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The purpose of this paper is to analyze the time-dependent reliability of harmonic drive.

The transient finite element analysis (FEA) of harmonic drive is established to calculate the stress under different loads. Combined with the residual strength model and random variables, the time-dependent reliability model of harmonic drive is deduced by the stochastic perturbation method and Edgeworth series. Based on accelerated life tests, the degradation parameters are estimated by maximizing likelihood function. Under variable load, the key stress from transient FEA is transformed into probability density function by kernel density estimation, and the residual strength model is modified by adding adjustment factors to deal with strength degradation under different loads.

The critical position of stress concentration from transient FEA is consistent with the fatigue fracture position at the accelerated life test sample. Compared with the time-dependent reliability method with equivalent circular-shell static stress or empirical degradation parameters, the proposed method has the smallest prediction error of failure life. Under variable load, the state function should be expanded to second-order series for avoiding error items relevant to variance. The failure life expectation under random variable load is smaller than that under constant load.

The time-dependent reliability method of harmonic drive is firstly proposed under constant and variable load. The transient FEA of harmonic drive is established to calculate the stress for strength analysis. The accelerated life test of harmonic drive is conducted for degradation parameters estimation. The adjustment factor is added to the residual strength model for strength degradation under different loads.

The purpose of variable loading conditions (392 N-785N-392N-785N) with break-in period were used to study interactions between zinc dialkyl dithiophosphate (ZDDP) 0.1 P% (phosphorus) and fine-grade molybdenum disulfide (MoS₂) 3%, in different mixtures of NLGI 2 lithium stearate grease. Four-ball wear tests were used to evaluate the tribological properties of different grease mixtures such as coefficient of friction and wear. ASTM 2266 as reported by earlier studies is useful, but it is not representative of real-life applications where variable loads and speeds and different break-in periods play a role and could change the results and the nature of tribofilms.

In this study, chemical and mechanical properties of tribofilms were examined. Moreover, design of experiment was used to examine the data and shorten experimentation time. Research described here is investigating variable loading conditions for real-life applications by using a break-in period of 2 min at the start to minimize asperities and establish a clean surface. Design expert (DOE) analyzes responses to reveal those variables that are single factor and those that are multifactor whether synergistically or antagonistically.

The results indicated that spectrum loading with break-in period showed reduction in wear when tested in greases with ZDDP/MoS₂ combinations. Ramping up or down the load every 7.5 min for a rotational speed of 1,200 rpm and a total of 36,000 revolutions or 30-min time slowed the wear properties of lithium-based grease under different MoS₂ and ZDDP concentrations. Experiments indicated that wear was largely dependent on the loading condition and ZDDP additives during specific break-in period at 1,200 rotational speed. It is believed that MoS₂ greases perform better under spectrum loading and under constant loading when mixed with ZDDP phosphorus.

This research indicates that there is a synergistic interaction between ZDDP, MoS₂ and variable loading especially when a break-in period is applied. The results indicated that wear was largely dependent on the specific speed used with spectrum loading as presented in the energy dispersive spectroscopy and the Auger electron spectroscopy analysis, and thus a 3% MoS₂ grease with ZDDP (phosphorus: 0.1 Wt.%) are needed to improve the wear resistance and improve the friction characteristics.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-01-2024-0016/

The non-stationary operational wind loads vary in time and site and has remarkable effect on wind turbine drive train. The purpose of this paper is to determine the effects of wind class 3 and 7 on the life of wind turbine drive train. The two-wind class 3 and 7 are described by average wind speed and weight factor and effects of two variables on wind energy generation and wind turbine drive train studied.

The load distribution method is used to calculate stress range cycles for wind class 3 and 7. To determine the rise of force on wind turbine drive train, the load cycle method is proposed. The fatigue damage model is studied with respect to influence of different wind speeds and wind shear factor and then results analysed accordingly. Also sensitivity analysis has been carried out to assess the percentage of drop of energy generation and rise of tangential force for wind class 3 and 7. Linear fit method is used to determine the inclination of wind variation and wind shear of wind class 3 and 7. In this regard, two practical wind sites fall under the wind class 3 and 7 and 1.5 MW wind turbine have been taken in to account.

