Gear Rim Research Articles

Numerical detection of shaft misalignments using a sensor‐integrating jaw coupling

AbstractShaft misalignments are one of the main causes of damage to couplings in machines. If they are not detected in time, they can lead to machine downtimes. When assembling a machine, however, it is not always possible to align the shafts perfectly. Elastic couplings are able to compensate for such misalignments up to a certain degree. To detect the present radial misalignment, the concept of a sensor‐integrating jaw coupling, developed to determine the transmitted torque, is used. In the teeth of the gear rim, boreholes are drilled and dielectric elastomer sensors (DES) are inserted. If the teeth deform during use of the coupling the DES will deform as well, leading to a change in capacitance, which can be detected. If the two shafts, which the coupling connects, are perfectly aligned to each other, each of the loaded teeth will deform uniformly. However, if there is a radial or angular misalignment, the deformation is different for each tooth, which can be determined with the help of the DES. To demonstrate this effect, a finite element model of the sensor‐integrating jaw coupling with misalignments is created, and numerical simulations are conducted. In this model, the hyper‐viscoelastic material behavior of (i) the gear rim of the jaw coupling and (ii) the DES is taken into account. From the mechanical simulation, the deformed state of the DES is obtained, which is used to compute the capacitance of the sensor. With the results of the numerical simulations, a symbolic regression is performed. The result is an analytical formula that makes the accurate detection of the present radial misalignment possible. The developed framework can later be easily programmed on a microcontroller which is integrated in the sensor‐integrating jaw coupling.

Experimental investigations and material modeling of an elastomer jaw coupling

Abstract This work investigates the hyper-viscoelastic behavior of a thermoplastic polyurethane IROGRAN A 92 E 5670 FCM used in the gear rim of a jaw coupling. The aim is to provide the material parameters for the modeling of jaw couplings in engineering tasks. Uniaxial compression tests were conducted at various temperatures and loading speeds to fit a hyper-viscoelastic material model. The material model uses the Yeoh free energy and the power law model with one Maxwell element. The parametrized material model showed very good results in comparison to experimental data. In addition, the influence of friction on the experiments was modeled, investigated, and discussed. Further component tests for a jaw coupling of size 28 were conducted with two different specimen types. The original gear rim and a modified gear rim with central boreholes for integrated sensors were used in the test. The influence of such a modification was investigated with four different loading cases, focusing on the torsion-torque characteristic and the relative damping. These component tests enable the validation of numerical models of jaw couplings.

Concept of a sensor-integrating jaw coupling for measuring operating data

In recent years, industry and research (i) have driven the development and application of data-driven machines and systems and (ii) have increasingly introduced predictive maintenance. One of the main challenges is the acquisition of representative data for these applications. In the scope of mechanical systems, machine elements are the key parts for measuring process relevant data. Thereby, elastic couplings offer a considerable potential for a wide range of applications. The present work describes a novel space neutral sensor-integrating gear rim of a jaw coupling for the measurement of torque, rotational speed and temperature. The mechanical modifications on the coupling and the applied dielectric elastomer sensor are outlined. Additionally, the electrical conceptualization and the measurement chains are described. A manufactured prototype of the sensor-integrating jaw coupling and a proof of concept are presented.

Helicopter Planet Gear Rim Crack Diagnosis and Trending Using Cepstrum Editing Enhanced with Deconvolution.

Detecting gear rim fatigue cracks using vibration signal analysis is often a challenging task, which typically requires a series of signal processing steps to detect and enhance fault features. This task becomes even harder in helicopter planetary gearboxes due to the complex interactions between different gear sets and the presence of vibration from sources other than the planetary gear set. In this paper, we propose an effectual processing algorithm to isolate and enhance rim crack features and to trend crack growth in planet gears. The algorithm is based on using cepstrum editing (or liftering) of the hunting-tooth synchronous averaged signals (angular domain) to extract harmonics and sidebands of the planet gears and low-pass filtering and minimum entropy deconvolution (MED) to enhance extracted fault features. The algorithm has been successfully applied to a vibration dataset collected from a planet gear rim crack propagation test undertaken in the Helicopter Transmission Test Facility (HTTF) at DSTG Melbourne. In this test, a seeded notch generated by an electric discharge machine (EDM) was used to initiate a fatigue crack that propagated through the gear rim body over 94 load cycles. The proposed algorithm demonstrated a successful isolation of incipient fault features and provided a reliable trending capability to monitor crack progression. Results of a comparative analysis showed that the proposed algorithm outperformed the traditional signal processing approach.

