Reliability analysis of aerospace planetary roller screw mechanism considering multiple failure modes

In recent years, time‐variant reliability issues have garnered widespread attention, particularly due to their consideration of the cumulative effects of material degradation and the time dependency of stochastic process loads. Methods based on the outcrossing rate are typically employed for time‐variant reliability analysis. However, they fail to effectively capture the correlations among multiple failure modes. To address this limitation, this paper proposes a time‐variant reliability analysis method that accounts for the correlation of multiple failure modes by integrating copula and PHI2. The method first utilizes Copula to analyze the correlations among various failure modes, followed by applying the PHI2 method for the time‐dependent reliability analysis of each individual failure mode. Ultimately, case studies confirm that the proposed method proficiently evaluates the time‐variant reliability of systems with multiple failure modes, yielding a maximum relative error below 5% compared to MCS and significant performance enhancements.

Time-varying loads, manufacturing errors, and assembly errors are the main factors leading to the performance degradation of the planetary roller screw mechanism. This paper proposes a comprehensive analysis method for the performance degradation of the planetary roller screw mechanism caused by time-varying loads and manufacturing and assembly errors. Firstly, a simulation analysis model of the planetary roller screw mechanism was established and its effectiveness was verified. A quantitative analysis was conducted on the influence of manufacturing and assembly errors on the load distribution, revealing the load-bearing mechanism under the influence of errors. Secondly, loading experiments were conducted on the planetary roller screw mechanism, and the degradation of its load-bearing performance was divided into the normal degradation stage, the accelerated degradation stage, and the failure stage. The experimental results prove that the initial transmission accuracy has a significant impact on the degradation of the load-bearing performance, determining the occurrence of the node where the accelerated degradation stage appears in the load-bearing performance. Thirdly, the wear status of the threads and gears was examined, and the results showed that material peeling was the main factor causing the degradation of load-bearing performance.

To reveal the dynamic characteristics of planetary roller screw mechanism, a dynamic model of planetary roller screw mechanism is developed in this study, which is based on the bond graph theory that accounts for friction, axial clearance, and screw stiffness. First, the bond graph models of friction, axial clearance, and load distribution are presented. Then, a bond graph model of the entire planetary roller screw mechanism for the dynamic analysis is established using the 20-sim software package, and the dynamic equations are solved using the Runge–Kutta–Fehlberg algorithm. Finally, the axial speed, axial acceleration, and contact force of the components are derived under different axial loads and with different axial clearances. Furthermore, the dynamic friction characteristics at different angular velocities of the screw and the dynamic stiffnesses for different axial clearances are also obtained. The results can provide a theoretical basis for planetary roller screw mechanism design with consideration of dynamic characteristics.

To reveal the dynamic load distribution characteristics of planetary roller screw mechanism under the high-speed operating conditions, based on the spiral surface equation and deformation coordination relationship, a static contact force calculation method of the roller-screw and roller-nut thread at the contact point is proposed, and a formula for calculating the contact angle after bearing is derived. On this basis, further considering the inertial force generated by using high-speed operation, a dynamic load distribution model for planetary roller screw mechanism thread was established. By comparing with the finite element contact model of planetary roller screw mechansim, the error is below 5%, which verifies the correctness of the model established. Finally, the influence of the parameters such as screw speed, axial load, pitch, and tooth flank angle on the distribution of dynamic load was analyzed. The results show that the inertia force causes the roller to have a tendency to move closer to the nut and away from the screw resulting in a decrease in dynamic contact force on the roller screw side and an increase in dynamic contact force on the roller nut side. The degree of uneven distribution of dynamic load is positively correlated with the screw speed and pitch, and negatively correlated with the tooth side angle. The size of axial load has a significant impact on the distribution of dynamic load.

Markov models are commonly used for unavailability analysis of redundant systems. However, due to the exploding states of Markov models for redundant systems, the states need to be merged to simplify the computation, which is called micro-Markov models. However, how to derive the failure rates and repair rates of the newly developed micro-Markov models has not been studied thoroughly. Therefore, this paper proposes detailed explanations and rules to derive the static unavailability by the micro-Markov models for thek-out-of-n:G systems with multiple failure modes. Firstly, two properties about applying the Markov models to the repairable system with independent multiple failure modes are presented. Based on these two properties, two rules are proposed for implementing the micro-Markov models. The micro-Markov models provide the exact same results for the repairablek-out-of-n:G system with multiple independent failure modes and repair mechanisms and approximate results for systems with multiple hybrid failure modes. A case study of safety integrity verification for safety instrumented systems is provided to illustrate the application of the proposed method. The conceptual comparison and numerical examples demonstrate the reasonability and usefulness of the proposed micro-Markov models.

