Tooth Profile Research Articles

Effects of cutter modification on the meshing characteristics of intersected beveloid gear and involute cylindrical gear

The parabolic cutter is introduced into the design of intersected beveloid gear and involute cylindrical gear pair, and the numerical model of the normal section tooth profile of the parabolic cutter is established. Based on the hobbing theory, the equation of the beveloid gear face of tooth machining with a modification cutter is derived. The mesh characteristics analysis model of gear pair is established, and the impacts of modification coefficients on meshing characteristics that contact pattern, transmission error, meshing stiffness, contact force, and tooth root stress are studied.

Research on hobbing accuracy of flexspline tooth profile of harmonic drive

Research on hobbing accuracy of flexspline tooth profile of harmonic drive

Research on the deformation characteristics of small module tooth during current-assisted splitting spinning of small module tooth-shaped part

Aiming at the problems such as low material utilization, poor strength and toughness of workpiece during manufacturing of small module tooth-shaped parts (SMTSPs) by traditional gear hobbing and shaping method, a current-assisted splitting spinning forming (CASSF) method was proposed to form SMTSPs with high performance requirements. A coupled electrical-thermal-mechanical finite element (FE) model was established based on the ABAQUS software, and the distribution of equivalent stress and equivalent strain, and deformation characteristics of small module tooth were investigated. The results show that the equivalent stress and equivalent strain decrease from tooth groove arc to the tooth crest arc and centre of the tooth groove at tooth profile surface. The distribution of equivalent stress and equivalent strain in the internal deformation region follows the same trend as the tooth profile surface from the centre of the tooth groove to the tooth groove arc, but increases from the tooth groove arc to the tooth crest. The material of small module tooth experiences three-directional stress state. The material in the gear tooth undergoes radial and axial elongation, and tangential compression, while in the tooth groove it undergoes radial compression, tangential and axial elongation.

Conceptual design and optimization of polymer gear system for low-thrust turbofan aeroengine accessory transmission

Abstract The advancement in materials and lubrication has significantly improved the load-carrying capability of polymer gears, making them ideal for replacing metallic gears in power transmission. However, this conversion is not as simple as substituting steel with polymer; it requires a thorough redesign of the structural parameters specific to polymer gears. To enable the metallic-to-polymer conversion of gear in power transmission, a model for optimizing polymer gear systems was developed. An investigation of the accessory transmission system of a low-thrust turbofan aeroengine was conducted. A comprehensive performance index for the accessory transmission was developed using combined weighting coefficients to achieve the optimization goals including total mass, transmission efficiency, maximum transmission error, and so on. The polymer gear system developed using the proposed optimization model demonstrated a 70.4% reduction in total mass compared with the metallic gear system, as well as a transmission error decrease of over 29% when compared with polymer gear systems with standard tooth profiles. The contribution analysis results demonstrated that optimizing the tooth width, pressure angle, and addendum height of polymer gears can significantly enhance the load-carrying capacity of the polymer gear system while maximizing tooth profile flexibility.

Simulation and analysis of propulsive performance for screw propulsion inspection robot

Screw propulsion mechanism is a kind of special walking mechanism suitable for traveling on the loose terrain, with the characteristics of small grounding specific pressure, strong trafficability and small turning radius. Based on this, a screw-propelled inspection robot for sandy land is designed. To evaluate the propulsive performance of the robot, The DEM-MBD coupling method was used to analyze the influence law of rotary-screw propulsor blade diameter, tooth profile Angle, lead and spiral blade number on the propulsive performance of screw-propelled inspection robot. The results show that the rotary-screw propulsor with larger blade outer diameter has stronger propulsion speed and better directivity, while its stability gradually deteriorates. The rotary-screw propulsor with smaller tooth Angle has better propulsive ability and stability. For the rotary-screw propulsor with single helix, the driving ability becomes stronger with the increase of the lead, and the stability deteriorates exponentially. When the pitch is similar, the directivity and stability of double helix are better than that of single helix and triple helix. The research results provide basic data for the performance optimization of screw propulsion mechanism and have practical significance.