Manufacturing of soft capacitive strain sensor based on dielectric elastomer material for an elastic element of a jaw coupling

In this work, we present a procedure for manufacturing a soft capacitive strain sensor in the form of a multi-layer electrical capacitor for further integration into the elastic gear rim of a jaw coupling. The dielectric elastomer sensor (DES) is based on an elastomeric substrate with alternating layers of conductive carbon black based ink as electrode layers and elastomeric film as a dielectric and electrical insulation. A variety of thin multi-layer sensors were produced to evaluate the manufacturing process. Additionally, using an LCR meter and a tensile test machine, the equivalent electrical capacitance (C) at the two sensor contacts and the applied force are measured, respectively. It is shown that C varies depending on the amount of sample strain caused by the applied force. By testing two versions of DES, a maximum change in capacitance of ΔC = 1.55 pF was achieved. The obtained characteristics show that the presented manufacturing process for the DES can be used as a soft strain sensor to measure the strain caused by the force applied to the elastic element between the jaw couplings.

Effect of Rim and Web Thickness on Tooth Root Stress of Spur Gear

This study investigated the impact of spur gear rim and web thickness on root stress. A finite-element analysis model (FEM) was utilized and validated through a gear-bending test. Four gears with different rim and web specifications, including a solid gear, were designed and tested using strain gages to measure their root stress. The 3D FEM was validated by comparing the measured root stresses with that analyzed by the developed FEM. Using this model, a parametric study was conducted by varying the web position, pressure angle, and module to investigate the effect of the backup ratio on the root stress ratio of the gear. A stress-ratio map was generated based on the results. This stress-ratio map was compared with the rim thickness factor (YB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${Y}_{B}$$\\end{document}) for external spur gears specified in ISO 6336-3. The comparison reveals that the rim thickness factor specified in ISO 6336 is overly conservative compared to values obtained in this study. Our results suggest that the thickness of both the rim and web should be considered to reduce the weight of spur gears. These findings can be applied to the design of lightweight spur gears.

Determination of Material and Fracture Properties of a Case-Hardened Planet Gear and Its Homogenisation Method to Obtain the Damage Mechanism Caused by Fragment Ingestion.

Before a new type of engine is introduced into civil aviation, it must comply with various safety regulations. These regulations include the analysis of secondary damage caused by the re-ingestion of a tooth fragment. The purpose is to prevent crack propagation through the gear rim, which would lead to catastrophic failure. In this context, identification of the initial crack location is crucial to determine the crack propagation path. Therefore, this paper presents a technique to determine and validate a constitutive material model and fracture locus for case-hardened spur gears. As the modelling of the surface-hardened layer is computationally intensive, it is necessary to homogenise the model. This paper comprehensively reviews and discusses the associated effects and errors. To determine the plastic behaviour of the case-hardened external gear (30CrNiMo8) and the nitrided internal gear (35CrAlNi7-10), the widely acknowledged Johnson-Cook material model is implemented using compression and Vickers indenter tests to define the necessary parameters. The fracture locus implementation is also based on the Johnson-Cook method and an axial shift of the fracture locus based on the hardness profile of the spur gears is determined by quasi-static pulsator tests. For validation, a project-specific gearbox test rig is used, enabling consistent ingestion of defined fragments. In addition, to check the likelihood of a tooth flank crack and to validate the results, a simplified ingestion experiment is performed.

