Tooth Load Research Articles

Performance evaluation of 3D-printed ABS and carbon fiber-reinforced ABS polymeric spur gears

Acrylonitrile butadiene styrene (ABS) polymer and carbon fiber reinforced acrylonitrile butadiene styrene (CF/ABS) spur gears were 3D-printed using fusion deposition modeling (FDM) with different fillet radii of 0.25, 0.50, and 0.75 mm. The performance of the fabricated gears was studied with the effect of fillet radius on varying load and speed conditions. The thermal properties of the gears were also investigated. The results indicated that 3D-printed CF/ABS spur gear exhibited better performance than the pure ABS. The 3D-printed CF/ABS gear with fillet radius of 0.25 mm recorded the highest wear and thermal stresses. However, the optimum performance was exhibited by the gear sample with highest fillet radius of 0.75 mm. Repeated gear tooth loading during service caused an increase in gear temperature due to the hysteresis and friction. Using optical microscopy, the tooth structures of both 3D-printed ABS and CF/ABS spur gears were analyzed before and after loading conditions to establish their failure mechanism. Evidently, various applications of the FDM 3D-printed spur gears depend on their different performances under loads and operating speeds. The methods and findings of this work can be regarded as helpful for future related work related to cellulosic reinforcing particles in a polymer matrix.

Study on gear contact stiffness and backlash of harmonic drive based on fractal theory

Contact stiffness and backlash in the harmonic drive significantly impact a robot's positioning accuracy and vibration characteristics. The height of the harmonic drive tooth pair is typically less than 1 mm, making the measurement and modeling of backlash and contact stiffness inherently complex. This paper proposes a contact stiffness and backlash model by establishing a correlation between fractal parameters and tooth contact load. To obtain the fractal roughness parameters of the real machined tooth surface, a combination of a noncontact optical profiler and the RMS method is employed. Subsequently, the study explores the influence of rough tooth surface and contact force fractal parameters on contact stiffness and gear backlash. The results demonstrate the substantial impact of surface topography parameters and contact force on contact stiffness and backlash. Specifically, an increase in the fractal dimension correlates with a reduction in gear backlash and contact stiffness. Conversely, the fractal roughness parameter exhibits the opposite effect. Notably, an increase in contact force enhances contact stiffness.

Efficient semi-analytic method for single tooth contact analysis of loaded spiral bevel gears

Accurately and fast calculation of single tooth load contact state of a gear pair is the basis for accurate calculation of multi-tooth load contact analysis. Therefore, this study proposed a semi-analytical quick single tooth load tooth contact analysis (Q-SLTCA) method. First, the ease-off tooth contact analysis (ease-off TCA) method was established, and a numerically stable initial contact stress distribution and contact ellipse analytical model was derived. Then, considering the influence of edge contact, the real-time division method of gear tooth slice was derived. Based on this, the equivalent principle of contact elliptical node and the load correction strategy were innovatively proposed. Then, the calculation method of the meshing characteristics of the tooth slice was established by coupling the boundary element method (BEM) with the equivalent cylindrical Hertz contact theory. The bending deformation, tooth root stress distribution, contact stress, contact deformation and meshing stiffness of the tooth slice were analyzed and calculated, and the instantaneous meshing stiffness of the single tooth was determined by combining the parallel method of the gear tooth stiffness. Finally, a single-tooth finite element method (FEM) meshing model was created for comparison with the method in this study, which verified the calculation accuracy and efficiency of the proposed method. This method can be easily developed into a quick multi-tooth load contact analysis algorithm, which can provide a new method for gear tooth crack and failure analysis.

Vibration optimization of spur gear based on GSA-SA algorithm.

To determine the optimal design parameters of spur gear under a specific condition, based on the basic theories of gear dynamics theory, gear meshing principle, tooth contact analysis and load tooth contact analysis, a six-degree-of-freedom vibration analysis model of spur gear pair is established, and a gravitational search-simulated annealing hybrid algorithm (GSA-SA) is used to optimize the gear addendum modification coefficient and profile modification parameters. The vibration response of the spur gear pair is evaluated through the optimization objective function established by the combination of the G1 method and variation coefficient method. The study shows that the optimized design parameters effectively reduce the level of the vibration, which proves the effectiveness of the optimization method, and the simultaneous optimization of the addendum modification coefficient and profile modification parameters of the gear has a better result than only optimizing the addendum modification coefficient or profile modification parameters. This method can be used for gear transmission system vibration optimization design in the automotive industry and shipbuilding.

