Gear Body Research Articles

Investigations on mesh stiffness functions in three-dimensional spur and helical gear models. Definitions and numerical simulations

A definition of mesh stiffness as a scalar function connecting spur and helical three-dimensional pinions and gears is presented along with its conceptual limitations. Since it relies on global parameters namely, variations in torque and transmission errors, it can therefore be applied to the vast majority of the models found in the literature. In parallel, a multi-foundation (MF) model of mesh interface is introduced with the objective of being as accurate as three-dimensional finite element (FE) simulations for highly reduced computational costs. Numerous results on mesh stiffness and tooth contact conditions are presented for unmodified spur and helical gears. It is shown that the proposed mesh stiffness functions based on global parameters are sound and that the MF and FE results compare well, particularly when gear body deflections are limited. The contributions of off-line of action contacts, elastic couplings when several tooth pairs are loaded and axial deflections in helical gears are analysed. Finally, the notion of mesh stiffness function representative of the elasticity of a pinion-gear pair for static and dynamic conditions is examined.

Calculation and Analysis of TVMS Considering Profile Shifts and Surface Wear Evolution Process of Spur Gear

Profile shift is a highly effective technique for optimizing the performance of spur gear transmission systems. However, tooth surface wear is inevitable during gear meshing due to inadequate lubrication and long-term operation. Both profile shift and tooth surface wear (TSW) can impact the meshing characteristics by altering the involute tooth profile. In this study, a tooth stiffness model of spur gears that incorporates profile shift, TSW, tooth deformation, tooth contact deformation, fillet-foundation deformation, and gear body structure coupling is established. This model efficiently and accurately determines the time-varying mesh stiffness (TVMS). Additionally, an improved wear depth prediction method for spur gears is developed, which takes into consideration the mutually prime teeth numbers and more accurately reflects actual gear meshing conditions. Results show that consideration of the mutual prime of teeth numbers will have a certain impact on the TSW process. Furthermore, the finite element method (FEM) is employed to accurately verify the values of TVMS and load sharing ratio (LSR) of profile-shifted gears and worn gears. This study quantitatively analyzes the effect of profile shift on the surface wear process, which suggests that gear profile shift can partially alleviate the negative effects of TSW. The contribution of this study provides valuable insights into the design and maintenance of spur gear systems.

Dynamic reduction technique for nonlinear analysis of spur gear pairs

In this study the dynamic response of a spur gear pair is analyzed using a novel nonlinear approach. The actual rolling motion and engagement of the system is simulated using a set of reduced order models obtained in a pre-processing phase using the minimal amount of master degrees of freedom without loss of accuracy or generality. The flexibility of the gear bodies is included by a refined finite element model, and no geometry simplification is introduced while also retaining all nonlinearity sources. To reduce the computational cost the time-varying mesh stiffness is also pre-computed and used depending on the instantaneous loading conditions. Contact loss is also taken into account, and reconnection events are treated as vibro impacts. The results are compared against high quality and demanding experimental results with a computational cost several orders of magnitude lower than models with similar accuracy. Different loading conditions are investigated during the sweep-up and down maneuvers. Mainly, the dynamic transmission error is analyzed, showing remarkable agreement with the test campaign’s results. Different nonlinear phenomena such as hysteretic jumps and sub- and super-harmonic resonances are correctly predicted by the proposed model in terms of both frequency and amplitude. This method allows quick and accurate nonlinear analyses overcoming current limitations and is open to further complications to include other components and effects.

