Abstract
Abstract. The required reliability of wind turbine gearboxes increases the requirements for large gear measurements. Extensive measurements to reliably assess the geometry of large gears in the single micrometer range are necessary. Due to an individually fixed measuring volume, standard methods like coordinate and gear measuring instruments reach their limits for large gears with diameters > 1 m. Therefore, a scalable optical measurement approach consisting of a single sensor in combination with a rotary table for multi-distance measurements with subsequent model-based evaluation of shape parameters of gears is presented. The scalable measurement approach is to be extended to a multisensory system in further work. As a fundamental shape parameter the mean base circle radius using the example of spur gears is determined. The base circle radius is used due to the geometric relationship to further shape parameters for example to the profile slope deviation. The theoretically achievable measurement uncertainty of the mean base circle radius due to sensor noise is estimated to less than 5 µm (k=2) for a small and a large gear, which verifies the scalability of the sensor system. In order to show a general proof of principle, two series of optical measurements on a gear with a diameter of 0.105 m are performed and referenced with a tactile measurement. As a result, random errors of 1.2 µm for k=2 are determined. The remaining systematic deviations to the reference value amount to 4.3 and 1.6 µm, respectively. Hence, the total measurement uncertainty is currently limited by systematic effects, and the defined aim of a total uncertainty of less than 5 µm (k=2) is narrowly missed by 1.5 µm. The random errors of 1.2 µm (k=2) show, however, that an adequate measurement precision is achieved and that the multi-distance measurement approach has the potential to reach the aimed measurement uncertainty with appropriate strategies to compensate for the systematic influences. The experimental and theoretical results prove the principle applicability of the proposed single sensor multi-distance approach for the precise inspection of gears.
Highlights
1.1 Motivation and measurement requirementsAround 90 % of the drive trains of installed wind turbines are based on gearboxes with diameters of 1 m (Crowther et al, 2011)
In order to prove the suitability of the measurement principle, the actual mean base circle radius is determined for a small spur gear
Simulations show that total uncertainties for the mean base circle radius of less than 5 μm (k = 2) are possible independent of the scaling of the gear
Summary
Around 90 % of the drive trains of installed wind turbines are based on gearboxes with diameters of 1 m (Crowther et al, 2011). Measurements of shape parameters of large gears with diameters > 1 m or modules > 10 mm with an uncertainty of single-digit micrometers are necessary to comply with the golden rule of metrology. Due to the size and mass of large gears listed, the quality inspection of the gear geometry is associated with a higher logistical effort when bringing the gear to the measurement system, in comparison to gears with diameters < 1 m. For this reason, mobile and scalable gear measurement systems are desirable to quantify the shape parameters of the gears with single-digit micrometer uncertainty with reduced logistical effort. Pitch diameter d in millimeters Mass m in kilograms Module mn in millimeters Number of teeth ZN Tolerances (total profile slope deviation fH αT ) in μm for quality class 5 Ratio of tolerances to diameter
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