Tooth Bending Research Articles

Spur gear tooth root stress analysis by a 3D flexible multibody approach and a full-FE contact-based formulation

This paper proposes an original method to determine the gear tooth root stresses from a 3D finite element (FE) flexible multibody approach and a full-FE contact-based formulation. The contact problem is dealt with an augmented Lagrangian formulation whereas the analysis is performed by a preconditioned gradient solver (PCG). Tooth flank modifications are directly introduced within the 3D model. This one is thus able to take into account straightforwardly tooth bending and Hertzian-like deformations as well as the micro-geometry effect. Simulations are performed for several mesh periods, without making any assumptions about load distribution, tooth and gear blank flexibilities, and possible premature or delayed contacts between tooth pairs in quasi-static conditions. A precise distribution of tooth root stresses associated with instantaneous contacts conditions is then computed. For this study, a single stage spur gear with micro-geometry modifications corresponding to an arc-shaped profile crowning is modeled. Several output torques are considered. The obtained results are compared to those obtained using a 2D FE ISO-based model, where external forces are applied along the theoretical line of action.

Experimental and numerical studies on the propagation paths of gear root cracks

Gear bending fatigue failure has a significant impact on the operational performance of advanced machinery, such as electric vehicles and wind turbines, potentially leading to failures and catastrophic consequences for transmission systems. Several methods are currently used to predict gear crack propagation; however, a comprehensive comparison of their accuracy and efficiency in predicting crack paths is lacking. In this study, the propagation path of root cracks in commonly used automotive gears was investigated using finite element (FE) analysis and experimental testing. Three mixed crack path prediction criteria were integrated to predict the gear root crack propagation using the commercial software ABAQUS by user-defined Python script. The impacts of gear crack parameters, including the gear initial crack length, on gear root crack propagation behaviour were analysed. The simulations were verified by the gear bending fatigue test using a single tooth bending test device. The results indicate that the simulation outcomes align with the experimental tests, demonstrating that all three criteria are effective in predicting gear root crack propagation behaviours.

Assessment of the Uniform Wear Bending Strength of Large Modulus Rack and Pinion Pair: Theoretical vs. Experimental Results

Due to long-term operation under low-speed and heavy-load conditions, large module gears and racks are inevitably subject to tooth surface wear. To investigate the changes in gear tooth bending strength, the Three Gorges ship lift was taken as the research object and a simulation test bench was established. An analytical method, a finite element method, and an experimental method were utilized to analyze the bending stress of gears under normal and various uniform wear conditions. The obtained results revealed that with the increase in wear degree and load, the bending stress of single-tooth meshing was significantly higher than that of double-tooth meshing, and the single-tooth meshing time also increased, which indicates that gear wear accelerated the process of performance degradation. Furthermore, the relative errors obtained by the three calculation methods were all at a low level. This investigation aims to provide a solid theoretical and experimental basis for the dynamic analysis of large module gear and rack transmission.

Dynamic behaviours of rack vehicle-track system considering rack flexibility under gear-rack mesh impact

ABSTRACT There are complex and large gradients for the rack vehicle running on the large mountain slope line. Under such a circumstance, the driving gear-rack interactions will be more intensified and could induce the larger tooth bending stress of the rack. At present, the dynamics modelling of the rack in the existing literature is generally treated as a rigid body or an infinite beam model, however, which is inconsistent with reality. To accurately simulate the vibration characteristics and bending stress of the rack structure, it is necessary to establish a detailed dynamic model considering the flexibility of the rack structure. In this study, the free beam and rod models are, respectively, used to describe the vertical and longitudinal flexibilities of the rack with the finite length. Then, the proposed rack dynamics model is introduced into a rack vehicle-track coupled system, and the developed dynamics model is validated by comparing the results from the simulation with the tested data. Finally, the vibration and bending stress features of the driving gear-rack engagement are analysed under different mounting deviations. The simulated results can give theoretical references for the design and structure optimization of the rack track structure.

Reverse engineering of geometric design parameters using shape information of non‐standard spur gear

AbstractIn this study, we conducted research on a method to reverse engineer geometric design parameters from the shape information of gears. The module and normal pressure angle were tracked using the bisection method, and the profile shift coefficient was extracted from the relationship between the working pitch circle diameter, center distance modification coefficient, and working pressure angle. It was confirmed that there are limitations to reverse engineering the shape using only a coordinate measuring machine or 3D scanner because various geometric information is additionally required to trace back the design requirements for gear strength. Finally, the gear tooth bending strength was calculated using finite element analysis and theoretical formula, and through this, the required level of gear strength design was inferred, and the verification of the gear reverse engineering method presented in this study was attempted.

