Search results for: stiffness matrix

Authors: Jiashang Jiang, Yongxin Yuan

Abstract:

In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping matrix and skew-symmetric gyroscopic matrix complied with the required eigenvalue equation are found under a weighted Frobenius norm sense.

Keywords: Model updating, damped gyroscopic system, partially prescribed spectral information.

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Authors: A. Sawangsuriya, T. B. Edil

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Microstructure and fabric of soils play an important role on structural properties e.g. stiffness and strength of compacted earthwork. Traditional quality control monitoring based on moisturedensity tests neither reflects the variability of soil microstructure nor provides a direct assessment of structural property, which is the ultimate objective of the earthwork quality control. Since stiffness and strength are sensitive to soil microstructure and fabric, any independent test methods that provide simple, rapid, and direct measurement of stiffness and strength are anticipated to provide an effective assessment of compacted earthen materials’ uniformity. In this study, the soil stiffness gauge (SSG) and the dynamic cone penetrometer (DCP) were respectively utilized to measure and monitor the stiffness and strength in companion with traditional moisture-density measurements of various earthen materials used in Thailand road construction projects. The practical earthwork quality control criteria are presented herein in order to assure proper earthwork quality control and uniform structural property of compacted earthworks.

Keywords: Dynamic cone penetrometer, moisture content, relative compaction, soil stiffness gauge, structural property.

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Authors: H. M. Mobarak, Helen Wu, Chunhui Yang

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In this study, an analytical model is developed to study crack breathing behavior under the effect of crack location and unbalance force. Crack breathing behavior is determined using effectual bending angle by studying the transient change in closed area of the crack. The status of the crack of a balanced shaft is symmetrical about shaft rotational angle and the duration of each crack status remains unchanged. The global stiffness of the balanced shaft is independent of crack location. Different crack breathing behavior for the unbalanced shaft has been observed. The influence of crack location on the unbalanced shaft stiffness can be divided into three regions. When the crack is located between 0.3L and 0.8335L, where L is the total length of the shaft, the unbalanced shaft is less stiff and when located outside this region it is stiffer than the balanced shaft. It was also found that unbalanced shaft stiffness has a maximum value with a crack at 0.1946L, a minimum value at 0.8053L and same value as balanced shaft at 0.3L and 0.8335L.

Keywords: Cracked shaft, crack location, shaft stiffness, unbalanced force.

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Authors: Yongxin Yuan, Kezheng Zuo

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In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

Keywords: Matrix equation, Generalized inverse, Generalized singular-value decomposition.

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Authors: Roozbeh Mansouri, Hassan Hadidi

Abstract:

Truss spars are used for oil exploitation in deep and ultra-deep water if storage crude oil is not needed. The linear hydrodynamic analysis of truss spar in random sea wave load is necessary for determining the behaviour of truss spar. This understanding is not only important for design of the mooring lines, but also for optimising the truss spar design. In this paper linear hydrodynamic analysis of truss spar is carried out in frequency domain. The hydrodynamic forces are calculated using the modified Morison equation and diffraction theory. Added mass and drag coefficients of truss section computed by transmission matrix and normal acceleration and velocity component acting on each element and for hull section computed by strip theory. The stiffness properties of the truss spar can be separated into two components; hydrostatic stiffness and mooring line stiffness. Then, platform response amplitudes obtained by solved the equation of motion. This equation is non-linear due to viscous damping term therefore linearised by iteration method [1]. Finally computed RAOs and significant response amplitude and results are compared with experimental data.

Keywords: Truss Spar, Hydrodynamic analysis, Wave spectrum, Frequency Domain

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Authors: Tanawat Limwathanagura, Chartree Sithananun, Teekayu Limchamroon, Thanyarat Singhanart

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The objective of this paper is to study the analysis and testing for determining the torsional stiffness of the student formula-s space frame. From past study, the space frame for Chulalongkorn University Student Formula team used in 2011 TSAE Auto Challenge Student Formula in Thailand was designed by considering required mass and torsional stiffness based on the numerical method and experimental method. The numerical result was compared with the experimental results to verify the torsional stiffness of the space frame. It can be seen from the large error of torsional stiffness of 2011 frame that the experimental result can not verify by the numerical analysis due to the different between the numerical model and experimental setting. In this paper, the numerical analysis and experiment of the same 2011 frame model is performed by improving the model setting. The improvement of both numerical analysis and experiment are discussed to confirm that the models from both methods are same. After the frame was analyzed and tested, the results are compared to verify the torsional stiffness of the frame. It can be concluded that the improved analysis and experiments can used to verify the torsional stiffness of the space frame.

