automation system, pitch and yaw. This offers the opportunity to analyze and optimize the interaction between the single components in the complete drive train system.
In the development of a gear unit, very different, and above all stringent, demands are made of the system. The aim is a design which meets functional, stress, deformation and vibration requirements, does not exceed weight limits and can be economically manufactured. Achieving a design with optimum vibration characteristics is therefore a key objective.
The theoretical determination of the vibration and sound characteristics of a gearbox design is a complex but necessary step, owing to stringent acoustic requirements. Interest in an optimized gear unit structure exists early in the drive train design stage. Verification of the environmental operating conditions of the gear unit, foundation, torque arm and, of course, the customer design for mounting the gear unit is also nonetheless required at an early stage.
In the development and design phase the greatest potential for reducing the level of noise is offered by controlling the structure-borne sound. Within certain limits, theoretical analyses enable the mechanical structure to be influenced so that, from the point of force excitation to the external structure surface, no vibration occurs in undesirable frequency ranges.
Radiation is the proportion of the surface vibration of a mechanical structure which passes into gaseous media and thus becomes airborne sound. This proportion can be theoretically determined only with difficulty. One way is the boundary element method (BEM), for which a number of commercial programmes are available. In considering the drive train components, while the mechanical structure is a most suitable factor for favourably influencing structure-borne sound, torsional vibration should also be considered at the same time.
The theoretical calculation is done using a three-dimensional model of the gear unit on the basis of the finite element method (FEM). Figure 4, right, shows a schematic diagram of a multi-stage structure-borne sound analysis. Initially the ‘virtual gear unit’ is decisive for the development of the gearbox and only later, in a subsequent developmental step, is it replaced by the data from an actual object.
Sound optimization is also rendered difficult by the variable speed operation of many wind turbines. Nonetheless, comparison between the results of a theoretical analysis and real measurement of the vibration characteristics of a 2 MW gear unit on the test rig shows the natural vibration modes of individual components can be assigned to the recorded measurements — and thus indicate the suitability of this method for determining the vibrational properties of the gearbox.
Natural vibration modes for combined helical planetary gear units can be fundamentally divided into four characteristic groups:
Basic vibration modes of the entire system and large subsystems, up to approx. 300 Hz
Natural bearing frequencies, from approx. 100 Hz
Natural frequencies of shafts, from approx. 200 Hz
Plate vibration modes, from approx. 450 Hz
The basis for determining the structure-borne sound level spectrum, or the overall level of the structure-borne sound, is the mechanical admittance. This property, a sort of transmission function, describes the readiness of the mechanical structure to vibrate.
Depending on the force applied on a tooth mesh of the gear, and taking into consideration suitable natural-mode-dependent damping, the structural speed is determined at a number of surface points. Depending on frequency, these points will be the Finite Element (FE) nodes or a selection of representative FE nodes. When carrying out analysis (using parametric variance methodology) only the proportions of the admittance which act at right angles to the surface are of special interest for optimization of the vibration characteristics.
For practical purposes it has been found that the tooth meshes important for structure-borne sound are those of the faster running helical gear stage, which are far more significant than those of the relatively slow-running planet gear stage. A component of the total spectrum of structure-borne sound can therefore be optimized if only the helical gear stages are considered.
As well as FEM, before the completely assembled gear unit is operated on the test rig, the gear unit structure or elements of it can be analyzed using other measuring techniques. As with the theoretical measuring technology — including associated software systems – these techniques offer a means of determining natural frequencies, vibration modes and transmission functions and thus visualizing operational characteristics.
Hammering down vibration
A typical torque arm of a gear unit in a simplified form is shown in Figure 5, overleaf The arrows show measuring points where 3-axis acceleration sensors are normally attached. Using a special hammer, to which a load cell is attached, the structure is excited into natural vibration by a regular striking. At the same time, measurement data is recorded at the three points.
Using a software system, the natural frequency and natural vibration mode of the real structure can then be determined from the measurement data, with the aid of a simple model.
