Helical Gearbox Research Articles

Application of the TOPSIS Method for Multi-Objective Optimization of a Two-Stage Helical Gearbox

Application of the TOPSIS Method for Multi-Objective Optimization of a Two-Stage Helical Gearbox

CIS2N: Causal independence and sparse shift network for rotating machinery fault diagnosis in unseen domains

Intelligent fault diagnosis (IFD) based on deep learning (DL) has demonstrated its powerful performance to promote the reliability and safe operation of rotating machinery. In industrial applications, working condition changes frequently, leading to models’ performance degeneration due to out-of-distribution (OOD) samples, such as vibration signals with unseen rotating speeds, loads, etc. To address this issue, domain generalization fault diagnosis (DGFD) has attracted increasing attention. However, mainstream DGFD methods are implemented from statical dependence, which fail to excavate intrinsic causal mechanisms and have limited performance and reliability. From a causal view, the causal independence and sparse shift network (CIS2N) is proposed to diagnose via causal mechanisms. Specially, a structural causal model (SCM) representing causal relations of features in IFD is given. Based on the SCM, it is derived that features are jointly independent and feature deviation between intervened sample pairs is sparse. The dependence among features is measured via the covariance matrices constructed by high-level features mapped by random Fourier features (RFF). Meanwhile the L1-distance between pairs of features with the same causal features (intervened pair) is calculated and optimized to realize shift sparsity. The effectiveness of the proposed CIS2N on DGFD is demonstrated on two real helical gearbox datasets.

Multi-Objective Optimization for Finding Main Design Factors of a Two-Stage Helical Gearbox with Second-Stage Double Gear Sets Using the EAMR Method

Multi-Objective Optimization for Finding Main Design Factors of a Two-Stage Helical Gearbox with Second-Stage Double Gear Sets Using the EAMR Method

Solving a Multi-Objective Optimization Problem of a Two-Stage Helical Gearbox with Second-Stage Double Gear Sets Using the MAIRCA Method

This paper provides a novel application of the multi-criteria decision-making (MCDM) method to the multi-objective optimization problem (MOOP) of creating a two-stage helical gearbox (TSHG) with second-stage double gear sets (SDGSs). The aim of the study is to determine the optimum major design components for enhancing the gearbox efficiency while reducing the gearbox volume. In this work, three primary design parameters are chosen to accomplish this: the gear ratio of the first stage and the coefficients of the wheel face width (CWFW) of the first and second stages. Additionally, the study is conducted with two distinct objectives in mind: the lowest gearbox volume and the maximum gearbox efficiency. Moreover, phase 1 and phase 2, respectively, are the two stages of the MOOP. Phase 2 handles the MOOP to identify the ideal primary design factors as well as the single-objective optimization problem to minimize the difference between the variable levels. Additionally, the Multi-Attributive Ideal–Real Comparative Analysis (MAIRCA) approach is selected to deal with the MOOP. The results of the study are utilized to determine the ideal values for three crucial design parameters in order to create a TSHG with SDGSs.

Multi-Objective Optimization of a Two-Stage Helical Gearbox with Second Stage Double Gear-Sets Using TOPSIS Method

The multi-criteria decision-making (MCDM) method was applied in a novel way in this study to the multi-objective optimization problem (MOOP) of designing a two-stage helical gearbox with double gear-sets in the second stage. Finding the best fundamental components to increase gearbox efficiency and decrease gearbox cross-section area was the aim of this study. Three main design factors were chosen for investigation in this work: the first stage gear ratio and the first and second stage coefficients of wheel face width (CWFW). Phase 1 solves the single-objective optimization problem to reduce the gap between variable levels, and phase 2 solves the MOOP to determine the optimal critical design factors. This additionally splits the MOOP into two phases. Additionally, the TOPSIS method was used as an MCDM approach to address the multi-objective optimization issue, and the entropy approach was used to compute the weight criteria. In this study, gearbox efficiency is calculated by considering power losses during idle motion. The multi-objective optimization of a helical gearbox with second stage double gear-sets is addressed using the TOPSIS technique for the first time.

