Gear Metrology Research Articles

Gear metrology – An update

Twenty years after the publication of a first CIRP Keynote Paper about gear metrology [32], this paper reviews again the state of the art in this area. Gear technology has changed and improved significantly during the past decades, which initiated substantial improvements in gear metrology, too. On the other hand, for up to 50% of gear inspection technologies used today, only minor changes are observed. Consequently, this update focuses on new or significantly improved techniques, such that only the combination of both this publication and [32] gives a comprehensive review of the state of the art in gear metrology. Gear technology in emerging markets, e.g., electric cars, large gears for energy systems, and micro gear drives, extends the scope of inspection tasks and requires new measuring methods and instruments, including optical sensors. Measured data, covering the entire gear flank of all teeth, need areal flank descriptions, areal evaluation methods, and areal deviation parameters. New calibration methods and artifacts will improve measurement uncertainties.

Novel alignment method for optical 3D gear metrology of spur gears with a plain borehole

In 3D optical metrology, novel approaches to characterise the geometrical quality of gears require a custom gear alignment process to produce reliable results. This study proposes a novel scan alignment method known as subsequent gear alignment (SGA). It emphasises on the proper alignment of the gear hole and follows the alignment of gears in real-world applications. Therefore, the SGA method increases the usability of the previously developed and published methods. The scanned data were first processed with both the commercial global alignment and SGA methods and then evaluated to obtain standard geometrical parameters. These were compared with those obtained by the tactile method, and the SGA method offered improved results over the global alignment method.

Comprehensive Areal Geometric Quality Characterisation of Injection Moulded Thermoplastic Gears.

Injection moulding is currently the most widely employed production method for polymer gears. Current standardised gear metrology methods, which are based on metal gear inspection procedures, do not provide the key information regarding the geometric stability of injection moulded gears and are insufficient for a thorough gear inspection. The study developed novel areal quality parameters, along with a so-called moulding runout quality parameter, with a focus on the injection moulding method. The developed parameters were validated on twenty-nine gear samples, produced in the same moulding tool using various processing parameters. The gears were measured using a high-precision structured-light 3D scanner. The influence of injection moulding process parameters on the introduced novel quality parameters was investigated. The developed moulding runout quality parameter proved to be effective in evaluating the shrinkage that can occur in the injection moulding process. The novel moulding runout parameter returned an average value of −21.8 μm in comparison to 29.4 μm exhibited by the standard parameter on all the gears, where the negative value points directly to mould shrinkages. The rate of cooling was determined to be the most influential factor for the shrinkage of the gear. The developed areal parameters demonstrated to be advantageous in characterising the deviations on the teeth more comprehensively.

3D Involute gear evaluation – Supplement: Measurements in double-flank contact

Equations for double-flank contact measurements as used in involute gear metrology are presented with their detailed mathematical derivations. All formulas can be applied to either internal or external and either spur or helical gears, even when considering profile shift. Moreover, a proposal for measurements using different stylus radii ensures comparability for the evaluation of the dimension over (or between) balls MdK. The influence of the stylus sphere radius on MdK is illustrated via a numerical example. All equations are derived for error-free gears. .

APPLICATION OF RULED SURFACES IN FREEFORM AND GEAR METROLOGY

An application of two ruled surfaces (i.e., surfaces generated by a motion of a straight line), a surface of hyperbolic paraboloid and a tangent surface of a cylindrical helix in freeform and gear metrology is introduced in this paper. Both surfaces have been implemented as the main functional figures in several artefacts – metrological calibration standards intended for testing the freeform capabilities of various measuring technologies (e.g., tactile point-to-point measurement and tactile scanning on coordinate measuring machine, optical scanning, computer tomography). Geometrical and mathematical properties of the surface used are summarised, CAD models of all the developed standards are presented and photos of the manufactured standards are shown.

