Closed-Form Calculation of Lead Flank Modification Proposal for Spur and Helical Gear Stages

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Uwe Weinberger ◽  
Michael K. Otto ◽  
Karsten Stahl
Keyword(s):  
Load Distribution ◽  
Degrees Of Freedom ◽  
Best Practice ◽  
Equation System ◽  
Constant Load ◽  
Calculation Model ◽  
Computing Power ◽  
Gear Mesh ◽  
A Value ◽  
Linear Equation System

Abstract Due to the growing need for gearboxes to be as lightweight and efficient as possible, it is most important that the gear mesh’s potential is utilized as well as possible. One way of doing that is to define a flank modification that optimally distributes the load over the flank. Best practice for defining a flank modification is to manually check out the load distribution and to define a value of the flank modification. In general, this is an iterative method to get an optimally distributed load. This method can also be automated. To do this, the deformations of the gearbox (shafts, bearings, gear mesh) are calculated. With those results, a modification proposal is calculated and applied to the calculation model. As soon as the values for the next additional modification proposal drop under a certain limit, the iteration is finished. This method consumes time and computing power. Additionally, since it is an iteration, it does not always converge. A new method for calculating the lead flank modification for all gear stages in the gearbox to be calculated is presented in this paper. The method shown in this paper uses additional degrees of freedom and equations, which are integrated into the linear equation system of the gearbox model. Those degrees of freedom and the equations apply the boundary condition to the model of a constant load distribution. By introducing additional factors in the equations, it is possible to calculate a lead flank modification for an arbitrary load distribution. By integrating these additional degrees of freedom and the equations, only one additional calculation is needed to get a modification proposal. Examples throughout this paper show the results of this method.

Closed Form Calculation of Lead Flank Modification Proposal for Spur and Helical Gear Stages

2019 ◽  
Author(s):  
Uwe Weinberger ◽  
Michael K. Otto ◽  
Karsten Stahl
Keyword(s):  
Load Distribution ◽  
Degrees Of Freedom ◽  
Best Practice ◽  
Equation System ◽  
Constant Load ◽  
Calculation Model ◽  
Computing Power ◽  
Gear Mesh ◽  
A Value ◽  
Linear Equation System

Abstract Due to the growing need for gearboxes to be as lightweight and efficient as possible, it is most important that the gear mesh’s potential is utilized as well as possible. One way of doing that is to define a flank modification that optimally distributes the load over the flank. Best practice for defining a flank modification is to manually check out the load distribution and to define a value of the flank modification. In general, this is an iterative method to get an optimally distributed load. This method can also be automated. To do this, the deformations of the gearbox (shafts, bearings, gear mesh) are calculated. With those results a modification proposal is calculated and applied to the calculation model. As soon as the values for the next additional modification proposal drop under a certain limit, the iteration is finished. This method consumes time and computing power. Additionally, since it is an iteration, does not always converge. A new method for calculating the lead flank modification for all gear stages in the gearbox to be calculated is presented in this paper. The method shown in this paper uses additional degrees of freedom and equations, which are integrated into the linear equation system of the gearbox model. Those degrees of freedom and the equations apply the boundary condition to the model of a constant load distribution. By introducing additional factors in the equations, it is possible to calculate a lead flank modification for an arbitrary load distribution. By integrating these additional degrees of freedom and the equations, only one additional calculation is needed to get a modification proposal. Examples throughout this paper show the results of this method.

Effect of an Original Gear Mesh Modeling on the Gearbox Dynamic Behavior

2007 ◽  
Author(s):  
Emmanuel Rigaud ◽  
Joe¨l Perret-Liaudet ◽  
Mohamed-Salah Mecibah
Keyword(s):  
Load Distribution ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Elastic Coupling ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Face Width ◽  
Building Process ◽  
Coupling Terms

Prediction of the vibratory and acoustical behavior of gearboxes is generally based on characterization of the excitation sources, overall modeling of the gearbox, modal analysis and solving of the parametric equations of motion generated by these models. On the building process of such large degrees of freedom models, the elastic coupling induced by the gear mesh is generally described by the parametric meshing stiffness k(t) along the line of action. This kind of model is not able to take into account the load distribution along the tooth face width, even though the resulting moment can constrain rotational angles associated to wheels tilting and flexural deformation of shafts. The scope of this study is to introduce the coupling terms between wheels associated to these phenomena. Some examples show how they can influence the gear modal characteristics and dynamic response and, consequently, the vibratory and acoustical response of the gearbox.

