Stress calculation on bevel gears with FEM influence vectors

In order to be able to carry out an optimal gear design with the aim of cost reduction and the careful handling of resources, load capacity is an important criterion for the evaluation of a gear. For the calculation of the flank and root load capacity, a precise loaded tooth contact analysis (LTCA) is necessary. With LTCA software like BECAL, influence numbers are used to calculate the deformation of the gear. These influence numbers are calculated with a BEM-module and considered for calculating the local root stress. This method simplifies the coupling stiffness in tooth width direction with a decay function and neglects the influence of local differences in tooth stiffness. In this publication, this simplification shall be questioned and evaluated.Therefore, a new method for calculating stress with FEM influence vectors is presented. This method enables the calculation of full stress tensors at any desired location in the gear with the efficiency of the influence number method. Additionally, the influence of local stiffness variations in the gear is taken into account. Various gear examples show the influence of material connections at the pinion root and the influence of the rim thickness of a wheel on the root stress. To validate the accuracy and the time efficiency of the new calculation method and to compare the results to current state-of-the-art simulations, a well-documented series of tests from the literature is recalculated and evaluated.

A numerical investigation on the hybrid spur gears: Stress and dynamic analysis

In this study, the effect of rim thickness of hybrid gears on the root stress, joint stress, tooth stiffness, natural frequency, and dynamic behavior are examined numerically. Hybrid gears consist of two materials, which are steel for the teeth-rim and hub regions of gear, carbon fiber reinforced plastic (CFRP) for the web region. Adhesive bonding is assumed for the joining of steel and composite materials. FE method is used to evaluate tooth root stress, joint stress, tooth deformation, and the natural frequency of hybrid gears. The adhesive is defined by cohesive zone modeling (CZM). Moreover, 2-DOF dynamic analyses are implemented to obtain dynamic factors and static transmission error. According to results, hybrid gears have substantial potential to reduce the mass of gear transmission systems with no adverse effect on root stress and dynamic factor if the design parameters are appropriately selected. Besides, rim thickness is found as a critical parameter for the hybrid gears since when its value changes from 0.5xm to 3xm, the root stress decreases 10% while the tooth stiffness and torque capacity increase 20% and 65%, respectively.

Vibration-Based Early Crack Diagnosis With Machine Learning for Spur Gears

Gear mechanisms are one of the most significant components of the power transmission systems. Due to increasing emphasis on the high-speed, longer working life, high torques, etc. cracks may be observed on the gear surface. Recently, Machine Learning (ML) algorithms have started to be used frequently in fault diagnosis with developing technology. The aim of this study is to determine the gear root crack and its degree with vibration-based diagnostics approach using ML algorithms. To perform early crack detection, the single tooth stiffness and the mesh stiffness calculated via ANSYS for both healthy and faulty (25-50-75-100%) teeth. The calculated data transferred to the 6-DOF dynamic model of a one-stage gearbox, and vibration responses was collected. The data gathered for healthy and faulty cases were evaluated for the feature extraction with five statistical indicators. Besides, white Gaussian noise was added to the data obtained from the 6-DOF model, and it was aimed at early fault diagnosis and condition monitoring with ML algorithms. In this study, the gear root crack and its degree analyzed for both healthy and four different crack sizes (25%-50%-75%-100%) for the gear crack detection. Thereby, a method was presented for early fault diagnosis without the need for a big experimental dataset. The proposed vibration-based approach can eliminate the high test rig construction costs and can potentially be used for the evaluation of different working conditions and gear design parameters. Therefore, catastrophic failures can be prevented, and maintenance costs can be optimized by early crack detection.

Analysis of tooth stiffness of nutation face gear

Purpose The purpose of this paper is to obtain the single-tooth stiffness, single-tooth time-varying meshing stiffness and comprehensive meshing stiffness of the internal and external face gears and to analyze the influence of the modulus, pressure angle and tooth width of each face gear on the single-tooth stiffness of the gear in nutation face gear transmission. Design/methodology/approach From the point of view of material mechanics, the gear teeth of nutation face gear are simplified as spacial variable cross-section beams. The shear deformation of gear teeth, the bending deformation of tooth root and the additional elastic deformation caused by the base deformation are gotten by simplified trapezoidal section method, thus the stiffness of nutation face gear teeth can be obtained. The comparison with finite element method results verifies the rationality of simplified trapezoidal section method for calculating the tooth stiffness of nutation face gear. Findings The variation of stiffness of internal and external face gears along the meshing line and tooth height in nutation face gear transmission is studied, and the variation laws of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained. Originality/value Nutation face gear transmission is a new type of transmission. The stiffness of face gear teeth is analyzed, and the variation rules of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained, which not only enriches the research of nutation face gear transmission but also has important guiding significance for the application of nutation face gear in engineering practice.

A Step Toward Fault Type and Severity Characterization in Spur Gears

Gear transmissions are widely used in industrial applications and are considered to be critical components. To date, the capabilities of gear condition indicators are controversial as some condition indicators can diagnose one type of fault at the early stages, yet cannot diagnose other types of faults. This study focused on fault detection and characterization based on vibrations in a spur gear transmission. Three different common local faults were examined: tooth face fault, broken tooth, and cracks at the tooth root. The faults were thoroughly analyzed to understand the fault manifestation in the vibration signature and to find condition indicators that are robust and sensitive to the existence and severity of the fault. The analysis was based on both experimental data and simulated signals from a well-established dynamic model of the gear system. The fault detection capability of common condition indicators, as well as newly defined condition indicators, was examined and measured using statistical distances. For each fault type, the investigated condition indicators were categorized according to their discrimination power between faulted and healthy states and the ability to rank the fault severity. It was concluded that faults that affect the involute profile throughout the tooth are easily detectable. Faults such as root cracks or chipped tooth, in which mainly the tooth stiffness is affected, are much more challenging to detect. It has been shown that while using a realistic model, the capabilities of different condition indicators can be tested, and the experiments can be replaced by simulations.

Enhanced application limits for crossed helical gearboxes using new geometries for smaller sliding paths or smaller contact pressures

Crossed-axis helical gear units are used as actuators and auxiliary drives in large quantities in automotive applications such as window regulators, windscreen wipers and seat adjusters. Commonly gear geometry of crossed helical gears is described with one pitch point. This article deals with an extended calculation method for worm gear units. The extended calculation method increases the range of solutions available for helical gears. In general, for a valid crossed helical gear pair, the rolling cylinders do not have to touch each other. In mass production of many similar gears, individual gears can be reused because they can be paired with other centre distances and ratios. This also allows the use of spur gears in combination with a worm, making manufacturing easier and more efficient. By selecting design parameters, for example the axis crossing angle or the helix angle of a gear, positive effects can be achieved on the tooth contact pressure, the overlap ratio, the sliding paths, the lubrication condition, the tooth stiffness and, to a limited extent, on the efficiency of the gearing. It can be shown that for involute helical gears, in addition to the known insensitivity of the transmission behaviour to centre distance deviations, there is also insensitivity to deviations of the axis crossing angle. This means that installation tolerances for crossed helical gearboxes can be determined more cost-effectively.