Analysis of the Effect of Shaft Misalignment on Tooth Bending Strength and Contact Stress of Helical Gear

Analysis of the Effect of Shaft Misalignment on Tooth Bending Strength and Contact Stress of Helical Gear

Fully ceramic versus steel gears: Potential, feasibility and challenges

The most common gear strength calculations performed in accordance with ISO/TC 60/SC 2 include surface durability and root bending strength. Typical geared power transmissions are characterized by high Hertzian contact stresses (surface durability) on the flanks – frequently in the order of 103 MPa – versus almost half an order magnitude lower first principal stresses on the tooth root (tooth bending strength). Therefore, the use of high strength special steel alloys is almost mandatory, especially in high-end applications, mainly to withstand the high contact stress values. Ceramic materials are typically characterized by high compressive strength versus very low flexural strength that at first glance makes them inefficient for gear transmissions since they are unlikely to withstand the tensile root stresses. Nevertheless, ceramic materials possess a number of advantages that makes them potential candidates for geared transmissions, such as their exceptional thermal properties, their low density (weight), their excellent wear characteristics and limited lubrication demands. The present work investigates the main challenges of using high-end ceramic gears and attempts to provide an insight on defining the design envelope of such gears to counter the main disadvantages. The increase of the normal pressure angle beyond the 25° limit set by ISO 6336 is primarily investigated, since in minimizes the tensile tooth root stresses, while also increasing the curvature of the contact surfaces without greatly increasing Hertzian stresses. Comparative assessment of the performance of fully ceramic gear designs versus their conventional steel counterparts is performed through quasi-static FEA simulations to set the basic design requirements for such gears and to promote further investigation of the feasibility of their usage in high power density applications.

Badanie czynników warunkujących stopień zużycia i zniszczenia zębów w mechanizmach przekładni zębatych

Transmission gears are very widely used in the modern construction of the machine. Even though electrical transmissions are used, mainly mechanical transmissions are widely used in the machine building industry as they are independent and better than other transmissions. Distributing power between the transmission mechanisms and working units of various machines, by changing the angle of momentum by adjusting the speed of the parts, it is possible to change the type of movement, turn the mechanism on and off, and change the direction of the transmission mechanisms. One of the most widespread types of transmission technology is gear transmission. Tens of thousands of kilowatt-hours of gears can be transmitted. The advantages of gear transmission in comparison with others are their ability to maintain their reliability and long-term functioning of the teeth, high value of the working coefficient (0.90–0.99), simple construction, lack of special service, simplicity of the transmission number and compactness of dimensions. The missing aspects of these transmissions are high precision in their preparation and installation, and low noise level. The main criterion for the working ability of the closed gear transmissions is the contact endurance of the active surface of the tooth. For this reason, the main dimensions of the transmission are determined by the contact tension and by teeth bending.

Effect of Initial Crack Position on Crack Propagation Behaviors of Heavy-Duty Transmission Gear.

The tooth bending fatigue fracture is caused by the alternating loads for the heavy-duty transmission gears. The crack initiation and propagation are the two major parts in the failure process. The crack propagation behavior is mainly affected by initial crack position except for the load and material properties. In this paper, the crack propagation model of a gear is established under the considering of crack initiation location by using extended finite element method (XFEM). The model accuracy is verified by testing results of strain and fractography by conducting the single-tooth bending fatigue experiment. The influence of crack initiation locations on subsequent crack propagation behavior is analyzed. The crack length in the tooth width direction and depth direction is faster when the initial crack is located in the middle of root surface. The crack growth rate is lower for the initial crack located in the surface close to the end surface of the gear.

Research on transformation method of bending fatigue test for single tooth bending fatigue and running gear based on minimum order statistics

Research on transformation method of bending fatigue test for single tooth bending fatigue and running gear based on minimum order statistics

Glass Fiber Reinforced Acrylonitrile Butadiene Styrene Composite Gears by FDM 3D Printing

Abstract3D printing of gears via fused deposition modeling (FDM) has been recently introduced as a low‐cost efficient manufacturing method. Different materials have been 3D printed and Acrylonitrile Butadiene Styrene (ABS) with excellent mechanical properties has been found to be promising. However, 3D printed ABS gears possess a high level of abrasion rate. This paper introduces a new class of ABS‐based gears reinforced by different amounts of milled E‐glass fibers and 3D printed by FDM with acceptable thermo‐mechanical properties and performance. A set of thermo‐mechanical tests is carried out to provide an insight into the influence of adding glass fibers on the glass transition temperature (Tg), hardness and teeth bending strength, teeth failure force, weight lost, abrasion resistance, mechanical wear, and performance of composite gears. The mechanical behaviors of driving and driven gears are examined in high and room temperatures with or without lubrication. Microstructure and gear profile analysis of 3D printed layers, worn surfaces, and fracture locations are also conducted by SEM images and profile projector. The newly developed glass fiber reinforced ABS gears reveal a high level of thermo‐mechanical performance in terms of hardness, mechanical strength, bending force, abrasion and wear resistance compared to pure 3D printed ABS gears.

