Stiffness Criteria Research Articles

Применение высокопрочной стали для создания полувагонов повышенной грузоподъемности

Purpose: substantiation of the possibility to increase the load capacity of gondola cars using high-strength steel in the car body structure. Methods: gondola cars load capacity changing analysis. Numerical research of the effect of the steel yield strength value on the mass of the beam structure according to the criteria of strength and stiffness for a beam on two hinged supports operating in bending, and also according to the buckling criteria of a compressed beam. Gondola car body structure finite element analysis in order to confirm the strength and buckling parameters with the normative requirements. Results: the analysis of load capacity of universal fouraxle gondola cars built in the period from the beginning of production of the first Russian cars up to the present time was performed. Results of the analysis of the effect of steel yield strength on the mass of the structure according to the strength criteria and stiffness for a beam on two hinged supports operating in bending, and also according to the buckling criteria of a compressed beam was presented. High-strength steel technical requirements for welded structures of freight wagons is considered. Parameters for evaluating the suitability of rolled high-strength steel for freight wagon construction are given. The results of strength and stability analysis of the gondola car model 12-6744 with high-strength steel, which confirm the design compliance of the car in terms of normative parameters of strength and stability with the requirements of the existing standards are given. The gondola car model 12-6744 advantages are described, as well as the economic effect of its operation for the consignor. Practical importance: the possibility of using high-strength steel to increase the load capacity of gondola cars is substantiated. The gondola car model 12-6744 with high-strength steel was designed. Its advantages are given, and the economic effect of operating such a wagon for the consignor is shown.

Bowstring-type inerter negative stiffness damper for vibration control of slender towers

The difficulty of practical installation restrains the application of tuned damping devices in the high-performance vibration control of slender towers. In order to address this issue, a novel Bowstring-type Inerter Negative Stiffness Damper (BINSD) is proposed. The BINSD is composed of an inerter-negative-stiffness-dashpot system connected between the tower and a mass block (or a massless node) located on a vertical prestressed cable like a bowstring. In order to determine the multiple optimal parameters of the proposed BINSD, analytical parametric optimizations are investigated for the following three aspects. Firstly, the optimal tuning frequency and damping ratios are obtained via an analytical approach considering H∞ and H2 norms. Secondly, the optimal negative stiffness is determined by balancing the static and dynamic performances, particularly for practical excitations with mixed static and dynamic components (such as wind). Thirdly, the optimal installation height is analytically derived to fulfil a least negative stiffness criterion, which leads to an economic realization in practice. Finally, the effectiveness of the presented BINSD and corresponding optimal design approaches is numerically validated by the wind- and seismic- induced vibration control cases of a wind turbine tower. The proposed optimal design approaches lead to a high-performance, economic, and feasible design of BINSD.

Shear fatigue behaviour of interfaces between bituminous layers using 2T3C hollow cylinder apparatus and Digital Image Correlation

Evaluating the shear fatigue behaviour of the interface between two bituminous layers is important in order to assure the structure can withstand repeated loadings. The 2T3C (Torsion-Traction-Compression sur Cylindre Creux, in French) hollow cylinder apparatus developed at the University of Lyon/ENTPE can apply torsion, tension, and compression on hollow cylinder samples. In this study, the apparatus is combined with 3D Digital Image Correlation (3D-DIC) to study the fatigue behaviour of the double-layered hollow cylinder samples with the interfaces with a tack coat made of emulsified bitumen. The fatigue failure was observed at the interfaces and not in layers. Six fatigue criteria are proposed to determine the fatigue life of an interface. They are: (1) the 50% reduction of stiffness criterion; (2) the maximal phase angle criterion, (3) maximal dissipated energy criterion, (4) slope change in the dissipated energy evolution curve criterion, (5) slope change in the stress evolution curve criterion, and (6) slope change in the displacement gap at the interface evolution curve criterion. The first criterion is more conservative in comparison with the last five criteria.