Influence of ring gear flexibility on the fatigue reliability of planetary gear systems in heavy helicopters

Flexibility of ring gear rims significantly affects the mechanical properties of planetary transmissions at both levels of gear tooth meshing and system power sharing, and is one of the important design factors determining the service reliability of large aviation planetary systems. Therefore, to analyze the mechanism by which the flexibility of ring gear rims affects the fatigue reliability of planetary systems, in the framework of the stress-strength interference theory, a reliability assessment model for the planetary system is constructed based on a calculation logic extension for the full probability formula. Starting from balancing evaluation accuracy and evaluation cost, a hybrid finite element method and a gear tooth lifetime transformation test are employed to provide load and strength input variables for the reliability model respectively. Finally, a mapping relationship from ring gear rim flexibility to planetary system fatigue reliability is established. For the specific design scheme of planetary systems, a lower limit of the ring gear rim thickness can be determined according to the requirements of reliability indexes, so that the balance between reliability and lightweight can be achieved to some extent.

Finite element based modeling and simulation of an elastomer gear rim

AbstractJaw couplings have become an indispensable part for industrial applications. Besides the compensation of radial, axial and angular misalignments, they are crucial for the reduction of torque shocks in drive systems. However, due to the complex material behavior of the elastic gear rim, which is typically made of thermoplastic polyurethane (TPU), there are few numerical models to describe the behavior of jaw couplings. In the present work, the material behavior of the gear rim is obtained by uniaxial loading‐unloading tests performed at different deformation rates and temperatures. By using experimental data, a hyperviscoelastic material model was fitted and a numerical model of a jaw coupling was realized in the finite element tool ABAQUS. Based on this model, (i) the relationship between torsion and torque as well as (ii) the deformation behavior of the gear rim was determined.

Development and research of the efficiency of a tractor transmission with a disc type gearbox

BACKGROUND: Modern tractors are equipped with gearboxes that are divided into three ranges, such as slow, operating and transport, for the sake of better power usage and fuel efficiency of the engine as well as getting higher performance. In addition, gearboxes must have a large number of gears, that leads to an increase in their mass and dimensions. An increasing mass of gearbox leads to additional high-quality metal consumption as well as energy costs for self-propelling of a tractor, which reduces its operational capabilities.
 AIMS: Increasing the number of gears and reducing the weight of gearboxes for agricultural tractors.
 METHODS: A disc-type gearbox (Patent RF No. 208805) has been developed to make it possible to increase the number of gears and reduce the weight of gearboxes for agricultural tractors. The feature of this gearbox is the gear disk with three gear rims on top and three on the bottom that is installed in its housing in addition to the usual gears and shafts. The implementation of the gear disk with gear rims makes it possible to reduce the number of gearwheels by more than half. The experimental gearbox is manual and interrupted-drive. It gives 18 forward gears and 18 reverse gears. Laboratory studies of a tractor with the experimental gearbox were carried out on a roller test bench. Load condition was arranged with the STEU-40 electric brake test rig in order to determine the transmission efficiency. During the testing, the torques on the gearbox input shaft and the tractor half shafts were measured. Reliability testing of the experimental gearbox, built in the LTZ-55 tractor, lasted for 2714 hours under the normal operation condition.
 RESULTS: The results of the transmission efficiency study at the 1st, 5th and 10th gears with different drive wheels torques as well as different oil temperatures revealed that the transmission efficiency is in the range of 0.75-0.96 at the transmission oil temperature of 16 to 60C, which corresponds to the numerical values of fixed-ratio transmissions of stock tractors. Operational tests of the tractor, equipped with the experimental gearbox, showed efficiency of gearbox during operation of 2714 hours.
 CONCLUSIONS: Laboratory studies of the LTZ-55 tractor, equipped with the experimental gearbox (Patent No. 208805), showed that the transmission efficiency improves with an increase in the drive wheels torque and the transmission oil temperature, and deteriorates with an increase in the gear number. The efficiency of the experimental transmission is in the range from 0.75 to 0.96, which corresponds to stock manual interrupted-drive transmissions of tractors. With an increase in oil temperature up to 60 C, the efficiency of the transmission greatens.

