Tooth Profile Research Articles

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.

High-precision measurement of gear tooth profile using line spectral confocal method

The optical measurement of gear tooth profile has the advantages of high efficiency and non-contact, but its measurement accuracy has not reached the accuracy of the existing contact method. Therefore, a line spectral confocal high-precision gear tooth profile measurement method is proposed. First, the gear optical measurement coordinate system is established using a standard mandrel and the optimal measurement position model for the measured tooth profile not blocked by the adjacent tooth is established. Then, to solve the problem that the tooth profile information contained in the optical measurement results and contact measurement results is inconsistent and cannot be directly compared, a virtual probe envelope filtering method for the tooth profile optical measurement data is proposed. Next, to verify the accuracy of the line spectral confocal gear measurement system, the tooth profile deviation measurement experiments using a two-accuracy-level gear involute master are conducted. The results show that the proposed line spectral confocal method has high measurement repeatability and accuracy. The maximum absolute difference between the tooth profile deviation measurement results and the verification results is 0.16 µm, and that the tooth profile deviation curve maintains highly consistent with the verification curve. Finally, the tooth profile deviation measurement experiments using a two-accuracy-level spur gear are performed. The results indicate that the maximum absolute difference between the tooth profile deviation evaluation results measured with the proposed method and the gear measuring center is 0.28 µm. The maximum absolute difference between the two profile deviation curves by point-to-point is 0.52 μm, and the average absolute difference is 0.16 μm. The proposed line spectral confocal method can realize the high-precision measurement of gear tooth profile.

A Novel Method for the Analysis and Optimization of End Face Stress in Cycloidal Gears Based on Conformal Mapping

In the realm of precision engineering, the evaluation of stress distributions in complex geometries, such as the end face of gears, is paramount for determining performance characteristics, including the fatigue life of transmission devices. This research introduces a methodology that combines the method of conformal mapping for multiply connected regions with a proposed global scaling factor. This combination facilitates the transformation of stress computations from intricate geometries to a unit circle. By employing this method as a foundation for surrogate models, and by incorporating the Bayesian-enhanced least squares genetic algorithm optimization technique, this study refines the end face stress distribution, particularly considering variations induced by tooth profile modification errors. The results delineate a design parameter domain that is conducive to achieving uniform stress distribution, offering a refined perspective and methodology for the design of cycloidal wheels.

Design for manufacturing of a spur gears profile modification based on the static transmission error for improving the dynamic behavior

This study presents a novel iterative algorithm for obtaining an improved profile modification for spur gears based on minimizing the peak-to-peak static transmission error. Two improved profile modifications, obtained with different initial constraints applied to the tooth profile, were calculated and characterized. The static behavior of the gears was analyzed using a finite element model, by which the modifications were compared considering the maximum contact pressure and peak-to-peak static transmission error. The dynamic behavior of the gears was analyzed using a lumped parameter model. The dynamic overload and the dynamic transmission error were evaluated under several working regimes. The grinding wheel profiles used to realize the proposed profile modifications and the total volume of material removed were calculated using a CAD model. The results showed that the proposed modifications lead to a significant improvement in the static and dynamic behavior of the transmission by reducing both the maximum dynamic overload and meshing noise. The profiles of the grinding wheel were found to be accurately represented by polynomial functions, thus a feasible manufacturing process can be obtained. The total volume of material removed was lower than that produced by commonly adopted profile modifications, thus reducing material waste and increasing the productivity of the manufacturing process compared to standard profile modifications.

