Modification Coefficient Research Articles

A Novel Comprehensive Method for Modeling and Analysis of Mesh Stiffness of Helical Gear

The mesh stiffness of gear pairs used in aerospace applications, such as geared turbofan, has a vital influence on vibration and noise. To compensate for the deficiencies of the conventional method that does not consider slice coupling and structure coupling simultaneously, a comprehensive mathematical model for computing the mesh stiffness of helical gears is established. In this novel model, the effect of structure coupling and slice coupling between neighboring sliced gears are considered. The effect of the axial component of meshing force is also taken into account simultaneously. The results obtained by the comprehensive model are consistent with the finite element method and it proves that the novel mathematical model is sound. The influences of the helical angle and addendum modification coefficient on mesh stiffness are studied. The results show that the mesh stiffness of helical gears would be decreased in multiteeth regions caused by structure coupling. With or without consideration of the axial component, the relative mean values of mesh stiffness become larger with an increasing helical angle. The fluctuation value of mesh stiffness decreases when a positive addendum modification coefficient is adopted. The addendum modification also changes the phase of mesh stiffness. This study is helpful for a vibration analysis of gear transmission systems.

A finishing method for the continuous generation of spur face gears with shaving cutters

Face gear drives have been widely applied in power transmission, but the finishing of continuous generation is a difficult problem. This is mainly because the teeth of face gears are on a plane, which leads to interference by worm grinding. Hence, a shaving method for face gears is proposed in this paper. This work studies the theory of face gear shaving, the causes of mid-concave phenomena based on load tooth contact analysis (LTCA), a solution for the modification coefficient of the shaving cutter and a control method for the cutter location point. The experimental results show that the maximum machining error is −12.7μm, that many generating lines appear and that the residual stress increases by 49.2% in comparison with that of the grinding tooth surface. The present study suggests that the shaving method for spur face gears can not only achieve the finishing of continuous generation but also improve the surface integrity of the gear.

Effects of bubble coalescence and breakup models on the simulation of bubble columns

This work investigates the effects of coalescence and breakup models on the radial distribution of gas holdup and local bubble size distribution in a laboratory scale bubble column operated at 0.11 m/s, 0.14 m/s, 0.19 m/s and 0.23 m/s. The results quantitatively show the influences of bubble coalescence due to various mechanisms, coalescence efficiency calculated by different models, modification coefficients for coalescence rates, critical energy required for breakup and bubble breakage caused by large scale eddies and viscous shear on numerical simulations. Furthermore, qualitative analysis is performed to analyze the effects of these factors. The performance of various models is evaluated (e.g. Han’s breakup model and Das’s coalescence model). Some optimized combinations of coalescence and breakup models that can be used to accurately predict the local gas holdup and bubble size distribution in laboratory scale bubble columns operated at heterogeneous regime are proposed.

Design optimisation of mating helical gears with profile shift using nature inspired algorithms

ABSTRACT Profile shift of the gear significantly affects its form, zone, stress factors, transversal and face load factors. In this paper, an optimum solution to the problem of mating helical gears design considering profile shift is given. The objective of the problem is to minimise volume taking into account tooth root bending strength, contact pressure, face width, and addendum modification coefficients as constraints. The design variables, namely, the module, the face width, the number of teeth, and profile shift coefficients of both gears are considered. Nature-inspired algorithms, namely, Simulated Algorithm (SA), Fire Fly Algorithm (FA), Cuckoo Search (CS), Particle Swarm Optimisation (PSO) and Teaching Learning-Based Optimisation (TLBO) algorithms are employed. Results of simulation with and without profile shift, performance of various algorithms are analysed and validated with literature. Results show that CS and PSO algorithms give the best optimum volume. They also significantly reduce volume by 1.91%, when compared to literature. CS algorithm gives the best optimum design parameters. Furthermore, results show the volume of the mating helical gears with profile shift is much lesser than the pair without profile shift.

Indicator Characterizing Carbonyl-Dependent Modification of Erythrocytic Superoxydismutase as a Biochemical Marker of Oxidative Stress in Coronary Heart Disease