Keywords: Space Frame, Student Formula, Torsional Stiffness, TSAE Auto Challenge

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Authors: Zuan-De Wang, Hou-biao Li, Zhong-xi Gao

Abstract:

In this paper, the backward Ussor iterative matrix is proposed. The relationship of convergence between the backward Ussor iterative matrix and Jacobi iterative matrix is obtained, which makes the results in the corresponding references be improved and refined.Moreover,numerical examples also illustrate the effectiveness of these conclusions.

Keywords: Backward USSOR iterative matrix, Jacobi iterative matrix, convergence, spectral radius

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Authors: Ahmed Noor Al-Qayyim, Barlas Ozden Caglayan

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Structural failure is caused mainly by damage that often occurs on structures. Many researchers focus on to obtain very efficient tools to detect the damage in structures in the early state. In the past decades, a subject that has received considerable attention in literature is the damage detection as determined by variations in the dynamic characteristics or response of structures. The study presents a new damage identification technique. The technique detects the damage location for the incomplete structure system using output data only. The method indicates the damage based on the free vibration test data by using ‘Two Points Condensation (TPC) technique’. This method creates a set of matrices by reducing the structural system to two degrees of freedom systems. The current stiffness matrices obtain from optimization the equation of motion using the measured test data. The current stiffness matrices compare with original (undamaged) stiffness matrices. The large percentage changes in matrices’ coefficients lead to the location of the damage. TPC technique is applied to the experimental data of a simply supported steel beam model structure after inducing thickness change in one element, where two cases consider. The method detects the damage and determines its location accurately in both cases. In addition, the results illustrate these changes in stiffness matrix can be a useful tool for continuous monitoring of structural safety using ambient vibration data. Furthermore, its efficiency proves that this technique can be used also for big structures.

Keywords: Damage detection, two points–condensation, structural health monitoring, signals processing, optimization.

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Authors: Muhammad Naseem Baig, Abdul Qudoos Khan, Jamal Ali

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Ground deformations in deep excavations are affected by wall stiffness and pile embedment ratio. This paper presents the findings of a parametric study of a 64-ft deep excavation in mixed stiff soil conditions supported by cantilever pile wall. A series of finite element analysis has been carried out in Plaxis 2D by varying the pile embedment ratio and wall stiffness. It has been observed that maximum wall deflections decrease by increasing the embedment ratio up to 1.50; however, any further increase in pile length does not improve the performance of the wall. Similarly, increasing wall stiffness reduces the wall deformations and affects the deflection patterns of the wall. The finite element analysis results are compared with the field data of 25 case studies of cantilever walls. Analysis results fall within the range of normalized wall deflections of the 25 case studies. It has been concluded that deep excavations can be supported by cantilever walls provided the system stiffness is increased significantly.

Keywords: Excavations, support systems, wall stiffness, cantilever walls.

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Authors: A. Dulaimi, H. Al Nageim, F. Ruddock, L. Seton

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This study aims at developing a novel cold asphalt concrete binder course mixture by using Ordinary Portland Cement (OPC) as a replacement for conventional mineral filler (0%-100%) with new by-product material (LJMU-A2) used as a supplementary cementitious material. With this purpose, cold asphalt concrete binder course mixtures with cationic emulsions were studied by means of stiffness modulus whereas water sensitivity was assessed by measuring the stiffness modulus ratio before and after sample conditioning. The results indicate that a substantial enhancement in the stiffness modulus and a considerable improvement of water sensitivity resistance is achieved by adding LJMU-A2 to the cold asphalt mixtures as a supplementary cementitious material. Moreover, the addition of LJMU-A2 to those mixtures leads to a stiffness modulus after 2-day curing compared to that obtained with Portland cement, which occurs after 7-day curing.