Investigating teeth root stresses of various spur gears using stress function and FEM

AbstractThe gear is the most efficient and reliable portion of the transmission system. In machine tools, gears are utilized to handle heavy loads. These gears are used indefinitely if the prerequisites are met. Gear tooth bending stress for numerous spur gears has been examined in this research. The influence of changing the pressure angles on the spur gear tooth root stress has been investigated. The purpose of this study is to look for a new way of finding the stresses generated in the roots of the gear teeth as well as the effect of changing pressure angles on these stresses. Solidworks 2021 uses parametric formulation to model gears, analyzed for deformation and maximum bending stress in ANSYS. The airy stress function is used to conduct the nominal root tooth stress. The enhancement percentages of modified cases are 5.92%, 1.70%, 10.70%, 17.22%, 10.86%, 24.32%, 20.91%, and 26.15% for the cases 2, 3, 4, 5, 6, 7, 8, and 9, respectively according to the stress function findings.

Binder jetting in gears

Due to near netshape production, powder metallurgically manufactured (PM) gears have a high potential to increase cost and resource efficiency. Compared to conventionally machined gears, the advantages of PM gears are the different local density distribution in the component and the potential integration of secondary design elements. These advantages are accompanied by the reduction of weight and the possibility of optimizing the NVH-behavior of a gear. PM gears may be manufactured by both, die pressing and additive manufacturing (AM). The powder bed-based additive manufacturing processes for metals can be classified into binder-based (e.g. Binder Jetting, BJT) and beam-based thermal processes (e.g. Laser Powder Bed Fusion, LPBF). Due to the specific process technology, the manufacturing of PM gears by die pressing is only economical for large batch sizes in series production. For small batches, AM offers an approach to manufacture gears that meet the requirements in terms of quality, strength, acoustics and economic efficiency of the manufacturing process.This report describes the potential of BJT gears made of stainless steel 17-4PH (X5CrN-CuNb16-4) with a relative density of ρ0,rel ≈ 99% regarding the tooth bending strength. The reliability of the process and thus the tooth bending strength can be increased further by a specific adjustment of process parameters. Subsequently, the gears are tested with regard to the tooth bending strength on the pulsator test rig. The results are summarized in a SN-curve.

MATHEMATICAL EXPRESSIONS FOR TEMPERATURE IN THE CONTACT ZONE OF TEETH OF THE GEAR MECHANISMS

Transmission gears are very widely used in modern machine building. Despite that electrical transmissions used in machine building industry, mainly mechanical transmissions are widely used in the industry. Because mechanical transmissions are independent and better than other transmisions. Distributing power between the transmission mechanisms and working units of various machines, changing the angle of momentum, by adjusting the speed of the parts, it is possible to change the type of movement, turn on and off the mechanism, change the direction of the transmission mechanisms. One of the most widespread types of transmission technology is the gear transmission. Tens of thousands of kilowatt-hours of gears can be transmitted. Advantages of gear transmission in comparison with others is their ability to maintain their reliability and long term functioning of the teeth, big value of the working coefficient (0,9 ÷ 0,99), simple construction, lack of special service, simplicity of the transmission number and compactness of dimensions. The missing aspects of these transmissions are high precision in their preparation and installation, and low noise level. The main criterion for the working ability of the closed gear transmissions is the contact endurance of the active surface of the tooth. For this reason, the main dimensions of the transmission are determined by the contact tension and by teeth bending. Keywords: gear wheel, tension, endurance, bending

Fatigue and Wear Performance of Autoclave-Processed and Vacuum-Infused Carbon Fibre Reinforced Polymer Gears

This study focuses on investigating the fatigue and wear behaviour of carbon fibre reinforced polymer (CFRP) gears, which have shown promising potential as lightweight and high-performance alternatives to conventional gears. The gears were fabricated via an autoclave process using an 8-layer composite made of T300 plain weave carbon fabric and ET445 resin and were tested in pair with a 42CrMo4 steel pinion and under nominal tooth bending stress ranging from 60 to 150 MPa. In-situ temperature monitoring was performed, using an infrared camera, and wear rates were regularly assessed. The result of the wear test indicates adhesive wear and three-body abrasion wear mechanisms between the CFRP gears and the steel counterpart. A finite element analysis was performed to examine the in-mesh contact and root stress behaviour of both new and worn gears at various loads and a specified running time. The results point to a substantial divergence from ideal meshing and stress conditions as the wear level is increased. The fatigue results indicated that the CFRP gears exhibited superior performance compared to conventional plastic and composite short-fibrous polymer gears. The described composite gear material was additionally compared with two other composite configurations, including an autoclave-cured T700S plain weave prepreg with DT120 toughened resin and a vacuum-impregnated T300 spread plain weave carbon fabric with LG 900 UV resin. The study found that the use of the T700S-DT120 resulted in additional improvements.