Meshing characteristics and dynamic characteristics of planetary transmission system with new tooth-type flexible ring gear

As one of the important components of the planetary transmission system, dynamic meshing characteristics of ring gear directly affect the performance of planetary transmission system load sharing and dynamic load factor. With the help of the flexibility of ring gear, the planetary gear system with flexible ring gear (FRG) can compensate for the uneven transmission torque of each branch caused by the machining error and installation error and improve the system's load sharing and dynamic load performance. An L-shaped FRG was developed in Italy to improve the traditional ring gear and was used in the latest AW101 helicopter with good feedback. By increasing the ring flexibility, the load distribution between planetary gears is more uniform, and the load-sharing performance of the system is significantly improved. Tooth wear and fracture caused by uneven load distribution can be improved. However, the structure has problems such as unbalanced loading, strength weakening, and stress concentration. In this article, the FRG's meshing and structural characteristics are analyzed in detail by constructing the parametric finite element model. Differences, advantages, and disadvantages of FRG and traditional ring gear are compared. A new type of tooth-type FRG is proposed. It has excellent structural flexibility meshing characteristics of tooth surface and avoids generating stress concentration. It improves the planetary gear train's load-sharing performance and overcomes tooth surface unbalanced loading and large amplitude fluctuation of loaded transmission errors.

Potential and Design Parameters of Polyvinylidene Fluoride in Gear Applications.

(1) Background: With the ever-increasing number of polymer materials and limited data on polymer gear calculations, designers are often required to perform extensive experimental testing in order to establish reliable operational data for specific gear applications. This research investigates the potential of a Polyvinyldene fluoride (PVDF) polymer material in gear applications, considering various loading conditions and different types of gear transmission configurations, including both self-mated mesh and steel/PVDF mesh. (2) Methods: PVDF gear samples were tested on a specially designed test rig that enables active torque control and temperature monitoring in order to obtain the necessary design parameters and failure modes. Each test for certain load conditions was repeated five times, and to fully investigate the potential of PVDF gear samples, comparative testing was performed for Polyoxymethylene (POM) gear. (3) Results: Tribological compatibility, tooth load capacity, and lifespan assessment, along with the types of failure, which, for some configurations, include several types of failures, such as wear and melting, were determined. Temperature monitoring data were used to estimate the coefficient of friction at the tooth contact of analyzed gear pairs, while optical methods were used to determine a wear coefficient. (4) Conclusions: The tribological compatibility of polymer gear pairs needs to be established in order to design a gear pair for a specific application. PVDF gear samples mated with steel gear showed similar lifespan properties compared to POM samples. Temperature monitoring and optical methods serve as a basis for the determination of the design parameters. PVDF is an appropriate material to use in gear applications, considering its comparable properties with POM. The particular significance of this research is reflected in the establishment of the design parameters of PVDF gear, as well as in the analysis of the potential of the PVDF material in gear applications, which gives exceptional significance to the current knowledge on polymer gears, considering that the PVDF material has not previously been analyzed in gear applications.

Investigation on the effect of strain rate on standard involute and asymmetric polymer gears using the newly design fixture for single tooth testing method