Tooth flank approximation with root point iteration – potentials and limits in gear metrology

Gear production demands high-precision metrology, for which a holistic evaluation approach of the geometric data is proposed to overcome current restrictions. The holistic approximation with integrated partitioning and iterative root point calculation can cope even with modified flanks and is validated for gear parameter estimation with systematic deviations <0.2 µm. Apart from low signal-to-noise-ratio cases, where the approximation suffers from the multidimensionality of the optimization, the accuracy of standard evaluation procedures is achieved. Furthermore, holistic approximation is able to perform the required mathematical separation of the integral geometric elements of a tooth flank automatically when determining unknown gear parameters.

Improved gear metrology based on the calibration and compensation of rotary table error motions

Geometric measurements of cylindrical gears are mainly conducted by either applying the generation principle or by coordinate measurements of points on a flank surface. In both cases, a rotary table (RT) is highly involved in the inspection process. The RT error motions and the misalignments of the gear axis with respect to the table’s effective rotary axis affects the measurement results, whose impacts increase with the gear dimensions. This paper presents the influence of such errors on gear measurements using both the classical line oriented and the areal inspection methods. A compensation method to remove these influences in gear evaluations is proposed using a RT, which was calibrated with a ball plate artifact. The methods are validated by measuring and evaluating a large gear artifact applying multiple strategies with and without compensation.

Virtual Model of Gear Shaping—Part II: Elastic Deformations and Virtual Gear Metrology

Elastic deflection of cutting tools relative to the workpiece is one of the major factors contributing to dimensional part inaccuracies in machining. This paper examines the effect of tool deflection in gear shaping and its effect on the gear's profile form error, which can cause transmission error and noise during gear operation. To simulate elastic tool deflection in gear shaping, the tool's static stiffness is estimated from impact hammer testing. Then, based on simulated cutter-workpiece engagement and predicted cutting forces, the elastic deflection of the tool is calculated at each time-step. To examine the effect of tool deflection on the profile error of the gear, a virtual gear measurement module is developed and used to predict the involute profile deviations in the virtually machined part. Simulated and measured profile deviations were compared for a one-pass external spur gear process and a two-pass external spur gear process. The simulated profile errors correlate very well with the measured profiles on the left flanks of the workpiece teeth, which are cut by the leading edges of the cutter teeth. However, additional research is needed to improve the prediction of the right flanks, which are cut by the trailing edges of the cutter teeth.

Future gear metrology based on areal measurements and improved holistic evaluations

Three existing major challenges in today's cylindrical gear metrology are: an increased need of holistic information on gear geometry; an increasing variety and use of flank modifications; and an improved feedback to the manufacturing process. This paper analyses the consequences of these challenges. They require a paradigm change in gear metrology concerning the sensing hardware (tactile vs. optical), measuring strategies (line oriented vs. area oriented), and evaluation methods. The latter includes a revision and update of the widely used gear deviation and modification parameters (e.g. fα, fβ, Fp, CHα, Cβ) and their effective determination by Chebyshev polynomials. Simulated and measured gear data are analyzed and a proposal for a revised set of gear deviation and modification parameters is presented.

A new calibration guideline for worm and worm-gear rolling testers

The evaluation and calibration of gear testers are considered as a key point to ensure the obtained results in gear metrology. Although ISO TC 60 working group has developed standards in this regard, the fact is that for the time being, there are not specific international standards for gear rolling tests. In this work, a periodical calibration guideline for gear rolling testers, particularly for worm gear transmission, is proposed, allowing the reduction of possible error sources in the measurement process. A series of tasks distributed over time are suggested in this work to maintain the accuracy of the gear rolling test machines.

Precision measurement of planar double-enveloping hourglass worms

The measurement of planar double-enveloping hourglass worms has always been a technical problem in the field of gear metrology. To solve this problem, we propose a new method and develop a measuring machine to inspect each deviation of the worms. In a cylindrical-coordinate system, the measuring principle adopts electronic generative metrology. The mathematical model of the worms is established according to the forming process of the worms. Based on the definitions of error items to be measured, the model of each deviation will be determined. The model could be transformed to the control path that leads the probe by controlling the movements of X axis, Y axis and Θ axis. In this process, probe radius compensation is necessary to correct the control path. At last, the helix deviations, the tooth profile deviations and the topologic deviations of a worm are inspected. It is the first time that the topologic deviation of this kind of worm is measured. The analysis shows that the deviations of the worm could be a reference to adjust the processing of the worms. The measuring machine could inspect the hourglass hobs, the cylindrical worms and the hobs as well.