Influence of tooth profile and surface roughness on wear of spur gears considering temperature

Influence of tooth profile and surface roughness on wear of spur gears considering temperature

Ex vivo study of molecular changes of stained teeth following hydrogen peroxide and peroxymonosulfate treatments

White teeth can give confidence and tend to be associated with a healthier lifestyle in modern society. Therefore, tooth-bleaching strategies have been developed, including the use of hydrogen peroxide. Recently, peroxymonosulfate has been introduced as an alternative bleaching method to hydrogen peroxide. Although both chemicals are oxidizing agents, their effects on the molecular composition of the stained teeth are yet unknown. In this study, the molecular profiles of teeth bleached with hydrogen peroxide and peroxymonosulfate were compared using Liquid Chromatography-Tandem Mass Spectrometry. Statistical analyses were used to assess the samples. In addition, reference spectral libraries and in silico tools were used to perform metabolite annotation. Overall, principal component analysis showed a strong separation between control and hydrogen peroxide and peroxymonosulfate samples (p < 0.001). The analysis of molecular changes revealed amino acids and dipeptides in stained teeth samples after hydrogen peroxide and peroxymonosulfate treatments. Noteworthy, the two bleaching methods led to distinct molecular profiles. For example, diterpenoids were more prevalent after peroxymonosulfate treatment, while a greater abundance of alkaloids was detected after hydrogen peroxide treatment. Whereas non-bleached samples (controls) showed mainly lipids. Therefore, this study shows how two different tooth-whitening peroxides could affect the molecular profiles of human teeth.

Options on Tooth Profile Modification by Hob Adjustment

The presented contribution focuses its attention on the research on the influence of the angular setting in a hobbing mill on the adjustment of the tooth profile created by this technology. The aspect of influence from the angular settings in the hobbing mill on the final shape of the gears is investigated. In this research, the effect of substituting the curvilinear profile of the cutting edges with a straight profile is analyzed, observing how this approach affects the final geometry of the gears. An important point of this research is also the comparison of different profiling methods using the hobbing mill, specifically when using a normal cut, which is perpendicular to the helix of the milling cutter, and also when cutting along the axial plane of the hobbing mill.

Tooth Profile Construction and Experimental Verification of Non-Circular Gear Based on Double Arc Active Design

The double arc pitch curve is a novel way for creating a non-circular gear tooth profile. Aiming at the problems of the rounding of non-integer teeth and the nonlinear equation system in the construction of double circular arc tooth profile, an active design method based on planetary gear transmission kinematics and gear-meshing theory is proposed. By studying the double arc pitch curve of the three engagement positions, combined with the uniform theory of the relative curvature of surfaces, the distribution characteristics of the solution of the nonlinear equation system are analyzed in depth, leading to the optimal solution of the characteristic parameter values of the pitch curve. Combined with UG modeling and ADAMS motion simulation, the gear engagement force and the angular velocity of the planetary gear around the center are compared and analyzed in the case of integer tooth ratio and non-integer tooth profile. The results show that the engagement force of the gear pair constructed by integer teeth is reduced by about 17%. The optimal combination of the numbers of teeth is determined by orthogonal experiments, on which trial production and hydraulic load tests are based. The results reveal that the torque of the product at a rated speed is about 2.6% higher than that of foreign prototypes, which verifies the effectiveness of the design method proposed in this paper.

Analytical and Experimental Investigation to Resolve Surface Related Fatigue Failure in Helical Gears

With the improvement of metallurgical process and tools it became possible to modify the material property of the steel to a desired possible level where its torque transmission capability can be enhanced. Case hardening and surface grinding is one such method which is used to leverage the surface durability and core strength of gears. With the enhancement in the torque transmission capability the load per unit area of face width also increased causing huge surface pressure. They are subjected to various conditions of load, speed, temperature, and ambient conditions. Micropitting is one such surface related failure which starts on tooth flank in terms of surface texture change. This may further grow in magnitude and result in catastrophic failure. This research work is performed to compare the results of analytical and experimental investigation for the possible micropitting initiative zone. Analytical approach is carried out by using the KISSsys model and the experimental work is carried out by using a dynamometer test rig to apply the load on the gearbox shaft for a defined load cycle. It was clearly visible that the micropitting has initiated below the pitch line of pinion. Tooth profile is later modified with lead and crown modification. After the application of this modification the tooth profile related failure was not visible for similar load testing cycle.