The results showed that the average rise of force on wind turbine drive train is 37.5% which can influence the drop in energy 34.7% for wind class 3. Similarly, the results of wind class 7 are showing that the average rise in force and drop in energy found to be 49.05% and 51.16%, respectively. The wind class 7 have higher tendency of wind fluctuations and weight factor that can cause a damage to wind turbine drive train components. The results showed that when wind speed increases to rated power 11.5 m/s the damages occurred and remain steady. Similarly, when weight factor increased from 0.18 to onwards the damage occurred. The increased wind loads increased the tangential loads on the wind turbine decreased life of the gearbox.

The results of study suggest that wind turbine should be design according to site specific wind environment for maximum energy generation and lowers the wind loads on the drive train component.

The paper attempts to establish the connection between structural reliability and structural optimization for the particular case of plastic structures. Along this line, the paper outlines a reliability‐based optimization approach to design plastic structures with uncertain interdependent strengths and acted on by random interdependent loads. The importance of such interdependencies, and of some of the other statistical parameters used as input data in probabilistic computations, is demonstrated by several examples of sensitivity studies on both the probability of collapse failure as well as the reliability‐based optimum solution.

Engineering components/structures are usually subjected to complex and variable loads, which result in random multiaxial stress/strain states. However, fatigue analysis methods under constant loads cannot be directly applied to fatigue life prediction analysis under random loads. Therefore, the purpose of this study is how to effectively evaluate fatigue life under multiaxial random loading.

First, the average phase difference is characterized as the ratio of the number of shear strain cycles to the number of normal strain cycles, and the new non-proportional additional hardening factor is proposed. Then, the determined random typical load spectrum is processed into a simple variable amplitude load spectrum, and the damage in each plane is calculated according to the multiaxial fatigue life prediction model and Miner theory. Meanwhile, the cumulative damage can be calculated separately by projection method. Finally, the maximum projected cumulative damage plane is defined as the critical plane of multiaxial random fatigue.

The fatigue life prediction capability of the method is verified based on test data of TC4 titanium alloy under random multiaxial loading. Most of the predicting results are within double scatter bands.

The objective of this study is to provide a reference for the determination of critical plane and non-proportional additional hardening factor under multiaxial random loading, and to promote the development of multiaxial fatigue from experimental studies to practical engineering applications.

Engineering components/structures with geometric discontinuities normally bear complex and variable loads, which lead to a multiaxial and random/variable amplitude stress/strain state. Hence, this study aims how to effectively evaluate the multiaxial random/variable amplitude fatigue life.

Recent studies on critical plane method under multiaxial random/variable amplitude loading are reviewed, and the computational framework is clearly presented in this paper.

Some basic concepts and latest achievements in multiaxial random/variable amplitude fatigue analysis are introduced. This review summarizes the research status of four main aspects of multiaxial fatigue under random/variable amplitude loadings, namely multiaxial fatigue criterion, method for critical plane determination, cycle counting method and damage accumulation criterion. Particularly, the latest achievements of multiaxial random/variable amplitude fatigue using critical plane methods are classified and highlighted.

This review attempts to provide references for further research on multiaxial random/variable amplitude fatigue and to promote the development of multiaxial fatigue from experimental research to practical engineering application.

Loading condition and minimizing friction and wear using molybdenum disulfide grease in aircraft engine bearings are the focus of this research. The relationship between the milled and unmilled MoS₂ (molybdenum disulfide) greases to its tribological properties, such as coefficient of friction, wear and chemical-mechanical properties of tribofilms, is examined for constant extreme pressure loading and spectrum or actual loading.

In this study, the design of experiments (DOE) approach was used to analyze the different loadings and speeds at a specific duration of 36,000 revolutions to examine the lithium base grease wear behavior with milled and unmilled MoS₂ powder. Load is treated as variable that simulates actual conditions under 1,200 and 600 rpm rotational speeds using the four-ball test with chromium steel ball bearing aircraft grade E52100.

