Gear Generation Research Articles

Implementation of an exact completing method of generation for face-milled spiral bevel gears with uniform depth taper

AbstractThis paper proposes an exact completing method of generation of face-milled spiral bevel gears with uniform depth taper. This method ensures localized bearing contact without kinematic transmission errors in both directions of rotation. Both sides of the tooth are generated simultaneously using the same set of basic machine tool settings. A tip relief on the tooth surfaces is the only required microgeometry modification to achieve a smooth transition of load between consecutive pairs of teeth. An analytical approach to determine the basic machine tool settings and select the grinding cutter parameters has been also developed. The selection of the nominal cutter radius follows the recommendations of Information Sheet AGMA 22849-A12. The basis for alignment error compensation has been also established. Tooth contact and stress analyses demonstrate the advantages and limitations of the proposed method, making it suitable for applications with higher power demands for the drive side than for the coast side.

Computerized generation, deviation correction and rapid tooth contact analysis of helical face gear

This paper delves into the generation of helical face gears using a grinding worm. It investigates the computerized generation process and explores the inherent geometric constraints associated with the application of a grinding worm for helical face gears. An approximate grinding method, tailored for helical face gears featuring large helix angles, is proposed, with an evaluation of the resulting theoretical deviations. Furthermore, a novel rapid computational approach for determining the bearing contact of helical face gear pairs is introduced and validated through Finite Element Analysis (FEA). The subsequent analysis comprehensively examines the effects of the machine tool positioning errors on tooth flank deviations, bearing contact, and transmission errors. A sensitivity matrix is developed to elucidate the relationship between machine tool positioning errors and the tooth flank deviations, leading to the proposition of a correction method for theoretical generating deviations. Finally, the paper introduces a tooth flank modification method for helical face gears and the meshing performance is highly improved.

A two-stage flank correction method for the continuous generation of face gears

Face gear pairs are particularly suitable for application in advanced equipment drivetrains with intersecting shafts. The continuous generation process of face gear tooth flanks using worms offers high machining efficiency, but achieving high accuracy in this process remains a considerable challenge. A two-stage flank correction method for face gears ground by worms on a computer numerical control (CNC) generator is proposed. This method comprehensively involves both the worm dressing and face gear grinding stages, considering the actual machine tool structure and constant offsets among its axes. Firstly, the machining kinematics for both stages are derived and the high-order tooth flank model of the face gears is developed. Secondly, the sensitivity of tooth flank deviations to variations in the kinematic coefficients is analyzed, and the deviations on both flanks of the tooth space generated with initial kinematics are measured. Finally, three cases of correction for the measured deviations are compared using the proposed method. Correcting only the grinding stage is effective and computationally inexpensive, and employing this case for manufacturing face gear tooth flank significantly reduces deviations.

A Modified Approach to the Rack Generation of Beveloid Gears

The purpose of this paper is to present an easier and more efficient method for the determination of the geometry of a bevelled gear tooth. Based on a method that provides an easier way for the rack generation of involute helical gears, the mathematical model of a beveloid gear is studied. The mathematical procedure for developing two-dimensional cross-sections has been extended to three-dimensional gear models. A computer programme is developed to obtain generating and generated surfaces. The proposed algorithm is compared with the previous studies for verification and validation. The results demonstrate that the coordinates obtained from the given method are nearly the same on the start and end points of the main gear parts, such as the involute and root fillets regions. Also, between the limits, the values can be considered acceptable. A coordinate deviation of the gear profile has been observed in the mathematical model, because of the profile shift. Modifications have been developed in the equations to eliminate these cases. The main advantage of the proposed method is to obtain mathematical models without carrying out some of the calculation steps used in previous studies. Eventually, this feature will provide an easier and faster method to develop computer-aided models of the beveloid gear types.

Methods for Creating Designs of Cardan Gears of Increased Resource for Land Vehicles and Agricultural Machinery

Spatial cardan mechanisms designed to transmit rotational motion between shafts, having angular displacement, differ in a variety of design solutions. Cardan gears are an articulation of one or more universal joints and tubular shafts. They compensate for axial movements, and also transmit torque at constant or variable angles between the connected units. During operation, the cardan transmission must function satisfactorily during the established service life, i. e., meet all the requirements arising from the peculiarities of its use. Therefore, the problem of improving cardan gears, increasing their reliability and ergonomicity on the basis of new design solutions optimized for dynamic parameters, materials used, manufacturing, assembly and operation technologies is relevant for modern technology. The paper presents a systematic approach to the creation of a new generation of cardan gears based on research in the field of operating conditions, materials science, materials technology, optimal design. It is shown that according to the results of the research, a new series of gimbal gears with improved technical characteristics has been created.