Taking the electro-mechanical servo system as the research object, considering the contact stiffness, friction and clearance of the main components in the electro-mechanical servo system, the analysis model of the electro-mechanical servo system based on Planetary roller screw mechanism (PRSM) is established by using AMESim software. The results showed that the response speed of the system slowed down when the friction of PRSM was taken into account. The larger the clearance or the smaller the stiffness, the greater the fluctuation amplitude of the system response. After the controller was adjusted, the steady-state error of the system caused by the load force can be reduced quickly.

In order to reveal the error coupling mechanism of thread pair and gear pair in the planetary roller screw mechanism (PRSM), a transmission error calculation model considering the error of gear and thread was established. This paper analyzed the thread pair error firstly, including assembly errors, eccentricity errors and errors caused by load. Secondly, the errors of gear pair including profile deviation, helix deviation and pitch deviation were analyzed, then the matrix of tooth surface flexibility coefficient was obtained by finite element method, and the transmission errors of the gear were further obtained. Thirdly, according to the structural characteristics of transforming rotating motion into linear motion and the same speed of roller gear and roller thread in the PRSM, the circumferential errors of gear were converted into axial error of nut. Thus, the coupling relation between gear pair and thread pair was established. Finally, the final transmission error curve was obtained. The final transfer error was a sine-like curve and the amplitude equaled to 0.02957 mm, which increased by 11.59% compared to the unconsidered gear errors, and the fluctuation was greater.

Despite the substantive literature on remaining useful life (RUL) prediction, less attention is paid to the influence of epistemic uncertainty and aleatory uncertainty in multiple failure behaviors in the accuracy of RUL. The research question in this study was: can uncertainties be quantified in predicting the RUL of systems with multiple failure modes? The first objective was to quantify the uncertainties in the prediction of RUL, considering known multiple failure modes. This objective used vibration data from accelerated degradation experiments of rolling element bearings. The second objective was to calculate the uncertainties in the prediction of RUL, considering the multiple failure modes as unknown. The experimental data used in this objective were from run-to-failure tests of Li-ion batteries. An analysis was performed on how the uncertainties affect the RUL prediction in systems with known multiple failure modes and systems where the multiple failure modes were unknown. A Bayesian neural network (BNN) was used to quantify epistemic and aleatory uncertainty while predicting RUL. The results of the qualitative uncertainties on RUL in systems with multiple failure modes were presented and discussed. Also, the study yielded an RUL uncertainty quantification model for multiple failure modes. The proposed framework's performance in the RUL prediction was demonstrated. Finally, the epistemic and aleatory uncertainties were quantified in the system's RUL. It was shown that systems that fail due to the same failure mode tend to have similar uncertainty values over time. The results in this paper may lead to the design of more reliable systems that exhibit multiple failure modes.

Lubrication condition has a strong effect on the service ability of planetary roller screw mechanism (PRSM), so how to effectively identify the lubrication condition of PRSM is highly important in practical industrial applications. A dynamic separable convolution residual convolutional neural network (DSC-RCNN) method is proposed in this paper for the lubrication condition identification of PRSM. In the proposed method, a dynamic separable convolution (DSC) is developed by adopting depthwise separable convolution and dynamic convolution. To verify the learning competence of the proposed method, the PRSM failure test is carried out firstly and vibration data of the PRSM with and without grease are collected in multiple working conditions. Then, three experiments are implemented. The first one is to obtain the optimal number of the depthwise separable convolution in the DSC. The second one compares the effect of the DSC unit and the dynamic convolution unit on the diagnosis capacity of the proposed method. The last one compares SVM, BSA-SVM, AEs, LSSVM, LSTM, VGG-13, and the proposed method. The results reveal the best number of the depthwise separable convolution, the optimal unit of the proposed model and indicate that the DSC-RCNN has enormous recognition and transfer learning abilities.

Portable electronic products subjected to transient shock may exhibit multiple failure modes in vicinity of the interconnects. Failure is often diagnosed by loss of functionality using techniques including the built-in self test, which provides limited insight into reliability and remaining useful life. In this paper prognostic framework for electronic systems has been developed with neural network based self organizing maps. The presented approach resides in the pre-failure space with a focus on electronic systems with multiple failure modes. Unsupervised learning of the neural net has been used to train the neural net for identification of individual failure modes. Feature vectors have been developed based on damage pre-cursors from time-spectral measurements. The clustered damage pre-cursors have been correlated with failure modes of the underlying damage. Several chip-scale packages have been studied, with leadfree second-level interconnects including SAC305, SAC405 alloys. Transient strain has been measured during the drop-event using digital image correlation and high-speed cameras operating at 100,000 fps. Continuity has been monitored simultaneously for failure identification. In addition, explicit finite element models have been developed and various kinds of failure modes have been simulated such as solder ball cracking, trace fracture, package falloff and solder ball failure. Fault modes predicted by simulation based pre-cursors have been correlated with those from experimental data. Activation of different neurons in the lattice for various failure modes and combinations of failure modes has been demonstrated. Previously the authors have developed techniques based on statistical pattern recognition for leading indication of impending failure and detection of damage initiation and progression [Lall 2006 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> , 2007 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> , 2008]. Early classification of multiple failure modes in the pre-failure space is new.