An impact-damping model of collision body with multi-point contact and external load, and its application in gear transmission

The damping term is an important component of the calculation model of the contact force of collision bodies because it simulates the energy dissipation of collision bodies during the contact-impact process. Therefore, an impact-damping model of a collision body with multi-point contact and external load is established by considering the restitution coefficient. The algorithm for solving this model is proposed based on iterative methods. Then, the accuracy of the established model is verified by the consistency between the calculated and tested results. The effect of multi-point contact and external load on the contact-impact process of the collision body is studied. The results show that the hysteresis damping factor increases from small to large when the collision body enters a stable state through repeated impacts. Further, the established damping model is applied to the dynamics model of a spur gear pair with backlash, extended teeth contact, and structure coupling effect of the gear body. The nonlinear dynamic characteristics, multi-state mesh, and teeth impact of the system are studied through the root-mean-square of transmission error, bifurcation diagrams with multi-mapping sections, and contact forces. The calculation results of the gear dynamics model with the impact-damping model are more consistent with the tested results than the calculation results of the gear dynamics model with the traditional damping model. Meanwhile, the connection between system resonance, response coexistence, teeth disengagement, and teeth impact is revealed.

Evaluation of vibration behavior at different sensing positions on gearboxes

Monitoring systems for rolling contacts in machinery are widespread. There are multiple solutions in various applications like Health Usage Monitoring Systems (HUMS) for Helicopters and smart bearings from different manufacturers. The number of solutions and possibilities is rising. This paper outlines how the vibrational behavior depends on the measuring position outside and inside the gearbox. The effect of the sensor location is evaluated by examining different locations close to the main excitation of gearboxes—the loaded tooth contact—as well as positions on the gearbox housing. Based on the results, recommendations for an optimal sensor position for gear vibration monitoring are given by considering the efforts of sensor integration. The results can be used to select sensors with the lowest cost to support the widespread gear vibration monitoring.Important locations for health monitoring are the gear meshes inside the gearbox. Due to the requirement of high power density, a compact design is mandatory. This does not allow for sensor application close to the gear meshes but only on the outside of the gearbox. An impediment of signal quality and less chance of early damage detection is the consequence. Hence, efforts have been made to directly integrate multiple sensors inside the gear body without negatively impacting the package.For the investigation of the vibration transmission behavior, an FZG gear test rig is selected. These standardized test rigs are approved and established all around the world for the creation and evaluation of various gear failure data. The presented test rig has been modified to be able to sense vibration in the gear wheel, at the gear wheel, and on the gearbox housing to evaluate different sensor positions and vibration sensors for their suitability on vibration measurement.

THE INFLUENCE OF THE OPTIMIZATION OF THE SPUR GEAR BODY ON THE MESHING STIFFNESS

The design of the body shape of spur gears has an effect on the deformation and thus also the stiffness of the gearing. The stiffness of the gearing is a parameter that significantly affects the noise level of transmission mechanisms. Determining the gear stiffness is difficult due to the shape of the gear teeth. The paper examines the influence of the shape and size of individual gear body parameters on gear deformation. Deformation is solved by finite element method. On the basis of the deformation of the gearing, the stiffness of the gearing is determined.

A novel semi-analytical method for fillet foundation deflection calculation in presence of a tooth crack propagating into the rim of a spur gear

Existing analytical approaches for calculating fillet foundation deflections in spur gear struggle to adequately address the complexities introduced by tooth cracks, particularly as cracks propagate into the gear body. The finite element methods are accurate but computationally expensive. In response to these challenges, the paper introduces a novel semi-analytical method based on elastic circular ring theory that is capable of calculating the fillet foundation deflection for both healthy and cracked conditions. To establish the usefulness of the method, the fillet foundation deflections obtained are further used to obtain the time-varying mesh stiffness. A methodology centered on compatibility conditions is employed to achieve load distribution during double tooth engagement. The results are verified using two three-dimensional finite element models. In addition, the effect of different hub hole radii, crack lengths and orientations on the fillet foundation deflections and TVMS are investigated. The outcomes suggest that the proposed semi-analytical approach demonstrates superior accuracy in the calculation of spur gear mesh stiffness compared to alternative methods.