A comparative study of fatigue behavior between S-shaped and involute POM gears

Abstract Applications of polymer gears have been gradually expanding from motion transmission to power transmission fields. Design of new gear teeth profiles plays a crucial role in meeting the requirement of replacing metallic gears with polymer ones. This work develops a computational framework consisting of tooth profile generation and fatigue life prediction of S-shaped and involute POM gears. The contact and bending fatigue performances of S-shaped and involute POM gears under oil lubrication are comparatively studied. It is found that the S-shaped profile reduces the tooth root stress by 25% and significantly improves the bending fatigue life by 10 times compared with the involute profile, especially under medium or high loading levels. Furthermore, the S-shaped gear with a single circular-filleted root curve benefits a 20% reduction of tooth root stress and a 30% increase in bending fatigue life compared to a double circular-filleted root curve S-shaped gear.

An exact system of generation for face-hobbed hypoid gears: Application to high reduction hypoid gear drives

The determination of the pitch cones for hypoid gears is already well defined either through numerical methods as those shown in the Standard ANSI/AGMA ISO 23509-B17 or through algorithms available in the specialized literature. However, a procedure to determine the gear tooth surfaces for hypoid gears directly from their pitch cones is still missing. An analytical approach to determine the basic machine-tool settings for the pinion and the wheel of hypoid gear drives is proposed here. It is based on the condition of exact generation, which means that the gears will operate under conjugate condition. It can be applied for generation of face-hobbed hypoid gears, produced either by the CycloCut or the CycloPalloid generation methods. A numerical example proves the goodness of the proposed methodology in a high reduction hypoid gear drive. The results of tooth contact and stress analyses prove that the bearing contact is localized and stable against misalignments, requiring just a small adjustment through the application of an optimum tip relief to the gear tooth surfaces to minimize the maximum contact pressure.

A Novel Asymmetric Face Gear Cut by Duplex Face-Milling With Multiple Auxiliary Flank Modification Motions

Abstract Face gear sets, comprising a face gear and a cylindrical pinion, are used in the crossed axes transmission with the advantages of easy assembly and a large gear ratio. Based on the geometry of a pinion tooth flank, the tooth surface of the face gear is derived and manufactured by gear hobbing or shaping processes. However, the hobbing and shaping processes to make a face gear require special machine attachments to achieve the spatial relationship between the gear cutter and the workpiece of the face gear. These special machine attachments are not always available in a typical gear-machining factory, so this study develops a manufacturing process that uses a standard spiral bevel gear generator and standard face-milling cutting tools to produce a face gear. The productivity and the gear quality of a face gear that is made using the proposed cutting method are similar to that for a spiral bevel gear that is produced by indexed duplex cutting. The machine settings for the spiral bevel gear generator are derived using the tooth surface of a face gear, which is conjugated to the tooth surface of specific pinion. This study uses a duplex face-milling method with multiple auxiliary flank modification motions to minimize the flank normal deviation between the conjugate and the generated face gear. A numerical example and a cutting experiment are performed to verify the feasibility of the proposed methodology.

Investigation on the generation of bevel gear by disk tool with curved tooth surface of trapezoidal tooth profile

A bevel gear pair with curved tooth surface is widely used for power transmission of intersecting shafts. The bevel gear pair with curved tooth surface has higher load bearing capacity than straight bevel gears, longer line length, quieter, center distance assembly error, and does not change the speed ratio. This paper proposes a disk cutter with curved tooth surface of trapezoidal tooth profile to generate a bevel gear pair. One continuously distributed a trapezoidal tooth profile with curved tooth surface on a disc into an imaginary disc cutter to generate a bevel gear pair with curved tooth surface. This method has never appeared in the literature. Therefore, a mathematical model of a disc cutter with curved tooth surface of trapezoidal tooth profile was established and used to generate the mathematical model of the bevel gear pair via the theory of gearing. Through the undercutting analysis, explore the undercutting conditions of the proposed disc cutter and determine the parameter size limit. Based on tooth contact analysis (TCA), the transmission error and the contact pattern of the bevel gear pair with curvilinear teeth is calculated under the assembly error of the bevel gear. The advantage of the proposed disc cutter is that the transmission error of the parabolic type without modification of the tooth surface of the bevel gear pair can be obtained.