Keywords: Binder course, cold mix asphalt, cement, stiffness modulus, water sensitivity.

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Authors: S. W. Lo, C.-H. Yu

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A new design of aerostatic thrust bearing is proposed for high static stiffness. The bearing body, which is mead of polymer covered with metallic membrane, is held by a circular ring. Such a support helps form a concave air gap to grasp the air pressure. The polymer body, which can be made rapidly by either injection or molding is able to provide extra damping under dynamic loading. The smooth membrane not only serves as the bearing surface but also protects the polymer body. The restrictor is a capillary inside a silicone tube. It can passively compensate the variation of load by expanding the capillary diameter for more air flux. In the present example, the stiffness soars from 15.85 N/μm of typical bearing to 349.85 N/μm at bearing elevation 9.5 μm; meanwhile the load capacity also enhances from 346.86 N to 704.18 N.

Keywords: Aerostatic, bearing, polymer, static stiffness.

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Authors: Lokendra K. Balyan

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In this paper, we present an algorithm for computing a Schur factorization of a real nonsymmetric matrix with ordered diagonal blocks such that upper left blocks contains the largest magnitude eigenvalues. Especially in case of multiple eigenvalues, when matrix is non diagonalizable, we construct an invariant subspaces with few additional tricks which are heuristic and numerical results shows the stability and accuracy of the algorithm.

Keywords: Schur Factorization, Eigenvalues of nonsymmetric matrix, Orthoganal matrix.

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Authors: Ber-Lin Yu, Jie Cui, Hong Cheng, Zhengfeng Yu

Abstract:

A sign pattern is a matrix whose entries belong to the set {+,−, 0}. An n-by-n sign pattern A is said to allow an eventually positive matrix if there exist some real matrices A with the same sign pattern as A and a positive integer k0 such that Ak > 0 for all k ≥ k0. It is well known that identifying and classifying the n-by-n sign patterns that allow an eventually positive matrix are posed as two open problems. In this article, the tree sign patterns of small order that allow an eventually positive matrix are classified completely.

Keywords: Eventually positive matrix, sign pattern, tree.

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Authors: Seok Min Choi, Minho Bang, Seuong Yun Kim, Hyungmin Lee, Won-Gu Joo, Hyung Hee Cho

Abstract:

The matrix cooling channel was used for gas turbine blade cooling passage. The matrix cooling structure is useful for the structure stability however the cooling performance of internal cooling channel was not enough for cooling. Therefore, we designed the rib configurations in the matrix cooling channel to enhance the cooling performance. The numerical simulation was conducted to analyze cooling performance of rib configured matrix cooling channel. Three different rib configurations were used which are vertical rib, angled rib and c-type rib. Three configurations were adopted in two positions of matrix cooling channel which is one fourth and three fourth of channel. The result shows that downstream rib has much higher cooling performance than upstream rib. Furthermore, the angled rib in the channel has much higher cooling performance than vertical rib. This is because; the angled rib improves the swirl effect of matrix cooling channel more effectively. The friction factor was increased with the installation of rib. However, the thermal performance was increased with the installation of rib in the matrix cooling channel.

Keywords: Matrix cooling, rib, heat transfer, gas turbine.

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Authors: S.K.Ayyaswamy, S.Balachandran, K.Kannan

Abstract:

Let G be a graph of order n. The second stage adjacency matrix of G is the symmetric n × n matrix for which the ijth entry is 1 if the vertices vi and vj are of distance two; otherwise 0. The sum of the absolute values of this second stage adjacency matrix is called the second stage energy of G. In this paper we investigate a few properties and determine some upper bounds for the largest eigenvalue.