Impacts of Rate of Change in Effective Stress and Inertial Effects on Fault Slip Behavior: New Insights Into Injection‐Induced Earthquakes

AbstractUnderstanding the physical mechanisms which link fluid injection with triggered earthquakes is critical in minimizing hazard in subsurface fluid‐injection operations. Currently, injection‐induced changes in effective stress on faults are considered as the main criterion in triggering seismic fault slip. However, rate of change in effective stress, together with inertial effects, are also be implicated in this criterion. We present a modified critical stiffness criterion to investigate the relative likelihood of triggering earthquakes during injection for different injection rate schedules (constant‐vs‐cycled‐vs‐increasing). A stability analysis of fault stress is used to define a critical stiffness as a function of magnitudes and rate of change in effective stresses. The relative potential for triggering earthquakes due to fluid injection is investigated using a coupled fluid‐flow‐deformation model. Polarities of change in critical stiffness are employed as an index to define the tendency for a transition from aseismic to seismic reactivation. During constant rate injection and self‐equilibration stages, the absolute magnitude of effective stress controls the transition. Conversely, the rate of change in effective stress dominates this transition when injection suddenly starts or stops, and inertial effects suppress the transformation to seismic slip. Cycling injection rates into a given fault is the most stable, followed by constant injection, with linear injection the least stable for the same total volume injected. High permeability reservoirs and strike‐slip faulting regimes reduce the potential of inducing seismicity. This work provides both new insights into assessing the seismic risks associated with injection and guidance for mitigation.

How Fault‐Normal and Shear‐Parallel Stiffness Influence Frictional Sliding Behavior

AbstractThe potential of faults to show earthquake‐generating slip instabilities depends not only on the intrinsic frictional properties of the fault zone, but also on the elasticity of the surrounding material. A velocity‐weakening fault is expected to show increasingly unstable frictional behavior with decreasing local elastic stiffness around the fault zone. Fault zone roughness can cause slip in the shear direction to be accompanied by fault‐normal movement, modulated by fault‐normal elastic properties, however these effects are poorly understood. Here, we systematically vary the stiffness surrounding the fault in both the shear‐parallel and fault‐normal directions, to investigate the origin of slip instabilities and changes in friction constitutive properties. We confirm the transition from stable sliding through slow slip to stick‐slip due to reduced fault‐parallel stiffness, and that the occurrence of different types of slip events can be explained by the ratio between shear and critical stiffness. In contrast, reducing the fault‐normal stiffness produces stick‐slip instabilities under conditions where the conventional critical stiffness criterion predicts stable sliding, and does not produce transitional slow slip events. Our data suggest that: (a) the stability criterion for frictional slip should be modified to incorporate fault‐normal stiffness, and (b) the unexpected slip instabilities may represent wrinkle‐like slip pulses, possibly due to a stiffness asymmetry introduced by lowering the fault normal stiffness on one side of the fault. This implies that earthquakes may occur when the fault‐normal stiffness, or bulk modulus for natural faults, is decreased and/or asymmetric across the fault zone, both of which may be common in nature.

Uneven Stiffness Coal Seam: A New Structural Factor Prone to Coal Burst Based on Stiffness Theory

The development of stiffness theory is constrained by its contradiction with engineering experience. Several easily overlooked details of stiffness theory were clarified, and a qualitative evaluation formula for the risk of coal burst was provided. Then a novel structure factor called uneven stiffness coal seam structure (USCS), which consists of high stiffness zone (HSZ), low stiffness zone (LSZ), and contiguous roof and floor, was proposed. Many areas prone to coal bursts, such as thinning zones, bifurcating areas, magmatic intrusion areas, and remnant pillar affected areas of coal seam, are the HSZs of USCSs. Comparative analysis of the uneven stiffness coal seam under different roof conditions and examination of the simplified trisection model of the USCS were conducted. Then 6 groups of 14 simplified 2D models using COMSOL5.2 was constructed based on controlled variable method to simulate different responses of the USCS with varying parameters under same working conditions. The results demonstrate the following: (1) coal bursts occur only when both the failure criterion and the stiffness criterion are simultaneously satisfied, the risk of coal burst (rCB) is the product of the risk of failure (rF) and the risk of instability (rI). (2) The pressure concentration function of USCS facilitates stress concentration from LSZ to HSZ, thus raising the rF in HSZ. The stiffness reduction function of USCS reduces the local mine stiffness (LMS) of the HSZ, allowing the system to meet the stiffness criterion even with a hard roof, thereby raising the rI in HSZ and reconciling the contrast between stiffness theory and engineering experience. Failures within HSZ of the USCS enables the roof strata to release bending deformation energy without roof breakage. (3) The normal stress of HSZ is positively correlates with the value of ERHRKHSL/KLSH; The LMS of the HSZ is positively correlated with the value of ERKL/KHHRSLSH. The USCS boasts significant advantages in integrating and harmonizing various existing theories and explaining multiple specific types of coal bursts. By applying relevant USCS findings, new explanations can be provided for engineering phenomena such as the time-delayed coal bursts, the inefficient pressure relief in ultra thick coal seams, and the “microseism deficiency” observed prior to certain coal bursts.

