This paper describes a new and efficient analytical methodology that is now used at Ford Motor Co. to evaluate any potential gear whine failure modes upfront in the design process for transmissions and axles. This method effectively combines analytical formulations for non-linear contact and finite element analysis to provide accurate and fast design analysis with drastic reduction in modeling and solution time compared to other conventional analytical methods. The paper presents how gear micro-geometry is integrated as part of the drivetrain system (transmission + driveshaft + axle) and analyzed as a fully coupled system to properly compute gear multi-mesh transmission error and the system dynamic response. A modeling method for a fully assembled multi-speed planetary transmission with rear axle and all internal components represented as flexible bodies is introduced. Gear transmission error was applied to induce gear dynamic force and transmission case vibration. Furthermore, CAE predictions are compared to experimental data to validate the simulation. Finally, planetary gear upfront design options are evaluated and optimized using design of experiments method.

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The paper presents the optimization approach to the process of computerized design of involute spur and helical gears. The basis of the proposed approach (named as the concept of dynamic blocking contour - DBC) is the procedure of optimizing the definition of shift coefficients of a pinion and gearwheel of a gear. Examples, considered in the paper, are obtained by means of the CAD system "Contour", where the proposed method is implemented. Versions of solving some tasks, arising in practical gear design, are shown. A new approach to computerized design of involute spur and helical gears is also considered in this paper, based on the synthesis of DBC method and the method of Direct Gear Design (DGD) which is intensively developing nowadays.

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The design of tooth surface for a low noise under the various load condition is very important. Gear noise is highly related to the transmission error. The optimal tooth surface for the reduction of transmission error is very difficult to determine analytically due to nonlinearity of transmission error and the satisfaction of several load conditions. The satisfaction of design variables in several load conditions leads to Pareto optimum of multi-objective optimization. Therefore, this study proposes the method to determine the optimal lead curve and robust design of the tooth surface, using the response surface method and multi-objective optimization. To do so, the effect of transmission error on candidate design variables by a screening experiment has been investigated using an analysis of variance and the design variables are selected. Then the fitted regression model is built with the statistic validation of the model. The model with constraints is solved to obtain the optimum design of the lead curve and the robust design for the tooth surface.

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Contact stress between meshing gear tooth flanks is one of the most important factors for the load capacity evaluation of a gear pair. A gear design system was developed using Tooth Flank Film Elements (TFFEs). The TFFEs enable boundary conditions for a contact problem in meshing teeth to be easily dealt with. In order to confirm the reliability of the gear design system, contact stresses between meshing gear flanks of spur gear pair subject to a static load were measured using pressure measurement film, and were compared with calculated ones. In the present paper, contact stresses of a gear pair with some parallel and crossed misalignments were measured, and were com-pared with calculated ones. As a result, even for a gear pair with some parallel misalignments, the Tooth Flank Film Elements can work well, and can yield reasonable contact stresses.

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The load capacity calculation of worm gear has been improved by the development of the new technical report ISO TR 14521 under the control of the ISO TC60/SC1/WG7. New rating criterions are proposed. The author provides the analyses of the actual TR improvements and gives the limits of application based on several examples. On the bases of experiments realised on test rigs and in order to improve the future of the worm gear load capacity calculation methods the author analyses the fact that the contact pressure is in general non uniform along the lines of contact in opposition to the bases of the TR which supposes a constant contact pressure. On the basis of the non uniform contact pressure, the author proposed a calculation method that can be easily adapted on a PC. At least an adaptation of the TR is proposed.

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The functions of the principal members of a flat-wheel harmonic drive are similar to the functions of a traditional harmonic drive, but the features of the flexible and the solid wheels are different. This paper reports on an analytical approximation method for tooth-load calculation based on backlash conditions of flat wheel harmonic drives. Deformation of teeth and the rotation of the flexible gear depending of loading torque are calculated. An experimental flat wheel harmonic drive is also introduced with measurement results.