Effect of strain rate on the single tooth strength of nylon-based gear has been investigated using a newly designed testing fixture. An adjustable single tooth testing fixture has been designed and developed for the purposed of single tooth loading test which is able to accommodate the gear with varying thickness. Injection molded nylon-6 and SLS (selective laser sintering) printed glass filled nylon-6 standard involute and asymmetric gear tooth have been investigated for their single tooth loading test at three different strain rates of 0.0003, 0.003, and 0.01 per sec. Single tooth strength for both injection and printed gear is found to increase with the increase in strain rate. Injection molded single gear tooth undergone bending failure whereas SLS printed gear tooth shows fracture failure. Resistance to single tooth deflection at higher strain rate has drastically increased for injection molded standard involute (IS) gear tooth by 23% whereas, asymmetric gear tooth IA20 followed by IA34 shows slight increment. SLS printed asymmetric gear tooth PAG20/34 exhibits maximum single tooth strength among all three types of printed gears at all the three strain rates. At higher strain rate of 0.01 per sec, single tooth strength dominates by tooth profile geometry whereas, at lower strain rate of 0.0003 per sec, it dominates by tooth profile geometry and microstructure.

In-fiber Bragg sensor measurements assess fluid effects on strain in the periodontal space of an ex-vivo swine incisor complex under mechanical loading

The purpose of this study is to determine whether in-fiber Bragg grating (FBG) sensors detect changes within the periodontal ligament (PDL) of ex-vivo swine tooth-PDL-bone complex (TPBC) when manipulating fluid content. Recording strain will allow for a better understanding of the biomechanics of viscoelastic load transfer from the tooth to the PDL during chewing and/or orthodontic tooth movement, as well as replication of these dynamics in regenerated PDL tissues. FBG sensors placed within the PDL of swine incisor teeth were used to measure strain resulting from an intrusive load. Specimens were mounted in a custom platform within an MTS machine and a compressive load was applied at 0.3 mm/s to a depth of 0.5 mm and held for 10 s. Median peak strain and load and median absolute deviation (MAD) were compared: dry vs. saline (n = 19) with bias-corrected bootstrap 95% CI. Dry vs. saline conditions did not statistically differ (median peaks of 5με, 103–105 N) and recorded strains showed high repeatability (MAD of 0.82με, 0.72με, respectively). FBG sensors did not detect the fluid changes in this study, suggesting that the deformation of tissues in the PDL space collectively determine FBG strain in response to tooth loading. The repeatability of measurements demonstrates the potential for FBG sensors to assess the strain in the PDL space of an in vivo swine model.

A double-layer iterative analytical model for mesh stiffness and load distribution of early-stage cracked gear based on the slicing method

To reveal the coupling relationship between the time-varying mesh stiffness (TVMS) and the load distribution along the tooth width direction (TWD) of gears with early-stage crack (ESC), a double-layer iterative analytical model for the TVMS and load distributions of gears is proposed considering the effects of the non-uniformly distributed load (NDL) along TWD caused by the ESC. In the proposed model, an analytical model of tooth torsional deformation and a parallel slice stiffness model of the tooth pair with ESC are separately developed based on the slicing method. On this basis, a double-layer iterative calculation method for the TVMS and load distributions is proposed, in which the coupling relationships between the slice stiffness and load distribution along TWD as well as the TVMS and load distribution between the meshing tooth pairs are respectively presented with the inner- and outer- layer iterations. Finite element (FE) models are established to verify the proposed double-layer iterative model. The effects of crack parameters and applied torque on the tooth torsional deformation, TVMS, and load distributions of the gear with ESC are finally investigated based on the proposed model. The results show that the proposed model can realize the accurate and fast decoupling calculation of the TVMS and load distributions of gears with ESC. This study can provide a basis for the establishment of the refined ESC fault diagnosis method and the rapid evaluation of the load distributions of gears with asymmetric errors or faults along TWD.

Dynamic modeling and analysis of planetary gear train system considering structural flexibility and dynamic multi-teeth mesh process

The structural flexibility of planetary gear trains (PGTs) is a significant factor that affects tooth loads and system vibrations, especially in heavy-duty wind turbine gearboxes. Therefore, it is crucial to investigate the influence mechanisms of complex structural deformations on tooth loads and system vibrations. In this work, a dynamic modeling approach is proposed for the complex carrier and ring gear based on the condensation theory of finite elements. The dynamic model of the sun shaft is modeled using the Euler-Bernoulli beam element, and the planetary gear set is modeled using the lumped parameter method. Then, the dynamic multi-teeth mesh process is developed using variable-speed characterization variables and virtual vibration line displacements. Lastly, the rigid-flexible coupling dynamic model of PGT is established and validated. The results indicate that treating components as rigid solids may lead to an underestimation of the impact of input torque variation on system vibrations. When the input torque remains stable, the tooth stiffness can be used to assess the overall change trend of tooth loads. However, when the input torque varies significantly, it is necessary to take into account the comprehensive structural deformations.