Multi-Objective Optimization of a Two-Stage Helical Gearbox Using MARCOS Method

In order to address the Multi-Objective Optimization Problem (MOOP) in building a two-stage helical gearbox, this work presents a novel application of the Multi-Criterion Decision-Making (MCDM) method. The aim of the study is to determine the optimal primary design factors that will increase gearbox efficiency while decreasing gearbox volume. Three main design parameters were chosen for assessment in this work: the first stage’s gear ratio, and the first and second stages’ Coefficients of Wheel Face Width (CWFW). In addition, the MOOP is divided into two phases: phase 1 solves the single-objective optimization problem to reduce the gap between variable levels, and phase 2 solves the MOOP to determine the optimal primary design factors. Furthermore, the Entropy approach was picked to compute the weight criteria, and the MARCOS method was chosen as an MCDM method to handle the multi-objective optimization issue. The following are important characteristics of the study: Firstly, the MCDM method (MARCOS technique) was successfully applied to solve a MOOP for the first time. Secondly, this work has looked into power losses during idle motion to calculate the efficiency of a two-stage helical gearbox. The results of the study were used in the design of a two-stage helical gearbox in order to identify the optimal values for three important design parameters.

Application of a Multi-Criterion Decision-Making Method for Solving the Multi-Objective Optimization of a Two-Stage Helical Gearbox

This paper provides a novel application of a multi-criterion decision-making (MCDM) method to the multi-objective optimization problem of designing a two-stage helical gearbox. This study’s goal is to identify the ideal primary design elements that increase gearbox efficiency while reducing the gearbox cross-section area. In this work, three primary design parameters were selected for investigation: the gear ratio of the first stage and the coefficients of wheel face width (CWFW) of the first and second stages. The multi-objective optimization problem was further split into two phases: phase 1 solved the single-objective optimization problem of minimizing the gap between the variable levels, and phase 2 solved the multi-objective optimization issue of identifying the ideal key design factors. Moreover, the multi-objective optimization problem was handled by the SAW method as an MCDM approach, and the weight criteria were computed using the entropy approach. This study’s significant characteristics are as follows: First, a multi-objective optimization problem was successfully solved using the MCDM approach (SAW technique) for the first time. Second, the power losses in idle motion were investigated in this work in order to determine the efficiency of a two-stage helical gearbox. From this study’s findings, the ideal values for three major design parameters can be determined for the design of a two-stage helical gearbox.

Helical Gearbox Defect Detection with Machine Learning Using Regular Mesh Components and Sidebands.

The current paper presents helical gearbox defect detection models built from raw vibration signals measured using a triaxial accelerometer. Gear faults, such as localized pitting, localized wear on helical pinion tooth flanks, and low lubricant level, are under observation for three rotating velocities of the actuator and three load levels at the speed reducer output. The emphasis is on the strong connection between the gear faults and the fundamental meshing frequency GMF, its harmonics, and the sidebands found in the vibration spectrum as an effect of the amplitude modulation (AM) and phase modulation (PM). Several sets of features representing powers on selected frequency bands or/and associated peak amplitudes from the vibration spectrum, and also, for comparison, time-domain and frequency-domain statistical feature sets, are proposed as predictors in the defect detection task. The best performing detection model, with a testing accuracy of 99.73%, is based on SVM (Support Vector Machine) with a cubic kernel, and the features used are the band powers associated with six GMF harmonics and two sideband pairs for all three accelerometer axes, regardless of the rotation velocities and the load levels.

A comparative study on ML algorithms and ANN on fault diagnosis of a two-stage helical gearbox

In the modern world, condition monitoring is crucial to the predictive maintenance of machinery. Gearboxes are widely used in machineries and auto motives to achieve the variable speeds. The major problem in gearbox is catastrophic failure due to heavy loads, corrosion and erosion, results in economic loss and creates high safety risks. So, it is necessary to provide condition monitoring technique to detect and diagnose failures, to achieve cost benefits to industry. The main purpose of this study to use Machine Learning (ML) algorithms and Artificial Neural Network (ANN) which are very powerful and reliable tool for fault detection and its most important attribute is its ability to efficiently detect non-stationary, non-periodic, transient features of the vibration signal. To do the vibration study, an experimental setup was created, and various faults were induced faults of various kinds that usually occurred in the gearbox. The gear in the gear train was subjected to vibration analysis which was captured via a sensor. Signal processing was carried out using MATLAB Toolbox. To automatically identify the flaws in the helical gearbox, an artificial neural network (ANN) and several machines learning methods, including KNN, decision tree, random forest, and SMV, were trained by creating a database from the experiment conducted. The outcomes showed potential in accurately classifying the faults. The results show that ANN has the highest accuracy of 99.6% with a 6.5662 seconds computational time while SVM has the lowest accuracy of 96% among them along with the highest computational time of 21.324 seconds.