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This paper describes a new method of profile design for strain wave gearing. At present there is a strong market demand for this device having improved performance. Especially, improved load capabilities are desired. The main elements covering load capabilities of strain wave gearing devices are the tooth bottom rim of the flexible external gear and the inner rolling contact surface of the wave generator, particularly, the fatigue strength at locations in the vicinity of the major axis thereof. The object of the present study is to reduce the stresses produced at these two locations. The principles of this method are based on two approaches. The one is the continuous meshing of teeth in the principal perpendicular section by satisfying the extend Euler-Savary's theorem. The latter condition is satisfied by the tooth contact condition along the tooth trace. Using these steps, we will get the useful guidance to profile design of this device.

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The mashing properties of the mismatched gear pair and the pre-control of contact mark of tooth surface have been researched in this paper, while the elastic deformation of tooth surface was taken into consideration. The theory of contact stress has been combined with the theories of spatial gear meshing. A new way and new method to control the quality of engagement of the spiral bevel gears and the Hypoid gears have been presented in this paper. For this purpose, the Baxter method, with which the conjugate curvature of line contact meshing can be calculated, has been extended into the case of spatial meshing of point contact.

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Coupled planetary drives can be obtained through coupling and fixing the base elements of two or more planetary drive units. Since planetary drives with three base elements are fundamental construction units of the coupled planetary drives, we carried out a general analysis of them to determine the properties of the coupled systems. We determined the directions of power-flows in each field of the transmission ratio, the kinematical-, dynamical- and efficiency equations, as well as self-locking power-flows and fields. Based on the results of research of planetary (differential) drives with three base elements we accomplished the analysis of several types of coupled planetary systems, such as 1 d-o-f coupled planetary drives with a closed circle, 2 d-o-f coupled planetary drives having constant transmission ratio, 2 d-o-f self-regulating continuously variable coupled planetary drive and a novel type of 2 d-o-f planetary mixers.

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This article deals with the well-founded methodology and the innovative design criteria, currently implemented on the AgustaWestland helicopter transmissions. These specific concepts constitute, by means of a combination of innovative features and practical experiences, a general design process for the definition of the future transmissions to come and for the continuous improvement of existing products. Both analytical predictions and experimental evidences, driving the design along parallel paths, have provided all necessary data for conceiving a logical flowchart, the end of which is a robust, light and durable transmission. Particular emphasis to quietness behaviour is indeed one specific objective of the new philosophy in gearbox design. Project peculiarities, design and analysis procedures, reliability indexes and achieved performance behaviour are presented. A number of practical and real case histories is outlined, providing examples of the actual implementation of this design and development approach.

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Conical involute gears came to be used in a wide range of applications. Recent years, the new applications of the conical involute gears are expected in the field of automobiles. In this paper, the analysis of tooth surface contact is reported using the conjugate surface for the practical design of conical involute gears. First, two coordinate systems that are rigidly connected to a pair of each conical gear are considered, and coordinate transformation between these two systems is explained. The conjugate surface of the conical gear is obtained as envelope of family of shapes made from relative motion of rotation to mate conical gear. Next, the conjugate surfaces are visualized with the generating line of the conical gear on the plane of contact with base cylinder, and theoretical tooth bearing are obtained. Finally, tooth bearing tests are executed and results of tests are in good agreement with the theoretical ones.

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The paper summarizes the research on the topic of improving the surface durability of conical gear drives for power transmission. The authors proposed a new concept for designing skew conical gear drives, which are designed in so-called approximate line contact combining with profile-shifted transmission. The contact patterns have a large major-to-minor-axis ratio, so that not only the surface durability can be increased, but also the sensitivity to edge contact can be reduced. A numerical method for loaded tooth contact analysis was also developed to solve the non-Hertzian contact problem of such a conical gear drive in approximate line contact. The feasibility of the design concept is verified both by FEM and by measuring the contact pattern on a test bench.

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The face hobbing process has been widely used in automotive industry. But few papers have been found regarding meshing of them. This paper presents mathematical models of two types of face-hobbed hypoid gears, non-generated and generated. First, based upon kinematical analysis of a cutting machine, a mathematical description of tooth surface generation is given. Second, based upon the theory of gearing and differential geometry, exactly conjugate surfaces are studied. Third, curvature analysis is performed. Last, a numerical model is validated by measuring loaded transmission error and loaded tooth contact pattern.

