Gear Form Research Articles

Numerical and Theoretical Analysis of a Spur Gear Using Composite and Conventional Materials

A spur gear is one of the most common forms of precision cylindrical gear. In the industry, reducing the weight of gears while keeping their useful properties has become an even more pressing challenge. As a result, the investigators have made many attempts to reduce the weight of the gears. Despite these efforts, the problem still requires more research. This study presented a spur gear's modeling and finite element analysis using different materials. A three-dimensional spur gear was designed, modeled, and simulated using ANSYS software. Five different materials, including two conventional materials (stainless steel and copper alloy) and three different composite materials, including 50% carbon fibers reinforced in epoxy resin, 1.5% filler containing acetal, i.e., Graphene Reinforced Acetal, and glass-filled polyamide. Composites were fabricated by varying the graphene quantity in Acetal nanocomposites. The spur gear stress was calculated theoretically using the Hertzian equation, and FEM was analyzed using ANSYS 14.0 under limited loading conditions and rotational speed. Although the obtained results showed that both methods were comparable, there was a significant difference between the two methods when 50% carbon fibers reinforced in epoxy resin matrix were used, which is Hertzian analysis was 250.13 MPa. In contrast, this result was reduced up to 152.13 MPa in FEM. The study concluded that among the different presented materials, 50% carbon fibers reinforced in epoxy resin matrix were the optimal material for spur gear fabrication due to their high strength and low density. Hence, the spur gear material can be replaced by 50% carbon fibers reinforced in the epoxy resin matrix.

Temperature field modelling in the form grinding of involute gear based on high-order function moving heat source

Grinding is one of the primary methods to enhance the tooth surface quality. For gear form grinding, due to the complexity of grinding movement and nonuniform grinding conditions of the tool and workpiece geometry, the accurate prediction for gear grinding temperature is difficult to achieve by using a single specific heat source shape. Therefore, a new temperature model based on high-order function curve moving heat source distribution in the grinding zone was established. Compared with the traditional models, using the new model can avoid assuming the heat source distribution shape in advance and greatly reduce the disadvantages caused by improper heat source shape assumptions under the nonuniform grinding conditions along the tooth profile. In this model, the analysis of geometry model of gear form grinding, characteristic parameters of abrasive grains and moving point heat source theory were comprehensively considered. Additionally, the finite element numerical simulation and gear grinding experiments were outperformed to analyze the gear grinding temperature. Comparison results show the highest temperature based on high-order function curve heat source appears earlier and closer to the front of the grinding contact arc compared with triangular and rectangular heat source distribution shapes. Furthermore, the tooth surface temperature in the grinding zone obtained by new model has better consistency with the experimental measurement results. The relative errors of the analytical and numerical simulation results of the maximum temperature are within 5.2 % and 6.4 %, respectively. These findings prove the accuracy and superiority of the temperature prediction model based on high-order function moving heat source distribution for gear form grinding, and it has a guiding role in the optimization of the workpieces with complex profiles in form grinding.

Loaded and unloaded tooth contact analysis of spiral bevel gears in consideration of misalignments

Bevel gear pairs are employed extensively in transmission systems, such as vehicle transmissions (rear axle drive), aircraft engines/turbines and helicopter gears, to transfer power between non-parallel shafts at high speed or high torque. The most complex form of bevel gear is the spiral bevel gear (SBG). SBG pairs are commonly used in applications that require high load capacity at higher operating speeds than are typically possible with other types of bevel gear. When manufactured in a metal-cutting process, spiral bevel gears can either be produced using single indexing (a face-milling method, which is considered in this study) or continuous indexing (a face-hobbing method). Due to manufacturing imperfections and the flexibility of components, the system might experience misalignments that intensify or exert a destructive effect on the gear vibration, which causes disruption in the stress distribution, thereby decreasing the lifetime of the gearbox. The main purpose of this study is to carry out loaded tooth contact analysis (LTCA) and unloaded tooth contact analysis (UTCA) for an SBG pair in the presence of two types of misalignment, axial and radial misalignment, and represent their effects on the mesh stiffness (MS). To calculate the MS, it is essential to determine the geometrical mismatch between two mating tooth profiles by means of UTCA. To conduct LTCA, three main approaches can be utilised: the finite element method (FEM) and experimental and analytical approaches. Due to the development of software packages during the last decade, Transmission3D-Calyx, an FEM-based software, is used in this study to carry out LTCA and UTCA. Finally, the MS for different misalignment cases is compared to represent the effect of misalignment on the SBG pair.