Approaches to reducing gear mass and their effects on gearing stresses and deformations

AbstractThis study compares empirical and topology optimization methods for reducing gear body mass. Specimens produced via empirical guidelines and topology optimization were compared to referent full-disc gear, focusing on stresses and deformations. Values were determined numerically (Ansys was used) and the calculation method was verified using ISO 6336. The empirical approach exhibited substantial increases in stress and deformation while topology optimization method had promising outcomes. While decreasing mass, it also diminished tooth root stress on the tensile side by 17.1%.

Mesh stiffness modeling and dynamic simulation of spur gears with body crack under speed fluctuation condition

The traditional method for calculating the time-varying mesh stiffness (TVMS) of cracked gears usually assumes that the root crack is solely located within the gear tooth. Accurate calculation becomes a challenge when the crack propagates into the gear body. In this paper, an improved model for calculating the TVMS of spur gears with crack propagation into the gear body is proposed based on a combined analytical finite element-potential energy method, and the accuracy of the proposed model is verified by the finite element method. A 5-degree-of-freedom (5-DOF) dynamic model with speed fluctuation is developed, taking into account the coupling shaft-bearing stiffness as the support stiffness. Subsequently, a dynamic simulation of a gear system with a gear body crack is conducted. The results indicate that the proposed analytical model can provide relatively accurate mesh stiffness for crack propagation into the gear body. The TVMS decreases as the crack length increases, the decrease in mesh stiffness becomes more significant when considering the influence of the crack on the gear body stiffness. The dynamic response obtained from the proposed dynamic model shows more pronounced pulse characteristics compared to the model that does not consider the influence of shaft stiffness. The low speed and heavy load conditions restrain the speed fluctuation of the gear system. The residual signal is more effective for identifying fault signals than the original signal. The proposed model can provide theoretical and methodological references for diagnosing faults in gear systems with crack propagation into the gear body.

Temperature control-based design of variable damping and lightweight gear bodies

Temperature control-based design of variable damping and lightweight gear bodies

Vplyv tvaru telesa na deformáciu čelného ozubenia

The article is devoted to the analysis of the influence of the basic parameters of the body of the spur gear on the deformation of the teeth in meshing. The problem is solved for spur gears of large dimensions, the semi finished product of which can be a weldment, casting or forging. Gear deformations are determined by the finite element method. Examples of simulation and subsequent processing of the results demonstrate the extent of the influence of individual parameters of the gear body on the deformation of the gearing. At the same time, the results point to suitable designs of shape and dimensions to achieve the desired deformation of the teeth but with the smallest possible weight of the gears.

The Use of SAW, RAM and PIV Decision Methods in Determining the Optimal Choice of Materials for the Manufacture of Screw Gearbox Acceleration Boxes

This article investigates material selection for components in worm gear reduction gearboxes, focusing on the worm shaft, gearbox casing, and worm gear body. The screw shaft’s and worm gear body’s material selection involved evaluating six criteria: hardness, tensile strength, yield strength, relative elongation, relative contraction, and impact strength. Gearbox casing materials were selected based on five parameters, including tensile strength, yield strength, relative elongation, impact strength, and hardness. The authors employed three Multi-Criteria Decision-Making (MCDM) methods, Simple Additive Weighting (SAW), Root Assessment Method (RAM), and Proximity Indexed Value (PIV) to assess material choices. Various methods, including Entropy, Logarithmic Percentage Change-driven Objective Weighting (LOPCOW), and Equal, determined weights for the criteria. Remarkably, consistent optimal material types emerged across all MCDM and weight determination methods, showcasing the robustness of the results. For screw shafts, C35 steel was identified as the optimal type. GC120- 04 stood out among nine materials for gearbox casing production. C35CrMo was determined as the best type among eight steel types for manufacturing the worm gear body. In summary, this study provides a comprehensive and objective approach to material selection for worm gear reduction gearbox components, offering valuable insights for decision-making in the mechanical engineering industry.