Aim To study the oxidative modification of red blood cell Cu,Zn superoxide dismutase (SOD) in patients with ischemic heart disease (IHD) in vivo and in vitro to substantiate the use of a new oxidative stress marker.Material and methods Red blood cell Cu,Zn SOD was measured by depression of nitrotetrazolium blue reduction by the superoxide anion generated in xanthine oxidase xanthine oxidation. Red blood cell Cu,Zn SOD was measured immunochemically. The biochemical study was performed in the control group (patients with low extremity fracture without known history of cardiovascular diseases and hyperlipidemia) and in groups of patients with acute myocardial infarction, stable angina, and decompensated heart failure. For evaluation of oxidative stress intensity in IHD patients, an empirical SOD oxidative modification coefficient (OMCSOD) was proposed, which is a Cu,Zn SOD activity / Cu,Zn SOD content ratio.Results The red blood cell Cu,Zn SOD activity was significantly decreased in all IHD groups compared to the control group. Furthermore, OMCSOD was also considerably decreased in IHD patients, which warrants the use of this biochemical index as an oxidative stress marker.Conclusion It was shown that the Cu,Zn SOD modification was induced by interaction of the enzyme molecules with a natural dicarbonyl, malonic dialdehyde, and OMCSOD can be used for evaluation of oxidative stress intensity in IHD patients.

A Macro-method for Including Bond–Slip Flexibility Within Fibre Element Formulation for Simulating Hysteretic Behaviour of RC Beam–Column Members

Fibre beam–column elements are frequently used in the nonlinear analysis of reinforced concrete (RC) frames. The “plane-sections remain plane” assumption in the fibre element formulation results in perfect–bond between rebar and surrounding concrete matrix, which neglects bond–slip added flexibility effects. This drawback affects the lateral stiffness, deformation, energy dissipation, yield displacement, and ductility of an RC member and consequently the RC structure. In this paper, a simple and effective method is presented for incorporating bond–slip flexibility within the plastic hinge of an RC member into fibre elements available in commercially developed computer programs. The developed macro-method modifies rebar elastic modulus using a rebar elastic modulus modification coefficient determined through a simplified and systematic formulation. Furthermore, in this study main design parameters contributing to rebar modulus modifications are determined. Although the developed formulation is simple, it has adequate accuracy and robustness which are verified using a large number of experimental test results.

Evaluation of deflection amplification factor for steel buckling restrained braced frames

In the common force-based design method prescribed in seismic codes, displacements of a structure under reduced seismic forces are amplified by a deflection amplification factor, Cd, to estimate inelastic displacements. The present study evaluates Cd for steel buckling restrained braced frames (BRBFs). For this purpose, six low-to mid-rise structures comprising 2- to 12-story BRBFs are considered, and nonlinear dynamic analyses are performed. Results indicate that the recommended Cd by ASCE 7 (i.e., Cd = 5.0) underestimates the inelastic maximum interstory drift ratio (IMIDR) of lower stories in BRBFs under the design earthquake. Furthermore, estimation of IMIDR in upper stories of mid-rise structures using Cd = 5.0 leads to acceptable results. Therefore, by applying the particle swarm optimization (PSO) algorithm, a new equation is proposed for Cd to more realistically estimate IMIDR in steel BRBFs under the design earthquake. In the case of roof displacement, the results show that for low-rise structures the recommended value of Cd = 5.0 significantly underestimates the inelastic maximum roof drift ratio (IMRDR). On the other hand, for taller structures Cd = 5.0 overestimates the IMRDR. Thus, another new equation is proposed using the PSO algorithm for CdRoof in order to better estimate the IMRDR. Moreover, effects of variation in strain hardening ratio on Cd and CdRoof are investigated. In the last part of this study, variations of the ratios of Cd and CdRoof to response modification coefficient (R) with ductility reduction factor (Rμ) are investigated.

Modified averaged vector field methods preserving multiple invariants for conservative stochastic differential equations

A novel class of conservative numerical methods for general conservative Stratonovich stochastic differential equations with multiple invariants is proposed and analyzed. These methods, which are called modified averaged vector field methods, are constructed by modifying the averaged vector field methods to preserve multiple invariants simultaneously. Based on the prior estimate for high order moments of the modification coefficient, the mean square convergence order $1$ of proposed methods is proved in the case of commutative noises. In addition, the effect of quadrature formula on the mean square convergence order and the preservation of invariants for the modified averaged vector field methods is considered. Numerical experiments are performed to verify the theoretical analyses and to show the superiority of the proposed methods in long time simulation.