Spin-Orbital Conversion with the Tight Focus of an Axial Superposition of a High-Order Cylindrical Vector Beam and a Beam with Linear Polarization.

In this paper, spin-orbital conversion in the tight focus of an axial superposition of a high-order (order m) cylindrical vector beam and a beam with linear polarization is theoretically and numerically considered. Although such a beam does not have a spin angular momentum in the initial plane and the third projection of its Stokes vector is equal to zero, subwavelength local regions with a transverse vortex energy flow and with the non-zero third Stokes projection (the longitudinal component of the spin angular momentum) are formed in the focal plane for an odd number m. This means that such a beam with an odd m has regions of elliptical or circular polarization with alternating directions of rotation (clockwise and counterclockwise) in the focus. For an even m, the field is linearly polarized at every point of the focal plane, and the transverse energy flux is absent. These beams can be used to create a micromachine in which two microparticles in the form of gears are captured in the focus of the beam into neighboring local areas in which the energy flow rotates in different directions, and therefore, these gears will also rotate in different directions.

A high-precision fitting and dressing method for the flex and circular rigid splines with involute tooth profile in gear form grinding

A high-precision fitting and dressing method for the flex and circular rigid splines with involute tooth profile in gear form grinding

Simulation and Compensation of Axial Geometric Errors for Cycloidal Gears Based on Form Grinding

To increase quality, reduce cycloidal gear noise, and avoid unnecessary vibration and shock, a compensation of axial geometric errors method is proposed based on the cycloidal gear form grinding. In the process of machining cycloidal gears, the relative position relationship between the grinding wheel and workpiece is affected by geometric errors of the motion axes, which has serious effects on the surface accuracy of the cycloidal gears. Combined with cycloidal gear form grinding kinematic principles, a geometric error model for each axis of a four-axis computer numerical control form grinding machine is established. By changing the compensation value of the geometrical errors on six degrees of freedom, the error of the cycloid gear tooth surface machined is obtained. Based on a sensitivity analysis of geometrical errors of each axis, the corrections are determined through an optimization process that targets the minimization of the tooth flank errors. The geometric errors of each axis of the cycloid gear grinding machine are compensated, and then, the cycloid gears produced by the machine are processed. Through the processing experiment, the error data of the actual processing before and after the compensation are compared, which indicates that the machining accuracy of the cycloid gear grinding machine is obviously improved. It has an important guiding significance in improving the precision and performance of large CNC form gear grinding machines.

Meshing Stiffness Calculation of Disposable Harmonic Drive under Full Load

Mechanical equipment in the field of aerospace that is used only once is called disposable machinery. As a piece of typical disposable machinery, disposable harmonic gear exhibit stiffness failure with a large load. This manuscript distinguishes disposable harmonic gear from conventional harmonic gear in terms of the application environment and structure. Then, this paper determines the single-tooth stiffness of the disposable harmonic gear under full load by using the non-uniform beam model and the improved energy method. In addition, the multi-tooth meshing in the disposable harmonic drive is considered, and the improved energy method is modified. Besides, the normal contact force and comprehensive elastic displacement at each meshing position are calculated according to the finite element model. Additionally, curves of the single-tooth stiffness and the comprehensive meshing stiffness are obtained. The theoretical results of the modified analytical method and FEM are compared to verify the correctness of the proposed method in terms of calculating the meshing stiffness of the disposable harmonic drive. Finally, FEM is used to obtain the failure form of the disposable harmonic gear under overload.