PLIC-FSR-SYS: System reliability analysis based on parallel learning of influential components with filtered sample region

Electromagnets are often used in indirect control for industrial applications. The ability of an electromagnet to control objects should decrease with performance degradation. And electromagnets product poses a danger to people and objects in the working environment. So, it is very difficult to analyze the reliability of electromagnetic performance degradation because of the complicated working condition. Failure Mode and Effect Analysis (FMEA) is the most commonly used tool for product reliability analysis. The new version of FMEA uses integer as evaluation value, which cannot represent the hesitation psychology of the evaluator. The Action Priority (AP) table of the FMEA describes the relationship between the evaluation of influencing factors and the risk level of the failure mode, which provides rules for determining the risk level of the failure mode. However, the AP table may result in multiple failure modes having the same ranking, which does not align with the intention of FMEA to prevent failures. Therefore, this paper proposes a reliability analysis method for electromagnetic performance degradation based on FMEA and FIS. Firstly, the Double Hierarchy Hesitant Fuzzy Linguistic Term Set (DHHFLTS) is used as the evaluation language to describe the hesitation psychology of evaluators. Secondly, the AP table of FMEA is used as FIS fuzzy inference rule. In this way, the idea of FMEA to determine the risk level of failure mode is retained and the problem of FIS fuzzy rule making is overcome. Then, FIS defuzzification AP table inference results to determine the risk ranking of failure modes. This avoids situations where the order of failure modes is equal. Finally, a performance degradation model of the electromagnet is constructed based on the Wiener process, and the calculation results of the new method are verified.

An anomaly detection and failure mode classification method has been developed for electronic assemblies with multiple failure modes. The presented prognostic health management method targets the pre-failure space of the electronic assembly life to trigger repair or replacement of impending failures. Presently, health monitoring systems focus on reactive diagnostic detection of failure modes. Examples of diagnostic detection include the built in self test and on-board diagnostics. In this paper, damage pre-cursors from time-spectral measurements of the electronic assemblies has been measured under applied vibration and shock stimulus. The time-evolution of spectral content of the damage pre-cursors has been studied using joint time frequency analysis in a full-field manner on the printed circuit assembly. Frequency moments have been used to build a feature vector. Evolution of the feature vector with damage initiation and progression has been studied under shock and vibration. The feature vector from multiple locations in the board assemblies has been mapped into a de-correlated feature space using Sammon’s mapping. Several chip-scale packages have been studied, with SAC305 and SAC405 leadfree second-level interconnects. Transient strain has been measured during the drop-event using digital image correlation and high-speed cameras operating at 100,000 fps. Continuity has been monitored simultaneously for failure identification. In addition, explicit finite element models have been developed and various kinds of failure modes have been simulated such as solder ball cracking, trace fracture, package falloff and solder ball failure. The neural net has been trained using simulated data-sets created from error-seeded models with specific failure modes. The neural net has then been used to identify and classify the failure modes in board assemblies experimentally. Supervised learning of multilayer neural net in conjunction with parity has been used to identify the hard-separation boundaries between failure mode clusters in the de-correlated feature space. The assemblies have been cross-sectioned to verify the identified failure modes. Cross-sections indicate that the experimentally measured failures modes correlate well with the position of the cluster in the de-correlated feature space.

Simulation of polymer electrolyte membrane fuel cell degradation using an integrated Petri Net and 0D model

The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bounds of system failure probability. The second method is SA based Nataf approximation, in which SA is used to estimate the probability density function (PDF) and cumulative distribution function (CDF) for the approximately linearized performance function of each failure mode. After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated, Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions, and then the system failure probability can be estimated directly by numerical simulation using the joint PDF. The third method is SA based line sampling (LS). The standardization transformation is needed to eliminate the dimensions of variables firstly in this case. Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions, and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space. By comparing basic concepts, implementations and results of illustrations, the following conclusions can be drawn: (1) The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function; (2) the second method can give the estimation of system failure probability, and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions; (3) the SA based LS method can obtain the estimator of system failure probability, which converges to the actual value along with the increase of sample size. The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability, and it is acceptable for the structural system both with a single failure mode and with multiple failure modes, therefore it has the widest applicability.