Gear Contact Research Articles

A new effective mesh stiffness calculation method with accurate contact deformation model for spur and helical gear pairs

This paper proposes a new effective mesh stiffness calculation method for spur and helical gear pairs, which is explicitly formulated by an original FE-analytical slice model for tooth local contact deformation, efficient FE model for gear global deformation and mathematical programming approach for gear contact. The original FE-analytical slice model comprehensively integrates the advantages of FE method, Hertz contact theory and slice approach, which can address the displacement datum and elastic interaction of tooth slices effectively, so that tooth contact deformation is determined accurately. The geometry modeling of tooth slices is established and the pressure configuration in the contact region of each slice is prescribed by Hertz distribution. A specified FE programming is developed to derive the tooth contact flexibility matrix accurately. Thus, the mesh stiffness can be effectively calculated by using the proposed method with the FE-analytical slice model. The local contact deformation of gear tooth and mesh stiffness of gear pairs under ideal and error conditions are simulated. The accuracy and efficiency of the proposed method are validated against the ANSYS benchmark and common existing methods.

Strategic discarding reduces seabird numbers and contact rates with trawl fishery gears in the Southwest Atlantic

Incidental mortality in trawl fisheries is a serious threat to seabird sustainability. Driven primarily by seabirds attracted to discards, limiting discard discharge through strategic batching is a best practice mitigation measure recommended by the Agreement on the Conservation of Albatrosses and Petrels (ACAP). However, studies supporting the efficacy of batch discarding are rare, limited to the south-western Pacific, and assess seabird numbers attending vessels only, not gear contact rates. The effectiveness of batch discarding in areas with different seabird communities, fishery assemblages, and natural prey availability is therefore unknown. Here we quantify both seabird numbers and gear contact rates in response to strategic discard discharge in the Falkland Islands trawl fleet for two high-risk species groups: black-browed albatross (Thalassarche melanophris) and giant petrel species (Macronectes spp.). Specifically, we test the effect of three different discharge treatments (zero, batch and continuous discarding) at two vessels. Bird abundance and contact rates were positively related, but zero discarding consistently reduced seabird numbers attending trawlers and eliminated contacts with warp cables and tori-lines. Batching significantly reduced bird abundance and contact rates at the vessel that stored all discards between batches. At the other vessel, however, intermittent release of hashed viscera diminished the mitigation effect. Our findings validate the generality of batch discarding as an effective mitigation measure in trawl fisheries where zero discarding is not possible, whilst highlighting the importance of complete waste storage.

Gear pitch rapid measurement by a point laser sensor

With the continuous improvement of the theory and method of gear measurement, the effectiveness of gear contact measurement is reduced, making it difficult to meet the need for 100% gear detection. To improve the measurement efficiency and make effective use of the full tooth surface data, a gear pitch rapid measurement method by point laser sensor is proposed. This method studies the principle of measuring the gear based on a laser point sensor, and the efficient model of collection and analysis of tooth surface data is established. Then the evaluation of the pitch deviation is completed, including the individual single pitch deviation, the single pitch deviation, the individual cumulative pitch deviation, and the total cumulative pitch deviation. Additionally, the pitch deviation of the multiple cross-sections is investigated, which may characterize the overall pitch deviation of the tooth surface. Compared to the gear measuring center P26, the experimental results show that the optical measurement of pitch deviation is feasible and efficient. Depending on the different measuring conditions, the offset status of the sensor can be selected to meet the different efficiency and accuracy requirements. The research and application potential of a point laser sensor in gear measurement is wide-ranging.