The computer modeling and analysis of complex dynamic structures of robotics from composite materials

The methods of designing and modeling dynamic stands from a composite material are considered. One of the complex elements of the stands is the elements that ensure the dynamic behavior of the channels of the stand: bearing supports, gear rims, gearboxes, motors, servo drives, etc. Approximation of these elements in numerical methods for calculating and studying dynamic structures (finite element method) is a difficult task. Direct approximation of these elements does not satisfy the adequacy. Various approaches are used to adequately approximate such elements. In this paper, a methodology is proposed that consists in determining the rigidity parameters of bearing supports, gear rims, gearboxes and motors. In the future, these elements are replaced by rod systems corresponding to the replaced elements in terms of stiffness parameters. The effectiveness of the proposed method is confirmed by a comparison with of available experimental methods. The shell structures and stands were modeled in ANSYS modeling module. The considered methods for designing stands can be applied to robotic systems, weaving machines and dynamic systems for various purposes, since they contain all the elements inherent in the considered stand. The finite element approximation of the stand was carried out by elements of various types.

Influence of arrangement of layers of composite material on the bearing capacity of a robotic system

The robotic system is considered as a rack made of composite material, which is under dynamic influence. A method for determining the reduced characteristics of a multilayer composite material is given. The simulation of the stand was carried out. To approximate the details of the movement of bench channels: bearings, gearboxes, gear rims, motors, an algorithm and a program for calculating the rigidity of these structures have been developed in order to approximate these elements in the finite element method by replacing such elements with a system of rod structures with rigidity identical to the replaced structures: bearings, gear crowns, gearboxes, motors. The convergence of the calculation results is checked by thickening the finite element mesh. The pinching along the base of the stand was taken as the boundary conditions. A technique has been developed for modeling a three-layer stand structure. The technique for modeling a three-layer structure consists in modeling a stand, assigning filler material to it, and creating shell bearing layers on the surface of the stand, assigning it the characteristics of a multilayer composite material. A layer-by-layer stress-strain state of a stand made of composite material has been obtained. The analysis of the influence of the orientation of the layers of a five-layer composite material on the stress-strain state of the HIL simulation bench has been carried out.

Computer modeling of robotic systems made of composite materials, analysis of the stress-strain state under dynamic influences

In the present study, a robotic system is considered: a multi-stage semi-natural simulation stand. The stand is designed to simulate the flight characteristics of aircraft instruments in laboratory conditions. The use of such stands can significantly reduce the cost of developing and testing aircraft instruments and contains all the attributes of robotic systems, which allows the developed method of computer modeling and analysis of stands to be applied in the field of robotic systems. The problem is solved by the finite element method. As a result of the study, a technique has been developed for approximating parts that carry out movements: gear rims, bearings, gearboxes, motors in the finite element method. Comparison with the available experimental studies showed the effectiveness of the developed methodology. As the stand material, a composite material is used, which has a high specific strength, which makes it possible to change the physical and mechanical characteristics depending on the location of the composite base in the layers of the multilayer composite structure. A technique has been developed for arranging the base layers in a multilayer composite to obtain maximum strength and rigidity of the stand, which is one of the main factors in the efficiency of the stand. The analysis of the behavior and stress-strain state of the bench under dynamic impact has been carried out.