The investigation of the effect of operating conditions in gearboxes on efficiency

Efficiency is a concept that evaluates the optimal utilization of resources, including time, energy, finances, or materials, in order to accomplish a particular goal or objective. As widely acknowledged, energy losses occur in systems involving relative motion between interacting machine elements due to friction. In the case of a gearbox, these losses can arise from tooth friction in the gear mechanism, friction in sealing elements, friction in roller bearings, and the influence of the lubricant used in the system, all of which are subject to environmental conditions. This study aims to experimentally determine the efficiency of the gearbox under various operating conditions by considering the gearbox as a comprehensive system encompassing all its components. A measurement system was designed in order to obtain the efficiency of a gearbox. Experiments and measurements were carried out via software support. The measurement system contains two torque transducers, electrical resistive load device, an electrical motor with temperature measurement thermocouple, and two stage helical gearbox. In experiments conducted through computer commands, input revolutions were incrementally increased with 400 rpm intervals within the range of 700–2700 rpm. Moreover, experiments were carried out at different lubricant levels in the gearbox. At the same time lubricant temperature was measured and effects to the gearbox efficiency were investigated. Subsequently, different lubricant with distinct viscosity indices were employed. As a result of this experimental design, regime efficiency values were obtained for each case. Thus, power loss of the gearbox system has been determined. These results were examined using a general full factorial design. Analysis of variance (ANOVA) tables were created and the effects of the parameters on the system and the efficiency results were determined by checking whether the parameters were interacting or not. Finally, regression analysis was performed and the regression function was obtained in order to develop a predictive model to estimate the efficiency of a gearbox.

Optimization of a Two-stage Bevel Helical Gearbox using Multiple Objectives to Increase Efficiency and Reduce Gearbox Bottom Area

This study aims to look at multi-target optimization of two-stage bevel helical gearboxes to determine the best major design factors for reducing gearbox bottom area (GBA) and increasing gearbox efficiency (GE). Grey relation analysis (GRA) and the Taguchi technique were used to address the problem in two steps. Prioritizing the closure of the variable level gap, the single-objective optimization problem was addressed, followed by the multi-objective optimization problem, which identified the ideal primary design variables. Additionally, the first-stage gear ratio, allowable contact stresses (ACS), and first and second-stage coefficients of wheel face width (CWFW) were calculated. The outcomes of the study were used to determine the best values for five essential design features of a two-stage bevel helical gearbox (BHG).

Experimental analysis of vibration and noise characteristics of helical gears with nano-lubricant additives

PurposeThe purpose of this study is to investigate the effects of nanoadditive lubricants on the vibration and noise characteristics of helical gears compared with conventional lubricants. The experiment aims to analyze whether nanoadditive lubricants can effectively reduce gear vibration and noise under different speeds and loads. It also analyzes the sensitivity of the vibration reduction to load and speed changes. In addition, it compares the axial and radial vibration reduction effects. The goal is to explore the application of nanolubricants for vibration damping and noise reduction in gear transmissions. The results provide a basis for further research on nanolubricant effects under high-speed conditions.Design/methodology/approachHelical gears of 20CrMnTi were lubricated with conventional oil and nanoadditive oils. An open helical gearbox with spray lubrication was tested under different speeds (200–500 rpm) and loads (20–100 N·m). Gear noise was measured by a sound level meter. Axial and radial vibrations were detected using an M+P VibRunner system and fast Fourier transform analysis. Vibration spectrums under conventional and nanolubrication were compared. Gear tooth surfaces were observed after testing. The experiment aimed to analyze the noise and vibration reduction effects of nanoadditive lubricants on helical gears and the sensitivity to load and speed.FindingsThe key findings are that nanoadditive lubricants significantly reduce the axial and radial vibrations of helical gears under low-speed conditions compared with conventional lubricants, with a more pronounced effect on axial vibrations. The vibration reduction is more sensitive to rotational speed than load. At the same load and speed, nanolubrication reduces noise by 2%–5% versus conventional lubrication. Nanoparticles change the friction from sliding to rolling and compensate for meshing errors, leading to smoother vibrations. The nanolubricants alter the gear tooth surfaces and optimize the microtopography. The results provide a basis for exploring nanolubricant effects under high speeds.Originality/valueThe originality and value of this work is the experimental analysis of the effects of nanoadditive lubricants on the vibration and noise characteristics of hard tooth surface helical gears, which has rarely been studied before. The comparative results under different speeds and loads provide new insights into the vibration damping capabilities of nanolubricants in gear transmissions. The findings reveal the higher sensitivity to rotational speed versus load and the differences in axial and radial vibration reduction. The exploration of nanolubricant effects on gear tribological performance and surface interactions provides a valuable reference for further research, especially under higher speed conditions closer to real applications.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2023-0220/