Simulation on coupling effects between surface wear and fatigue in spur gear

A surface wear prediction method is used to determine the wear rate of the tooth surface. This method employs the Archard’s wear model together with the gear contact mechanics model. An equivalent calculation model based on Hertzian contact theory and fracture mechanics is used to investigate crack initiation and crack propagation. The virtual crack extension (VCE) method is employed to analyze the propagation process from the initial crack to occurrences of tooth surface pitting. A life prediction method on the wear-fatigue coupling is developed. The crack propagation process and pit shapes are determined by the iterative analysis. The relationship between service life and the remaining distance from the crack tips to the tooth surface is determined. The damage mechanism of wear-fatigue coupling is explored. The results of the comparative analysis show that the wear of tooth surface affects the cracks propagation characteristics, reduces the service life and even can change the failure mode. The simulated pit shapes and crack propagation process are in good agreement with the results of other literature. The analysis method of wear-fatigue coupling damage can well simulate the damage process and predict service life in spur gear.

Crack nucleation and propagation modeling for lubricated spur gear contacts of rough surfaces

In this study, a rolling contact fatigue model for lubricated gear contacts of rough surfaces is proposed, considering both crack nucleation and propagation stages. A boundary element approach is implemented to describe surface roughness topography effect on near surface stress concentration, with surface tractions yielded from mixed EHL analysis. A fatigue criterion is employed to find crack nucleation position and life. Assuming mode II crack opening mechanism, stress intensity factor range is determined and used to arrive crack propagation life. Through comparisons to experiments, model capability is demonstrated. Simulation results show important roughness effect on crack propagation as well as crack nucleation.

Using variable modulus to modify a rack cutter and generate a gear pair

In this paper, two normal imaginary helical rack cutters were first established. One of these cutters is a skewed-rack cutter with an asymmetrical straight edge. The other is a rack cutter with an asymmetric parabolic profile. Second, the gear’s tooth surface of the asymmetric parabolic rack cutter is modified to be barrel-shaped based on a variable modulus. The tooth thickness of the gear is gradually reduced along the face width of the tooth from the middle of the tooth surface. Then the coordinate relationship between the gears’ blanks and the imaginary helical rack cutters was established. Through the differential geometry, crowned and uncrowned helical gear pairs were generated. Because of human factors, when the gear pair is installed, it is easy to cause the gear pair edge contact. It is necessary to add artificial assembly error settings through the tooth contact analysis to investigate the kinematic errors and contact conditions of the crowned and uncrowned helical gear pair. The mathematical models and analysis methods proposed for the crowned imaginary rack cutter using variable modulus should be useful for the design and production of double crowned helical gears with asymmetric parabolic teeth.

Методика расчета на прочность глобоидной червячной передачи

Worm gears are widely used in mechanical engineering. Recently, worm gears with a globoid worm attract a considerable interest. To improve the quality characteristics of globoid gears, their geometric dimensions and parameters, as well as the production technologies are being improved. It is also important to have a methodology for calculating the strength, which is, however, currently unavailable, and the state standards cover the issue of determining and calculating only the transmission geometry. In this regard, the development of the technique for calculating the contact and bending strength of a globoid worm gear appears relevant. The basic areas of the research are gear enhancement, production technology improvement, the gearing pattern study, working surfaces mathematical simulation, 3-D modeling, and the transmission calculation. The contact strength calculation is based on the Hertz’s formula taking into account the geometric features of globoid worm gears. The authors developed the calculation of the bending strength of the worm gear teeth based on the helical gear calculation method. The paper presents data on the influence of the mechanical properties of the materials of a worm and a worm gear wheel on the gear contact strength, gives the computed coefficients estimated values. The authors note that the dynamic load factor can increase significantly with the wear of the gear working surfaces. The research findings can be used to develop the design calculation technique, as well as to improve it to take into account the effect of transmission wear and working temperature on the operation duration.

Dynamic Simulation and Analysis of Engagement Process for Logarithmic Spiral Bevel Gear Based on Accurate 3D Model

Based on the accurate 3D model of logarithmic spiral bevel gear, the operation of spiral cone gear engagement is analyzed and simulated by ANSYS. Through the nonlinear static contact analysis of different positions, the stress change rule and the maximum contact stress is obtained. Compared with the theoretical contact stress strength rule, this paper also analyzes the dynamic operation situation of the gear pairs, obtains the dynamic contact situation rule at different engagement times and different rotating speeds, the influence of the rotating speed on the gear contact characteristics is compared too. The static, dynamic performance and change rules of the gear engagement is obtained, which lay a solid foundation for the further research, design and manufacture of spiral bevel gears.