Influence of orientation of layers of a multilayer composite material on the stressed state of a robotic structure under dynamic loading

The paper developed a method for calculating the stress-strain state of a robotic structure made of composite material under dynamic action. The bearing capacity of multilayer composite materials is affected by the location of the warp threads of the composite material. By changing the orientation of the layers, it is possible to change the bearing capacity of the composite material. In the present work, such a study was carried out for a robotic system made of a composite material under the action of a dynamic operational load. An eight-layer composite material with different layer orientations was considered. Carbon fiber was used as the basis. As a robotic system stand was considered, designed to simulate flight characteristics in laboratory conditions. The simulation of the stand was carried out. The bench was approximated by finite elements. The convergence of the results of the finite element model of the stand was checked by condensing the finite element mesh and comparison the results obtained. Robotic systems are equipped with elements that move the channels: bearings, gear rims, gearboxes, motors. In the present study they were replaced in the finite element model with a system of bar elements of identical stiffness. The design of the stand was a three-layer structure, consisting of external carrier layers of an eight-layer composite material and a filler layer between the carrier layers of lightweight material in the form of foam and used to absorb shear stresses and prevent the bearing layers from approaching. Calculation and analysis of the design of the stand for dynamic load is carried out, the stress-strain state of the stand is obtained for different arrangement of the layers of the composite material.

Динамика процессов взаимодействия элементов гусеничного движителя при наезде первого опорного катка на неровность

The article focuses on the dynamics of high-speed tracked vehicle caterpillar drive elements and their interaction when moving over unevenness. Such movements are accompanied by the previously insufficiently studied effect of the caterpillar drive free branch capturing by the drive wheel gear rim in its front location, which leads to the destruction of the structural elements of the power unit. The paper presents the results of dynamic wave processes in a caterpillar drive obtained using mathematical modeling. The model, in which the dynamic system is presented as an elastic rod on an inertialess elastic foundation, takes into account the inertial dynamic loads in the caterpillar drive formed by the soil microprofile. It also allows us to analyze with satisfactory accuracy the dynamic excitation process of transverse vibrations in a free branch. The computational and experimental results of studying the dynamic process of free-branch transverse wave oscillations (when the first roller wheel hits an unevenness) demonstrate that due to the significant inertial force influence, the caterpillar oscillations amplitude increases significantly, which increases the likelihood of its capture by the drive wheel gear rim. The free branch transverse oscillations amplitude does not significantly depend on the design parameters. The determining factor is the pretensioning force. When the first track roller hits an unevenness, it is not a controllable value and, in the limiting case, can be reduced to zero. To reduce the likelihood of the drive wheel being caught by the gear rim, it is necessary to introduce an additional track tensioning mechanism and an appropriate control system into the design of the caterpillar mover with the front location of the drive wheels.

Geometric calculation of non-circular gear segments of the planetary mechanism in rotary hydraulic machines

The article discusses the improvement of the methods of geometric design of positive-displacement hydraulic machines with floating satellites. At the first stage, based on standard methods, an “average” round-link planetary mechanism, having the number of teeth as in the designed hydraulic machine, is calculated. At the second stage, the same-type cyclic functions characterizing the paths of the center of the satellite in the coordinates associated with each of the central gearwheels are specified. At the third stage, the coordinate arrays of the satellite in a variety of its positions are calculated. The angular position of the satellite relative to one of the profiled gearwheels (for example, the sun gearwheel) provides equidistance of the centroid of this gearwheel to the path of the center of the satellite. The angular position of the satellite relative to the other profiled wheel is determined by its running around the first wheel. At the final stage of the design, the satellite is constructed in a variety of positions, and the profile of the corresponding non-circular gear rim is obtained as an envelope of the family of satellite curves-profiles.

An analytical approach for calculating thin-walled planet bearing load distribution

With the development of planetary gear trains (PGTs), more planet gears are designed as thin-walled structures to reduce the weight and accommodate the larger bearings so that the transmission system can achieve higher power density, improved reliability, and better compactness. However, this would make the planet gear fragile, where it could easily deform and thus influence the load distribution on the bearing. To address this problem, this study investigates the effect of the planet gear rim deformation on the bearing load distribution and its service life. By incorporating the Timoshenko three-dimensional (3D) curved beam theory and the transfer matrix method, a novel analytical model was developed that computes the planet gear rim deformation and the bearing loads. The validation of the model was conducted using a finite element (FE) simulation. Based on the proposed model, the internal states, including forces and deformations, of the planet gear rim along the circumference were examined, and the effects of the planet gear parameters and the bearing clearance on the bearing load distribution and service life were analyzed. The results show that the deformation of the planet gear rim has a significant effect on the contact load, pressure distribution, and service life of the bearing. On this basis, an optimal rim thickness that gives the maximum bearing life was obtained for different planet helix angles and bearing clearances, which can provide design guidance for the planet gear bearing with higher reliability.