Research on Noise Reduction Modification Design of High Speed EMU Traction Arc Toothed Cylindrical Gears

Aiming at the deficiencies of the traction helical gear transmission system when the EMU is running at high speed, this paper proposes and designs a kind of arc toothed cylindrical gear adapted to the traction of higher speed EMU. A parametric arc toothed cylindrical gear model was constructed using CREO, and its dynamic contact characteristics and acoustic response characteristics were analyzed under sustained operating conditions using the finite element boundary element method. The design of a tooth profile combined with the radius of the arc toothed line of the comprehensive trimming program put forward a virtual trimming prototype method through MATLAB and CREO reconstruction gear, and trimming before and after the gear transmission simulation experiments occurred for comparison and analysis. This study shows that the traction arc toothed cylindrical gear comprehensive modification method proposed in this study achieves better dynamic performance optimization, effectively reduces the contact stress and radiation noise of the gear transmission, and provides a theoretical basis for the development of a new generation of high-speed EMU stock traction drive systems.

Stability prediction and optimization of multi-regenerative weak stiffness grinding system based on microstructured tool

Chatter is a serious problem in grinding, which will directly affect machining accuracy, efficiency, tool wear and even damage machine tools. In order to understand and avoid grinding chatter, a stability prediction and optimization method of multi-regenerative weak stiffness grinding system based on microstructured tool is innovatively proposed. It is the first time to use microstructured tools to ensure the system stability without sacrificing the material removal rate, which offers promise for weak stiffness grinding. Firstly, a multi-random geometric model of microstructured grinding wheel is established, considering the shape, distribution, microstructure patterns and truing conditions of abrasive grains. On this basis, considering the regulating effect of microstructure patterns on workpiece regeneration delay and tool wear delay of grinding system with large aspect ratio, a multi-regeneration stability model based on microstructure tool is established. Then, the experiments of grinding wheel microstructuring, internal thread grinding and profile measurement are carried out. The results show that the theoretical model established can accurately predict the grinding stability boundaries. The microstructure types can be arranged in descending order according to the optimization degree of grinding chatter: composite type, cross type, oblique type and linear type. Compared with the grinding wheel without microstructures, the microstructured grinding wheel can increase the speed limit deviation by 12.2 % − 54.0 %, which basically solves the chatter problem at high rotation speed. The wear resistance of microstructured grinding wheel is improved by 44.2 %, the tooth profile angle error and bottom fillet radius of workpiece are reduced by 92.3 % and 90.4 % respectively, and the maximum tooth height difference and average tooth height error are reduced by 90.6 % and 87.5 % respectively.

A Novel Tooth Modification Methodology for Improving the Load-Bearing Capacity of Non-Orthogonal Helical Face Gears

This study proposes a double-crown tooth surface modification technology that improves the load-carrying capacity of non-orthogonal helical tooth surface gears. The tooth modification is determined by a modified rack-cutter, and its feed motion is related to an intentionally designed transmission error. The novelty of the tooth modification design is that the transmission error can be pre-designed. First, changing the tooth profile of the tool enables preliminary modification along the tooth profile direction; second, by modifying the interaction between the tool and the machined gear, subsequent fine adjustments are made to the contact path. This two-stage tooth modification strategy not only retains the advantages of the traditional method but also significantly improves the balance of the load distribution on the tooth surface through an original contact path modification strategy. Through systematic tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), it was verified that the new method reduces contact stress and tooth root bending stress and improves the gear’s resistance to misalignment errors. This research provides the basis and motivation for further exploring and improving this tooth profile modification technology to solve the challenges faced by more complex gear systems.

Effect of recycled powder and gear profile into the functionality of additive manufacturing polymer gears

PurposePolymer laser powder bed fusion (PBF-LB/P) is an additive manufacturing technology that is sustainable due to the possibility of recycling the powder multiple times and allowing the fabrication of gears without the aid of support structures and subsequent assembly. However, there are constraints in the process that negatively affect its adoption compared to other additive technologies such as material extrusion to produce gears. This study aims to demonstrate that it is possible to overcome the problems due to the physics of the process to produce accurate mechanism.Design/methodology/approachTechnological aspects such as orientation, wheel-shaft thicknesses and degree of powder recycling were examined. Furthermore, the evolving tooth profile was considered as a design parameter to provide a manufacturability map of gear-based mechanisms.FindingsResults show that there are some differences in the functioning of the gear depending on the type of powder used, 100% virgin or 50% virgin and 50% recycled for five cycles. The application of a groove on a gear produced with 100% virgin powder allows the mechanism to be easily unlocked regardless of the orientation and wheel-shaft thicknesses. The application of a specific evolutionary profile independent of the diameter of the reference circle on vertically oriented gears guarantees rotation continuity while preserving the functionality of the assembled mechanism.Originality/valueIn the literature, there are various studies on material aging and reuse in the PBF-LB/P process, mainly focused on the powder deterioration mechanism, powder fluidity, microstructure and mechanical properties of the parts and process parameters. This study, instead, was focused on the functioning of gears, which represent one of the applications in which this technology can have great success, by analyzing the two main effects that can compromise it: recycled powder and vertical orientation during construction.