State of Art of Gear Contact Fatigue Theories

State of Art of Gear Contact Fatigue Theories

Finite Element Analysis of Mg Alloy Based Gear Set Using ANSYS

Now magnesium alloy is the lightest metal materials of in engineering application, it has a wide application in automobile sector, aerospace, biomedical and other fields. Magnesium alloy gear is utilized in the present research, and a gear-pinon cad model is utilized by utilizing finite element software ANSYS, under loads. Here the model is designed in ANSYS SpaceClaim then imported to ANSYS commercial software and determine the contact stress of mating gears for other different materials and results comparing with Mg alloy gear. Gears a major component utilized in the field of engineering and technology, these fears have played a major role in transmit of puissance. Contact stress is generally the deciding factor for kenning the requisite dimensions of gears. Research on gear action has substantiated fact that adjacent to. In the gears contact stress is main parameter, the contact stress is dependent on involution of the model and material properties, as the material property transmutes the contact stress will withal change. The modal analysis and harmonic replication are required for analysis of gear systems. The aim of this project is to determine the contact stress and frequency replication of gear for sundry materials. The modal analysis is carried out token the mode shapes & natural frequency, and the harmonic analysis is withal done for different materials like Mg alloy, Cast iron and Al alloy.

Research on dynamic load spectrum of electric vehicle transmission system based on underdamping characteristic

Overall, the electric vehicle transmission system shows an underdamped characteristic. Under changeable road conditions and high-frequency response for the motor, the resulting dynamic load environment may cause multiple failure modes, such as contact fatigue failure and bending fatigue fracture, for the transmission component, which limits the electric vehicle transmission component lifespan and system reliability. To reflect the dynamic load characteristics of the electric vehicle transmission system using a permanent magnet synchronous motor as a power source and accurately calculate the dynamic load of the transmission system, a high-speed helical gear-rotor-bearing coupling mechanical model for the electric vehicle transmission system was built based on simulating actual operation working conditions of the electric vehicle and considering the external load excitation caused by the Electromagnetic torque of the permanent magnet synchronous motor and vehicle driving resistant change as well as internal excitation caused by gear time-varying meshing rigidness and meshing error. Through simulation calculation of the mechanical model, the dynamic meshing force of the gear pair and dynamic contact force of the support bearing was obtained. Based on the Hertz contact theory, the stress-time history was obtained for the key parts, the rain flow counting method was adopted for the statistics collection and analysis of the stress-time history, and the fatigue load spectrum for various key parts of the transmission system was obtained. The result lays a foundation for the fatigue life prediction and reliability analysis for the pure electric vehicle transmission system.

Influence of Different Modified Gears on the Vibration and Noise of Electric Vehicle Reducer

The tooth profile crowning modification was applied onto paired gears for reducing the noise of an electric vehicle reducer. The simulated gear contact spots are compared before and after modification, and are validated by a contact spot experiment. Based on the rigid-flexible coupling model of the gear transmission system, the time-varying meshing stiffness, time-varying meshing force, and the vibration and noise of the gear pairs with different modified gears obtained by simulating calculation are analyzed. The results showed that the selection of modified gear has a great influence on the modification effect. In the way of tooth profile crowning, it is not advisable to modify the pinion independently, as it may increase the frequency and degree of meshing impact between the helical gear pair, making the transmission become less smooth; while modifying the wheel and pinion at the same time can effectively reduce the time-varying meshing stiffness and force, and the vibration and noise. Also, the optimized gear modification scheme is verified by the noise test.

