Gear Quality Research Articles

Study of laser texturing assisted abrasive flow finishing for enhancing surface quality and microgeometry of spur gears

This paper reports on study of laser texturing assisted abrasive flow finishing (LT-AFF) process of the hobbed spur gear (HSG) to further improve their microgeometry, surface finish, micohardness, microstructure, wear resistance, and material removal rate (MRR) as compared to AFF process. Preliminary experiments were conducted to identify optimum values of power and focal length of the continuous fiber laser of 1064-nm wavelength, and number of passes for laser texturing of the HSG made of 20MnCr5 alloy steel. Identified optimum values were used to produce homothetic texture on flank surfaces of HSG in a direction perpendicular to the lay profile generated by hobbing. Influence of laser texturing was studied by comparing deviations in microgeometry, average and maximum surface roughness values, microhardness, wear resistance, and MRR of HSG directly finished by AFF and laser-textured hobbed spur gears (LTHSG) finished by AFF. Previously optimized value of viscosity of AFF medium was used during finishing of HSG and LTHSG. Deviations in total profile, total lead and total pitch, and radial runout were used to indicate deviation in microgeometry of the spur gears. Results reveal that AFF of LTHSG reduced surface roughness and errors in microgeometry and improved microhardness, microstructure, wear resistance, and MRR than direct of AFF of HSG. Improved microgeometry and surface quality of spur gears will lead to their increased operating performance and service life thus reducing their running noise and vibrations and preventing their premature and failures. This research proves that productivity of AFF process can be improved significantly by laser texturing for finishing the spur gears.

A perspective on gear meshing quality based on transmission error analysis

Gears are one of the most important elements in power transmission systems. Their use is present in many industries due to their various advantages. Durability, constant transmission ratio, reduced size, high efficiency, suitability for a wide range of powers are some of the benefits. But gears also feature a number of drawbacks like vibration of the gear meshing system generating an undesirable noise. The main source of such a noise is the transmission error that result from misalignment of the gear, tooth profile errors and tooth deflections. This article is a state of the art on the theory of transmission error components that influences gear meshing. The errors of static transmission in gears may have several causes. One originates in the function of the gear mechanism which transmits the rotation and torque between axes and generates forces on the teeth, thus modifying their geometry due to elastic deformation. Another undesirable consequence that would be present even if tooth deflections were insensitive is caused by manufacturing errors such as profile, eccentricity, pitch or even assembling errors. One of the best known methods of reducing transmission error of a gear pair is the profile correction. This paper describes the main differences between static and dynamic transmission errors. It will be shown the most common methods of detecting the transmission error using analytical methodology, optimization algorithms, hybrid numerical/ Finite-Element Analysis and experimental researches in order to establish the dynamic behaviour of the gear pairs under different operating conditions.

Laser line triangulation for fast 3D measurements on large gears

The causes of geometrical deviations from the production process and the prediction of application properties, such as noise behavior, wear or material fatigue, are only possible by having detailed information about the gear geometry. The gold standard for the gear quality inspection is represented by dimensional measurements with a tactile sensor system. As a result for industrial applications, the slow serial measurement leads to the compromise of a random inspection of the gear geometry. For the purpose of a faster and more extensive surface acquisition, a laser line triangulation sensor is investigated providing 1280 points at a line width of 25 mm with up to 200 lines/s. The results at the tooth of a large cylindrical involute gear with a pitch circle diameter of 922 mm and a face width of 246 mm show the qualification for fast three-dimensional measurements of the convex and reflective surface. The detection of the complete profile line at once is possible. It is shown that the measurement deviation of laser line triangulation can be minimized by increasing the dynamic threshold. The measurement deviations amount to ± 8.2 µm and can be attributed to random and systematic errors. Compared to the standard gear inspection, an acceleration factor of 5700 was attained. An optical scanning of the complete tooth flank provides the prerequisite for an identification of surface defects in the form of breakouts and blemish.