Residual stress evolution for tooth double-flank by gear form grinding

In gear form grinding, the complexity of tool-workpiece geometries affects the grinding force and heat distribution along the tooth profile, thus resulting in difficulties in the calculation of residual stress. Specifically, the stress and heat generated on the newly machined tooth flank were influenced by the former grinding passes. Unfortunately, this issue was ignored in the previous research. To fill this gap, this paper presents a thermal-mechanical coupling calculation model considering the differences in gear double-flank, and a new heat source optimization algorithm is proposed. Firstly, according to the kinematic analysis of gear form grinding, the Lagrange interpolation method is used to solve unevenly distributed moving heat sources on the curved surface. Secondly, based on the theory of plastic increment combined with the von Mises yield criterion considering work hardening, the relationship between the temperature and the grinding stress on the first grinding tooth flank and the second grinding tooth flank is obtained through load cyclic loading. Finally, the residual stress field in the final state of all tooth flanks is obtained through the release procedure. The gear grinding experiments were conducted to verify the model, and the comparison results showed good consistency. The influence of unevenness in gear form grinding is not only reflected in the stress distribution along the tooth profile, but also on the different flanks. Based on the correlation law between the processing parameters and the residual stress on the tooth flanks, the optimal machining parameter range is obtained. The study provides an important reference for the understanding of gear form grinding mechanisms and the optimization of the grinding process.

Modelling and experiment for grinding forces of gear form grinding considering complete tooth depth engagement

Grinding is an essential gear finishing method. Grinding force analysis and prediction are critical to understand grinding mechanisms. By using a geometry model for gear form grinding and surface grinding mechanisms, a theoretical model was established to calculate the gear form grinding force. By considering the complete tooth depth engagement between tooth grooves and wheel profiles during form grinding, three segments of the involute, transition arc and tooth bottom line, which were included in complete tooth groove profiles, were analysed using the model. Contact relations among the normal grinding depth, wheel equivalent radius, wheel linear velocity and wheel profile were obtained. In addition, grinding experiments were outperformed on the basis of the single tooth, and the unknown coefficients of the form grinding force calculation model were acquired. The effects of the grinding depth, feed speed and grinding speed on grinding force were analysed using the grinding force model. The comparison of the predicted values of the form grinding force model with the experimental results, indicated that the relative errors of tangential and normal grinding forces are within ±10% and ±12%, respectively. The results confirmed the accuracy of gear form grinding force calculation model. These findings play a key role in parameter optimisation during gear form grinding.

Analysis and experimental study of metal streamline configuration in hot rolling forming of spiral bevel gears

Analysis and experimental study of metal streamline configuration in hot rolling forming of spiral bevel gears

Prediction and test of stable transmission time of spiral bevel gear during a loss-of-lubrication event in helicopter transmission system

PurposeThis paper aims to establish a prediction model of stable transmission time of spiral bevel gear during a loss-of-lubrication event in helicopter transmission system.Design/methodology/approachTo observe the temperature change of spiral bevel gear during working condition, a test rig of spiral bevel gear was developed according to the requirements of experiments and carried out verification experiments.FindingsThe prediction is verified by the test of detecting the temperature of oil pool. The main damage form of helicopter spiral bevel gears under starved lubrication is tooth surface burn. The stable running time under oil-free lubrication is mainly determined by the degree of tooth surface burn control.Originality/valueThe experimental data of the spiral bevel gear oil-free lubrication process are basically consistent with the simulation prediction results. The results lay a foundation for the working life design of spiral bevel gear in helicopter transmission system under starved lubrication.