Optimising the Geometric Parameters of a Gear in a Tractor Transmission Under Constraints Using Kisssoft

Abstract We optimise the speed gears in a tractor transmission with KISSsoft software under three constraints: input power torque, transmission system volume and the gear ratio for each speed. This study aimed to optimise the module, face width, gear quality, centre distance, number of teeth, helix angle, addendum modification coefficient and pressure angle for each speed while considering the above constraints based on an optimisation chart. Tooth bending stress, tooth contact stress, contact ratio and specific sliding were considered during optimisation. Additionally, the effects of changes in a module on the gear profiles, overlap ratio, number of teeth and weight of the gear pair were examined. Strength calculations of gear pairs that were optimised and defined for all geometric parameters with KISSsoft were calculated with the mathematical model described in ISO 6336, and results were then compared. Finally, backlash was minimised for all gear pairs as defined with geometric parameters, and all dimensions and tolerances were determined for gear inspection after manufacturing. A concept design was also presented. We conclude that both the KISSsoft results and mathematical model results are within the range of the target value.

Analogy test rig for the generation of tooth flank fractures at large gears (WZL-double pulsator)—commissioning and first test results

As a result of the enhanced of load-carrying capacity with regard to pitting and tooth root breakage, generation of tooth flank fractures became more frequent. This type of damage differs from existing fatigue damages on the tooth flank in that crack initiation takes place below the case hardened surface layer and the tooth breaks in the area of the active tooth flank. An isolated investigation of tooth flank fractures is currently not possible because there is no analogy test rig available that can reproduce both, the compressive stress due to Hertzian contact flattening as well as the tensile stress due to tooth bending. For this reason, a test rig concept is being developed, manufactured and put into operation in the DFG research project “Analogy test rig for tooth flank fractures”, which allows the generation of tooth flank fractures in absence of other damage types. This report deals with the commissioning of the WZL-Double Pulsator as well as first test results. The FE model of the analogy test rig is validated by measuring tooth root strains with strain gauges and comparing them with the calculated strains. Finally, the commissioning is carried out and first tests are performed.

Comparison of Tooth Bending Strength of Speed-increasing and Speed-reducing Involute Spur Gears

Comparison of Tooth Bending Strength of Speed-increasing and Speed-reducing Involute Spur Gears

Investigation of the heavy duty truck gear drive failure

For heavy vehicle systems, within the power transmission chain from the driving machine to the working components (wheels), gears have a large share of application in the form of gearboxes, differentials and speed reducers. Their purpose is to achieve the highest possible output torque at the working components. In one heavy-duty truck, the gearbox lost its working capacity due to the failure of its vital parts: a tapered roller bearing and a helical gear. The analysis presented in this paper, conducted on the basis of experimental and analytical methods, showed that, due to inadequate installation of the bearings’ outer ring in the gearbox housing in one intermediate shaft support, the roller bearing performed its elementary function in very unfavorable working conditions of mechanical and thermal nature. Due to the damage accumulation, the roller bearing gradually lost its working capacity. As a result, the intensity of the working conditions of the entire gearbox increased. At the moment when they reached the critical value from the aspect of the gear teeth bending strength, volumetric destruction occurred, i.e fracture of the helical gear tooth, and thus the cessation of gearbox power transmission.

Modal analysis of spur gears for varied teeth root cracks characteristics: finite element analysis (FEA) simulations

Gear failure is considered the main alarming and undesirable event in gearboxes. Usually, cracks happen by fatigue caused due to cyclic loading. Fatigue stress is focused on the teeth root because of the small tooth fillet radius. This causes progressive damage to gear teeth which causes teeth failure, and hence, a damaged gear. This work shows a numerical framework to identify and quantify cracks' existence at the teeth root of spur gears. The problem is numerically analysed through finite element-based simulation with ANSYS by conducting a modal analysis. There are nine cases of gears with different cracks on their tooth; these cracks are varied by their number (single or multiple), Crack Length Percentage (CLP %), and location. The FEA is used to simulate all nine cases to predict the bending natural frequency of teeth and to investigate the effects of the variation of the crack by looking at the natural frequency of the teeth bending as well as the deformation level. Results revealed that the teeth bending natural frequency decreases as the CLP% increases. In addition, the gear stiffness is calculated based on the natural frequency and gear’s mass and it is indicated that the stiffness decreases as the CLP% increases, while the deformation level increase with CLP%.