Analysis and multi-response optimization of gear quality and surface finish of meso-sized helical and bevel gears manufactured by WSEM process

This paper studies influence of and optimizes pulse-on time, pulse-off time, servo voltage, and feed rate of wire on microgeometry and surface finish of stainless steel meso-helical gears (MHG) and meso-bevel gears (MBG) manufactured by wire spark erosion machining (WSEM) process. Microgeometry of MHG was evaluated in terms of error in total profile and total cumulative pitch and that of MBG in terms of error in single pitch and total cumulative pitch. Average and maximum surface roughness values were used to evaluate their surface finish. Twenty-nine experiments with two replicates were conducted using Box-Behnken approach of response surface methodology thus manufacturing 58 meso-helical gears and 58 meso-bevel gears. It was observed that higher pulse-on time and servo voltage, and lower pulse-off time and feed rate of wire yield poor microgeometry and surface finish of MHG and MBG. Desirability function analysis based multi-response optimization was used to identify optimum WSEM parameters to manufacture the best quality of MHG and MBG. The optimized values of the responses were validated experimentally. It was found that WSEM can attain up to DIN 6 quality in microgeometry of MHG and MBG. SEM micrographs of the best quality MHG and MBG revealed accurate and uniform bore, tooth profile, flank surfaces free from burrs and sharp edges and without any undercut at root. Microstructural examination of these gears showed flank surfaces free from cracks, globules and pores. This study proves that WSEM is economical and technically superior process for near net-shape manufacturing of high quality MHG and MBG.

Surface quality assurance of ring gear during precision stamping of gearwheels

The article highlights the main factors, defining the surface quality of ring gear during hot bulk precision stamping. It offers enhanced techniques of surface quality of stamped ring gear.

Differential Gear Bending Stresses in the Presence of Misalignments and Run-out

Automotive differential gears are usually operating at very low speed and high load conditions and hence are usually designed to be protected against the root bending fatigue failure. Depending on application requirements and lubrication regime, surface failures may occasionally be encountered as well. Mainstream existing design procedures published by AGMA are based on analyzing one single gear pair engagement while up to four potential engagements, between two side gears and two differential pinions, exist. There are also differential designs with three or four differential pinions that increase potential number of engagements to, respectively, six and eight. Usually, the hypoid gear loading is divided by number of side gears, two, also differential pinion loads are usually assumed to be equal; this is a good estimate when no misalignments are present. When misalignments are present, load sharing between the differential pinions becomes greatly imbalanced. This study tries to come up with a simplified analytical approach to evaluate overload factor between the differential pinions as a result of misalignments realized by differential gears inside a differential case. The total indexing run-out quality of gears is also studied through treating it as a source of misalignment. This study will help designers to evaluate the effects of tolerance limits and differential case machining errors on differential gear bending lives.

A novel tooth surface modification method for spiral bevel gears with higher-order transmission error

To reduce the running noise and vibration of spiral bevel gears, we present a novel method for designing high-contact-ratio spiral bevel gears with the higher-order transmission error (HTE) based on the function-oriented design. According to the design HTE curve and contact path, the pinion target tooth surface can be acquired by correcting the conjugated tooth surface derived from the mating gear. We establish a mathematical model for the computerized numerically controlled cradle-style pinion generator with the following design parameters: tool parameters, initial machine settings, and polynomial coefficients of the auxiliary tooth surface correction motion. An optimal model was developed to solve for the polynomial coefficients. TCA and LTCA results show that the HTE spiral bevel gears designed with the auxiliary tooth surface correction motion meets the design requirements. The meshing quality of the HTE spiral bevel gears is also better than that of gears designed using the parabolic transmission error (PTE). The tooth surface correction method proposed in this paper can serve as a basis for modifying high-contact-ratio (HCR) spiral bevel gears.

A heuristic synthesis of multistage planetary gearbox layout for automotive transmission

The automatic transmission system is very crucial for the high-speed vehicles, where the planetary or epicyclic gearbox is a standard feature. With the increase in design intricacies of planetary gearbox, mathematical modelling has become complex in nature and therefore there is a need for modelling of multistage planetary gearbox including the shifting scheme. A random search-based synthesis of three degrees of freedom (DOF) high-speed planetary gearbox has been presented in this paper, which derives an efficient gear shifting mechanism through designing the transmission schematic of eight speed gearboxes compounded with four planetary gear sets. Furthermore, with the help of lever analogy, the transmission power flow and relative power efficiency have been determined to analyse the gearbox design. A simulation-based testing and validation have been performed which show the proposed model is efficient and produces satisfactory shift quality through better torque characteristics while shifting the gears. A new heuristic method to determine suitable compounding arrangement, based on mechanism enumeration, for designing a gearbox layout is proposed here. An important finding on automotive gear shift quality due to closer gear ratio is also reported in this work.

