Mesh Force Modelling and Parametric Studies for Compound Oscillatory Roller Reducer

A compound oscillatory roller reducer (CORR) with a first-stage gear transmission and a second-stage oscillatory roller transmission is presented. The transmission principle of oscillatory roller transmission is introduced, and the tooth profile equation of the inner gear is derived. The analytical model of mesh force considering the installation errors and manufacturing errors is proposed. Then, parametric studies considering different errors on the mesh force are conducted. Results show that the design parameters are significant factors for mesh force. The mesh force is reduced by 17% as the eccentricity of disk cam increases from 2.5 mm to 4 mm. When the radius of the movable roller increases from 7 mm to 20 mm, the mesh force decreases by 8%. As the radius of disk cam increases from 125 mm to 170 mm, the mesh force is decreased by 26.5%. For the impacts of errors, the mesh force has a noticeable fluctuation when these errors exist including the manufacturing error of disk cam, the installation error of disk cam and the manufacturing error of movable roller change. The prototype of the reducer is manufactured and preliminary run-in test proved the feasibility of the transmission principle.

Hob cutter shaping for internal straight thread

Резьба используется во многих механизмах и достаточно часто для разъемных соединений деталей судовых машин. Для повышения долговечности внутренней цилиндрической резьбы и производительности процесса ее нарезания предлагается новая методика «профилирования червячной фрезы для нарезания внутренней цилиндрической резьбы методом огибания. В данной статье приведено аналитическое определение сопряженных профилей цилиндрической внутренней резьбы и инструмента. Рассматривается метод профильных нормалей для профилирования червячной фрезы при нарезании внутренней резьбы способом огибания, основанный на применении теории матриц. Червячная фреза в осевом сечении имеет конкретный криволинейный профиль, для его получения необходимо знать расчетные зависимости торцового профиля резьбы, и уравнения ее винтовой поверхности и осевого профиля. Для возможности образования витков резьбы необходимы определенные зависимости скорости резанья фрезы и резьбы, а для формирования внутренней резьбы - ее поверхность должна набегать на зубья червячной фрезы. Эти задачи решены с помощью разработанной системы уравнений для изготовления фрез при нарезании внутренней цилиндрической резьбы способом огибания методом профильных нормалей. Расчетный механизм профилирования инструмента - фрезы для нарезания цилиндрических внутренних резьб – может применяться для формообразования конических внутренних резьб. Threads are used in many mechanisms and frequently in detached connections of marine engines elements. The new technique of hob cutter shaping for internal straight thread is proposed in order to increase durability of the internal cylindrical thread and to improve its cutting performance process. The article gives analytical definition of conjugate profiles of internal straight thread and of a tool. It also deals with the method of profile normals for shaping hob cutter whilst cutting the internal thread by enveloping. The method applies the matrix theory. There is some curved profile in the hob cutter axial section. In order to obtain that profile, it is necessary to know the calculated dependence of a thread transverse profile and its helical surface and axial profile equation. Special dependences of thread speed range and cutting are required to produce turns of the thread. To form internal thread – its surface is to slide on cutter teeth. All the mentioned tasks can be solved by the system of equations for cutters manufacture with cutting internal straight thread applying enveloping with the method of profiles normals. The calculation mechanism for shaping the tool – the hob cutter for internal straight threads – can be used for making internal taper threads.

Analytical Description of Neck Profile during Tensile Testing of Cylindrical Specimens

One of the problems of studying the rheological properties and plasticity of metals and alloys from the results of tensile tests of cylindrical specimens is the need to determine the stress triaxiality value, which depends on the shape and size of the neck formed. An analytical description of the neck profile makes it possible to increase the accuracy of experimental measurements of its dimensions, in particular, the radius of curvature in the smallest cross-section of specimen. This paper is devoted to searching a universal neck profile equation that allows calculating the radius of neck curvature regardless of the nature of the material hardening curve and the stage of strain localization. The exact surface equation is established and its accuracy is estimated for hardening and softening material.

Representation of solutions to wave equations with profile functions

In many applications, solutions to wave equations can be represented in Fourier space with the help of a dispersion function. Examples include wave equations on periodic lattices with spacing [Formula: see text], wave equations on [Formula: see text] with constant coefficients, and wave equations on [Formula: see text] with coefficients of periodicity [Formula: see text]. We characterize such solutions for large times [Formula: see text]. We establish a reconstruction formula that yields approximations for solutions in three steps: (1) From given initial data [Formula: see text], appropriate initial data for a profile equation are extracted. (2) The dispersion function determines a profile evolution equation, which, in turn, yields the shape of the profile at time [Formula: see text]. (3) A shell reconstruction operator transforms the profile to a function on [Formula: see text]. The resulting function is a good approximation of the solution [Formula: see text].