Computerized generation and surface deviation correction of face gear drives generated by skiving

This paper presents the computerized generation and surface deviation correction of face gears generated by skiving. Firstly, the mounting relation among the skiving cutter, the virtual shaper, and the being-generated face gear is defined and the velocity relation analyzed. Secondly, the equations for the rake face angle and back flanks of the skiving cutter are defined, and the profile of the cutting blade obtained. Based on the kinematics of the generation movement of the skiving cutter, the surfaces of the face gear teeth are derived. The influence of the parameters of the cutter profile on the face gear surface topology is studied. Thirdly, the correction of the face gear tooth surface deviation has been achieved to some extent by adjusting the cutting depth, the rotation angle of the face gear, and the cutter offset distance during the process of machining. Finally, the simulation of the proposed machining process has been verified with VERICUT. The results show that the deviation of the face gear tooth surface is consistent with that obtained by the computerized generation as proposed in this paper.

A model for the intensity of fishing gear

Industrial fishing, instrumental in feeding the world's population while providing a livelihood to many people, also presents a variety of hazards to the health of the ocean, including the accumulation of derelict fishing gear. Although direct evidence of harm from derelict gear is abundant, efforts to quantify and assess the threats posed by it are confounded in part by the tremendous diversity of fishing gear and techniques. In this paper, we advance a novel analytic framework for describing the use of fishing gear that can be applied to evaluate the environmental impacts that arise from fishing activity. We model fishing as a unit process comprising three successive characterizations, each of which can be observed and validated independently: the intensity of fishing effort, the material intensity of gear, and the intensity of the environmental effect. We present the method as an open-source computation system with a library of gear models that can be reviewed and extended by the research community. We apply the program to estimate the generation of derelict gear for several different gear types and discuss how it can be expanded to advance the understanding of the impacts of industrial fishing at the global scale. This article met the requirements for a Gold–Gold JIE data openness badge described at http://jie.click/badges.

Mathematical model of the worm wheel tooth flank of a double-enveloping worm gear

This paper presents a novel method for determining the worm wheel tooth flank surface. The worm wheel model is developed according to the theory of gearing and the gear generation mechanism. Two cases are considered simultaneously. In one case, the worm wheel is generated by the hourglass worm hob with a rectilinear tooth axial profile, while in the other case, it is generated with an arc (concave and convex) tooth axial profile. The contact lines between the hourglass worm hob and worm wheel surfaces are determined. Surface formation generated during processing by the tool external edge and formation so-called region II was presented. The manner of separating regions on the worm wheel tooth flank surface was developed. Because the difference between the parameters that describe the tool side surface, only the flowchart of the algorithm for determining the worm wheel tooth side surface of rectilinear profile is presented. For the arc profile, the algorithm flowchart is analogous. The proposed procedures and the developed computer-aided worm wheel generating program allow obtaining complete mathematical representation of worm wheel tooth flank surface.

Computerized Generation of Asymmetric Straight Bevel Gear

To carry out any type of analysis and study the gear drives, the primary steps include the graphical representation of the gear drive under consideration. In this study, the mathematical formulations of the tooth surface, tooth root surface, and tooth root transition surface of symmetric straight bevel gear were formulated based on the planning principle. The proposed modification has been done on the mathematical formulation of the symmetric tooth profile to consider the effect of asymmetric tooth profiles (which are characterized by different pressure angles on the loaded and unloaded sides). As a result of this study, a computer program based on the above mathematical formulation has been built to represent the final shape of symmetric and asymmetric teeth profiles of straight bevel gear for different design parameters.

Применение сосредоточенных обмоток для мощных синхронных ветрогенераторов

Low-power machines were commonly considered as the main application field of concentrated windings. However, a lot of paper have recently been published, which address both the theory of these windings and specific cases of their application for large synchronous machines. The article presents an analysis of the parameters of concentrated windings having various configurations intended for use in high-power gear and gearless wind generators. In assessing the winding, not only the high winding factor value was taken into account, but also the star of slot EMFs, harmonic spectra of the MMFs and EMFs, the cogging torque component and torque pulsation under load, as well as emerging losses. It is shown that the well-known advantages of concentrated windings over distributed windings can be fully realized by choosing the appropriated numbers of slots and poles.

Principle and Method for Machining Face Gear with Developable Ruled Surface

The tooth surface of a face gear is recognized as un-developable ruled surface in tradition, which result in the problem that face gear generation using simple cutter with high efficiency and accuracy puzzled people for a long time. Applying the traditional shaping method for face gear generation in derivation of the tooth surface position vector, a space straight line equation was established by using this vector, to illustrate that the tooth surface of the traditional face gear could be considered as developable ruled surface constituted by space lines family, the position vectors of the developable ruled surface were established respectively based on involute, rack and considering the spatial position relationship in meshing. Elaboration and proposition of the principle and method that were used to generate the face gear with the developable ruled surface by straight edged cutter in line contact, and representation of the generated surface model. Furthermore the developable ruled surface was compared to the traditional surface, the normal difference between the two kinds of surfaces is on micro-scale. Numerical examples shows that the normal distance is no more than 1/70 of modulus, the developable ruled surface to which was performed simple longitudinal crowning is able to mesh with the involute surface of the pinion correctly, and demonstrates acceptable geometric meshing performance.