On simultaneous improvement of wear characteristics, surface finish and microgeometry of straight bevel gears by abrasive flow finishing process

Improvement in operating performance, service life and transmission efficiency and reducing the noise of straight bevel gears (SBG) requires their better wear resistance, surface finish and microgeometry. Viscosity of the medium used in abrasive flow finishing (AFF) process and finishing time play very important role in achieving these objectives. This paper reports on simultaneous improvement of wear characteristics, surface finish and microgeometry of SBG by abrasive flow finishing (AFF) process by studying the effects of viscosity of AFF medium and finishing time so as to identify their optimum values through twenty experiments. Average and maximum surface roughness were used to study improvement in surface finish while, microgeometry was evaluated in parameters of pitch deviation and runout. Friction force, coefficient of friction, specific wear rate coefficient, wear volume, microhardness and microstructure of the worn surfaces were used to study the wear characteristics and wear mechanism of the best finished SBG. Use of AFF has significantly improved the wear characteristics, surface finish and microgeometry and quality of SBG. Reduced wear characteristics will reduce the frictional heating which will result in lower operating temperature of the bevel gears. Lower wear volume will improve their service life and mechanical efficiency. Microstructure study of the AFF best finished bevel gear flank surfaces revealed that they are free from hobbing cutter marks, cracks, burrs, pits, surface roughness peaks, thermal distortion. The worn flank surface of the best finished bevel gear have shown very less amounts of worn debris, pits and displacement of material and indicate scuffing mode of wear. This work helps in establishing AFF as an economical, sustainable and productive alternative process for finishing the gears made of any material which can simultaneously improve surface finish, wear characteristics, microgeometry and quality of the bevel gears.

Comparative analysis of numerical methods for the determination of contact pattern of spiral bevel gears

PurposeThis paper aims to present a comparison of numerical methods for determining the contact pattern of Gleason-type bevel gears. The mathematical model of tooth contact analysis and the finite element method were taken into consideration. Conclusions have been drawn regarding the usefulness of the considered methods and the compatibility of results. The object of the analysis was a bevel gear characterised by an 18:43 gear ratio and arc tooth line, and manufactured according to the spiral generated modified-roll method.Design/methodology/approachThe mathematical model of tooth contact analysis consists of both the mathematical model of tooth generating and the mathematical model of operating gear set. The first model is used to generate tooth flanks of the pinion and the ring gear in the form of grids of points. Then, such tooth surfaces are used for the tooth contact analysis performed with the other model. It corresponds to the no-load gear meshing condition. The finite element method model was built on the basis of the same tooth flanks obtained with the former model. The commercial finite element method software Abaqus was used to perform two instances of the contact analysis: a very light load, corresponding to the former no-load condition, and the operating load condition. The results obtained using the two models, in the form of the contact pattern for no-load condition, were compared. The effect of heavy load on contact pattern position, shape and size was shown and discussed.FindingsThe mathematical models correctly reproduce the shape, position and size of the contact pattern; thus, they can be reliably used to assess the quality of the bevel gear at the early stage of its design.Practical implicationsDetermination of the correct geometry of the flank surfaces of the gear and pinion teeth through the observation of contact pattern is a fundamental step in designing of a new aircraft bevel gear.Originality/valueA possibility of the independent use of the mathematical analysis of the contact pattern has been shown, which, thanks to the compatibility of the results, does not have to be verified experimentally.