Keywords: Second stage spectral radius, Irreducible matrix, Derived graph

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Authors: M. M. Bagheri, G. Doudak, M. Gong

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The in-plane rigidity of light frame diaphragms has been investigated by researchers due to the importance of this subsystem regarding lateral force distribution between the lateral force resisting system (LFRS). Where research has lacked is in evaluating the impact of out-of-plane raigidity of the diaphragm on the deflection of shear walls. This study aims at investigating the effect of the diaphragm on the behavior of wood light-frame shear walls, in particular its out-of-plane rigidity was simulated by modeling the floors as beam. The out of plane stiffness of the diaphragm was investigated for idealized (infinitely stiff or flexible) as well as “realistic”. The results showed reductions in the shear wall deflection in the magnitude of approximately 80% considering the out of plane rigidity of the diaphragm. It was also concluded that considering conservative estimates of out-of-plane stiffness might lead to a very significant reduction in deflection and that assuming the floor diaphragm to be infinitely rigid out of plan seems to be reasonable. For diaphragms supported on multiple panels, further reduction in the deflection was observed. More work, particularly at the experimental level, is needed to verify the finding obtained in the numerical investigation related to the effect of out of plane diaphragm stiffness.

Keywords: Deflection of light-frame wood shear walls, out-of-plane stiffness of the diaphragm, initial stiffness.

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Authors: Z. Adnan, M. M. Habib

Abstract:

The laboratory tests for measuring the effects of small strain to the shear strength and maximum stiffness development of post-cyclic degradation of hemic peat are reviewed in this paper. A series of laboratory testing has been conducted to fulfil the objective of this research to study the post-cyclic behaviour of peat soil and focuses on the small strain characteristics. For this purpose, a number of strain-controlled static, cyclic and post-cyclic triaxial tests were carried out in undrained condition on hemic peat soil. The shear strength and maximum stiffness of hemic peat are evaluated immediately after post-cyclic monotonic testing. There are two soil samples taken from West Johor and East Malaysia peat soil. Based on these laboratories and field testing data, it was found that the shear strength and maximum stiffness of peat soil decreased in post-cyclic monotonic loading than its initial shear strength and stiffness. In particular, degradation in shear strength and stiffness is more sensitive for peat soil due to fragile and uniform fibre structures. Shear strength of peat soil, τ_max = 12.53 kPa (Beaufort peat, BFpt) and 36.61 kPa (Parit Nipah peat, PNpt) decreased than its initial 58.46 kPa and 91.67 kPa. The maximum stiffness, G_max = 0.23 and 0.25 decreased markedly with post-cyclic, G_max = 0.04 and 0.09. Simple correlations between the G_max and the τ_max effects due to small strain, ε = 0.1, the G_max values for post-cyclic are relatively low compared to its initial G_max. As a consequence, the reported values and patterns of both the West Johor and East Malaysia peat soil are generally the same.

Keywords: Post-cyclic, strain, shear strength, maximum stiffness.

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Authors: Guangbin Wang, Liangliang Li, Fuping Tan

Abstract:

In this paper, we obtain some new subclasses of non¬singular H-matrices by using a diagonally dominant matrix

Keywords: H-matrix, diagonal dominance, a diagonally dominant matrix.

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Authors: Mahmoud Miri, Soleiman Maramaee

Abstract:

Because of architectural condition and structure application, sometimes mass source and stiffness source are not coincidence, and the structure is irregular. The structure is also might be asymmetric as an asymmetric bracing in plan which leads to unbalance distribution of stiffness or because of unbalance distribution of the mass. Both condition lead to eccentricity and torsion in the structure. The deficiency of ordinary code to evaluate the performance of steel structures against earthquake has been caused designing based on performance level or capacity spectrum be used. By using the mentioned methods it is possible to design a structure that its behavior against different earthquakes be predictive. In this article 5- story buildings with different percentage of asymmetric which is because of stiffness changes have been designed. The static and dynamic nonlinear analysis under three acceleration recording has been done. Finally performance level of the structure has been evaluated.

Keywords: Seismic analysis, torsion, asymmetric, irregular building, stiffness source.

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Authors: Xinjian Kou, Linlin Li, Yongju Zhou, Jimian Song

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We introduce the redundancy matrix that expresses clearly the geometrical/topological configuration of the structure. With the matrix, the redundancy of the structure is resolved into redundant components and assigned to each member or rigid joint. The values of the diagonal elements in the matrix indicates the importance of the corresponding members or rigid joints, and the geometrically correlations can be shown with the non-diagonal elements. If a member or rigid joint failures, reassignment of the redundant components can be calculated with the recursive method given in the paper. By combining the indexes of reliability and redundancy components, we define an index concerning the structural robustness. To further explain the properties of the redundancy matrix, we cited several examples of statically indeterminate structures, including two trusses and a rigid frame. With the examples, some simple results and the properties of the matrix are discussed. The examples also illustrate that the redundancy matrix and the relevant concepts are valuable in structural safety analysis.