Transmission performance evaluation of non-circular spur bevel gear based on a novel isochronal measurement method

This paper aims to study the transmission performance evaluation of non-circular spur bevel gear (NCSB-gear) based on a novel isochronal measurement method. Firstly, the mathematical model of NCSB-gear is established. Then a novel isochronal measurement method is proposed, and the actual tooth surfaces are reconstructed by non-uniform rational B-spline interpolation. The advantages of the proposed method are discussed based on the geometric characteristics of tooth surface and measurement fitting error. A pair of forged NCSB-gears is measured through a coordinate measurement machine and the maximum tooth surface fitting error by the proposed method reduces 2μm compared with the traditional method. Moreover, deviation tooth contact analysis (DTCA) and load tooth contact analysis (LTCA) are conducted to evaluate the transmission performance. Finally, the transmission performance of measured NCSB-gear is obtained by a gear rolling tester. By comparing the TCA calculation of different measurement methods, it is found that the relative error of the maximum transmission error based on the isochronal measurement method reduces 4.719% compared with the traditional measurement method, thus verifying the validity of the proposed measurement method.

Use of sun gear orbits to obtain the load sharing in planetary transmissions and its impact in the tooth load

The present work assesses the possibility of using the orbits described by the sun gear in order to analyse the load sharing ratio in planetary gear transmissions. Furthermore, the current work is extended to observe the impact of the floatability and different tangential pinhole position errors in the load borne in a single contact between a pair of teeth in comparison to the load per planet. Therefore, it highlights the inaccuracy of the load sharing ratio (LSR) as an indicator of the overload in one tooth of the planet. Moreover, the use of the orbits represented with respect to a rotating reference provides helpful information to determine the overloads and underloads in the planets due to the existence of a tangential error in sequentially phased transmissions. Therefore, this proposal provides a simpler solution to the measurement of the LSR in planetary transmissions with different numbers of planets than the use of strain gauges.

Fatigue Reliability Prediction Method of Large Aviation Planetary System Based on Hierarchical Finite Element

The reliability of planetary equipment determines the economic affordability and service safety, to a large extent, for a helicopter transmission system. However, with the continuous improvement of the progressiveness and large-scale degree of new aviation planetary equipment, the contradiction between reliability design indexes and R&D economy is also gradually highlighted. This paper takes the large aviation planetary system as a research object, aims to accurately evaluate the system reliability level formed in design processes, and deeply excavates the inherent characteristics of the planetary system in functional realization and builds a system fatigue reliability evaluation model accordingly. An advanced hierarchical finite element technology is used to calculate dangerous tooth load histories under the influence of system global elastic behavior, and the tooth probability fatigue strength is obtained through the gear low-cycle fatigue test and life distribution transformation method, so as to provide economic load and strength input variables, respectively, for the reliability model. This prediction method can provide targeted structural optimization guidance in the development and design of the large aviation planetary system and significantly reduce the cost of reliability index realization for this kind of large-scale, high-end equipment in design iteration processes.