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When shaft angle Σ, offset E and gear ratio i0 are given, it is clarified how the lengthwise contact ratio common to all kinds of gear is defined and how the pitch cones of hypoid gear are chosen to obtain the equal lengthwise contact ratios of drive and coast sides as follows. (1) Σ, E and i0 determine the field of relative velocity in the static space, points Pw having the same relative velocity Vrsw draw a line element Lpw of cylinder around the instantaneous axis and the Lpw is also the intersection of the surfaces of action. In the case of cylindrical and bevel gears, the Lpw coincides with the instantaneous axis because of Σ → 0 or π or E → 0. (2) By rotating the Lpw around the axes of pinion and gear, the pitch hyperboloids are drawn respectively, which are the pitch surfaces common to all kinds of gear because the Lpw is the intersection of the surfaces of action. (3) The tooth trace is defind as the curve which the path of contact put on the Lpw draws in the coordinate system which rotates with each gear respectively. (4) The lengthwise contact ratio is defined as the one calculated along the Lpw. (5) In the case of hypoid gears, equal lengthwise contact ratios of drive and coast sides can be realized by choosing the pitch cones contacting at Pw so that the intersection between the pitch cone and the surface of action coincides with the Lpw and the resultant pitch angle of cone is different from Wildhaber's one and almost equal to the inclination angle of the instantaneous axis, which is shown in the design examples.

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It is the research on the face gear expected as a substitution of the bevel gear and hypoid gear. First, the geometrical design method of the face gear was introduced, and how to decide an effective engagement area under the design parameter was explained. In continuing, how to avoid the influence of machining and assembling error on tooth bearing of the face gear was shown. So, in this paper, on the face gear with modified tooth flank by some methods, for example, the conventional method which modifies tooth profile of pinion, the influence of machining and assembling error on tooth bearing was investigated by tooth contact analysis (T. C. A.). And the new method which modifies gear tooth surface was proposed on condition that the hardened gear-teeth finishing process could be carried out by the general-purpose Multi-Tasking machine. A numerical example was presented based on the proposed method.

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The tooth surfaces of conjugate gears are slightly modified in some cases in order to provide the insensitiveness to manufacturing errors and misalignments. When the tooth surfaces of the conjugate gears are modified, the line contact in meshing of gear teeth turns into a point contact. In this case, the progressive direction of contact point on the gear tooth surface concerning with the meshing progress has an influence on the performance of the gears. The progressive direction of tooth meshing has not been almost considered in gear kinematics so far, so that gear manufacturers could not get the standard tooth contact pattern on the tooth surface, and gear engineers could not know the real meaning of the tooth meshing. In this paper, the meshing of gear teeth is discussed and the progressive direction of tooth meshing is made clear based on gear kinematics. As examples of hypoid and worm gears, slide lines and contact lines are calculated numerically. The results show that the progressive direction of tooth meshing is the direction of the relative velocity between meshing gears. We understand loosely the tooth meshing which is the most fundamental phenomenon in the gears. The tooth meshing means the sliding contact of a pair of slide lines.

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The present paper presents a numerical model able to simulate the quasi-static loaded behavior of a pinion rack with variable ratio. The three main steps are: -Tooth profiles, depending on a given kinematics law, -Unloaded kinematics simulations, to obtain the potential contact zones and to compute the distances between the meshing surfaces, -Instantaneous load sharing computation. Results such as the pressure distribution, meshing stiffness, transmission error and stresses at the tooth roots are provided. The model needs at several steps a CAD model. This one is automatically generated. All the process is briefly presented and the paper is focused on the two first main steps.

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The plunger harmonic transmissions and the principle of its operation is considered as the construction of a new kind of mechanisms for the transformation of movement. The problem of geometrical synthesis of a gear engagement of plunger harmonic transmission with circular working surface of the plunger and the traj ectory of its movement by a circumscribed arc of a fixed radius is formulated and solved. The theoretical solution is illustrated by a numerical example from the practice of design of a plunger transmission of an experimental reducer.