Model Based Damage Identification Using Output Spectral Densities

1999 ◽  
Vol 123 (4) ◽  
pp. 691-698 ◽  
Author(s):  
A. Nauerz ◽  
C.-P. Fritzen
Keyword(s):  
Degrees Of Freedom ◽  
Damage Identification ◽  
Reference Model ◽  
Equation System ◽  
Measurement Information ◽  
Spectral Densities ◽  
First Case ◽  
Linear Equation System ◽  
Measured System ◽  
Second Procedure

A damage identification method utilizing an existing computational model and output spectral densities is presented. The problem covered here is the detection, localization and quantification of damage in real vibrating elastomechanical structures. The damages are localized by means of changes in the dynamic characteristics between a reference model and the actual, measured system. The main contribution is that the exact measurement of the input signals is ignored. These signals are assumed to be an ergodic random process, whose statistical properties such as mean and covariances must be estimated. Power spectral densities allow random excitations to be dealt with. The lack of measurement information is treated by means of the dynamic condensation technique and the Kalman Bucy filter technique. In the first case the size of the model matrices are reduced to the number of measured degrees of freedom (dof). In the second procedure the measured responses are expanded to the size of the model matrices. With equally sized measurement and model matrices a linear equation system for the desired parameter changes is derived by using the sensitivity approach. The equation system for this inverse problem is usually ill-conditioned and must be regularized in some way. One possibility is to reduce the subset of parameters to be in error. The algorithm is applied to a beam structure and a measured laboratory structure, a multi story frame, in which artificial damage is introduced by weakening one column between two stories. So, it is shown that the location and the size of the corresponding stiffness decrease can be detected.

PARALLEL COMPUTING OF NUMERICAL SCHEMES AND BIG DATA ANALYTIC FOR SOLVING REAL LIFE APPLICATIONS

2016 ◽  
Vol 78 (8-2) ◽  
Author(s):  
Norma Alias ◽  
Nadia Nofri Yeni Suhari ◽  
Hafizah Farhah Saipan Saipol ◽  
Abdullah Aysh Dahawi ◽  
Masyitah Mohd Saidi ◽  
...  
Keyword(s):  
Big Data ◽  
Parallel Computing ◽  
Parallel Algorithm ◽  
Sparse Matrices ◽  
Real Life ◽  
Poor Performance ◽  
Equation System ◽  
Numerical Schemes ◽  
Linear Equation System ◽  
Data Analytic

This paper proposed the several real life applications for big data analytic using parallel computing software. Some parallel computing software under consideration are Parallel Virtual Machine, MATLAB Distributed Computing Server and Compute Unified Device Architecture to simulate the big data problems. The parallel computing is able to overcome the poor performance at the runtime, speedup and efficiency of programming in sequential computing. The mathematical models for the big data analytic are based on partial differential equations and obtained the large sparse matrices from discretization and development of the linear equation system. Iterative numerical schemes are used to solve the problems. Thus, the process of computational problems are summarized in parallel algorithm. Therefore, the parallel algorithm development is based on domain decomposition of problems and the architecture of difference parallel computing software. The parallel performance evaluations for distributed and shared memory architecture are investigated in terms of speedup, efficiency, effectiveness and temporal performance.

Dynamic Characteristics of Double Helical Planetary Gear Train With Tooth Friction

2015 ◽  
Author(s):  
Fengxia Lu ◽  
Rupeng Zhu ◽  
Haofei Wang ◽  
Heyun Bao ◽  
Miaomiao Li
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Friction ◽  
Planetary Gear ◽  
Gear Train ◽  
Variable Step Size ◽  
Step Size ◽  
Planetary Gear Train ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Nonlinear Dynamics Model

A new nonlinear dynamics model of the double helical planetary gear train with 44 degrees of freedom is developed, and the coupling effects of the sliding friction, time-varying meshing stiffness, gear backlashes, axial stagger as well as gear mesh errors, are taken into consideration. The solution of the differential governing equation of motion is solved by variable step-size Runge-Kutta numerical integration method. The influence of tooth friction on the periodic vibration and nonlinear vibration are investigated. The results show that tooth friction makes the system motion become stable by the effects of the periodic attractor under the specific meshing frequency and leads to the frequency delay for the bifurcation behavior and jump phenomenon in the system.

Teaching Materials of Problem-Based Linear Equation System with Two-Variables for Eighth-Grade Students in Junior High School

2021 ◽  
Vol 1 (1) ◽  
pp. 119-123
Author(s):  
Nurhayati Abbas ◽  
Nancy Katili ◽  
Dwi Hardianty Djoyosuroto
Keyword(s):  
High School ◽  
Linear Equation ◽  
Junior High School ◽  
Junior High ◽  
Equation System ◽  
Eighth Grade ◽  
Teaching Material ◽  
Teaching Materials ◽  
Linear Equation System ◽  
Eighth Grade Students

This research is motivated by the lack of mathematics teaching materials that can make students learn on their own. The teaching material can be created by teachers as they are the ones who possess the knowledge about their students’ characteristics. Further, learning materials are a set of materials (information, tools, or texts) that can aid teachers and students to carry out the learning process. The two-variable linear equation system (SPLDV) is one of the mathematics materials taught to eighth-grade students of junior high school; it contains problems related to daily life. However, it is found that this material is still difficult to master by most students. Therefore, it is necessary to develop the SPLDV teaching materials that can help students learn and solve problems as well as be used as examples by teachers in developing other materials. This research aimed to make problem-based SPLDV teaching materials. The research method refers to the Four-D Model by Thiagarajan, Semmel, and Semmel (1974). It consisted of defining, designing, developing, and disseminating. The results showed that problem-based SPLDV teaching materials could be used in learning activities as the students and the teachers had shown their positive responses after going through expert assessments. This study also suggested that the teachers use this teaching material and adopt teaching materials for other similar materials.

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