INFLUENCE OF LUBRICANT ON THE TECHNICAL LEVEL OF HIGH-SPEED GEARBOXES WITH ASYMMETRICAL PROFILE

The issues of efficiency improvement in hydrodynamic (liquid) or limit (semi-liquid) modes of friction of gears with an asymmetric profile and the effect of the liquid on tooth damage, power loss and temperature in contact, as well as the role of an elastic medium that dampens shocks and changes contact lines, are considered. In many gears, the tooth load per tooth is much higher and applied for longer periods of time. The asymmetrical shape of the tooth reflects this functional difference. In the case of asymmetric gears, the standard symmetrical toothed tool rail is modified by changing the pressure angle of one of the side surfaces. However, this simplistic approach to the design of an asymmetric transmission significantly limits the ability to maximize the performance of a wide range of possible applications of these transmissions. As the frequency of impact interactions increases, the lubricating layer of high-speed gears with an asymmetric profile ceases to respond to pressure changes, and the load value, which determines the smallest layer thickness over time, approaches the minimum stationary component of the spectrum of dynamic loads. At the same time, noise and vibration levels are slightly reduced. Therefore, in the calculations of the strength, contact endurance and seizure of high-speed gears with an asymmetric profile, the complex influence of the criterion parameters of the lubricant must be taken into account not only when determining the allowable stresses, but also when determining the amount of dynamic load amplification due to the impact interaction of the teeth.

NEZHEBOVSKY V.V., BEREZHNYI R.A., PERMYAKOV O.A., KLOCHKO O.O., RYABCHENKO S.V., USTINENKO O.V. SYSTEMS OF THE PARAMETERS OF THE CONDITION OF THE WORKING SURFACES AND DIMENSIONS ACCURACY OF THE CYLINDRICAL HARDENED GEAR WHEELS OF THE CLEANING COMBINED UKD

The issues of efficiency improvement in hydrodynamic (liquid) or limit (semi-liquid) modes of friction of gears with an asymmetric profile and the effect of the liquid on tooth damage, power loss and temperature in contact, as well as the role of an elastic medium that dampens shocks and changes contact lines, are considered. In many gears, the tooth load per tooth is much higher and applied for longer periods of time. The asymmetrical shape of the tooth reflects this functional difference. In the case of asymmetric gears, the standard symmetrical toothed tool rail is modified by changing the pressure angle of one of the side surfaces. However, this simplistic approach to the design of an asymmetric transmission significantly limits the ability to maximize the performance of a wide range of possible applications of these transmissions. As the frequency of impact interactions increases, the lubricating layer of high-speed gears with an asymmetric profile ceases to respond to pressure changes, and the load value, which determines the smallest layer thickness over time, approaches the minimum stationary component of the spectrum of dynamic loads. At the same time, noise and vibration levels are slightly reduced. Therefore, in the calculations of the strength, contact endurance and seizure of high-speed gears with an asymmetric profile, the complex influence of the criterion parameters of the lubricant must be taken into account not only when determining the allowable stresses, but also when determining the amount of dynamic load amplification due to the impact interaction of the teeth.

Load share model based gear loss factor prediction in high contact ratio spur gear drive

Gear loss factor is considered to be a crucial parameter, and is governed by factors like contact load, sliding velocity, contact ratio, etc. Sliding power loss is a function of the gear loss factor and friction coefficient. It depends on the contact tooth load and its contact surfaces. A small decline in the gear loss factor and variation in the friction coefficient reduces the energy consumption which improves gear efficiency significantly. Hence, accurate prediction of the gear loss factor is important. This paper deliberates on measuring the contact load of High Contact Ratio (HCR) non-standard gear drive, using the finite element contact model. The input for the gear loss factor is obtained from a 2D elastic contact model using ANSYS. In the previous works the load is considered as a rigid hypothetical element, but in the real case it is varying at each instantaneous contact point. To address this, a more accurate method of predicting the power loss using the contact load share model is proposed. The effectiveness of this technique, built on the computational data and its accuracy are examined. Based on the accuracy, the load share model was suggested to be the most effective one compared to other techniques. The results show that the proposed model provides an effective tool for making reliability assessments on power loss and efficiency of high contact ratio gear drives under diverse operating conditions.

Damage mechanisms and tooth flank load capacity of oil‐lubricated peek gears

AbstractPlastic gears are increasingly being utilized in higher performance ranges. Operating under oil lubrication can reduce friction and heat input. By running under oil‐lubricated conditions, tooth damage such as abrasive wear recedes into a secondary role, and fatigue damage such as pitting becomes relevant for the durability of the gears. Polyether ether ketone (PEEK) is suitable for use in demanding operating conditions due to its very high strength properties, even at higher temperatures. In this work, the stress conditions affecting the tooth flank and the damage behavior of oil‐lubricated PEEK gears are investigated and tooth flank strength parameters were determined for different temperature levels. Theoretical studies on the stress distribution on the tooth flank show the necessity to apply adapted profile modifications in order to reduce undesired stress conditions in the extended meshing area. In experimental investigations, the damage behavior of oil‐lubricated PEEK gears is examined and the influence of temperature on the gear load capacity is discussed.