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A large improvement in gear cutting productivity is needed to reduce CO_2 emissions. A substantial improvement in productivity can be expected for face-hobbed hypoid gears by changing from the conventional wet cutting process to a high-speed dry cutting process. To facilitate the switch to a dry cutting method, changes are needed in materials, tools, cutting conditions, and cutting machines. Highly accurate synchronization between the cutter axis and the work axis and a system for high-speed dry cutting are necessary for the cutting machines. However, conventional face milling machines do not have such a synchronizing system. The aim of this study is to achieve high-speed dry cutting of face-hobbed hypoid gears on conventional face milling machines. A prototype of a hypoid cutting machine using the face milling method and equipped with a synchronizing system was developed. This machine is able to cut face-hobbed hypoid gears at high speed in a dry cutting process. Concretely, the rotary encoder arrangement, spindle stiffness and the machine's drivetrain system were optimized. Machining accuracy was improved by adopting measures based on an analysis of vibration from intermittent cutting and the drivetrain. Management of heat generated by dry cutting was optimized and a chip evacuation device was added. With these measures, the target machining accuracy and tool life were achieved after conducting several cutting trials. As a result, cutting conditions were found that facilitate high-speed dry cutting of face-hobbed hypoid gears.

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Tooth surface modification of hypoidgears is inevitable operation to obtain excellent gears with good performance. However in the case of the face hob cutting, it is considerably complicate for gear engineers, because both side of tooth are cut at once. In this paper, the authors present the procedure to obtain the correction values of machine settings for tooth surface modification in the case of face hob cutting and report that the modification of pressure angle and spiral angle can be achieved perfectly for individual demand of both tooth flanks with little influence on other characteristics of tooth surface. The usefulness of this procedure was certificated by cutting test using the prototype machine.

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This paper describes cutting methods for a face gear meshing with a large helix pinion with a small number of teeth. This type of face gear may be cut with the hob having the same profile of the pinion. But, it is known that interference between the hob tooth flank and gear blank and the profile error based on a cutter feed are apt to occur. In this paper, mechanisms that the interference and the profile error occur are investigated numerically. And, the cutting conditions for no interference and smaller profile errors are shown. Cutting tests of the face gear were conducted on the hobbing machine with a tangential feed attachment. Moreover, meshing tests were conducted using the face gear cut by applying the proposed method. As the results, good contact patterns with smooth meshing were obtained.

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This study reports the method of forging of spiral bevel gear of arbitrary axial angle. In the case of spiral bevel gear, line contact of pinion and gear tooth surface should be changed to point contact to avoid wrong performance of power transmission. The authors made two ideas for crowning of gear tooth surfaces to obtain point contact for forging gears. One idea proposes that the trace of the contact points on pinion and gear surfaces lies along the tooth profile of pinion and gear surfaces, namely the trace lies perpendicular to the lengthwise direction of gear tooth. The trace can be set arbitrarily on the gear tooth. The other idea can be used for the trace of contact points on pinion and gear surfaces lies along the direction of tooth trace of the gear teeth. The numerical data are calculated and used for CAD/CAM systems for processing the metallic mold for forgoing of spiral bevel gears. Tooth contacts of forged gear set are confirmed by the 3D drawing of tooth surfaces. Master gears of electrode to work metallic mold to forge a pair of spiral bevel gears were made and running test and tooth contact testing. The running test shows the low noise running and contact mark coincide well with the contact mark calculated and drawn by 3D expression by the theory proposed in this report. And the authors succeeded in forging of the pair of pinion and gear by the two method by the idea proposed in this paper.

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Surface finish rolling experiments were carried out using rollers and helical gears of 1.5Cr-0.2Mo alloyed sintered steel having the density of 7.00〜7.60 g/cm^3. A two roller dies transverse CNC form rolling machine was employed. Two kinds of FEM model of 2-dimensional and 3-dimensional were proposed to simulate the surface densification process of rollers. Pore structures in the densified surface layer were examined and the effects of initial density of P/M material on densification properties were compared and evaluated. The experimental results show that the surface densification of P/M material with the initial density of 7.25 g/cm^3 or more has possibilities to make the part surface to a depth fully dense by optimizing the rolling condition. The simulation results in 3-dimensional model agree well with the experimental ones in the surface densification behaviors.