Best Fitting Methods for The Mud Profile Equations

In order to understand the dynamics of shoreline changes due to natural and anthropogenic causes, it is imperative for a coastal manager to comprehend the shore profile characteristics which are dependent on the sediment-wave interaction and can be depicted in a profile equation. Moreover, it is possible to derive the power form for the profile equation of a sandy coast based on the argument of wave energy dissipation per unit bed area and unit time. By using this same argument and considering the phenomenon that the main cause of wave damping over a muddy coast is due to energy absorption by the soft mud bottom, the mud profile equation can also be formulated. The aim of this study was to observe the mud profile equation geometry using best fitting method and to compare the characteristic features of the mud profiles using the field observation data. Shore profile data were measured from the muddy coast of Pantai Cermin in the eastern coast of North Sumatera Province. The data obtained were fitted to both the sand and mud profile equations. The procedures and results of the two best fitting methods, the nonlinear regression and the least square based trial and error search, were exhibited and compared. Several noteworthy features of the mud profile equation were found to be the same with the sand profile equation in describing the profile data. In order to provide a better profile and shoreline stabilization, it is recommended to use more complete observation data and good knowledge of shore profile by the coastal manager.

Nonlinear Dynamic Analysis of a Trochoid Cam Gear

A trochoid cam gear (TCG) is a kind of precise transmission device with high performance, such as non-backlash, high-precision, low noise, etc. However, the nonlinear dynamics has not been studied. In the present paper, the nonlinear dynamic differential equation of the TCG is constructed. First, the trochoid equation and the tooth profile equation are deduced to satisfy the conditions of the continuous transmission. Second, a pure torsional nonlinear dynamic model is established to further construct the nonlinear model of the TCG according to a Lagrange equation. Finally, the dynamic characteristics of the TCG are investigated. For the short amplitude coefficient K, break of quasiperiodic torus is the main reason for the chaotic vibration. By increasing K, the performance of TCG can be improved to maintain stable motion.

Analysis of Wind Effect on High-Rise Building for Different Terrain Category

This paper analyzed the effect of wind loadings on high-rise building for different terrain categories. The wind speed and design wind pressure for the different terrain categories adopted for this study were calculated as per logarithmic wind profile equation and BS6399-2:1997 respectively. Also, the nodal displacement of a 3D high-rise building model with reference to the calculated design wind loads were performed using finite element analysis software(STADDPROV8I). From the result obtained, it was shown that Terrain category IV when compared to other terrain categories recorded lower wind speed and pressure from the ground to a height of about 10m. The writers also observed that at greater terrain category(TC4), the wind speed and pressure tends to be much higher at the top floors(10m-48m) of the high-rise building whereas, terrain categories (TC3, TC2, TC1) recorded lower wind speed and pressure at that same height(10m-48m). this disparity however was discovered to be due to a phenomenon known as gust effect. Also, the nodal displacement for the different terrain category (TC4, TC3, TC2 and TC1) on each floor of the high-rise building increased uniformly in respective pattern as the height of the 3D model increases. In conclusion, the authors therefore remark “the greater the terrain category, the lowest is the wind speed in the roughness sub layer and the longer height it takes to reach gradient wind speed”.

VOLUME AND TAPER EQUATIONS FOR COMMERCIAL STEMS OF Nothofagus obliqua AND N. alpina

ABSTRACT Timber volume of standing trees is essential information for management decisions. The increasing need to optimize the potential capacity of forests maintaining their conservation, requires the quantification of the different potential possible timber products. The aim was to adjust taper equations to determine volumes of different timber products for commercial stems of Nothofagus alpina and N. obliqua. Trees of both species were randomly selected in harvesting areas of Lanin National Park (Argentina). Trees were felled and cut into commercial logs, measuring diameter with bark at different heights up to the beginning of the crown, and for each tree the diameter at breast height and total height. Five taper equations were selected and non-linear regression processes were employed for the fittings. We obtained the volume through the integration of the stem profile equation and the rotation in the space thereof through solid of revolution. The Bennet and Swindel (1972) model was selected for both Nothofagus species, obtaining similar equation parameters and differences were observed at the top of the stems of larger trees. For this the use of an integrated model is not recommended. With the obtained equations it is possible to: (i) estimate volume at different heights and for different commercial diameters, and (ii) predict the height at which both species reach to a certain diameter. The model presented some statistical limitations (e.g. multicollinearity), however, the fitting of the equation and the easy understanding of the outputs support it as a useful tool in a broad range of forest applications.

Analysis on Contact Stress after Gear Meshing and Finite Element of Stiffness

According to APDL language of ANSYS, this paper establishes the ideal identity model of tooth profile and gear based on ideal tooth profile equation, and it gets the ideal gear profile in meshing period and change curve of maximum contact stress with position of gear meshing. The result indicates that the contract stress distribution of ideal gear profile presents certain regularity with meshing state of double gear. Gear module can not change the stiffness value of gear meshing; increasing the number of driving wheel can reduce meshing stiffness. Finally, this paper gets the curve of meshing stiffness changes with load. The result indicates that the effect of load on deviation and tooth profile and gear meshing is larger than that on idea tooth profile and stiffness of gear meshing.