This method can be applied to individual elements or whole structures, though here, too, ‘boundary conditions’ have to be taken into consideration. In the case of large structures, though, excitation can be difficult because of the high energy input necessary.
If the load-dependent excitation of the structure on the test rig is brought about by the existing tooth mesh, the method can be used analogously and the operating behaviour of the structure analyzed. The recorded measuring data are now applied to the simplified structure model. The result is the operating vibration of the structure in the practical test. Theoretical analyses can thereby be verified.
Generally prototype gear units for wind turbines are subjected to comprehensive tests during the development process. These tests include those at various load levels and speeds, taking into consideration the wind turbine power curve, up to overload. They include:
measurement of the sound and vibration behaviour
measurement of temperature on bearings and other components
inspection of contact patterns of tooth meshes
measurement of load distribution in the tooth meshes
test of the oil cooling and lubrication systems
dismantling of the gear units for inspection of the components
function test over a longer period with up to 200% of rated power
During these tests the power curve of the wind turbine is run through in stages to determine the sound-vibration characteristics of the gear unit. The airborne sound is determined by the sound intensity method. Structure-borne sound characteristics are measured with a large number of acceleration sensors at various positions on the gear unit. This method may be used both on a test rig and on the turbine.
Since the actual carrying characteristics of the real teeth have a substantial effect on the load-carrying capacity of the gear units as well as on the load-dependent excitation in the gear unit, they are analyzed with visual contact pattern checks at various load stages.
In this process the teeth are painted with dye which wears off in operation. The contact surface then becomes visible which can be compared with the theoretical calculation.
The contact patterns in the planet gear stage cannot be viewed during the tests, however. The distribution of load across the tooth width and the division of load between the individual branches are determined by measurements. The method used also allows the excitation to be evaluated at various load stages. The load distribution is not constant on the circumference of the carrier either. Because of the mass of the gear unit, the gear starts to tilt relative to the planet carrier within the stiffness characteristics of the surrounding elements, the bearing stiffnesses and the bearing backlash.
Once the load factors have been evaluated from the actual device, a comparison with the calculated values is possible. Perhaps surprisingly, a comparison with various loadings reveals a drop in the load factor with increasing load. This is as a result of a better width contact with higher loads.
Similar to the evaluation of the load factors is the determination of the load sharing factors and dynamic factors. These load magnification factors cannot be easily separated by measuring technology. For designs constructed today, where four planets are used in the main stage of the gearbox, more favourable values could not be determined than those set out in standards or calculation requirements of certifying companies such as Germanischer Lloyd and Det Norske Veritas.
After the prototype gear units have passed this series of comprehensive tests and measurements, all the gear units are dismantled and inspected in detail. The inspections give further information about the connections, excitations and effects in the system at the same time as helping to verify the accuracy of the measuring data evaluation.
Lightening the load
Gear units are already being built that will accommodate an output of up to 6 MW, and current trends would suggest this figure is set to rise over the coming years. The aim in developing such systems is a robust design which meets functional, stress, deformation and vibration requirements, which does not exceed specified weight limits and which can be economically manufactured.
Naturally great importance is attached to the trialling of prototypes to guarantee the availability and safety of the systems. Prototype tests — comprising sound and vibration measurements, analyses of the temperature characteristics of rolling bearings, contact pattern inspection by optical methods, indeed a host of different techniques — are applied in order to ensure the optimum gear unit design. Designs featuring improved vibrational characteristics are becoming increasingly important too. Wind turbine developments have become the focus of increasing public interest and awareness, particularly when it comes to their visual appearance and acoustic characteristics. While the options are limited with respect to the appearance of a turbine, stringent demands are made of wind turbine drive trains, where good design based on sound theoretical and experimental results can yield significant improvements in terms of their acoustic properties.
Dr Ralf Dinter is Manager of Engineering and R&D at Winergy AG, his colleague Dr Volker Kreidler is chief technology officer and Michael Krollmann is product manager.