Optimization of vane pump structure based on modal characteristic analysis

In order to ensure the good stability and reliability of the vane pump, the modal characteristics of the mechanical structure were studied and analyzed through finite element simulation and impact modal testing. Based on the stiffness criterion, an optimization plan was proposed for the structure of the vane pump without reducing the natural frequency. Adopting tetrahedral adaptive mesh method, the mesh quality of the modal simulation model was verified to ensure the accuracy and efficiency of the calculation. In modal testing, force sensors and acceleration sensors were arranged reasonably. The excitation signal would be transmitted to the integrated vibration testing system for processing, and modal analysis and processing would be carried out through LMS Test Lab. Based on curve fitting, the spectrum and modal parameters of the tested structure could be obtained. The influence of different curvature radius of cover plates on natural frequencies were studied, and the results show that increasing the curvature radius within a certain range can enhance stiffness and improve processability.

Design and evaluation of hollow frame structures for the development of urban-centric two-passenger electric vehicles

This paper focuses on the design and evaluation of hollow frame structures for the development of two-passenger electric vehicles targeted for urban use. The primary problem addressed is the lack of focused research on efficient, lightweight, and safe electric vehicle frame designs, particularly for urban transportation needs. Through 3D simulation and Finite Element Analysis (FEA), this paper successfully develops a hollow frame design with dimensions of 2,148×800×640 mm and a weight of 40.77 kg that meets strength and stiffness criteria. The analysis shows that the design has an adequate safety margin with a safety factor of 2.053e+01. ASTM A36 steel is chosen as the material, balancing strength, stiffness, and cost. The results offer an innovative and practical solution to urban transportation issues, with broad potential applications in the electric vehicle industry. In particular, this study focuses on the specialized needs of urban-centric, two-passenger electric vehicles. The Finite Element Analysis (FEA) used here serves as a robust validation method, effectively reducing the need for extensive physical testing. This accelerates the R&D process and opens possibilities for future studies on alternative materials and dynamic loading conditions. The study's limitations and future research directions are also discussed. Moreover, the study's computational methods offer an eco-friendly alternative to traditional physical prototypes. This aligns with sustainability goals and provides methodologies for future studies. With rising urban populations, the demand for efficient vehicles is increasing. This study paves the way for city-focused, two-passenger electric cars that meet modern urban needs and sustainability goals

An Experimental Investigation of Fatigue Performance for A Flexure Spring

In order to prevent a free-piston Stirling cryocooler failure during mission life, the flexure spring's fatigue life is most critical and important. In the current research, an effort is made to examine fatigue life. The fatigue life testing of cryocooler flexures is frequently discussed in the literature. However, more information is needed about the economic approach and hardware needed for the testing. This research paper adopts the FEA approach of flexure spring and outlines the criteria for flexure fatigue testing. A moving coil linear motor was also designed and selected for the oscillating shaft and bending special-purpose flexure spring stack to validate stiffness criteria. The 108 no. of cycles required to validate the fatigue limit were also attained using the approach in a few days when testing at a relatively high frequency.

A Study on Numerical Analysis of High-Temperature And Oxidation Damage of C/C Composites

Due to coupling of oxidation damage and mechanical damage,failure mechanism of C/C composites is complex under high-temperature and oxidation environment.In this paper,establishment of cumulative damage analysis method is based on coupling of oxidation damage and mechanical damage.Based on this method,high-temperature and oxidation damage model of C/C composites is established: Initial damage criterion and degradation mode of stiffness in mechanical damage model are modified by oxidation state parameter;Diffusion coefficient of oxygen in oxidation damage model is modified by mechanical damage parameter.Through joint simulation of multiple physical fields of MATLAB and ABAQUS,oxidation damage and mechanical properties of C/C composites under high-temperature and oxidation environment are studied,which has a certain reference significance for structural failure prediction of C/C composites.