Three Stage Helical Gearbox: A Review of Materials - Scope and Challenges

Many research articles on various helical gearbox stages are accessible in reputable journals. The majorities of earlier research, despite the fact that triple step helical gearboxes have several benefits, were confined on single step and double step helical gears. Lately, most researching experts who work in this field have started paying close attention to the importances of three stage helical gearboxes. Throughout this research, authors seek to carry out an exhaustive evaluation of the current triple step helical transmission articles for examining the most widely used survey designs, approaches, tools & techniques. The above investigation expansively analysed 315 journal articles on helical gearbox various stages and then used content analysis procedure with an inductive method of research for carrying out an organized review of 45 literatures on three step helix transmission box that appeared in different scientific publications over the preceding two decades. Apart from this; the study presents a broad assessment of currently utilized materials, several future possibilities and problems in employing different materials for various parts of gearbox and its casing. This important research finding indicates there’s an enormous potentiality towards dominating the area of research as well as continuing more chances for exploring growth of three stage helical gearboxes, which provides novel career opportunities for both experts and industrial professionals.

Optimization of a Two-stage Helical Gearbox with Second Stage Double Gear Sets to Reduce Gearbox Mass and Increase Gearbox Efficiency

This work aims to identify the key design components for lowering gearbox mass and raising gearbox efficiency by multi-target optimizing a two-stage helical gearbox (THG) with second-stage double gear sets (SSDGS). In the study, the Taguchi technique and grey relation analysis (GRA) were applied to handle optimization work in two phases. The single-target problem was addressed first to narrow the separation between variable levels, and then multi-target work was addressed to establish the best primary design variables. The first and second-stage CWFW coefficients, as well as the allowed contact stresses (ACS) and the gear ratio of the first stage, were computed. The outcomes of the study can be applied to determine the best values for the main essential design factors of a THG with SSDGS.

Applicability of Numerical Simulation to the Classification of Fluid Dynamic Loss in Aeroengine Transmission Gears

Abstract In high-speed gear systems for aeroengines, reducing the fluid dynamic loss, which accounts for the majority of power loss, can significantly improve fuel economy. However, few practical numerical examples are available regarding high-speed gas–liquid two-phase flows involving gear meshing and gear shrouds (gear enclosures, which are effective for loss reduction). Therefore, in this study, the porosity method for object boundaries including the gear meshing, the volume of fluid method, and the surface compression method for the gas–liquid interface was used as fast and numerically stable calculation methods. In addition, a gap was provided at the contact surface of the gear tooth surface to improve the calculation stability, and the oil properties were set considering the difference between the flow resistance in a two-phase flow and that in a single-phase flow (due to the separation of oil particles) to improve the calculation accuracy. To validate the numerical simulation method, a two-axis helical gearbox with a maximum peripheral speed of 100 m/s with specifications equivalent to aeroengine gears was used, and the air flow, oil flow, and fluid dynamic losses were validated. Once the practical accuracy was confirmed, the numerical simulation was used to understand the relationship between air and oil flows, torque, and the effect of the shroud. Consequently, the fluid dynamic loss could be classified phenomenologically.

Multi-objective Optimization of a Two-Stage Helical Gearbox to Improve Efficiency and Reduce Height

Multi-objective Optimization of a Two-Stage Helical Gearbox to Improve Efficiency and Reduce Height

Detecting Helical Gearbox Defects from Raw Vibration Signal Using Convolutional Neural Networks.