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This paper shows the transient phenomenon of chip formation and behavior in simulation tests of hobbing by using a high-speed video camera. Scratches occur on tooth surfaces and cutting edges chip when the chip jams between the tooth and the cutting edge. As a result, tooth surfaces degrade and abnormal tool wear occurs in dry hobbing. Chips produced by hobbing are classified roughly into three types; the "U", "J" and "I" types are represented in this paper. This paper presents findings of the "J" and "I" type-chip movements in flytool simulation tests. In the "J" type-chip, a part of end side of the chip produced by the top cutting edge is often jammed into the finished surface being pushed by the chip from the side cutting edge. The "I" type-chip flows from the root to the tip side of the cutting edge, and the pointed end of the chip is jammed into the space in down cut method. In up cut method, the chip flows to the root side on the rake face, and the jam of chips occurs as well as the case of down cut method. Jamming mechanism in hobbing is discussed from the results of flytool tests.

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In gear hobbing, High Speed Steel (HSS) hob is one of the most useful tools. However, the improvement of productivity by HSS gear hobbing is reaching critical limit, because the hardness of HSS hob decreases rapidly when in the high temperature of 600℃ or more. Therefore, it is important that improving productivity for gear manufacturing is increased by using carbide tipped hob with heatproof. However, damage might occur in the tool at the early stage when the cutting condition is mistaken, and the tool life be shortened extremely. Therefore, when carbide tipped hob is applied for gear cutting, it is important to understand the characteristic of it enough, and to understand the condition for the tool life. In this study, the factor of the damage of the carbide tool is systematically examined.

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Relief grinding for involute helical pinion cutters with no profile error is realized by through grinding with a trapezoid-like grinding wheel. As a calculation example, an involute helical pinion cutter with semi-topping and protuberance cutting edges is used. First, a method for calculating the grinding wheel profile to finish the tooth flanks of the pinion cutter with the exact cutting edges is proposed. Next, the profile errors of cutting edges after regrinding are calculated and evaluated by means of the tooth profile of the work gear being shaped with the reground pinion cutter. As the result, it was found that the profile errors and changes in shapes of the semi-topping and protuberance cutting edges after regrinding are very small. Finally, the usefulness of the proposed methods was confirmed through the grinding tests of the pinion cutter.

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The development of industry consecutively requires more exact and more efficient power transmission techniques. In order to create efficiently meshing gears it is mandatory to manufacture the gears with accurate geometrical shape. This is especially true for worm gears in hypoid or spiroid drives. The goal of our study is to work out an applicable mathematical approach for handling and classifying shape errors in worm gear manufacture.

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In the last years the demand for grinding machines of large module gears increased very strong. New productive solutions were developed. The profile grinding technology was improved. By using the fast feed rate grinding it is possible to do rough grinding with much higher specific metal removing rates. Also the non-productive auxiliary times are reduced. Before grinding the gears they are measured completely with high-speed measuring. Based on these results the grinding process will be optimized to prevent grinding times without contact of grinding wheel and gear. Another possibility to increase quality and productivity is the combination of processes in one machine. The grinding of the gear teeth, the bore and the face of a planetary gear will be executed in one machine. The results are presented. The continuous generating grinding was further developed. Now it is possible to grind large module gears up to a gear diameter of 1000 mm and a module of 10. The productivity could be increased significant. The specifics and the problems in comparison with profile grinding are discussed. An outlook to future developments is given.

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Current trends in gear manufacturing include shorter production lead time and a rising number of gear variants due to a larger variability of product configuration. Both trends create the requirement for a reduction of lot sizes and an increasing frequency of machine change-overs. The latter is additionally intensified by a continued decrease of cycle time through high performance machining processes (Fig. 1). Different gear grinding processes, i.e. discontinuous profile grinding and continuous generating grinding, are well known but have individual strengths and limitations. In the past, gear manufacturers were often limited to the selection of the type of gear grinding process depending on single-function gear grinding machines that were available. Considering the increasing number of different gear variants, technical and economic advantages can be achieved by selecting the optimum gear grinding process depending on the individual workpiece requirements instead. Gear grinding machines offering full flexibility regarding process and tool selection are required. In view of the increasing change-over frequency, methods to reduce set-up time are being emphasized, particularly allowing frequent change-overs between the different types of grinding processes and tools.[figure]