Dynamics analysis of spur gears considering random surface roughness with improved gear body stiffness

In previous calculation of gear mesh stiffness, the gear body is typically treated as a deformable elastic ring, and the stiffness of the gear body is determined using Sainsot's empirical formula. In this paper, a new calculation method for determining the gear body stiffness based on the analytical finite element-potential energy method is proposed, and its feasibility is verified by the finite element method. A new nonlinear dynamic model for a spur gear system is established, taking into account the time-varying backlash and random surface roughness. This model aims to investigate the dynamical responses of the gear system under various parameters, including rotational speed, shaft hole radius and surface roughness. The results indicate that the proposed method for calculating the stiffness of the gear body is significantly more accurate than Sainsot's empirical formula, as it closely aligns with the finite element method. This leads to a more precise calculation of the time-varying mesh stiffness. The gear dynamics model incorporating random surface roughness exhibits a heightened degree of realism and complexity in its dynamic phenomena. This study provides a valuable reference for the future development of dynamic gear systems.

An Analysis Model for Predicting Windage Power Loss of Aviation Spiral Bevel Gears Under Optimal Injection Jet Layout

With the increasing rotating speed of aviation spiral bevel gears, the load-independent windage power loss caused by hydrodynamic behavior has a greater impact on transmission efficiency. An analytical model is established to predict the windage power loss of spiral bevel gears with oil injection lubrication. The improved model regards the total windage losses as the sum of oil–gas dragging effects on the tooth flank, toe/heel, circular cone surface, circumference of the teeth, and tooth root. Then the numerical method and analytical method are combined to calculate windage losses. A multi-objective NSGA-II optimization algorithm is used to optimize the jet layout parameters. The rationality and accuracy of this model are verified by comparing the calculation results of an example with data sets of existing experimental findings and computational fluid dynamics (CFD) simulation results. The calculation results show that compared with the tooth profile assumption method in the existing literature, the improved calculation formula of windage dragging effect on tooth flank can better reflect the influence of oil injection lubrication layout parameters on windage loss and make the windage loss calculation more accurate. Finally, the influence of gear body parameters, working conditions parameters, geometric parameters, and injection lubrication layout parameters on the windage loss is examined. This research provides a theoretical basis and methodological guidance for optimization design of reducing windage power loss.

Dynamic investigation and experimental validation of a gear transmission system with damping particles

Due to recent technological advances, preciseness in gear transmission has evolved into an essential goal, in which vibration is one of the critical issues. This study demonstrated an experimental platform for a proposed construction model on the spur gear pair, in which damping particles were filled into six through-cavities in gear bodies to verify decreases in vibration. The experimental design involved variable control of input rotational speed, filling ratio, particle size, and material to investigate the damping particles’ behavior. Subsequently, operating both ADAMS and EDEM software established a reliable two-way coupling analysis model. The results confirmed that the filling damping particles effectively reduced system vibration, and both simulation and experimental tests demonstrated a consistent impact. In addition, the damping particle behavior indicated that high rotational speed was more effective in vibration reduction, and increased filling ratio decreased radial vibration. Increases in particle diameter only contributed slightly to vibration reduction. Moreover, although density increase significantly reduced vibration, bead elasticity did not impact vibration. Finally, the dynamic behavior of damping particles with the greatest reduction impact was achieved by applying a soft lead bead in a 5-mm diameter, 48% filling ratio, and the system working at a rotational speed of 600 rpm.

DESIGN OPTIMIZATION OF GEAR WHEEL BODIES IN ORDER TO REDUCE WEIGHT

Design solutions for the shape of the gear bodies depend on several factors such as the size of the wheel, material, production method or use. Cast forged or welded gears are used for larger gear wheels. One of the requirements for gear shape solutions is weight reduction. Such an effort can be achieved by changing the dimensions of the given wheel, while maintaining the required stiffness of the gearing. The paper is devoted to the problem of optimizing the shape of gears in order to reduce the weight of the gears, but while maintaining the best possible stiffness of the teeth.