Computerized approach for design and generation of face-milled non-generated hypoid gears with low shaft angle

A computerized approach for the design and generation of face-milled non-generated hypoid gears with low shaft angle has been proposed. A new method for pitch cone design based on two mathematical iterations has been developed and applied for hypoid gears with low shaft angle. The gear blank parameters are obtained from the Standard ANSI/AGMA ISO 23509-B17 and the machine-tool settings for the wheel determined based on an existing approach. Then, the determination of the machine-tool settings for the pinion is based on the application of the local synthesis method. A method to find the required addendum coefficient for the wheel based on the avoidance of singularities on the active surfaces of the pinion as well as numerical methods to check for undercutting, pointing of the top land, and smoothness of the root land have been developed and applied. Therefore, the selected design parameters of hypoid gears with low shaft angle allows gear geometry parameters to be obtained for acceptable geometries of pinion and wheel. The developed approach for design and generation of hypoid gears with low shaft angle is verified by some numerical examples.

A finishing method for the continuous generation of spur face gears with shaving cutters

Face gear drives have been widely applied in power transmission, but the finishing of continuous generation is a difficult problem. This is mainly because the teeth of face gears are on a plane, which leads to interference by worm grinding. Hence, a shaving method for face gears is proposed in this paper. This work studies the theory of face gear shaving, the causes of mid-concave phenomena based on load tooth contact analysis (LTCA), a solution for the modification coefficient of the shaving cutter and a control method for the cutter location point. The experimental results show that the maximum machining error is −12.7μm, that many generating lines appear and that the residual stress increases by 49.2% in comparison with that of the grinding tooth surface. The present study suggests that the shaving method for spur face gears can not only achieve the finishing of continuous generation but also improve the surface integrity of the gear.

Technological Aspects in Manufacturing of Non-Circular Gears

The construction and manufacture of non-circular gears is one of the most difficult issues in machine technology. Due to the limited technological capabilities of traditional machines and tools, past manufacturing methods were unable to calculate the assumed shape of the tooth line and its profile. Modern manufacturing methods using computer numerical control allow for the generation of non-circular gears with free-form tooth profiles and curvilinear teeth in their lengthwise direction. These methods are also used to manufacture internal gears. This article provides a review of the methods of machining non-circular gears and presents the results of the research on the Fellows method using a shaper cutter, as well as the wire electrical discharge machining method.

Generation, TCA and Stress Analysis of the Face Gear Drive with a Tapered Involute Pinion

Generation, TCA and Stress Analysis of the Face Gear Drive with a Tapered Involute Pinion

Predicting optimal combinations of by‐catch reduction devices in trawl gears: A meta‐analytical approach

AbstractGlobal efforts to reduce unwanted catches have led to the development of a vast array of by‐catch reduction devices (BRDs), in particular for mixed trawl fisheries. Some of these BRDs could likely benefit from being combined. However, the number of possible combinations would be prohibitive to be tested experimentally. Therefore, in this study we propose a meta‐analytical approach that combines the data available on BRDs tested independently in a fishery and predict the theoretical selectivity of all possible combinations of those devices. This allows to identify promising BRD combinations, worth experimental investigation and flexible trawl configurations, where the selectivity can be substantially modified by adding or removing one BRD, thus aiding fishermen in adapting to high variability in catch composition and quota availability. To illustrate the approach, we used BRDs developed for the well‐studied Nephrops (Nephrops norvegicus, Nephropidae) directed mixed trawl fishery in the Skagerrak and Kattegat seas. We predicted the selectivity of 100 BRD combinations for Nephrops, cod (Gadus morhua, Gadidae) and haddock (Melanogrammus aeglefinus, Gadidae), compared them in terms of absolute selectivity and performance under realistic catch scenarios, from both single‐ and multispecies perspectives, and identified 15 BRD combinations that could be worth future experimental investigation. The meta‐analytical approach makes best use of existing knowledge and leads to new insights about the potential for improvement and flexibility in trawl selectivity. This could benefit a variety of mixed trawl fisheries and help developing a new generation of more flexible gears, with multiple BRDs integrated in their structure.