Measurement Method of Temperature of the Face Gear Rim of a Spiroid Gear.

Spiroid gears are used to transfer heavy loads with a significant reduction in input speed. Like most toothed gears, they are lubricated with oil whose physical properties change with temperature fluctuations, affecting the durability and reliability of the gear. Bearing this in mind, gear designers plan systems for measuring oil temperature during gear operation at the design stage. The authors of this paper are of the opinion that, in the case of spiroid gears, it may be insufficient to measure only oil temperature during gear operation. It seems that the working temperature of a pair of mating wheels has a decisive impact on the durability and reliability of the gear. The measurement of oil temperature in a tested gear should be treated as a supplementary measurement with the measurement of temperature on the toothed wheels as the basic measurement. Taking into consideration the above, an innovative test bench was designed and built, making it possible to observe how working parameters of the gear (torque and rotational speed) affect the temperature of the lubricating oil, but most of all, the working temperature of the pair of mating wheels. This paper presents, among others, the results of research on the impact of the rotational speed of the input shaft and load on the distribution of temperature on the toothed rim of the face gear.

Fatigue Reliability Design Method for Large Aviation Planetary System Considering the Flexibility of the Ring Gear

As the foundation and core of various heavy aircraft transmission systems, the reliability level of large-scale aviation planetary mechanism restricts the economic affordability and service safety for the aircraft to a great extent. This paper takes the heavy helicopter planetary mechanism as the research object, and aims to improve the fatigue reliability level of the system. The fatigue load history of the gear teeth under the coupling of global elastic behavior of the system is calculated using a hierarchical finite element method, and the fatigue strength distribution of gear teeth is fitted based on the gear low circumference fatigue test with the minimum order statistics transformation method to provide cost-effective load and strength input variables for the system reliability prediction model. Based on this, a mapping path from the key structural elements of large-scale aviation planetary mechanism to the system reliability indexes is established, and then a new method of reliability-driven multi-objective optimization design for planetary mechanism structural dimensions is proposed. Finally, the influence law of ring gear rim thickness on the fatigue reliability of the planetary gear train is analyzed and the NSGA-Ⅱ genetic algorithm is used to determine the optimal stiffness matching result of the rim size of the designated type of large aviation planetary system. The stiffness potential of the core structural elements is maximized as a way to balance the contradiction between reliability and lightweight requirements of a large aviation planetary system.

Deformation and Response Analysis of Spur Gear Pairs with Flexible Ring Gears and Localized Spalling Faults

For the analysis on the deformation of flexible ring gears in spur gear pairs, the complete flexible ring is discretized, and the boundary condition is added to the connecting points to develop a calculation method for the flexible deformation. The ovality index is used to describe the deformation degree of flexible ring gears, then the influences of ring-gear width and the spalling defects on the flexible deformation of ring gears are discussed. The result shows that the flexible deformation of ring gears is caused by the gear pair meshing force, and the deformed shape is close to an ellipse. In the single-tooth meshing interval of gear pairs, the main form of deformation is being stretched, and while in the double-tooth meshes, the main form is bending deformation. When the width of the ring gear rims is increased, the flexible deformation of the ring gears can be effectively suppressed, and the vibration amplitude of the gear pairs can be reduced. Additionally, when there is a localized spalling fault on gear pairs, the sudden changes in the deformation of flexible ring gears are generated by the shock of the meshing force. Finally, through the finite element analysis model and the experiment, the mathematical model of gear pairs with flexible rings is confirmed.