FACTORS AFFECTING THE ACCURACY AND REPEATABILITY OF INDUSTRIAL ROBOT POSITIONING

Industrial robots refer to the most complex products of mechanical engineering and electronic equipment in terms of their labor intensity, accuracy, and a class of manufacture as well as quality requirements. Both static and dynamic positioning inaccuracies occur during their operation. Static positioning depends mainly on such parameters as joint axis geometry and angle offset. Non-geometric parameters include compliance (elasticity of joints and bonds), gear form errors (eccentricity and gear errors), gear backlash, and temperature-related expansion. Dynamic positioning is only relevant for large robots that are subject to high speeds and accelerations. Positioning accuracy is affected by the design features of the robot, the control system, the speed of movement and rotation of the manipulator, temperature, and vibrations, both inherent and caused by the robot's location in production. This research examines the sources of positioning inaccuracy and gives recommendations for improving the positioning characteristics of robots.

Fringe direction weighted autofocusing algorithm for gear tooth flank form deviation measurement based on an interferogram.

When measuring the form deviation of the gear tooth flank with laser interferometry, due to the limitation of the depth of field of the lens, focused and defocused regions exist in the interferogram simultaneously. The introduced errors that were generated by these defocused regions decrease the measurement accuracy. Therefore, the evaluation of definition for interferograms is necessary for image processing. However, the gradient of gray, which performs by fringes, makes it difficult for traditional algorithms to evaluate its definition. This paper proposes a method based on nonsubsampled contourlet transformation (NSCT) combined with fringe direction as weighting coefficients to solve the problem. First, the information about the directions of these fringes in interferograms was evaluated. Then, the NSCT method was applied to interferograms so that several sub-images in different scales and directions can be achieved. Based on these sub-images and directions information, an improved function for definition evaluation was conducted. Lastly, a series of simulations and experiments was carried out to verify its feasibility and accuracy.

Error analysis and compensation of cycloid gear form grinding based on multi-body system error topology theory

Error analysis and compensation of cycloid gear form grinding based on multi-body system error topology theory

Rotating Biological Contactor Wastewater Treatment using Geotextiles, Sugarcane Straw and Steel Cylinder for green areas irrigation

Due to the recent climatic and economic developments in the Middle East, the region has become on the verge of water poverty. It has become imperative to reconsider the policy of water spending and rationalization of consumption and to consider recycling all types of water, thus in this study, two identical stages of the RBCs system were used to treat wastewater after its primary treatment at Zenin wastewater treatment plant in Giza, Egypt. Different materials were used in the treatment process such as geotextile, (in two different forms), circular discs and discs in the form of gear, with 15 discs per RBC stage, a steel cylinder, in addition to a plastic bottle with holes with sugarcane straw inside. The rotation speeds were varied between 5, 8 and 10 RPM, with 40% submergence for the geotextile discs of the normal circular shape and for the rest of the materials a rotation speed of 5 RPM were used, where it was found later that it gave the best results. The hydraulic retention time ranged between one, two, and three up to seven days. It was found that the best results obtained at HRT of 3 days. Results showed that the removal rates of BOD, COD and TSS were almost 82%, 86.7% and 81.5% at 5RPM for normal circular discs shape respectively, while for gear shaped discs removal rates were almost 83.7%, 91% and 81.3% respectively. For sugarcane straw plastic bottle, BOD, COD and TSS removal rates were almost 64.86%, 69.49 and 68.18% at 5RPM respectively, noting that sugarcane straws removal rates were the lowest among the rest of materials. Removal rates were almost 86.9%, 94.4 and 82.14% for BOD, COD and TSS respectively at 5RPM for steel cylinder. Steel cylinder showed the highest removal rates among all other materials.

Probability distribution model of gear time-varying mesh stiffness with random pitting of tooth surface

Pitting is one of the fault forms of gears, which directly causes a reduction in gear time-varying meshing stiffness (TVMS). In this paper, the probability distribution model of gear TVMS is established with random pitting. Firstly, a distribution model of tooth surface pitting is proposed based on the Monte Carlo method, which considers the relationship of tooth surface fault degree and pits number. Then, the TVMS with different characteristics of pitting is calculated by combining image processing. Pits number and distribution parameters of pitting are taken as random variables. The probability distribution models of TVMS with random pitting of tooth surfaces are established. Furthermore, the influence of pits number and distribution parameters on gear meshing stiffness are investigated. The results show that the probability distribution models of TVMS of gears with random pitting agree well with the normal distribution with angular displacement.