Optimization of Recycled Glass Fibre-Reinforced Plastics Gear via Integration of the Taguchi Method and Grey Relational Analysis

The increase in demand for industrial gears has resulted in the increase in usage of plastic-matrix composites particularly glass fibre-reinforced plastics as the gear materials. The usage of these synthetic fibers is to enhance the mechanical strength and the thermal resistance of the plastic gears. Nevertheless, the production of large quantities of these synthetic fibre-reinforced composites poses a serious threat to the ecosystem. Comprehending to this fact, the present work aimed at investigating the effects of incorporating recycled glass fibre-reinforced plastics in various compositions particularly on dimensional stability and mechanical properties of gear produced with diverse injection moulding processing parameters setting. The integration of Grey relational analysis (GRA) and Taguchi method was adopted to evaluate the influence of recycled glass fibre-reinforced plastics and variation in processing parameters on gear quality. From the experimental results, the blending ratio was found as the most influential parameter of 56.0% contribution in both improving tensile properties as well as in minimizing shrinkage, followed by mould temperature of 24.1% contribution and cooling time of 10.6% contribution. The results obtained from the aforementioned work are expected to contribute to accessing the feasibility of using recycled glass fibre-reinforced plastics especially for gear application.

Influence of tribological conditions on cold forging of gears

Gears are integral and vital machine elements in the field of drive and transmission technology. With regard to economic and ecological aspects, cold forging represents a promising approach compared to conventional cutting processes for producing highly-loadable gears. A possible extrusion process for manufacturing helical gears is the so-called “Samanta”-process. In comparison to conventional extrusion processes, an additional ejector system is avoidable. Thus, in particular for helical gears, a negative impact on the gear quality by the ejector operation is prevented. Furthermore, the process chain during the component production cycle is shortened which leads to a more efficient production. The achievable gear accuracy as well as insufficient tool life are major challenges while establishing the “Samanta”-process in industry. To enable an industrial application, basic process understanding as well as knowledge about the influences on the process results is required. For influencing component and process properties within cold forging, approaches from the tribological system can be generally used. The aim of this study is to analyze the influence of the friction conditions on selected component and process properties within cold forging of gears by the “Samanta”-process. For adjusting the occurring friction, various lubrication systems were applied, which have been qualified using a double cup extrusion test (DCE-test). The results reveal that the lubrication system determines the friction conditions during forming. Within cold forging of helical gears by the “Samanta”-process, the friction influences the resulting strain hardening of the components and the required maximum forming force as well as the energy amount.

Performance of pulsed-electrochemical honing and pulsed-electrochemical finishing in improving quality of bevel gears

This article presents a comparative study concerning performance of pulsed-electrochemical honing (PECH) and pulsed-electrochemical finishing (PECF) in straight bevel gear finishing. Performance of these processes were compared in terms of average percentage difference in the considered parameters of surface features of bevel gear namely average percentage differences in average surface roughness ‘PDRa’, maximum surface roughness ‘PDRmax’ and depth of surface roughness ‘PDRz’, micro-geometry (i.e. average percentage differences in single pitch error ‘PDfp’, adjacent pitch error ‘PDfu’, cumulative pitch error ‘PDFp’, and percentage difference in runout ‘PDFr’) and finishing productivity (i.e. material removal rate ‘MRR’). Microstructure and microhardness were also considered as measure for performance assessment. Observed results show PECH is proficient in simultaneously improving all the considered responses of bevel gears by more than 50% as compared to PECF. The PECH-finished gear additionally displayed unrivalled microstructure and better microhardness when contrasted with PECF-finished gear. These changes will upgrade the working-life and operating performance of the finished gear.

Exploring WSEM Process for Manufacturing Meso Helical and Bevel Gears

This paper presents an experimental investigation with objective to explore and establish WSEM (wire spark-erosion machining) process as a technically superior alternative for manufacturing the best quality and closed to net-shape meso helical gear (MHG) and meso bevel gear (MBG) made of stainless steel (SS 304). Effect of variable WSEM parameters namely servo voltage ‘SV’, pulse-on-time ‘Ton’, peak current ‘IP’, pulse-off time ‘Toff’, feed rate of wire ‘WF’, wire tension ‘WT’, dielectric flow rate ‘WP’ and percentage cutting speed ‘CS’ on gear cutting rate (GCR) and average surface roughness (Ra) are studied. The experiments were planned and designed according to one-variable-at-time approach of ‘Design of Experiments’ to determine the variation in gear cutting rate and average surface roughness with WSEM process parameters. It was observed that servo voltage, pulse-on-time and peak current significantly affect the GCR and Ra. Gear quality standard up to DIN quality number 7 for error in single and error in total pitch of MBG; and DIN quality number 7 and 6 for error in total profile and error in total pitch respectively of MHG were achieved by WSEM process. This study explores capabilities and superiority of WSEM to manufacture closed to net-shape MHG and MBG.

