Mathematical models and dynamic contact analysis of involute/noninvolute beveloid gears

This study investigates an approach for parametric modeling and dynamic contact analysis of involute/noninvolute beveloid gears. Firstly, the mathematical models of involute/noninvolute beveloid gear pairs are derived based on the theory of gearing and the generation mechanism. Then the parametric modeling programs of involute/noninvolute beveloid gears are developed to automatically generate exact model via a Matlab code. Subsequently, a numerical example of intersecting axes beveloid gears is presented to evaluate the dynamic stress distribution and dynamic transmission error. Finally, the dynamic contact characteristics of involute and noninvolute beveloid gears are calculated by three-dimensional dynamic contact finite element method, respectively. The results show that the noninvolute beveloid gear pairs can relieve the high dynamic stress and contact shock problem of intersecting axes beveloid gear pairs

Análise do contacto de engrenagens cónicas com dentado espiral: simulação numérica e validação experimental

Dissertação de mestrado integrado em Engenharia MecânicaO objetivo deste trabalho é, principalmente, o estudo de engrenagens cónicas com dentado espiral. No entanto, no início da análise foram utilizadas engrenagens cilíndricas de dentes retos, por serem um mecanismo mais simples de analise e compreensão do seu comportamento. Para a análise, de ambas, recorreu-se a simulações por elementos finitos, usando o software Abaqus. Em primeiro lugar, foi feito um estudo da arte, para se conhecer melhor o mecanismo de transmissão estudado, as engrenagens. Num modo geral, foram estudados todos os tipos de engrenagens, mas foram analisadas, de um modo mais profundo, os dois tipos de engrenagens utilizados neste estudo (cilíndricas de dentes retos e cónicas de dentado espiral). Nesse mesmo estado da arte, foi feita uma pequena pesquisa sobre os processos de fabrico das engrenagens. Para estudo das engrenagens, foram analisadas as tensões (tensão segundo critério de Von Mises e a tensão normal s22). Este estudo levou em linha de conta aspetos de natureza operacional, tais como o desalinhamento involuntário dos eixos dos elementos da transmissão, bem como a correção do dentado e binário aplicado. Analisaram-se, ainda, alguns aspetos da simulação, que influenciam a análise do comportamento das engrenagens, tais como, influência do número de dentes e refinamento da malha. Por fim, foram analisados os resultados, comparados os comportamentos das engrenagens e retiradas conclusões.The objective of this work is, mainly, the study of bevel gears with spiral teeth. However, at the beginning of the analysis, straight teeth cylindrical gears were used, as they are a simpler mechanism to analyse and understand their behaviour. For the analysis of both, finite element simulations were used, using the Abaqus software. Firstly, a study of the art was made, in order to better understand the studied transmission mechanism, the gears. In general, all types of gears were studied, but the two types of gears used in this study (cylindrical straight teeth and conical spiral teeth) were further analysed. In this same state of the art, a little research was done on the manufacturing processes of the gears. To study the gears, the stresses were analysed (stress according to Von Mises criteria and the normal stress s22). This study took into account aspects of an operational nature, such as the involuntary misalignment of the axles of the transmission elements, as well as the correction of the gear and applied torque. Some aspects of the simulation were also analysed, which influence the analysis of the behaviour of the gears, such as, influence of the number of teeth and mesh refinement. Finally, the results were analysed, the gears' behaviour was compared and conclusions were drawn

Modelling and prevention of meshing interference in gear skiving of internal gears: Conference Proceedings [Modellierung und Vermeidung von Freiflächeninterferenz beim Wälzschälen von Innenverzahnungen]

Gear skiving is a highly productive process for machining of internal gears which are required in large quantity for electric mobility transmissions. Due to the complex kinematics of gear skiving, collisions of the tool and workpiece can occur during the process. Models exist to check for collisions of the tool shank or collisions in the tool run-out. While these models are sufficient for the process design of external gear skiving, at internal gears meshing interferences between tool and workpiece can appear outside the contact plane on the clearance face of the tool. To test for meshing interference requires comprehensive assessment of workpiece, tool and process kinematics. Currently, this is often done by time consuming CAD-simulation. In contrast, this paper presents an automated geometrical model for the analysis of meshing interference. The test for collisions is thereby performed along the whole height of the tool and especially includes constructive clearance angles and eccentric tool positions. The model is developed for user-friendly implementation and practical applications. The model for avoiding meshing interference in gear skiving is validated on two different process applications. In doing so, influences of the tool and process design on the interference situation are investigated, compared and discussed. Furthermore this new approach enables the prevention of meshing interference or tooth tip collisions in the early tool design by adjusting the process kinematics or the tool design itself. The maximal viable tool height can be quantified and recommendations for improving the clearance face situation are suggested