Analysis of Track Bending Stiffness and Loading Distribution Effect in Rail Support by Application of Bending Reinforcement Methods

Railway track is a linearly inhomogeneous object that consists of geometrical and elastic discontinuities such as bridges, transition zones, rail joints and crossings. The zones are subjected to the development of local instabilities due to quicker deterioration than the other tracks. Until now, there have been no efficient approaches that could fully exclude the problem of accelerated differential settlements in the problem zones. Many structural countermeasures are directed at controlling the sleeper/ballast loading with the help of fastenings/under-sleeper pad elasticities, sleeper forms and additional bending stiffness reinforcements. However, the efficiency of the methods is difficult to compare. The current paper presents a systematic approach in which the loading distribution effect in the rail support by application of two bending reinforcement methods is compared: auxiliary rail and under-sleeper beam. The study considers only the static effects to reach a clear understanding the influence of the main factors. The track equivalent bending stiffness criterion is proposed for comparing reinforcement solutions. The analysis shows that the activation of the bending stiffness of the reinforcement beams depends on the relative ratio of the rail fastenings stiffness and track support stiffness under sleepers (or under the under-sleeper beam). The comparison demonstrates that conventional auxiliary rail reinforcement solutions are ineffective due to their weak bending because of the high elasticity of fastening clips and the main rail fastenings. The share of an auxiliary rail is maximally 20% in the track bending stiffness and cannot be significantly improved by additional rails. The under-sleeper beam-based reinforcement solutions show noticeably higher efficiency. The highest effect can be achieved by the activation of the horizontal shear interaction between the under-sleeper beam and the rail. The additional track bending stiffness of the under-sleeper-based solutions is about 3.5 times more of the rail one and could be potentially increased to 6–10 times.

Embedded paired explicit Runge-Kutta schemes

Recently, Paired Explicit Runge-Kutta (P-ERK) schemes were introduced to accelerate the solution of locally-stiff systems of equations. P-ERK schemes use different numbers of active stages based on local stiffness criteria, significantly reducing computational cost relative to classical explicit Runge-Kutta schemes. In the current work we present a framework for incorporating an embedded pair within the original P-ERK formulation. By design, the embedded scheme has a slightly smaller stability limit than its corresponding base scheme. When combined with a suitable controller, the difference between the base and embedded solution approximations can be used to adapt the time step size to be as close as possible to, without exceeding, the stability limit of the base scheme. Numerical results using the high-order flux reconstruction approach for spatial discretization of the compressible Navier-Stokes equations are presented for flow over a circular cylinder, a plunging and pitching NACA 0012 airfoil, and a stalled NACA 0020 airfoil. It is demonstrated that adaptive time stepping using embedded P-ERK schemes yields excellent agreement with reference data, while being up to seven times less computationally expensive than classical embedded pairs for all cases.

Effects of phyllosilicate content on the slip behavior of fault gouge: Insights from room-temperature friction experiments on quartz–talc mixtures

Shallow slow slip events (SSEs) occur on the shallowest reaches of subduction megathrust faults. To investigate how phyllosilicate fraction in quartzo-feldspathic sediments influences the style of fault slip behavior, we conducted frictional sliding experiments on various binary mixtures of quartz and talc using a biaxial testing apparatus at room temperature, room humidity, sliding velocities of 2 or 0.66 μm/s, and a normal stress of 10 MPa. With increasing talc content, the steady state coefficient of friction decreases from 0.7 to 0.2 in association with a transition from velocity-weakening (VW) to velocity-strengthening (VS) behavior. For the gouges with 0–10 wt% talc, fault slip behavior, following velocity steps, transitions from regular stick slips via sustained oscillations to attenuated oscillations with talc content. The oscillations emerge only in a narrow range of talc contents (i.e., 4–10 wt%) at near velocity-neutral conditions. The observed transition is attributed to an increase in the stiffness ratio K = k/kc, where k is the elastic stiffness of the system and kc is the critical stiffness of the fault, although K is larger than 1 for both stick-slip and sustained-oscillation behaviors, and thereby the critical stiffness criterion is not satisfied. We also find that for unstable slip events, the smaller the stress drop magnitude, the slower the peak slip velocity. Our results suggest that mixed gouges containing VW and VS materials show velocity-neutral behavior and facilitate the nucleation of shallow SSEs, although finely tuned rate-and-state friction parameters are required to allow spontaneous slow slip.