Method to Estimate Lateral Earth Pressure on High-Filled Cut-and-Cover Tunnels

High-filled cut-and-cover tunnels (HFCCTs) can be used in northwestern China to reclaim usable land. Because of the ultra-high backfill used in HFCCTs, the stress on the cut-and-cover tunnel (CCT) will change. However, The calculation method adopted at present for earth pressure usually result in either overestimation or underestimation. Different from vertical earth pressure, lateral earth pressure (LEP) can help stabilize the structure of HFCCTs. The current methods for estimating LEP rely mainly on Rankine's theory or empirical formulas. Using conventional methods has led to errors between actual values and estimated values, and such deviation increases with an increase in the backfill height over the CCT. Due to the complex soil-arching effect, the current methods used for calculating LEP for HFCCTs need to be modified. These modifications need to consider characteristics of the CCT, mechanical properties of the backfill soil, and the geometry of the landform. In this work, several influential factors were identified through numerical analysis using the finite element method and propose four corresponding coefficients of modification: k0, the cross-sectional shape of the CCT; k1, the mechanical properties of the backfill; k2, the width of the CCT; and k3, the coupled effect of the slope angle and ratio of the width of the valley floor to the width of the CCT. Because current methods and specifications may overestimate the LEP for HFCCTs in valleys, a general equation was formulated for modifying the LEP coefficient. Also, this general modification equation was verified that agrees well with the numerical analysis results for different cases.

Seismic Performance of Eccentrically Braced Frames with Shear Link

The push-over nonlinear evaluation of four eccentrically braced frame performance was conducted to assess the plastic deformation and location of plastic hinges in buildings with six, nine, twelve and fifteen stories. The excessive plastification of out-of-beam members is revealed in the majority of these buildings while the AISC design provision allows the moderate plastification in these members. Therefore, the beams out of link might be in danger of fracture of web and flange. Likewise, this was controversial evidence in Chrischurch earthquakes. In order to modify this problem either using fixed connection of braced members or using the very short shear links which have less end moment force than out-of-link beams moment strength are recommended. By this modification, the response modification coefficients are calculated for these buildings which are almost equal to the provision value. The maximum plastic rotation of shear links recommended by provisions (0.08 radian) is the upper ultimate limit to prevent emerging of out-of-link member`s instability.

Incremental dynamic analysis and FEMA P695 seismic performance evaluation of a cold‐formed steel–framed building with gravity framing and architectural sheathing

SummaryThe objective of this paper is to present incremental dynamic analysis (IDA) and seismic performance evaluation results for a two‐story cold‐formed steel (CFS)–framed building. The archetype building was designed to current U.S. standards and then subjected to full‐scale shake table tests under the U.S. National Science Foundation Network for Earthquake Engineering Simulation (NEES) program. Test results showed that the building's stiffness and capacity were considerably higher than expected and the building suffered only nonstructural damage even at excitations in excess of Maximum Considered Earthquake levels for a high seismic zone. For the archetype building, three‐dimensional finite element models at different modeling fidelity levels were created using OpenSees. The models are subjected to IDA using the far‐field ground motion records prescribed in Federal Emergency Management Agency (FEMA) P695. Seismic performance quantification following the FEMA P695 procedure shows that if the modeling fidelity only follows the state‐of‐the‐practice, ie, only includes shear walls, unsafe collapse margin ratios are predicted. State‐of‐the‐art models that account for participation from CFS gravity walls and architectural sheathing have overall performance that are consistent with testing, and IDA results indicate acceptable collapse margin ratios, predicated primarily on large system overstrength. Neglecting the lateral force resistance of the gravity system and nonstructural components, as done in current design, renders a safe design in the studied archetype, but largely divorced from actual system behavior. The modeling protocols established here provide a means to analyze a future suite of CFS‐framed archetype buildings for developing further insight on the seismic response modification coefficients for CFS‐framed buildings.

Research on Intelligent Evaluation System of Load-bearing Capacity of Existing Reinforced Concrete Bridge

The intelligent evaluation system of existing reinforced concrete bridge “BLP” is a special software for the load-bearing capacity rapid analysis and evaluation of the existing reinforced concrete bridge, which was developed by the Highway Research Institute of the Ministry of Transport. Based on the parametric modelling method, it can quickly and easily establish the finite element plane model of the bridge structure for the static analysis of ultimate bearing capacity limit states and serviceability limit state, under variety norms. And it can easily and quickly build variable-section beams and rebars, with the special module. According to the comprehensive modification method of the load-bearing capacity evaluation, it can automatically recommend checking sections, and automatically calculate partial modification coefficient of resistance effect, and conveniently judge the safety coefficient of the sections, and quickly get the results of bridge load-bearing capacity. In summary, this system can significantly improve the work efficiency and accuracy of load-bearing capacity for exiting reinforced concrete bridge. This paper introduces in detail the characteristics of the intelligent analysis technology, calculation principle and real bridge application examples of the system.