A study on the gearbox (speed reducer) defect detection models built from the raw vibration signal measured by a triaxial accelerometer and based on convolutional neural networks (CNNs) is presented. Gear faults such as localized pitting, localized wear on helical pinion tooth flanks, and lubricant low level are under observation for three rotating velocities of the actuator and three load levels at the reducer output. A deep learning approach, based on 1D-CNN or 2D-CNN, is employed to extract from the vibration image significant signal features that are used further to identify one of the four states (one normal and three defects) of the system, regardless of the selected load level or the speed. The best-performing 1D-CNN-based detection model, with a testing accuracy of 98.91%, was trained on the signals measured on the Y axis along the reducer input shaft direction. The vibration data acquired from the X and Z axes of the accelerometer proved to be less relevant in discriminating the states of the gearbox, the corresponding 1D-CNN-based models achieving 97.15% and 97% testing accuracy. The 2D-CNN-based model, built using the data from all three accelerometer axes, detects the state of the gearbox with an accuracy of 99.63%.

Application of the Taguchi Method and Grey Relational Analysis for Multi-Objective Optimization of a Two-Stage Bevel Helical Gearbox

This paper introduces a novel approach to deal with the multi-objective optimization of a two-stage bevel helical gearbox by applying the Taguchi method and Grey Relation Analysis (GRA). The goal of the study is to find optimal main design factors that minimize the gearbox volume and maximize the gearbox efficiency. To accomplish this, five main design parameters were selected: the coefficients of wheel face width (CWFW) of the bevel and the helical gear sets, the allowable contact stresses (ACS) of the first and the second stages, and the gear ratio of the first stage. Furthermore, two single targets were investigated: minimum gearbox volumes, and maximum gearbox efficiency. Also, the multi-objective optimization problem is solved through two steps: Step 1 for closing the gap between variable levels and Step 2 for determining the optimal main design factors. The study’s findings were used to introduce the optimum values of five major design parameters for designing a two-stage helical gearbox.

Multi-Objective Optimization of a Two-Stage Helical Gearbox Using Taguchi Method and Grey Relational Analysis

This paper presents a novel approach to solve the multi-objective optimization problem designing a two-stage helical gearbox by applying the Taguchi method and the grey relation analysis (GRA). The objective of the study is to identify the optimal main design factors that maximize the gearbox efficiency and minimize the gearbox mass. To achieve that, five main design factors. including the coefficients of wheel face width (CWFW) of the first and the second stages, the allowable contact stresses (ACS) of the first and the second stages, and the gear ratio of the first stage were chosen. Additionally, two single objectives, including the maximum gearbox efficiency and minimum gearbox mass, were analyzed. In addition, the multi-objective optimization problem is solved through two phases: Phase 1 solves the single-objective optimization problem in order to close the gap between variable levels, and phase 2 solves the multi-objective optimization problem to determine the optimal main design factors. From the results of the study, optimum values of five main design parameters for designing a two-stage helical gearbox were first introduced.

Measuring instantaneous angular speed using a gear wheel as material measure to detect pitting damage during an endurance test

Gearbox condition monitoring is mostly carried out using accelerometers at the housing. The long transfer path interferes with the information on damaged gears. Therefore, new technologies such as measuring the instantaneous angular speed (IAS) are gaining interest. But these require constructive changes in the power-transmitting elements. Therefore, this contribution uses magnetoresistive (MR) sensors and a minimally invasive integration approach to measure IAS. Three sensor classes are integrated: accelerometers at the gearbox housing, MR sensors, which use a gear wheel as a material measure and MR sensors, which use an encoder magnet at the end of the shaft. These sensor concepts are introduced by Koch et al. 2022 [1] and applied to a 3-stage bevel helical gearbox in this contribution. The first results are on artificial tooth flank damage. Therefore, this contribution focuses on real fatigue pitting damage.A back-to-back test stand is set up for the endurance test. The tests are carried out with an overload load at a constant speed to generate fatigue pitting damage. The results are evaluated in the frequency domain by exploring the gear mesh frequency (GMF) and sidebands modulated with the shaft frequency of the damaged pinion. Results show that with all sensor concepts, the damages can be detected. Influences when using a gear wheel as a material measure are described for one measurement concept. A feature to compare the damage-specific information over the endurance test is introduced and the influence of the transfer path is evaluated through analysis of the relative rise of damage-specific amplitudes.