МОДЕЛЮВАННЯ НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ ТОНКОСТІННИХ КУПОЛІВ З ПОЛІКАРБОНАТУ ДЛЯ РАЦІОНАЛЬНОГО ПРОЕКТУВАННЯ

The paper contains the further developed of method for calculating thin-walled dome systemswithout a stationary foundation. Have been carried out the detailed analysis of the fundamental design solutions for frameless collapsible spherical polycarbonate domes, which are used by modern world manufacturers of these structures. Have been done a brief description of the momentless theory of the operation of spherical shells, which is adapted for polycarbonate domes. Have been considered a simplified analytical model of the stress-strain state of a spherical shell with an equatorial diameter of up to5 m under the influence of climatic influences for the subsequent verification of detailed models. Have been developed highly detailed finite element models of domes of different sizes, taking into account technological openings and structural stiffeners (support ring and door frame) under the wind, snow, ice loads and under other climatic influences. Have been identified the fragments with the highest stresses from various loads and forms of the deformation of the structure.Have been considered separately the issues related to the loss of shape stability, position and balance of a thin-walled spherical shell, as a light temporary structure. Have been proven that the worst influence on the dome structures is the windinfluence, based on the stability criterion. Have been determined the estimated value of the aerodynamic lifting force from wind effects on the dome. Have been proven that the lifting force far exceeds the stabilizing force of the weight of a thin-walled dome. Have been revealed with the help of the performed calculations, it was that a frameless spherical polycarbonate dome inevitably БУДІВЕЛЬНІ КОНСТРУКЦІЇНАУКОВО-ТЕХНІЧНИЙ ЖУРНАЛ “СУЧАСНІ ТЕХНОЛОГІЇ, МАТЕРІАЛИ І КОНСТРУКЦІЇ В БУДІВНИЦТВІ”84loses its balance stability due to the action of wind loads and requires unfastening with anchors. Have been proposed a rational method for anchoring dome structures at temporary earthen construction sites using geo-screws or metal screw piles. Have been revealed the addiction between the radius of curvature of a spherical dome and the rational thickness of polycarbonate based on the criteria of stiffness and strength. Have been formulated the constructive recommendations regarding the rational design of polycarbonate dome systems. Have been developed the technological regulations for the further safe operation of domes, and have been outlined the directions for further scientific research on this topic

Analytically optimal parameters of supplemental brace-damper system in single-degree-of-freedom structure based on stability maximization criterion

In this study, optimal parameters (i.e., optimal additional stiffness ratio α and damping ratio λ) for supplemental brace-damper system in a single-degree-of-freedom (SDOF) structure are analytically derived. Different from the design formulations for supplemental brace-damper system proposed by Londoño, which are essentially fitting formulae through extensive parametric study, analytically optimal parameters for supplemental brace-damper system are derived by combining the research work by Londoño and the stability maximization criterion (SMC). Similar to Optimum Brace Stiffness (OBS) criterion and Optimum Damper Size (ODS) criterion proposed by Londoño, SMC-based OBS criterion and SMC-based ODS criterion are respectively proposed to assure a desired structural performance represented by the targeted overall damping ratio of the considered system. Through numerical study, it is demonstrated that the seismic response of the proposed SMC-based OBS criterion and SMC-based ODS criterion excellently agree with those of the existing OBS criterion and ODS criterion, respectively.

Experimental and Numerical Investigations of RC Frame Stability Failure under a Corner Column Removal Scenario

In recent decades, interest in the resistance of buildings and structures to progressive collapse has been increasingly sparked in research communities. Although several experimental, numerical, and analytical research projects on the robustness of building frames under a column removal scenario have been implemented, some aspects of this problem remain understudied. These aspects encompass failure mechanisms of reinforced concrete frames with slender columns, as well as criteria used to evaluate such failures. This paper focuses on experimental and numerical investigations of the structural behavior and failure of a scale reinforced concrete frame with slender columns under a sudden corner column removal scenario. In addition, we analyze the stability failure mechanism of a reinforced concrete frame with slender columns and the tangent stiffness criterion, which allow for evaluation of the ultimate state of a structure subjected to an accidental impact. A scale physical model of a reinforced concrete frame of a multistory building was designed and tested using the theory of functional similarity. For numerical study purposes, a finite element model was made that exactly the same as the test frame. We validated the findings by comparing simulation results and experimental data. The studies on the behavior of a reinforced concrete frame subjected to quasistatic loading with unequal concentrated loads identified the load transfer between columns through beams. Although these effects were minor in the frame under consideration, they can become more significant in cases of long-term loading. Numerical simulation and physical modeling of an accidental impact allowed for identification of the mechanism of load capacity exhaustion triggered by stability failure. Such failure was fragile. The moment of stability failure of the column of the experimental frame corresponded to the extremum on the force–displacement curve, indicating that zero tangent stiffness was reached. Hence, a criterion of tangent stiffness can be proposed for evaluation of the ultimate state of a structure subjected to an accidental impact.