Investigations on surface quality of WEDM-manufactured meso bevel and helical gears

ABSTRACTThis article presents investigations on and analysis of surface finish of meso bevel and helical gears made of stainless steel (SS 304) manufactured by wire electric discharge machining (WEDM) process using thin soft plain brass wire of 0.25 mm diameter. Effects of eight WEDM process parameters, namely, peak current, pulse-on time, pulse-off time, wire feed rate, wire tension, servo-gap voltage, dielectric pressure, and cutting speed on average and maximum surface roughness of the meso bevel and helical gears have been studied by conducting 31 experiments using one-factor-at-a-time approach to identify their optimum ranges/values for further experiments. Tooth profile, microstructure, microhardness, and topography of tooth flank surface have been studied for the best quality meso gears. Average and maximum surface roughness of tooth flank surfaces of meso bevel and helical gears increase with increase in peak current, servo-gap voltage, pulse-on time, wire feed rate, wire tension and cutting speed, and decrease with increase in pulse-off time while dielectric pressure does not significantly influence surface roughness. This work establishes that WEDM process can be an economic and sustainable manufacturing alternative for net-shaped meso-sized bevel and helical gears having better surface finish which will eliminate need of any subsequent finishing processes.

A new digitized reverse correction method for hypoid gears based on a one-dimensional probe

In order to improve the tooth surface geometric accuracy and transmission quality of hypoid gears, a new digitized reverse correction method is proposed based on the measurement data from a one-dimensional probe. The minimization of tooth surface geometrical deviations is realized from the perspective of mathematical analysis and reverse engineering. Combining the analysis of complex tooth surface generation principles and the measurement mechanism of one-dimensional probes, the mathematical relationship between the theoretical designed tooth surface, the actual machined tooth surface and the deviation tooth surface is established, the mapping relation between machine-tool settings and tooth surface deviations is derived, and the essential connection between the accurate calculation of tooth surface deviations and the reverse correction method of machine-tool settings is revealed. Furthermore, a reverse correction model of machine-tool settings is built, a reverse correction strategy is planned, and the minimization of tooth surface deviations is achieved by means of the method of numerical iterative reverse solution. On this basis, a digitized reverse correction system for hypoid gears is developed by the organic combination of numerical control generation, accurate measurement, computer numerical processing, and digitized correction. Finally, the correctness and practicability of the digitized reverse correction method are proved through a reverse correction experiment. The experimental results show that the tooth surface geometric deviations meet the engineering requirements after two trial cuts and one correction.

Radial and tangential error analysis of double-flank gear measurement

To clarify or interpret the measurement results of double-flank gear measurement (DFGM), the mathematical model of radial and tangential error analysis of double-flank gear measurement is established. Using differential method, the mathematical model of surface-to-surface contact stage is concerned, and also the tip-to-surface interference stage is involved. The error sources including the base radius error (or profile slope deviation) and the tooth space angle error (or single pitch deviation) of the gear to be measured are concerned. A case study of the gear parameter with the gear contact ratio 1.77 is discussed to explain the tooth contact process, in which the critical contact points are listed for determining the rotation angle. The radial and tangential composite deviations are simulated under different sign combination or different value of the error sources to cover as many results as possible. The simulation results are compared with the measurement results on a gear measuring device (GMD) using double flank rack probe (DFRP), whereby the simulation parameters are determined through the gear profile slope deviation and the single pitch deviation of the gear measured on a Gear Measuring Center Klingelnberg P26. The curves of the simulation results and the measurement results on GMD are consistent to each other. For gear grade 6 according to ISO 1328-1:2013, the allowable value of the total profile deviation is 11.5 μm. The simulation results are compared with the measurement results on a gear measuring device (GMD) based on double flank rack probe (DFRP). The difference between the peak to peak value of the simulation results and the mean line of the measurement results within the evaluation range is 1 μm in radial direction and 1.3 μm in tangential direction, which means the simulation results has better consistency with the measurement results. The radial and tangential error analysis of DFGM can not only be used in simulation of the results, but also in interpreting the DFGM measurement results, which is helpful for gear measurement and quality control.