Standard conforming involute gear metrology using an articulated arm coordinate measuring system

Standard conforming involute gear measurements were taken by a manually operating articulated arm system and the respective task-specific measurement uncertainties were estimated. User-friendly templates were developed to provide almost unambiguous and repeatable measurement results. They allow the metrologist to easily detect and gather the single measurement points according to existing guidelines and standards commonly used in gear metrology. The research activities were carried out at the Physikalisch-Technische Bundesanstalt (PTB), Germany in the Department of Coordinate Metrology. Measurements were taken on a robust and highly accurate large gear measurement standard of PTB, in the following called the gear standard. This gear standard materializes a left-hand and a right-hand gear as well as a spur gear. The 1 m outside diameter of the gear standard is similar to the gears used in wind power plants. A commercial articulated arm coordinate measuring system was used for the measurements. A high temperature stability of ±0.2 °C was provided to minimize thermal influences. The results of profile and helix measurements will be presented. This worldwide first investigation, on the basis of a calibrated involute gear standard, gives users of the articulating arm system quantitative information on a task-specific performance of a representative gear measurement.

The influence of manufacturing method on the running-in of gears

Striving for higher gear transmission efficiency by using a low-viscosity transmission lubricant affects the lubricant film thickness. To keep the Λ-ratio (the ratio between the film thickness and the surface roughness) intact, more effort must be put on the surface topography. This paper presents a study of how running-in affects the dry elastic contact area ratio in spur gears using real surface topographies from three common manufacturing methods (green-shaving, honing, and grinding). The test gears were manufactured in case-hardened steel, similar to 20MnCrS5. Surface topography measurements were used as input to a contact analysis boundary element software program. An important hypothesis used in this work is that the dry elastic contact area ratio, i.e. the ratio between real and nominal contact area, can be used as a measure of the contact conditions in gears. It is concluded that running-in differs significantly for the studied manufacturing methods and that the dry elastic contact area ratio gives a consistent description of these changes. The shaved gears have the highest dry elastic contact area ratio after running in, where the ground gears have the lowest dry elastic contact area ratio. The increase in dry elastic contact area ratio is about 30 per cent for the shaved gears, 12 per cent for the honed gears and less than 5 per cent for the ground gears. Extreme value parameters, such as Rp and Rz, showed relatively good correlation to dry elastic contact area ratio. However no genuine correlation could be found between dry elastic contact area ratio and two-dimensional (2D) surface roughness parameters. Furthermore, traditional gear metrology form parameters do not serve as a good measure on the changes occurring during the running-in.

Interpretation of bevel gear topography measurements

The bevel gear manufacturing process is characterized by several steps, beginning with gear design requirements and the optimization of meshing properties and ending with extending the cutting and grinding tool life. The rolling process of a gear set is currently optimized by simulating and calculating corrections for the generating movements of the cutter axis. The basis to calculate manufacturing corrections is a measurement of the flank topographies, obtained from the first cut gear. Therefore, the detected flank form deviations serve as the main issue in the subsequent simulations and calculations. Bevel gear metrology is based on a point-wise description of nominal flank geometry, which is not directly ‘visible’ since CMMs or gear measuring instruments (GMI) are able to scan rapidly across the bevel gear flank. This definition of nominal geometry is different from cylindrical gear metrology, which detects deviations through the recreation of the rolling process. Despite the different measuring methods, some of the evaluation parameters were taken over from the ‘cylindrical world’, which leads to several potential problems and misinterpretations. This paper presents common and uncommon evaluation methods, causing different topography results. These differences lead to specific correction calculations in the manufacturing process and impact the closed loop process in a significant way.

