Flächenhafte numerische Beschreibung, Ausrichtung und Auswertung von Zylinderrädern (3D-Surface-like Numerical Description, Alignment, and Evaluation of Involute Cylindrical Gears)

Stöbener

et al. 2021

Sensors

The demand for extensive gear shape measurements with single-digit µm uncertainty is growing. Tactile standard gear tests are precise but limited in speed. Recently, faster optical gear shape measurement systems have been examined. Optical gear shape measurements are challenging due to potential deviation sources such as the tilt angles between the surface normal and the sensor axis, the varying surface curvature, and the surface properties. Currently, the full potential of optical gear shape measurement systems is not known. Therefore, laser triangulation and confocal-chromatic gear shape measurements using a lateral scanning position measurement approach are studied. As a result of tooth flank standard measurements, random effects due to surface properties are identified to primarily dominate the achievable gear shape measurement uncertainty. The standard measurement uncertainty with the studied triangulation sensor amounts to >10 µm, which does not meet the requirements. The standard measurement uncertainty with the confocal-chromatic sensor is <6.5 µm. Furthermore, measurements on a spur gear show that multiple reflections do not influence the measurement uncertainty when measuring with the lateral scanning position measurement approach. Although commercial optical sensors are not designed for optical gear shape measurements, standard uncertainties of <10 µm are achievable for example with the applied confocal-chromatic sensor, which indicates the further potential for optical gear shape measurements.

on the tooth flank of tooth Z results from an addition of a radial vector

and a tangential vector

in the workpiece coordinate system ( x , y ). The vector

has the length of the geometry parameter base circle radius r b of the spur gear while the angle

depends on position parameters

.…”

Section: Measurement Principlementioning

confidence: 99%

“…In order to solve the inverse problem, the geometric model of the nominal involute is fitted to the measured data by iteratively minimizing the sum of the squared plumb line distances

i.e., by using a nonlinear least-squares method. According to [ 17 , 21 ], the plumb line distances to the nominal involute of a spur gear are determined by

…”

Section: Measurement Principlementioning

confidence: 99%

Gear Shape Measurement Potential of Laser Triangulation and Confocal-Chromatic Distance Sensors

Pillarz

Stöbener

et al. 2021

Sensors

“…According to [ 9 , 20 , 21 ], a measured actual point

on the individual tooth flank can be described by adding the nominal point P of a spur gear to the deviation to the nominal geometry in the normal direction

of the surface, the plumb line distance d plu . According to Figure 1 , each nominal point

of tooth Z of a spur gear can be calculated by vector addition of a radial component

, a tangential component

in the workpiece coordinate system ( x’, y’ ) and the translation vector

to the workpiece coordinate system.…”

Section: Measurement Principlementioning

confidence: 99%

“…According to [ 20 , 22 ], the plumb line distances to the ideal involute can be calculated to

whereby the corresponding rolling angles

to the root point of the plumb line distances on the involutes are determined implicitly. The parameter r I

is the radius of the detected actual point in polar coordinates within the workpiece coordinate system and

describes the corresponding polar angle to the radius r I .…”

Section: Measurement Principlementioning

confidence: 99%

Gear Shape Parameter Measurement Using a Model-Based Scanning Multi-Distance Measurement Approach

Pillarz

Fischer

2020

Sensors

To reduce wind turbine failures by defective drive trains, deviations in the geometry of large gears (diameter ≳ 1 m) must be extensively determined with single-digit micrometer uncertainties. Fixed measuring volumes limit standard measuring methods like coordinate and gear measuring instruments for large gear measurements. Therefore, a model-based scanning multi-distance measurement approach for gear shape parameters is presented. The measurement approach has a scalable design and consists of a confocal-chromatic sensor, rotary table as a scanning unit and model-based signal processing. A preliminary study on a midsize spur gear demonstrates the general feasibility of the model-based scanning multi-distance measurement approach. As a result, the mean base circle radius as the fundamental gear shape parameter is determined with an uncertainty of <5 μm. The calibration and adjustment of the sensor arrangement were performed with a known calibration gear. Scalability is not experimentally validated in this article. However, simulations verify the scalability of the measurement approach in a first step. For gears with 1 m in diameter and varying tooth flank geometries, the estimated achievable uncertainty of the mean base circle radius is still <5 μm. Therefore, the model-based scanning multi-distance measurement approach is a promising alternative for gear inspection.

“…The nominal position P N of any point on a flank of a gear can be determined in (x, y, z)-coordinates as a function of a few parameters (according to [7][8][9]): -rolling angle $, -position in z-direction, -base circle radius r b , -rotational position of the gear q, -number of teeth n, -base helix angle b b…”

Section: Calculation Of Deviations For Each Flankmentioning

confidence: 99%

Areal parameters for the characterisation of gear distortions

Stöbener

Materialwissenschaft Werkst

Fuhrmann

et al. 2012

Gear distortion is influenced by several effects which might originate in various steps of the entire production chain. To understand the distortion mechanisms including interactions between different influencing parameters, a system approach for the whole production process is required. As distortion is not constrained to the toothing but also effects the gear's base body, an extended measuring strategy (compared to the standard) has been devised. Based on this strategy, an areal evaluation has been developed and new quality parameters describing the deviations of the whole gear and of each tooth have been defined. In contrast to the standard evaluation, the new quality parameters consider the relationship between different measured lines. This offers the possibility to determine the influences of the base body deviations on the toothing distortion and to separate them from the intrinsic toothing deviation. This paper describes the developed strategies and methods and compares them with the standard inspection process.Keywords: gear / distortion / areal evaluation / measurement strategy / cmm / Der Verzug von Zylinderrädern wird durch verschiedene Effekte beeinflusst, die in unterschiedlichen Teilen der Fertigungskette auftreten können. Um die Verzugsmechanismen inklusive der Wechselwirkungen zwischen den einzelnen Einflussgrößen vollständig zu verstehen, ist ein Systemansatz für den gesamten Fertigungsprozess erforderlich. Da der Verzug nicht nur auf die Verzahnung beschränkt ist, sondern am gesamten Zylinderradkörper auftreten kann, ist (verglichen mit dem Standard) eine aufwändige Messstrategie für Zylinderräder entworfen worden. Basierend auf dieser Strategie konnte eine flächenhafte Auswertung inklusive neuer Qualitätspara-metern entwickelt werden, welche sowohl die Formabweichungen des gesamten Zylinderrades als auch die der einzelnen Zähne beschreiben. Die Auswertung berücksichtigt im Gegensatz zum Standard-Verfahren die Beziehungen zwischen den einzelnen gemessenen Linien. Damit ergibt sich die Möglichkeit, die Einflüsse der Grundkörperverformungen auf den Verzahnungsverzug zu bestimmen und sie von denen der Verzahnung zu separieren. Der Artikel beschreibt die entwikkelten Strategien und Methoden und vergleicht sie mit dem standardisierten Mess-und Auswerteprozess.