Basic Study on Calculation of Cutting Forces Useful for Reducing Vibration in Skiving

In order to improve the accuracy of skived gears by means of reducing vibrations that are often observed during the cutting process, a simple model for calculating the cutting forces of skiving process is presented and also its effectiveness was discussed. The model is characterized by simple geometrical calculations, and the cutting forces were assumed as sum of vectors that represent the penetration of cutting edges. In the model, multiple cutting edges that are simultaneously meshing with the workpiece were considered. Distinguished oscillating frequencies of the calculated cutting forces and the natural frequencies of the clamped workpiece and of the cutter were carefully analyzed in order to predict the cutter rotation speed that was most likely to reduce undesired vibrations. Processing experiments conducted at several cutter rotation speeds showed that the predicted cutter rotation speed which could significantly reduce undesired vibrations was very effective and enabled the quality of a skived gear to be improved. Consequently, the proposed calculation model was enough effective and useful for operation conditions such as cutter rotation speed being determined.

Cloud-based shaft torque estimation for electric vehicle equipped with integrated motor-transmission system

In order to improve oscillation damping control performance as well as gear shift quality of electric vehicle equipped with integrated motor-transmission system, a cloud-based shaft torque estimation scheme is proposed in this paper by using measurable motor and wheel speed signals transmitted by wireless network. It can help reduce computational burden of onboard controllers and also relief network bandwidth requirement of individual vehicle. Considering possible delays during signal wireless transmission, delay-dependent full-order observer design is proposed to estimate the shaft torque in cloud server. With these random delays modeled by using homogenous Markov chain, robust H∞ performance is adopted to minimize the effect of wireless network-induced delays, signal measurement noise as well as system modeling uncertainties on shaft torque estimation error. Observer parameters are derived by solving linear matrix inequalities, and simulation results using acceleration test and tip-in, tip-out test demonstrate the effectiveness of proposed shaft torque observer design.

Investigations on microgeometry of meso bevel and meso helical gears manufactured by WEDM process

This article reports about investigations on microgeometry of meso bevel and meso helical gears manufactured by wire electro discharge machining (WEDM) process. Effects of eight WEDM parameters (namely, peak current, pulse-on time, pulse-off time, servo-gap voltage, wire feed rate, wire tension, dielectric pressure and percentage cutting speed) on single pitch error and total pitch error for meso bevel gear and total profile error and total pitch error for meso helical gear were studied. A total of 31 experiments for meso bevel gear and 31 experiments for meso helical gears were conducted using one-factor-at-time approach to identify optimum ranges/values of the eight WEDM parameters for further experiments. It revealed existence of optimum ranges of servo-gap voltage, pulse-on time, pulse-off time, and percentage of the cutting speed to minimize microgeometry errors in meso bevel and helical gears and that use of higher values of peak current, wire feed rate, wire tension, and dielectric pressure yields better quality of meso bevel and helical gears. The best quality meso helical gear has better quality (DIN 6, DIN 6, and DIN 8) than the best quality meso bevel gear (DIN 7, DIN 7, and DIN 10) for single pitch error, total pitch error, and radial runout; whereas for successive pitch error, reverse is true. Meso helical gear has better surface finish (R a 1.1 μm and R max 7.3 μm) than meso bevel gear (R a 1.3 μm and R max 8.0 μm). Examination of tooth profiles of the best quality meso gears by scanning electron microscopy revealed that they have uniform tooth profiles that are free from burrs, nicks, asperities, dimples, undercutting at the root, and sharp edges on both end faces of the gears. It also revealed that tooth flank surfaces are free from micro-cracks, pores, and globules. The present work proves that WEDM has potential to be a better alternative for manufacturing better quality net-shaped meso bevel and helical gears which will not require any further post-manufacturing processing.