Dynamics and Stability of Magnetic-Air Hybrid Quasi-Zero Stiffness Vibration Isolation System

With the improvement of machining accuracy, external low frequency vibration has become one of the most important factors affecting the performance of equipment. The theory of quasi-zero stiffness vibration isolation shows favorable low frequency vibration isolation effect. However, the theory, mechanical properties and dynamics of the system still need to be studied and expanded. Based on our previous research on the structure of a magnetic-air hybrid quasi-zero stiffness vibration isolation system, the nonlinear mechanical expression of positive and negative stiffness structure has been analyzed in this paper, to improve application of the system and provide a theoretical basis for sequential studies of active control. To provide the judgment criteria and basis for the application of quasi-zero stiffness, a more accurate quasi-zero stiffness mechanical model was to be established, and the judgement criterion and stability of quasi-zero stiffness was to be discussed and analyzed. Then, the dynamical model based on external low frequency vibration was developed, to investigate the stability and natural frequency. At the same time, the influence of different feedback parameters on the amplitude frequency characteristics has been discussed, which provides a basis for the future study of active control. Finally, we carried out simulation and experimental analysis to verify the stiffness of high static and low dynamic and the low frequency vibration isolation effect of the vibration isolation system.

Effects of reinforcing steel tanks with intermediate ring stiffeners on wind buckling during construction

Many tank structures may not be stable during the construction phase, and this may lead to their becoming vulnerable to buckling under environmental loading conditions such as wind. Installing intermediate ring stiffeners of the proper size at the mid-height of the cylindrical shell may be the most effective way to stabilize these structures, especially under the effects of wind action. In the study, analytical and numerical studies were conducted to identify the required strength and stiffness for the intermediate ring stiffener. First, a new cylindrical shell-to- intermediate ring stiffness ratio was derived by considering curved beam and shell membrane theories. For strength criteria, the tributary height and the effect of shell- ring interaction on the internal forces and moments were examined by making use of Linear Analysis (LA) and Geometrically Nonlinear Analysis (GNA). The stress resultants developed in the intermediate ring stiffener were identified so that they could be used as strength criteria. For stiffness criteria, by considering the changes in the buckling resistance based on the developed stiffness ratio, an expression to compute the minumum intermediate ring stiffness was determined. In addition, Geometrically Nonlinear Analysis including Imperfections (GNIA) was also performed to examine the effect of the geometric imperfections on buckling strength of the steel tank with an intermediate ring stiffener, taking different imperfection amplitudes into account. The developed design equations in simple algebraic form can be utilized for the structural stability of cylindrical steel tanks during erection.

Topology Optimization of a Bell Crank Lever Based on Stiffness and Mass using Finite Element Analysis

The following paper represents the topology optimization of a bell crank lever used in trucks. Current trends indicate a steep rise in the use of topology optimization in all fields. There arises a need for such optimized parts in the automotive industry to increase the overall efficiency of any vehicle. The aim of the present research is to optimization of a bell crank lever arm made of AISI A514 Steel used in trucks and maximizes its performance based on criteria of stiffness and mass. Initially, the model is subjected to loading conditions in accordance with a worst-case scenario and optimized accordingly. The optimized and existing bell crank lever is subjected to static analysis using FEA. Results show a 22 % mass reduction of the crank (3395.71 grams to 2641.02 grams) and a 40% stiffness increase (389.32N/mm to 644.988N/mm) which suits the purpose of the study.

An experimental method for determining the service life and reliability of the CNC lathe main spindle bearing assembly

The main spindle bearing assembly (MSBA) plays an important role in the quality and service life of CNC machine tools and industrial equipment. The MSBA is usually evaluated based on the allowable wear or the stiffness independently combined with the vibration characteristics. Therefore, it is very important to determine the service life of MSBA when the wear reaches the allowable value, and the stiffness is reduced to the allowable value. This paper studies the simultaneous relationship of wear, stiffness, and vibration characteristics of MSBA in a CNC lathe. The results show that the service life of MSBA is different when evaluated based on each criterion (wear or stiffness). The stiffness of the MSBA is reduced to the allowable limit [J] = 200 N/μm with a Root Mean Square (RMS) value of about 5.75 mm/s2. The wear of the MSBA reaches the allowable limit [δa] = 5 μm with an RMS value of about 4.5 mm/s2. The life of MSBA calculated according to the stiffness criterion is about 1.18 times higher than that calculated based on the wear criterion. The average life of MSBA with standard lubrication according to the wear criterion reaches ∼15,799 h and RMS reaches ∼2.4508 mm/s2.