Keywords: Structural robustness, structural reliability, redundancy component, redundancy matrix.

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Authors: Nursyarizal Mohd Nor, Ramiah Jegatheesan, Perumal Nallagownden

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Newton-Raphson State Estimation method using bus admittance matrix remains as an efficient and most popular method to estimate the state variables. Elements of Jacobian matrix are computed from standard expressions which lack physical significance. In this paper, elements of the state estimation Jacobian matrix are obtained considering the power flow measurements in the network elements. These elements are processed one-by-one and the Jacobian matrix H is updated suitably in a simple manner. The constructed Jacobian matrix H is integrated with Weight Least Square method to estimate the state variables. The suggested procedure is successfully tested on IEEE standard systems.

Keywords: State Estimation (SE), Weight Least Square (WLS), Newton-Raphson State Estimation (NRSE), Jacobian matrix H.

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Authors: Pravin Gaikwad, Prakash Mahanwar

Abstract:

The main objective of incorporating natural fibers such as Henequen microfibers (NF) into the High Density Polyethylene (HDPE) polymer matrix is to reduce the cost and to enhance the mechanical as well as other properties. The Henequen microfibers were chopped manually to 5-7mm in length and added into the polymer matrix at the optimized concentration of 8 wt %. In order to facilitate the link between Henequen microfibers (NF) and HDPE matrix, coupling agent such as Glycidoxy (Epoxy) Functional Methoxy Silane (GPTS) at various concentrations from 0.1%, 0.3%, 0.5%, 0.7%, 0.9% and 1% by weight to the total fibers were added. The tensile strength of the composite increased marginally while % elongation at break of the composites decreased with increase in silane loading by wt %. Tensile modulus and stiffness observed increased at 0.9 wt % GPTS loading. Flexural as well as impact strength of the composite decreased with increase in GPTS loading by weight %. Dielectric strength of the composite also found increased marginally up to 0.5wt % silane loading and thereafter remained constant. 

Keywords: Henequen microfibers (NF), polymer composites, HDPE, coupling agent, GPTS

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Authors: Mehdi Modabberifar, Sanaz Jabary, Mojtaba Ghodsi

Abstract:

Stiffness sensing is an important issue in medical diagnostic, robotics surgery, safe handling, and safe grasping of objects in production lines. Detecting and obtaining the characteristics in dwelling lumps embedded in a soft tissue and safe removing and handling of detected lumps is needed in surgery. Also in industry, grasping and handling an object without damaging in a place where it is not possible to access a human operator is very important. In this paper, a method for object handling is presented. It is based on the use of an intelligent gripper to detect the object stiffness and then setting a programmable force for grasping the object to move it. The main components of this system includes sensors (sensors for measuring force and displacement), electrical (electrical and electronic circuits, tactile data processing and force control system), mechanical (gripper mechanism and driving system for the gripper) and the display unit. The system uses a rotary potentiometer for measuring gripper displacement. A microcontroller using the feedback received by the load cell, mounted on the finger of the gripper, calculates the amount of stiffness, and then commands the gripper motor to apply a certain force on the object. Results of Experiments on some samples with different stiffness show that the gripper works successfully. The gripper can be used in haptic interfaces or robotic systems used for object handling.

Keywords: Gripper, haptic, stiffness, robotic.

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Authors: Ivandic Kreso, Spiranec Miljenko, Kavur Boris, Strelec Stjepan