Duncan Dowson: Pioneer of elastohydrodynamic lubrication of gears

The paper briefly reviews Duncan Dowson's ground-breaking contribution to the theory of elastohydrodynamic lubrication in relation to the understanding of lubrication of gear tooth contacts. His early work with Higginson on numerical modelling of elastohydrodynamic lubrication finally explained how gears can operate successfully, and avoid wear, due to the generation of a stiff, protective oil film. The resulting minimum film thickness equation stands as a reliable reference formula for calculations in gear design standards. The paper includes examples of how elastohydrodynamic lubrication theory has been developed by the present authors and their co-workers, and applied to aid the design of engineering components such as worm gears, thrust rims and profile-modified helical gears. Also included is its extension to include the important effects of surface roughness at the asperity level (micro-elastohydrodynamic lubrication) and its relevance to the current, troublesome problem of micropitting.

Gear life and failure mode versus meshing stress in polyacetal/carbon black nanocomposite gears

The life and failure mode of polyoxymethylene (POM) and POM/carbon black (CB) spur gears were assessed under different torque levels. A new experimental approach was performed to obtain the transition torque of polymer based gears by employing the online temperature monitoring and step-loading. The gear life versus contact stress was experimentally investigated and a life prediction model was proposed. Dynamic mechanical thermal analysis (DMTA) assessment was employed to determine the viscoelastic behavior of gear materials. The POM/CB gears exhibited improved load capacity, heat performance and service life. The POM/CB gear material demonstrated higher storage modulus and lower hysteresis heating as compared to pure POM gear material. The addition of CB nanoparticles switched the failure mode from fracture to tooth thinning and tooth tip plastic deformation at lower levels of torque (6, 8 and 10 Nm). At higher torque levels (12 and 14 Nm), the POM/CB gears showed 52% and 65.2% increases in the service life, compared to the pure POM gears, and finally failed under thermal material flowing.

Analysis of Tooth Surface Contact Stress of Involute Spur Gear

Through the establishment of a pair of spur gear contact models, based on Hertz contact theory, the tooth surface contact stress is calculated; then the Ansys finite element analysis software is used to simulate and analyse the stress distribution. Through the analysis and comparison of the two results, it is proved that the contact stress calculated by Hertz theory is relatively small, which is close to the results of the finite element simulation analysis. Theoretical calculation can verify the accuracy of the finite element simulation analysis model, and the finite element simulation analysis provides an effective way to accurately calculate the contact stress of the tooth surface.

Analytical solution to contact characteristics for a variable hyperbolic circular-arc-tooth-trace cylindrical gear

Abstract. The variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear is a new type of gear. In order to research the contact characteristics of the VH-CATT cylindrical gear, tooth surface mathematical models of this kind of gear pair are derived based on the forming principle of the rotating double-edged cutting method with great cutter head in this regard. Then, according to the differential geometry theory and Hertz theory, the formula of the induced normal curvature and equation of the contact ellipse are derived based on the condition of continuous tangency of two meshing surfaces, which proves that the contact form of VH-CATT cylindrical gear is point contact. The present work establishes analytical solutions to research the effect of different parameters for the contact characteristic of the VH-CATT cylindrical gear by incorporating elastic deformation on the tooth surface, which have shown that the module, tooth number and cutter radius have a crucial effect on the induced normal curvature and contact ellipse of the VH-CATT cylindrical gear in the direction of tooth trace and tooth profile. Moreover, a theoretical analysis solution, a finite element analysis and the gear tooth contact pattern are carried out to verify the correctness of the computerized model and to investigate the contact type of the gear; it is verified that the contact form on the concave surface of the driving VH-CATT cylindrical gear rotates from dedendum at the heel to the addendum at toe and is an instantaneous oblique ellipse due to elastic deformation of the contact tooth profile, and the connecting line of the ellipse center is the contact trace path. It is indicated that the research results are beneficial for research on tooth break reduction, pitting, wear resistance and fatigue life improvement of the VH-CATT cylindrical gear. The results also have a certain reference value for development of the VH-CATT cylindrical gear.