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In recent years, the demand for precision machining of planetary gears has increased due to the requirement of reduced noise and vibration in automotive transmissions. For ring gears (one of the components of the planetary gear system), the conventional method of finishing has been gear shaping or helical broaching followed by heat treatment. To meet the increasing requirement of the aforementioned demand, mass produced planetary gear systems, must be hard gear finished after heat treatment with high accuracy and efficiency. This paper presents a new gear grinding machine developed specifically for economical finish grinding of automotive internal ring gears in mass production.

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When invented approximately thirty years ago, gear honing was (only) a surface polishing process with small materials removal rate. Up until a few years ago, the industry thought that even the large gears (diameter up to 280 mm), crank shafts, gears with collision contours necessitating the use of small cross axis angles were not honable in terms of an insufficient material removal process. Innovations in the tools and technology and ultimately in the areas of machines and controls have enabled us to turn gear honing into an economic hard-fine finishing process that fulfils the contemporary increased gear quality requirements. The special surface generated by gear honing, in combination with induced compressed residual stress, have had a positive effect on durability and noise emission of the gears. The latest development prove that there is lots of room for improvements in the relatively young gear honing process, but nevertheless, gear honing has been established in the gear industry.

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Now, tooth contact evaluation is done with visual check in visible area. But the results of visual examinations are too subjective. Therefore, automation and accuracy enhancement of tooth contact evaluations are required. We tried new evaluation of tooth contact in the near-infrared area. Therefore, a near-infrared camera and infrared lights were used in this research. First of all, the evaluation of near-infrared images of tooth contact was done. Second, tooth contact images by image binarization, which is indispensable to automation, were evaluated. Third, boundary part of the tooth contact was extracted by differential operation. Finally, the effectiveness of the tooth contact evaluation proposed in this research was compared with the tooth contact calculated from the tooth surface. As a result, the high S/N images were obtained by using near-infrared area. Moreover, we clarified the effectiveness of new evaluation of tooth contact to examine the automation of tooth contact evaluation.

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We developed a new diagnostic method by using a laser beam. First, the tooth surface is irradiated by a zonal laser beam from oblique direction, and then an irradiated laser beam line is shifted along the height of the tooth according to gear revolution. The variations of laser reflection between the initial and the present conditions are compared, and it can estimate the condition on the tooth surface. Next, we developed the method to scan the length of the pitting area from the laser reflection data using a computer. To put this method into practical use, the laser sensor was fixed in the gearbox, and the laser reflection from the lubricated gear was measured. These experiments were carried out under the condition of force-feed lubrication. As a result, this method could detect all occurrence of the pitting in the dry condition. To improve the accuracy of the detected length of the damage area, the definition of the value of the first-stage threshold and smoothing of the different data was important. Furthermore, to apply this method to a helical gear, we made the three-dimensional model which located the relation between the helical gear and the laser sensor, and derived the conditional equation that the helical gear can be irradiated by the laser sensor along the tooth trace of the helical gear. By using this equation, we can diagnose the helical gear as well as a spur gear.

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A pair of screw compressor rotors consists of a male and female rotor which have a unique profile each. The rotors mesh with each other and the male rotor drives the female by its leading lobe surface contact like the gears in an oil-injected screw compressor. The pair of rotors has transmission error caused by tolerances and misalignment. The transmission error can increase undesirable noise and vibration. An easy and fast method to calculate and predict the transmission error is proposed to reduce this noise. This method is based on a calculation of clearance distribution along the sealing line between the rotors. The transmission error can be calculated by comparing the male and female rotor rotation angle, when the rotors' leading surfaces contact each other as in virtual meshing. This method was experimentally shown to have enough accuracy for practical use. An oil-free screw compressor needs high accuracy in the setting of its timing gears. Virtual meshing can be applied to the phase adjustment of their settings. This method can predict their margins of backlash on both the leading and trailing sides, including hot condition during the machine operation.