Effects of diaphragm flexibility on the seismic design acceleration of precast concrete diaphragms

A new seismic design methodology for precast concrete diaphragms has been developed and incorporated into the current American seismic design code. This design methodology recognizes that diaphragm inertial forces during earthquakes are highly influenced by higher dynamic vibration modes and incorporates the higher mode effect into the diaphragm seismic design acceleration determination using a first mode reduced method, which applies the response modification coefficient only to the first mode response but keeps the higher mode response unreduced. However the first mode reduced method does not consider effects of diaphragm flexibility, which plays an important role on the diaphragm seismic response especially for the precast concrete diaphragm. Therefore this paper investigated the effect of diaphragm flexibility on the diaphragm seismic design acceleration for precast concrete shear wall structures through parametric studies. Several design parameters were considered including number of stories, diaphragm geometries and stiffness. It was found that the diaphragm flexibility can change the structural dynamic properties and amplify the diaphragm acceleration during earthquakes. Design equations for mode contribution factors considering the diaphragm flexibility were first established through modal analyses to modify the first mode reduced method in the current code. The modified first mode reduced method has then been verified through nonlinear time history analyses.

Density regulation of mixed and mono-specific forest stands as a continuum: a new concept based on species-specific coefficients for density equivalence and density modification

AbstractA wealth of recent research has improved our understanding of the structure, growth and yield of mixed-species stands. However, appropriate quantitative concepts for their silvicultural regulation remain scarce. Due to the species-specific stand densities, growing area requirements and potential over-density, the density and mixing regulation in mixed stands is much more intricate than in monospecific stands.Here, we introduce the species-specific coefficients: density equivalence coefficients (DEC), for density equivalence; and density modification coefficient (DMC), for density modification in mixed species stands. DEC is suitable for the conversion of the stand density and growing area requirement of one species into that of another species. DMC estimates the modification of maximum stand density by tree species mixing using as reference the maximum stand density of one of the species.First, we introduce the theoretical concept of these coefficients. Second, we derive the mean values of these coefficients based on long-term experiments using different mixtures of European beech. Third, we apply DEC and DMC for flexible regulation of the stand density and mixing proportion. Thus, silvicultural regulation of monospecific stands and mixed-species stands forms a continuum, where monospecific stands represent an extreme case of mixed-species stands.Lastly, we discuss the advantages and limitations of these concepts. Future directions comprise the inclusion of additional species, their integration in guidelines and simulation models, and their establishment for the quantitative regulation of experimental plots and the practical implementation in forest stands.

Eritrocytic Parameters of the Blood of Calves with Different Birth Weights

In the conditions of a dairy farm with the help of the standard clinical, instrumental and laboratory methods the research on particularities of Eritrocytic parameters of the blood of calves (n=299) with different birth weights was carried out. It is shown that Holstein calves with normal intrauterine growth, born with body weight from 36.5 to 29 kg, have no reliable differences in red blood cell count. With a 1 kg reduction in body weight, there is a trend towards hyperchromia, but an increase in weight deficiency promotes of hypovolemia, hypochromia, and polycythaemia. In newborns with a body weight of 27.9–26.9 kg, polycythaemia is derived from hypovolemia, but, with a more pronounced weight deficiency, the role of erythrogenesis disorder in the pathogenesis of the syndrome increases. Hypochromia is a consequence of hematopoietic organs dysfunction and transmembrane loss of hemoglobin. Herein membrane destruction is caused by the increase in the content of toxical metabolites in the blood (sorptivity of red blood cells by 10–12 percent), and by a higher level of adrenaline (modification coefficient of membranes by adrenaline by 20–30 %). This indicates that the response of the fetus to the factors that inhibit its development is similar to a metabolic response against stress. At strong underweight body (b.w. less than 25 kg) exhausting of adaptive capability is observed with the increase in the blood level of toxical metabolites (sorptivity of red blood cells by 15 %), level of membrane destruction (level of ectoglobular hemoglobin in 2,8 times), and heterogeneity of red blood cells. Thus, in newborns with a body weight of less than 29 kg, the significant disturbances in the structure and functions of red blood cells were revealed, which gave grounds for stating that they had antenatal hypotrophy. Herewith, the severity of hematological changes depends on the degree of weight deficiency. Initially, it is hypovolemia and the resulting polycythemia, but, erythropoiesis disorders, and destruction of their membranes with increased polycythemia, and the development of hypochromia occur with the increasing severity of hypotrophy.

Experimental study on the effect of substrate slope on continuously released heptane spill fires

The slope of ground has a significant impact on the spread and burning process for spill fires on land. In this paper, a series of continuous spill fire experiments were conducted on a fireproof glass sheet with different slope angles (0.5°, 1°, 3°) to study the effects of slope on fuel spread and burning behaviors. The results show that the spread process can be divided into four phases based on time-dependent spread area. The maximum spread area and spread rate both increased greatly with increasing slope angle for a constant discharge rate, while the effect of slope on the steady burning area was only slight. The burning rate in the quasi-steady burning phase tends to be a little lower with increasing slope. It is proved that the burning rate at the quasi-steady burning phase is lower than that of pool fires under the same burning size and the corresponding ratio is close to 0.32, independent on the discharge rate and the slope angle. Then, a simple modification coefficient was introduced and a burning rate model of spill fires was developed, which provide a basis for liquid layer simulation under the burning conditions.