Damage-Induced Dynamic Tooth Contact Forces in Spur Gears with Root Cracks

<div class="section abstract"><div class="htmlview paragraph">A finite element/contact mechanics formulation is used to analyze the dynamic tooth forces that arise from damage-induced vibrations in spur gear pairs. Tooth root crack damage of varying sizes are analyzed for a wide range of speeds that include resonant gear speeds. The added localized compliance from tooth root crack damage leads to a re-distribution of the forces on the individual gear teeth in mesh. At speeds away from resonance, smaller dynamic forces occur on the damaged tooth and larger dynamic forces occur on the tooth that engages immediately after it. These dynamic tooth contact forces cause additional transient dynamic response in the gear pair. For certain speeds and sufficiently large tooth root cracks, the damage-induced dynamic response causes large enough vibration that tooth contact loss nonlinearity occurs. For some speeds near resonance, the damage-induced vibrations cause teeth that normally lose contact to remain in contact due to vibration. Tooth contact loss nonlinearity in this cause briefly seizes but then occurs again after several mesh cycles when the damage-induced transients diminish. The features of the dynamic tooth loads shown in this work may be used in analyses that predict the propagation of damage, determine conditions that will likely cause healthy teeth to become damaged, and give insight into the fundamental mechanisms driving vibration in damaged geared systems.</div></div>

The Influence of Different Occlusal Loading on Six Restorative Materials for Restoration of Abfraction Lesions—Finite Element Analysis

The aim of the study was to analyze the occurrence of stress on teeth with abfraction lesions restored with six different restorative materials, and by introducing the tensile strength parameters to calculate the safety factor of the material under the load (ratio between the strength of the material and the maximum stress). Three-dimensional models of the mandibular premolar are created from a microcomputed tomography images. An abfraction lesion is modeled on the tooth. The stress of the dental tissues and six restorative materials under functional and nonfunctional occlusal loading of 200 (N) are analyzed by finite element method. CTAn program 1.10 and ANSYS Workbench (version 14.0) were used for analysis. Results are presented in von Mises stress. Oblique loads caused ≈ four times higher stress in restorative materials than the axial ones. It is noticeable that high values of von Mises stress are measured at the bottom of the sharp lesion, even up to 240 MPa, that are significantly reduced after the restoration. The highest stresses at the restorative material are present at the lower (gingival) margin of the restoration. The highest stresses under both types of loads are measured in nanohybrid composite (Tetric EvoCeram, Ivoclar Vivadent). The lowest values of the stress are measured in the flowable composite (Tetric Flow, Ivoclar Vivadent), but at the same time, the highest value of the stress is measured in the surrounding dental tissues on the tooth restored with the flowable composite. The microhybrid composite (Herculite XR, Kerr), with the highest safety factor, is the material that best withstands the stresses it is exposed to. The obtained safety factor did not exceed the critical limit, except for the glass ionomer cement, with the safety factor lower than 1. The type of tooth loading has the greatest influence on the intensity of stress. The value of the obtained stresses in the restorative material and dental tissues differ due to the different mechanical properties of the materials. Restoration of noncarious lesions significantly reduces extremely high stress values at their bottom.

Increase wind gearbox power density by means of IGS (Improved Gear Surface)

Increasing gearbox power density is a key factor in reducing the levelized cost of wind energy (LCOE). The tooth root and flank load carrying capacity of gears are strongly affected by surface conditions. Additional finishing methods such as shot peening (SP) and superfinishing (SF) significantly increase the gear load capacity, but these effects have not yet been adequately considered in the current ISO 6336 standard or in any other gear standards.Based on the experimental results, an estimation of the safety margin increase is calculated for a wind gearbox part. Additional fatigue tests are needed to confirm this increase.