Gear wear prediction based on the theorem of degradation entropy generation

Tooth surface material loss caused by gear wear alters the surface morphology of gears, which impacts their vibration, noise, and remaining lifespan. Although gear wear modeling and prediction have been extensively studied, this paper proposes a novel approach based on the theorem of degradation entropy generation (DEG). A point-by-point calculation method is introduced to determine the degradation coefficient for each measurement point on the tooth profile, accounting for varying working conditions along the tooth profile during the actual meshing process of the gear pair. First, the FZG gear’s bearing capacity is tested. Next, a surface roughness profilometer is employed to in-situ measure the tooth profile after each load stage. The profile deviation curve and the amount of profile wear following each load stage are obtained by processing the measured profile morphology data. Then, the pitting safety factor for each point on the tooth surface is calculated according to the ISO 6336–22:2018 standard and used to correct the degradation coefficient for that point. Finally, the entropy generation of the system during each load stage of the FZG gear is calculated. The degradation coefficient suggested in the DEG theorem is employed to link gear wear with system entropy generation, realizing gear wear modeling and prediction. The results demonstrate that the gear wear calculation method based on the DEG theorem can accurately predict the evolution of tooth profile surface morphology during the experimental process. This research provides a unified calculation method for surface morphology evolution caused by gear wear during service.

Reverse design of involute helical gear pairs considering machining errors based on IMAGEWARE and HYPERMESH

Gears inevitably contain errors during the manufacturing and installation process, which can increase the vibration and noise of the gear system. The finite element model with error can accurately solve the variation of vibration and noise and meshing characteristics of such gear systems. This paper develops a combined analytical and simulation method for involute helical gears when machining errors are included. First, the tooth profile accurate point clouds of the involute gear are derived by cutting the tooth blank with the rack and the coordinate transformation function. Subsequently, the gear is reconstructed by the IMAGEWARE and UG. With HYPERMESH's powerful node editing capabilities, sinusoidal profile errors can be assigned to gears. Also, the intersection of the error gear with the tooth blank is used to find the apex, which has an essential effect on noise. Finally, the difference in static transmission errors of gears with and without errors is analyzed by ABAQUS. The results show that gears containing errors increase the peak-to-peak values of transmission errors, i.e., increasing noise. The method proposed in this paper can provide a basis for modeling and analysis of meshing characteristics of special gears that cannot be directly parameterized or gears with various errors.

Contact Analysis for Cycloid Pinwheel Mechanism by Isogeometric Finite Element

Cycloid drives are generally used in precision machinery requiring high-reduction ratios, such as robot joint (RV) reducers. The contact stress of cycloidal gears greatly affects lifetime and transmission performance. Traditional finite element method (FEM) has less computational efficiency for contact analysis of complex surface. Therefore, in this paper, isogeometric analysis (IGA) was employed to explore the multi-tooth contact problem of the cycloid pinwheel drive. Based on the nonuniform rational B spline (NURBS) curved surface generation method, the NURBS tooth profile of the cycloid gear was reconstructed. In addition, the NURBS surface of the cycloid gear–pin tooth–output pin was generated via the element splicing method. A geometrical analysis model of cycloid pinwheel drive was established to solve the contact force of the meshing pair under different input angles and compared with the finite element method in terms of convergence, resultant accuracy, and solving timeliness. The results show that isogeometric analysis has higher accuracy and efficiency than the finite element method in calculating the contact stress and contact force. The error of the IGA is only 8.8% for 10 × 10 elements in contact, while the error of the finite element method reaches about 40%. The method can improve the contact simulation accuracy of the cycloid drive and provides a reference for the design evaluation of RV reducer.

Friction power loss of continuous sine tooth profile planetary reducer

In this paper, a sine tooth planetary reducer with one tooth difference is proposed. For the proposed reducer, the equations of the oil film thickness, the meshing sliding and rolling friction power loss, and the friction power loss of the bearings for the reducer are proposed. Using these equations, the oil film thickness distribution, the meshing sliding and rolling friction power loss of the sine gear reducer plus the friction power loss of the bearings on eccentric shaft section are analyzed. The power loss of the reducer is measured and compared to the calculated values. Results show that the measured ratio of the friction power loss to input power is 27.90 %, and the calculated one is 26.53 %. The difference between them is 1.65 %. This illustrates analysis about lubrication and friction power loss of the reducer.