An experimental and theoretical study of subharmonic resonances of a spur gear pair

This study focuses on a class of dynamic behavior observed in spur gear pairs as a parametrically excited system. Stiffness at the gear contact interface that couples the gear bodies is a periodically time-varying due the fluctuation of number of tooth pairs in contact. In presence of such stiffness fluctuation as part of the excitations, various published studies predicted subharmonic resonances near speeds that are integer multiples of the speed at which the primary resonance occurs, with little or no validation. This study presents an extensive experimental investigation to show such subharmonic resonances and various associated period-n motions (n≥2) under both transient and steady-state conditions. A test set-up and a pair of test gears developed for this purpose are described along with solutions to various measurement and data processing challenges. Two different models of the gear pair, a purely torsional discrete model and a deformable-body model, are employed, and their predictions are compared to the measured period-1 and period-n motions to assess their accuracy.

Deep nitriding—contact and bending strength of gears with increased nitriding hardening depth

The load carrying capacity of gears can be significantly increased by nitriding. However, the required nitriding hardening depth depends on the stress level and the gear size. In order to achive a high fatigue resistance and durability of nitrided gears an adequate nitriding hardening depth is necessary. In industrial practice, a nitriding hardening depth (NHD) of about 0.6 mm is currently regarded as the upper limit that can be reached within a reasonable time and cost. This also limits of the load carrying capacity of nitrided gears, in particular with increasing gear sizes. Therefore, case hardening is the main treatment used with increasing gear sizes, although nitriding provides some advantages over case hardening. However, with an increased nitriding hardening depth, a significant increase in the load carrying capacity of nitrided gears for medium and larger gear sizes could be expected, which will be discussed in this publication. In order to evaluate the expected potential of the load carrying capacity of nitrided gears with an increased nitriding hardening depth of NHD ≈ 0.8 to 1.0 mm (deep nitriding heat treatment) made out of the materials 31CrMoV9 (1.8519), 30CrNiMo8 (1.6580) and 32CDV13 (alloy for aerospace applications according to AIR 9160), experimental investigations were carried out, which will be discussed in this publication. Both, the tooth root bending strength and the flank load carrying capacity were investigated.

Tribofilm Formation of Simulated Gear Contact Along the Line of Action

In this paper, an experimental simulation method was used for evaluating the tribofilm formation in rolling/sliding contact at different points in the line of action. A ball-on-disc test method was employed by which the pressure and slide to roll ratio of gear contact could be simulated. In order to reach a general conclusion, four different oils and two surface roughness were involved in the experiments. The tribofilm evolution was captured using spacer layer interferometry method, and the correlation of tribofilm with the location at the line of action was studied. Results showed that there is a threshold pressure for the tribofilm formation around which the tribofilm growth rate is maximum. Above this threshold pressure, the tribofilm formation is not stable, and the wear is dominant. Below this threshold pressure, the tribofilm growth rate rises by increasing the pressure and the gear contact is safely protected by a stable tribofilm.Graphic

Basic Theory and Design Method of Variable Shaft Angle Line Gear Mechanism

In this paper, a novel line gear mechanism is proposed; it is called the variable shaft angle line gear mechanism (VSALGM). VSALGM has two rotational degrees of freedom, one is the rotation of the two gears with a constant transmission ratio, and the other is the relative swing of the two gears shafts. First, a novel contact model of VSALGM composed of one driven contact curve and one driving line teeth working surface (DLTWS) was proposed. With the concept, the basic design equations for VSALGM were derived on the basis of the space curve meshing theory of line gear. Moreover, the design criterion of pressure angle for VSALGM was analysed and proposed on the basis of the contact model. A basic design method for VSALGM was thus developed. A design example was given, and prototypes were manufactured using three-dimensional (3D) printing. Kinematic experiments and gear contact spot testing were carried out on a self-made kinematic test rig by the prototypes. The results show that the VSALGM designed in this paper can achieve a continuous, smooth and stable meshing transmission while the shaft angle is continuously changed within its setting range.