Evaluation of Seismic Performance Factors for High-rise Steel Structures with Diagrid System

Diagrid system is a new tubular structural system in tall buildings which requires seismic performance factors (R, Ω0, Cd) for seismic design according to the loading and design codes. By considering the fact that the current codes do not include these factors, this paper aims to evaluate them based on the FEMA P695 methodology. For this purpose, five archetypes have been developed in a way that the structure story heights and span lengths are respectively equal to 4 and 6 meters; this makes the diagonal angles equal to 53.13 degrees. The response modification coefficient (R-factor) of the archetypes was calculated by the Uang method through iteration in analysis and design in OpenSees and ETABS software, respectively. Two types of analysis were carried out: non-linear static analysis (pushover analysis) and non-linear incremental dynamic analysis (IDA); the first evaluates ductility, μT, and over-strength factors, Ω, and the second evaluates “collapse margin ratio (CMR)”. At the end, computed “adjusted collapse margin ratio (ACMR)” was controlled by acceptable values of ACMR in the FEMA P695. Based on the results, the values of R-factor, over-strength factor, Ω0, and deflection amplification factor, Cd, are proposed to be 2.5, 2.0 and 2.5, respectively.

Tooth modification and loaded tooth contact analysis of China Bearing Reducer

China Bearing Reducer (CBR) is a one-stage cycloid speed reducer, which has the advantages of large transmission ratio, large load, high precision, high stiffness, and compact structure. The profile modification quality and manufacturing error of cycloid gear are the key factors affecting the transmission accuracy. In this paper, the structure of CBR is introduced first. By means of tooth contact analysis, a new parabolic profile modification method is proposed to improve the transmission accuracy. Then, by using Hertzian contact theory, force equilibrium equations and deformation compatibility conditions, a loaded tooth contact analysis algorithm of CBR is proposed to analyze the loaded transmission characteristics. According to the designed manufacturing error, the objective function is established to minimize the transmission error under nonload condition, and the particle swarm optimization algorithm is used to solve the optimal modification coefficients. Finally, the CBR25 is manufactured with the optimum modification coefficients, and the manufacturing error is measured in coordinate measuring machine to verify that it meets the design requirements. The optimal modification coefficients of CBR25 under nonload are solved based on particle swarm optimization model. Then the optimal modification coefficients are substituted to loaded tooth contact analysis to analyze the meshing contact force, contact deformation, and transmission error of CBR25. The transmission error of the CBR25 is tested on the testing rig. The error between the measured results and the calculated results of loaded tooth contact analysis is within 5%, which shows the correctness of the loaded tooth contact analysis algorithm. At the same time, the operation stability of the CBR25 is improved by using the optimal modification method.

Analysis of the Effect of the Addendum Modification Coefficient for Contact Surfaces of Spur Gear

Abstract The spur gear is widely used in many types of machines and appliances that is why the research of the connection analysis of them (Tooth Contact Analysis, TCA) is very important because of the development of these gears. The TCA analysis is a complex task because the mathematical description, the CAD modelling process, the overall designing process, the manufacturing process of the gears and the definition of the mechanical parameters have to be known. After the gear designing process the gear pairs have to be analysed by TCA method to determine the typical dimension of the mechanical parameters in case of given load. Knowing of the result we can reason for the appropriate gear geometry of the given construction and working conditions.

Analysis of mesh stiffness of herringbone gear considering modification

Herringbone gear is a key component in the reducer. Its mesh stiffness is an important parameter in gear dynamics research. In this paper, an improved Velex method is proposed to calculate the mesh stiffness of herringbone gears, and compared with Weber method and Finite Element Method (FEM), the accuracy of the method is proved. Meanwhile, the influence of helix angle and modification coefficient on the stiffness of the gear is analyzed by Weber method. The results show that the two parameters have different degrees of influence on the mesh stiffness of the herringbone gear, which provide a theoretical basis for the design of the herringbone gear transmission. Finally, by the calculation of the stiffness of the herringbone gear, the difference between the herringbone gear and the helical gear is compared and analyzed, and the conclusion that the herringbone gear is not a simple superposition of the helical gear is obtained. Because of the difference between the helical gear and the herringbone gear, it is of great value to the stiffness analysis of the herringbone gear.