Research on Time-Varying Meshing Stiffness of Marine Beveloid Gear System

Beveloid gears have the advantages of compensating for axial error, providing smooth transmission, and eliminating turning error. Therefore, they are widely used in applications that require high transmission accuracy and stability. However, research on calculating the time-varying meshing stiffness of beveloid gears is still limited, and there is an urgent need to propose a method that can calculate the meshing stiffness of beveloid gears quickly and accurately. We first established the tooth profile expressions, assuming a pair of beveloid gears meshing with the same rack, and the contact line equations of parallel axis beveloid gear pairs were derived. Next, we analyzed the contact process of beveloid gears. We propose an analytical algorithm based on the slicing method to calculate the meshing stiffness of helical gears, straight beveloid gears, and helical beveloid gears. Then, the influence of different parameters on the meshing stiffness of helical beveloid gears was analyzed by changing the respective parameters. Finally, the finite element method (FEM) was used to verify the correctness of the analytical results, and then the errors were analyzed. The study demonstrates that the results obtained from the analytical algorithm we proposed have the same magnitude as those obtained by the FEM for the time-varying meshing stiffness calculation of beveloid gears.

Investigation of Effect of the Tooth Profile Modification on the Engagement Characteristics of the Gear Pair

As a vital component in the electric vehicle, the higher requirements for the gear precision are urgently needed in the service environment with high speed and heavy load. The tooth profile modification can greatly improve the accuracy and strength of the gear transmissions. Therefore, accurately obtaining the optimum modification parameters of the gear system under the action of specific loads is the premise of the research of gear vibration and noise reduction. The time-varying mesh stiffness calculation model is established in this paper considering the coupling effect of the tooth profile errors and structural coupling effect. The minimum variations of the loaded static transmission error are selected as the objective function to obtain the optimum modification parameters of gear pair. In addition, the effect of torque, modification amount and modification length on the engagement characteristics of the gear pair are studied. The research can provide some references for the design and optimization for the gear transmission system in the electric vehicle.

Features of processes of high-speed milling with a complex profile tool in the processing of aluminum alloys and composite materials

Complex computational and experimental studies substantiate rational modes of milling of complex contour equiaxed surfaces with high accuracy of shape, dimensions and roughness parameters. Bars made of nanostructured carbide composite (produced by extrusion of WC-Co-Al2O3 bimodal powder mixtures) with increased strength, crack resistance and heat resistance were used as a workpiece material for the manufacture of new original tool designs. The combination of these properties is a necessary prerequisite for the effective operation of the developed designs of multi-blade cutters at high cutting speeds and under conditions of variable cyclic loads. A more complex kinematics of the joint rotational movement of the tool during milling dictates the need for new approaches when assigning rational cutting modes. To obtain reliable calculation formulas, numerical experiments were previously carried out, including simulation of the processing process using the VisualStudio integrated development environment, which supports WindowsForms technology. The ability to display graphical 3D objects was implemented using an additional software product in the form of the Open CASCADE geometric core. Numerical experiments using MathCAD software products and based on the analytical provisions proposed in the work made it possible to evaluate the influence of cutting conditions, geometric parameters of the cutting part of the tool (profile and number of teeth), kinematics of relative movement in the “tool – part” system on the shape of surfaces and contour parameters (roughness obtained during milling. A technique, algorithm and program for the automated calculation of cutting conditions has been developed, which has been verified during full-scale experiments and the manufacture of complex profile parts from aluminum alloys for drives of aerospace products (in the form of a RC profile and parts of a pinion transmission of guidance mechanisms). At the same time, on the basis of a 3D model of products, control programs for CNC machines were created using MasterCAM. The practical significance and technical and economic efficiency of the proposed design and technological solutions is to increase productivity and reduce the complexity of processing (in comparison with the basic options) through the use of new multi-edge carbide tools for high-speed milling (including when processing composite materials).