Analysis of the Transmission Error of Spur Gears Depending on the Finite Element Analysis Condition

Finite element analysis is widely used to predict the structural stability and tooth contact performance of gears. This study focused on the effect of finite element modeling conditions of a spur gear on the simulation result and the model simplification. The gear body and teeth, teeth width, configuration of mesh, frictional coefficient, and simulation time interval (gear mesh cycle division) were selected for model simplification for gear analysis. The static transmission error during a single-gear mesh cycle was calculated to represent the performance of the gear, and the elapsed time was measured as a simplification factor. Contact stress distribution was also checked. The differences in maximum transmission error and elapsed time depending on the model simplification methods were analyzed. After all simplification methods were estimated, an optimal combination of the methods was defined, and the result was compared with that of the most detailed modeling methods.

An Improved Load Distribution Model for Gear Transmission in Thermal Elastohydrodynamic Lubrication

The gear drive generally operates in elastohydrodynamic lubrication (EHL) contacts, and the existence of oil film effectively reduces wear and improves transmission stability. However, little research has been devoted to studying the effect of lubrication characteristics on load distribution of gear transmissions. In order to investigate the coupling effect between the lubrication behavior and load distribution, an analytical load distribution model suitable for EHL contact spur gear pairs is proposed. The non-Newtonian transient thermal EHL solution, flexibility of meshing teeth, structural coupling deformation of the gear body and extended tooth contact are considered in the deformation compatibility condition for iteratively solving the load distribution. A parametric analysis is performed to determine the influence of load torque and rotation speed on load sharing ratio and loaded static transmission error. The transient lubrication behaviors based on the proposed load distribution model is compared with that obtained from the traditional model. A series of comparisons with different models demonstrated the correctness, significance and generality of the present model. The results show that it is necessary to consider the thermal EHL calculation into the iterative solution procedure of load distribution model for EHL contact gear pairs. The proposed model is a useful supplement for an accurate study of thermal EHL characteristics of gear transmissions.

An analytical method for the meshing characteristics of asymmetric helical gears with tooth modifications

This paper establishes a time-varying meshing stiffness (TVMS) analytical method for asymmetric helical gear pairs based on the potential energy principle and slice method. The method considers the adjacent teeth' influence on the deformation of the gear body part. The proposed method is verified the reasonableness by finite element (FE) analysis. The basic parameters of asymmetric helical gear such as helical angle, pressure angle and tooth width are estimated for the meshing characteristics. The results show that the increase of helix angle, pressure angle of the driving side, normal modulus and tooth width will affect the contact ratio and maximum meshing stiffness of helical gears. The variation of these parameters can minimize the fluctuation of the TVMS curve when the overlap contact ratio reaches an integer. The variation trend of the loaded-static transmission error (LSTE) is opposite to that of the TVMS curve. The load share ratio (LSR) on a pair of gear pairs will decrease with the increase of the degree of reattachment. Furthermore, the influence of tooth modifications on TVMS is estimated by using the proposed method. The mean value of stiffness is reduced after the tooth modifications. The TVMS curve changes more gently after the tooth tip modification.

Load carrying capacities of gears with a lattice structure body

Lattice structures are type of topology structures that have complex geometry, composed of multiplicated unit cells through which a pattern is generated. Lattice structures are of great interest in engineering due to their strength-to-weight ratio. There has been an increasing trend for their application as infill patterns in a variety of engineering parts and elements. However, the complexity of the lattice geometries, makes them difficult to be produced by conventional methods. Therefore, additive manufacturing technologies have been used as technologies for production of parts containing lattice structures. In this research, the focus is placed on analyzing various unit cell structures and their application in conventional gears as their structure body. One specific lattice structure is chosen and generated. Several characteristics of the lattice structure can vary, like the cell size, density, wall thickness etc. The lattice shape will remain the same for all the analysis. The lattice is optimized by weight reduction and maintaining load carrying capacity of the gears. Different samples are examined using FEM (Finite Element Method) in terms of determination the load carrying capacity. The results for the optimized gear body structures are elaborated, conclusions are drawn and recommendations for application of gears with a specific lattice structure are provided.