Force reduction by electrical assistance in incremental sheet-bulk metal forming of gears

Producing load-adapted and functionally integrated components by flexible and resource efficient processes has gained importance within industries like the automotive sector in recent years. A promising new class of processes that enables a local adaption of the sheet thickness is Sheet-Bulk Metal Forming (SBMF). While the incremental procedure (iSBMF) only requires a moderate forming force, forming of high strength steels leads to a tool load resulting in a significantly reduced tool life. One approach to reduce tool loads is the utilization of the so called electroplastic effect (EPE). This study for the first time identifies the potential of the EPE on a temporary reduction of the forming force during the iSBMF of gears targeting an improvement of the tool life. The steel grades DC04 and HSM700 HD are characterized considering the EPE under uniaxial tension. Based on the characterization, the current density and temperature increase are modelled numerically and analytically for the incremental gear forming process. Moreover, the impact of EPE on strain hardening, grain texture and forming force is determined. By a local insulation of the forming tool based on a PVD coating and the application of an electrical current, a temporary force reduction of up to 55 % is observed whereas the strain hardening effect remains almost unaffected.

Numerical study of sheet-bulk forming process of high strength steel 16MnCr5

The sheet-bulk metal forming (SBMF) technology provides a new processing method for gears. This manufacturing technology is greatly affected by process parameters, deformation conditions and material properties. Defects such as holes, tearing and insufficient filling of materials are easy to occur during forming process. In order to understand the mechanism of this process, finite element modelling and simulations are carried out on the sheet-bulk forming of gears. Equivalent stress and material flow are analyzed by combining point tracking method. The mechanism of incremental sheet-bulk forming of gears technology is clarified. The phenomenon of insufficient filling of initial teeth caused by restricting material flow is emphatically explained.

Analysis and experimental study of cycloid gear form grinding temperature field

Form grinding is the finishing process of the cycloid gear of RV reducer. In order to avoid the tooth surface burn of the cycloid gear during the grinding process and improve the grinding efficiency, the heat distribution ratio and the convection heat dissipation coefficient during the grinding process are calculated. The computer simulation software ANSYS 17.0 is used to calculate the instantaneous temperature field of the tooth surface during the grinding process of the cycloid gear. The distribution of the instantaneous temperature field of the tooth surface along the axial of the gear is obtained. According to the characteristics of the YK7350B gear grinding machine, the grinding process parameters is reasonably selected, and the grinding experiment is carried out. The metallographic structure of the burned section of the experimental part was observed by the ProgRes C5 metallographic measuring instrument to verify the simulation results. The research is beneficial to predict the temperature field distribution of the tooth surface of the cycloid gear and select the grinding process parameters reasonably.

Computational Design and Optimization of Non‐Circular Gears

AbstractWe study a general form of gears known as non‐circular gears that can transfer periodic motion with variable speed through their irregular shapes and eccentric rotation centers. To design functional non‐circular gears is nontrivial, since the gear pair must have compatible shape to keep in contact during motion, so the driver gear can push the follower to rotate via a bounded torque that the motor can exert. To address the challenge, we model the geometry, kinematics, and dynamics of non‐circular gears, formulate the design problem as a shape optimization, and identify necessary independent variables in the optimization search. Taking a pair of 2D shapes as inputs, our method optimizes them into gears by locating the rotation center on each shape, minimally modifying each shape to form the gear's boundary, and constructing appropriate teeth for gear meshing. Our optimized gears not only resemble the inputs but can also drive the motion with relatively small torque. We demonstrate our method's usability by generating a rich variety of non‐circular gears from various inputs and 3D printing several of them.