Micro gear validation: improving the correlation between virtual and physical testing

Downsizing mechanical systems requires the consideration of technological environment and restrictions. Nominal dimensions can be miniaturized, but shape and material deviations cannot be scaled down in the same way. In design these effects have to be considered and thus analyzed and evaluated in the very early activities. Simulation and test methods have to be adapted to the special characteristics of microtechnology. The present paper provides a strategy to validate micromechanical systems by means of virtual and physical testing. A standard test approach in macroscopic gear metrology, the tangential composite inspection, is used as validation tool for both test approaches. The results are very promising and show a good correlation between both miniaturized tests procedures.

Influence of reinforcement on composite gear metrology

Injection molded polymer composite gears are being used in many power and motion transmission applications. In order to widen the utilization of reinforced polymers for precision motion transmission and noise less applications, the quality or accuracy of molded gears should be increased. Since the injection molded gear quality is significantly influenced by the material shrinkage behaviour, there is a need to understand the influence of fiber orientation on part shrinkage behaviour and hence the gear quality. Unreinforced and 20% short glass fiber reinforced Nylon 6/6 spur gears were injection molded in the laboratory and computer aided simulations of gear manufacturing was also carried out. Results of the mold flow simulation of gear manufacturing were correlated with the actual fiber orientation and measured metrological parameters of the molded gears. Actual orientation of the fibers near the tooth profile, weld line region and injection points of molded gears were observed using optical microscope . Fiber alignment along the tooth profile restricts shrinkage and induces anisotropic shrinkage, which significantly decreases the deviation of involute profile parameter from the design value. Fibers embedded in the molded skin surface increases the gear tooth profile form and lead form deviations. Non-alignment of fibers across the gear tooth section increases the tooth thickness, tooth-to-tooth spacing and radial runout deviations from design values.

An international comparison of involute gear profile and helix measurement

The results from the first international comparison of profile and helix measurements between the national metrological institutes (NMIs) or their representatives of Germany, USA and UK are presented. The comparison was organized and coordinated by the UK National Gear Metrology Laboratory. The results from measurements on a 200 mm diameter helix master and a 200 mm diameter profile show that differences in slope error parameters are within the measurement uncertainty claimed by individual NMIs. The results should become the basis for the mutual acceptance of measurands for gears, in the calibration measurement capability list of EUROMET.

Gear Metrology

Gear drives represent key components for all kind of vehicles, machine tools, aircrafts, household appliances as well as a broad variety of industrial equipment and toys. The designers are confronted with increasing demands concerning lifetime, power transmission and noise emission, whereas the size and weight of gear drives is constantly reduced. Thus, the measurement of gears and gear tools is of decisive importance for gear production. This paper reviews the state-of-the-art of gear metrology, where tactile probing methods dominate almost exclusively. It summarizes new modelling and measuring principles, enabling a superficial description and inspection of gears. Especially optical measuring methods, the inspection of micro gears and alignment problems are discussed in detail. A final section reports the actual accuracy limits of gear measurements. It points out that a significant reduction of the measuring uncertainty associated with gears, standards and instruments is an urgent need for the production of high-precision gears.

The accuracy of image analysis methods in spur gear metrology

This paper describes the design of an involute spur gear inspection system in which measurements are made using a video camera and image analysis software. The measurement accuracy possible using low-cost CCTV cameras is investigated, and the possible sources of error identified. It is concluded that the measurement accuracy is comparable to that of current methods for tolerance inspection of spur gears and the low cost and ease of use make image analysis measurement systems an attractive alternative.

The Use Of Optical Gratings In Gear Metrology

Historically gear metrology machines have worked on the principle of generating motions by mechanical means, such as friction drive discs, straight edges, levers and sine bars. The gear error is then a difference reading measured by a small displacement transducer, for example a dial indicator or LVDT probe. Machines of this type are still commonly used, but the advent of optical gratings has now revolutionised gear metrology. The paper describes their development and use in CNC machines for the measurement of gear profile, helix and pitch errors and for the composite measurements of transmission error and backlash of a gear pair. The outcome is that much more data can be obtained than hitherto, more quickly and in a more helpful form. Despite these improvements there is a need for further research to take full advantage of the more comprehensive data, which can assist in quality control and performance prediction. The CNC machines are capable of development to still higher accuracies when the market need arises.