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This article discusses the possibility of using dilatometer tests (DMT) together with in situ seismic tests (MASW) in order to get the shape of G-g degradation curve in cohesive soils (clay, silty clay, silt, clayey silt and sandy silt). MASW test provides the small soil stiffness (G_o from v_s) at very small strains and DMT provides the stiffness of the soil at ‘work strains’ (M_DMT). At different test locations, dilatometer shear stiffness of the soil has been determined by the theory of elasticity. Dilatometer shear stiffness has been compared with the theoretical G-g degradation curve in order to determine the typical range of shear deformation for different types of cohesive soil. The analysis also includes factors that influence the shape of the degradation curve (G-g) and dilatometer modulus (M_DMT), such as the overconsolidation ratio (OCR), plasticity index (IP) and the vertical effective stress in the soil (s_vo'). Parametric study in this article defines the range of shear strain g_DMT and G_DMT/G_o relation depending on the classification of a cohesive soil (clay, silty clay, clayey silt, silt and sandy silt), function of density (loose, medium dense and dense) and the stiffness of the soil (soft, medium hard and hard). The article illustrates the potential of using MASW and DMT to obtain G-g degradation curve in cohesive soils.

Keywords: Dilatometer testing, MASW testing, shear wave, soil stiffness, stiffness reduction, shear strain.

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Authors: Minghui Wang, Luping Xu, Juntao Zhang

Abstract:

Based on the conjugate gradient (CG) algorithm, the constrained matrix equation AXB=C and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Iterative method, symmetric arrowhead matrix, conjugate gradient algorithm.

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Authors: S. O. Adeosun, E. I. Akpan, S. A. Balogun, A. S. Abdulmunim

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SiC reinforced Aluminum samples were produced by stir casting of liquid AA1200 aluminum alloy at 600-650ºC casting temperature. 83µm SiC particles were rinsed in 10g/l, 20g/l and 30g/l molar concentration of Sncl₂ through cleaning times of 0, 60, 120, and 180 minutes. Some cast samples were tested for mechanical properties and some were subjected to heat treatment before testing. The SnCl₂ rinsed SiC reinforced aluminum exhibited higher yield strength, hardness, stiffness and elongation which increases with cleaning concentration and time up to 120 minutes, compared to composite with untreated SiC. However, the impact energy resistance decreases with cleaning concentration and time. The improved properties were attributed to good wettability and mechanical adhesion at the fiber-matrix interface. Quenching and annealing the composite samples further improve the tensile/yield strengths, elongation, stiffness, hardness similar to those of the as-cast samples.

Keywords: Al-SIC, Aluminum, Composites, Intermetallic, Reinforcement, Tensile Strength, Wetting.

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Authors: Norsinnira Zainul Azlan, Hiroshi Yamaura

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This study is concerned with a new adaptive impedance control strategy to compensate for unknown time-varying environment stiffness and position. The uncertainties are expressed by Function Approximation Technique (FAT), which allows the update laws to be derived easily using Lyapunov stability theory. Computer simulation results are presented to validate the effectiveness of the proposed strategy.

Keywords: Adaptive Impedance Control, Function Approximation Technique (FAT), unknown time-varying environment position and stiffness.

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Authors: Dhruba Das

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In this paper, a method has been developed to construct the membership surfaces of row and column vectors and arithmetic operations of imprecise matrix. A matrix with imprecise elements would be called an imprecise matrix. The membership surface of imprecise vector has been already shown based on Randomness-Impreciseness Consistency Principle. The Randomness- Impreciseness Consistency Principle leads to defining a normal law of impreciseness using two different laws of randomness. In this paper, the author has shown row and column membership surfaces and arithmetic operations of imprecise matrix and demonstrated with the help of numerical example.

Keywords: Imprecise number, Imprecise vector, Membership surface, Imprecise matrix.

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Authors: Tian Baoguang, Liang Chunyan, Chen Nan

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In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_i are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_i<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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Authors: A. H. Elkholy, A. H. Falah

Abstract:

A new approach has been developed to estimate the load share and distribution of worm gear drives, and to calculate the instantaneous tooth meshing stiffness. In the approach, the worm gear drive was modelled as a series of spur gear slices, and each slice was analyzed separately using the well-established formulae of spur gear loading and stresses. By combining the results obtained for all slices, the entire envolute worm gear set loading and stressing was obtained. The geometric modelling method presented allows tooth elastic deformation and tooth root stresses of worm gear drives under different load conditions to be investigated. Based on the slicing method introduced in this study, the instantaneous meshing stiffness and load share are obtained. In comparison with existing methods, this approach has both good analysis accuracy and less computing time.

Keywords: Gear, load/stress distribution, worm, wheel, tooth stiffness, contact line.

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