The results indicated that ball-milled MoS₂ grease tests showed reduction in wear and friction under all conditions, especially spectrum or actual loading. Unmilled MoS₂ powder exhibited worse wear outcomes than the milled one. The SEM and AES analyses indicated that a tribofilm is formed on the wear surface of the milled powder grease, especially at variable loading and initially at lower loads in the ramp-up tests that significantly enhanced the contact characteristics and prevented abrasion at higher loads.

This research indicated that the wear resistance in actual loading might be due to frictional heating generated during the ramping-up conditions where it provided a protective film that enhanced the steady-state friction for the duration of the test. Several researchers used ASTM standards to work on constant loading conditions. This is the first time that reduced milled MoS₂ powder showed significant improvement in grease performance.

This study aims to explore and empirically test variables influencing material delivery schedule inaccuracies?

A mixed-method case approach is applied. Explanatory variables are identified from the literature and explored in a qualitative analysis at an automotive original equipment manufacturer. Using logistic regression and random forest classification models, quantitative data (historical schedule transactions and internal data) enables the testing of the predictive difference of variables under various planning horizons and inaccuracy levels.

The effects on delivery schedule inaccuracies are contingent on a decoupling point, and a variable may have a combined amplifying (complexity generating) and stabilizing (complexity absorbing) moderating effect. Product complexity variables are significant regardless of the time horizon, and the item’s order life cycle is a significant variable with predictive differences that vary. Decoupling management is identified as a mechanism for generating complexity absorption capabilities contributing to delivery schedule accuracy.

The findings provide guidelines for exploring and finding patterns in specific variables to improve material delivery schedule inaccuracies and input into predictive forecasting models.

The findings contribute to explaining material delivery schedule variations, identifying potential root causes and moderators, empirically testing and validating effects and conceptualizing features that cause and moderate inaccuracies in relation to decoupling management and complexity theory literature?

Bearings in electric machines often work in high speed, light load and vibration load conditions. The purpose of this paper is to find a new fatigue damage accumulation rating life model of ball bearings, which is expected for calculating fatigue life of ball bearings more accurately under vibration load, especially in high speed and light load conditions.

A new fatigue damage accumulation rating life model of ball bearings considering time-varying vibration load is proposed. Vibration equations of rotor-bearing system are constructed and solved by Runge–Kutta method. The modified rating life and modified reference rating life model under vibration load is also proposed. Contrast of the three fatigue life models and the influence of dynamic balance level, rotating speed, preload of ball bearings on bearing’s fatigue life are analyzed.

To calculate fatigue rating life of ball bearings more accurately under vibration load, especially in high speed and light load conditions, the fatigue damage accumulation rating life model should be considered. The optimum preload has an obvious influence on fatigue rating life.

This paper used analytical method and model that is helpful for design of steel ball bearing in high speed, light load and vibration load conditions.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2019-0180/

Load forecasting is important to any electrical grid, but for the developing and third-world countries with power shortages, load forecasting is essential. When planed load shedding programs are implemented to face power shortage, a noticeable distortion to the load curves will happen, and this will make the load forecasting more difficult.

In this paper, a new load forecasting model is developed that can detect the effect of planned load shedding on the power consumption and estimate the load curve behavior without the shedding and with different shedding programs. A neuro-Fuzzy technique is used for the model, which is trained and tested with real data taken from one of the 11 KV feeders in Najaf city in Iraq to forecast the load for two days ahead for the four seasons. Load, temperature, time of the day and load shedding schedule for one month before are the input parameters for the training, and the load forecasting data for two days are estimated by the model.

To verify the model, the load is forecasted without shedding by the proposed model and compared to real data without shedding and the difference is acceptable.

The proposed model provides acceptable forecasting with the load shedding effect available and better than other models. The proposed model provides expected behavior of load with different shedding programs an issue helps to select the appropriate shedding program. The proposed model is useful to estimate the real demands by assuming load shedding hours to be zero and forecast the load. This is important in places suffer from grid problems and cannot supply full loads to calculate the peak demands as the case in Iraq.