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In this paper an approach to measure gears transmission error (TE) by means of optical encoders is discussed and the consequent software tool is presented. Two incremental encoders with 18000 angular divisions and sinusoidal outputs have been used and a 5 MHz for channel data acquisition card has been utilized to acquire the signals. A Matlab software has been created to manage the whole data acquisition and processing: setting the proper frequency of acquisition, the discrete signals acquired from the two encoders are reconstructed by interpolation, improving the accuracy of the acquisition. Moreover, the one-per-revolution signals of the two encoders can be used to measure TE always from the same pair of teeth in contact. Data are elaborated and transmission error curves can be plotted for any number of revolutions of the input shaft and always from a selected pair of teeth in contact. By means of this procedure, transmission error can be measured for different values of torque and speed. Comparisons between experimental measurements and theoretical results of a validated numerical model are shown to confirm the validity of the measurement system.

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Although the double flank gear rolling test is widely used for controlling accuracy of gears because of its stability in applications, it is considered difficult to use it for detecting all the components of gear inaccuracy. The authors previously proposed a method for detecting tangential composite deviations with the double flank gear rolling test based on the difference between the tooth flank contact point on the line of action during the machining of its tooth form and the contact point during the measurement, and validated the method theoretically and experimentally. The authors are further advancing a study on providing a perfect accuracy guaranty of micro module master gears with modules less than 0.2, which is impossible to do with conventional gear measuring instrument.

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The high precision gear is strongly required for advanced quality on Motion and Power Transmissions which is the fundamental technology of many fields, such as automobiles, construction machines and robots. And the improved evaluation technology (accuracy measurement etc.) of the gear is becoming indispensable. Then the high precision gear measuring machine, that have new system which reduces the error factors of the conventional machine, is being developed. It will improve the gear measuring technology spectacularly and the measurement uncertainty of the tooth profile, which is most important for the accuracy of the gear, will be reduced by one digit. And Osaka Seimitsu Kikai Gear Measuring Center (GMC) recently was accredited as JCSS (International MRA) gear calibration laboratory, which satisfies the requirements of ISO/IEC17025 concerning the competence of the calibration laboratory. And this high precision gear measuring machine is expected to contribute to improve gear calibration uncertainty.

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A complete measurement result consists of the measurement value and its measurement uncertainty. The knowledge of the uncertainty is, above all, of economic importance as it is a prerequisite for making a reliable statement on the quality of a measurement. Based on a traceable determination of measurement results, the production processes can be evaluated and controlled in a targeted way. Particularly with regard to the manufacture of highly accurate workpieces with constantly decreasing tolerances this leads to less complaints and thus to high cost savings. The determination of the measurement uncertainty is, however, complex and has, as a matter of principle, to be estimated for each measurement individually. Therefore, the method of the "Virtual Coordinate Measuring Machine" (VCMM) has established itself for some time now in coordinate metrology for a realistic, fast and automatic determination of the measurement uncertainty on prismatic workpieces. Within the scope of a German research project, the Physikalisch-Technische Bundesanstalt (PTB), in cooperation with partners from industry, has transferred this approach to the gear metrology. The aim was the development of an industry suited procedure for a computer-simulated determination of an ISO-compliant measurement uncertainty for involute gear measurands. Thus, the extended VCMM for gear measurements guarantees traceable gear measurements and provides the prerequisites for a modern quality management system.

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The reduction of the vibration and noise of gears is an important issue in mechanical devices such as vehicles and wind turbines. The characteristics of the vibration and noise of gears are markedly affected by deviations of the tooth flank form of micrometer order; therefore, strict quality control of the tooth flank form is required. The gear measuring instrument is generally calibrated by an involute helicoid artefact. In the tooth flank form measurement of the involute helicoid artefact, the setting error of the involute helicoid artefact largely affects the measurement result. The laborious setting operation is required for the calibration of the gear measuring instrument. Therefore frequent calibration of the gear measuring instrument has not been realized. In this study, evaluation method of the gear measuring instrument using multiple-tooth involute helicoid artifact is proposed to reduce the effect of the setting error. The efficiency of this method is confirmed by the measurement simulation using a computer program.

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