A study of teeth generation for arbitrary-shaped sprockets

ABSTRACT In the noncircular sprocket designing process, drawing the teeth cannot be automatically performed using any function in the drawing software, and it needs complicated manual operations and adjustments. The accuracy and time waste are big problems here. This paper proposes a procedure to automatically generate a complete 3D sprocket design from a set of sprocket pitch coordinates. Japanese standard tooth profile (JIS B 1801) is used as an example model in the procedure development. First, the tooth profile equation is derived using the theory of gearing in a particular coordinate system. Subsequently, the coordinate transformation matrix is built to attach the tooth profile on every sprocket pitch coordinate in the correct direction, remove some coordinates surpassing the outer diameter limit, and build the complete 3D sprocket profile. The proposed procedure can be implemented into programming languages with the sprocket pitch coordinate file as the input and the set of sprocket teeth coordinate as the output. With the proposed procedure, a 3D design of any shape sprocket can be generated quickly and accurately.

Grinding wheel profile design and temperature field analysis of the pinion for internal meshing gear with curve configuration

To further develop the performance testing and practical application of internal meshing gear with curve configuration, the grinding manufacturing method is proposed in this paper. Based on basic principle of internal meshing gear with curve configuration, Newton’s iterative method is used to derive the contact line condition equation during the process of form grinding. Then, the spatial coordinate transformation relationship of the pinion is established, and normal profile of the grinding wheel is derived. An improved transversal algorithm is proposed to analyze the tooth profile error after form grinding simulation, and the results verify the correctness of the designed grinding wheel. A meshing model with single tooth is established. The effects of different parameters on the grinding temperature field under dry and wet grinding conditions are simulated respectively, which will be helpful to the optimization and control of temperature in grinding process. The research results lay the essential theoretical foundation and engineering analysis for practical form grinding applications of the new internal gears. Further study on experimental analysis of grinding manufacturing process of the new tooth surfaces will be carried out.

Study on small modulus modified gear damage fault and electromechanical coupling vibration characteristics under multiple working conditions

The fault of transmission system seriously affects the life of robot joints, so it is urgent to study the crack of the displacement wheel set. Firstly, the tooth profile equation of the modified gear is established, and the time-varying mesh stiffness (TVMS) is obtained. Secondly, the multi-degree-of-freedom electromechanical coupling dynamic equation is established. Finally, the vibration displacement under steady state, start-up and shock conditions is analyzed. The results show that: (a)The positive displacement can increase TVMS, while negative displacement is the opposite. (b) The appearance of cracks accelerates the damage to two adjacent teeth. (c) The decrease of TVMS increases with the increase of crack depth. (d) The crack causes the gear pair to generate vibration shock, and the vibration displacement increases significantly in the case of broken teeth. (e) Statistical analysis of the vibration displacement reveals that the root means square value can detect early cracks, and the kurtosis index can predict life. (f) Cracks have a large effect on the transient process at start-up and shock, but the effect of cracks is weakened during no-load steady-state operation.

Spiral bevel gears: Bifurcation and chaos analyses of pure torsional system

The goal of this paper is to provide a detailed analysis of the complex dynamic scenario of spiral bevel gears by considering the torsional shaft stiffness. The dynamic model takes into account: time-dependent stiffness and non-smooth nonlinearity due to the backlash, i.e., teeth contact loss. The time-varying meshing stiffness is evaluated by means of a nonlinear finite element model, which allowed an accurate evaluation of the global and local teeth deformation in both directions: forward and reverse motions. Due to intentional tooth profile errors, e.g., profile modification, manufacturing error, or assembly error, the loaded and unloaded tooth contact analyses were conducted. The dynamic model was validated by comparisons with a verified SDOF model in terms of linear natural frequencies and nonlinear dynamic response. The present study provides amplitude frequency diagrams and bifurcation diagrams; for specific regimes, periodic, quasiperiodic, and chaotic responses were found. The dynamic behavior of the systems was evaluated using various tools such as modal analysis, nonlinear time series analysis, spectra, 3D-phase diagrams, and Poincaré maps. This study proves that decreasing the DOFs of the system can lose some dynamics. Different phenomena have been found such as trapping and boom-and-bust cycle. The dynamic response of different cases is evaluated by estimating the largest Lyapunov exponent and the correlation dimension. It is found that the system undergoes complex dynamic phenomena including nT-periodic, trapping, and aperiodic motions, which are evidenced in 3D-bifurcation diagrams, spectra, Poincaré maps, and 3D-phase diagrams. The chaotic motion found in this study is an undesirable behavior from a practical point of view, which can be avoided by adjusting the designed parameters. The results provide a basis for parameter design and dynamic characteristic control of the spiral bevel gear drive system.