Automatic handling of gear data for Industry 4.0 applications

TCC (graduação) - Universidade Federal de Santa Catarina. Campus Joinville. Engenharia Aeroespacial.Engrenagens possuem diversas informações de geometria, manufatura e metrologia, que podem ser agrupadas em arquivos padronizados para intercâmbio de dados, como o GDE. Este trabalho pretende automatizar a criação e manipulação de arquivos GDE, facilitando a obtenção de versões digitais de engrenagens reais, as digital shadows, para diferentes usos finais. Por meio de programação em Fortran e C e com auxílio de medições de topografia de engrenagens reais, foram criadas rotinas que promovem a automatização do processo. A verificação da representatividade dos arquivos gerados foi realizada avaliando as nuvens de pontos e modelos 3D gerados, e simulações foram conduzidas com o programa Zako3D para confirmação da compatibilidade dos arquivos com o mesmo. As rotinas criadas apresentaram excelente desempenho ao permitir a criação automática de arquivos GDE e seu preenchimento de maneira fácil e rápida, com necessidade mínima de ação do usuário. Os objetos digitais resultantes são fidedignos e funcionam propriamente com o programa de simulação utilizado.Gears have several geometry, manufacturing and metrology information, which can be grouped in standardized files for data exchange in automatic procedures, such as Gear Data Exchange (GDE) files. This work intends to automate the creation and manipulation of GDE files, making it easier to obtain digital versions of real gears, the digital shadows, for different end uses. Through programming in Fortran and C and with the aid of topography measurements of real gears, routines that promote the automation of the process were created. The representativeness of the generated files was verified by evaluating the point clouds and 3D models generated, and simulations were conducted with an in-house developed tooth contact analysis software to confirm the compatibility of the files with it. The routines created showed excellent performance by allowing the automatic creation of GDE files and their filling in an easy and fast way, with minimal need for user action. The resulting digital objects are reliable and work properly along with the simulation software used

Virtual Model of Power Skiving Cutting Mechanics

Power skiving is a high-speed gear cutting operation which involves feeding a rotating cutting tool into a synchronously rotating workpiece at an angled orientation, creating a continual chip removal cutting action. It is capable of quickly machining both internal and external gears. The process has recently gained more interest from industry due to its potential to increase the productivity of gear manufacturing. However, power skiving is prone to vibrations and chatter, requiring stiff, well-controlled machine tools for effective implementation. Furthermore, methods for planning power skiving processes have not matured as much as those for more traditional machining processes, such as milling, turning, and drilling, which creates difficulties for its implementation. Mechanistic models to predict cutting forces and other process outcomes have been widely used for traditional machining operations. These models can be invaluable in industry as tools to aid in the planning and optimization of cutting operations in order to maximize quality, minimize tool wear, and to reduce process time, among other measures of performance. The basis of these models is always the accurate prediction of cutting forces. This sort of modelling has not previously been performed for power skiving, and would be a valuable addition to research into the process. The kinematics of power skiving are straightforward, but result in a complex cutting action. A power skiving process consists of multiple passes at set radial depths of cut. The workpiece and tool rotate as a pair of meshing gears, and the tool is fed axially along the width of the gear at a radial cutting depth. The tool is oriented at a cross-axis angle with respect to the workpiece so that the rotational motion results in the cutting edge being fed through the tooth gaps of the gear to remove material. Homogeneous transformation matrices are established to be able to represent points and vectors in a tool, workpiece, or machine coordinate system. A wide range of local cutting conditions occurs due to the relative velocity between the tool and workpiece, which has been calculated. The kinematics of power skiving are modelled and validated by comparing simulated tool positions with axial position data from the controller of a DMG NT5400 DCG mill-turn machine during experimental trials. Cutting force predictions are made by applying the kinematics in a dexel-based cutter-workpiece-engagement engine to extract data representing a 3D uncut chip. The dexel data comprising the chip is then used to create a two-dimensional point cloud by intersecting the dexels and their outer contours with the established tool rake geometry. Delaunay triangulation is used on the point set to create a cross-section of the chip, with a set size threshold eliminating triangles that are unlikely to be part of the geometry. The chip geometry triangles are associated with points along the discretized cutting edge, and an oblique model using the local cutter geometry and relative velocity establishes the local cutting forces, their component directions (tangent, feed, and radial), and cutting angles (rake and inclination). The local cutting forces across the cutting edge are summed to create a total cutting force prediction. During experimental trials, data was captured using a wireless force measurement system and then filtered to reduce the noise. The measured cutting forces are compared to those produced by the model. It is found that predictions are made within 4--10% average RMS error, and 10--15% peak RMS error for cases where the tool geometry and coefficients are well defined. More trials are needed, however, to validate processes with thinner chips as well as helical and internal gears. To reduce the computation time for simulation results, a partial workpiece simulation is used. A workpiece representing a single gear tooth gap is used in the simulation, and the results are processed using superposition to reconstruct the forces for a full cylindrical workpiece. While a 2--3% error was introduced (in numerically stable cases), in large part due to transient effects in the starts and ends of passes. This method reduced the simulation time by around 93%. The partial workpiece is then used to perform a simulation with alternating ramping-in and constant-depth passes on a wide workpiece. The results of this simulation establish a relationship between previous cutting depth, incremental cutting depth, and cutting parameters (in this thesis, the average total cutting force). With these relationships, new power skiving processes are planned by setting target thresholds and determining the incremental cutting depths. Planning was successfully performed to create processes with more consistent forces compared to the traditional planning approach, though more intelligent process limit targets are still being explored

Mechanical Engineering

The book substantially offers the latest progresses about the important topics of the "Mechanical Engineering" to readers. It includes twenty-eight excellent studies prepared using state-of-art methodologies by professional researchers from different countries. The sections in the book comprise of the following titles: power transmission system, manufacturing processes and system analysis, thermo-fluid systems, simulations and computer applications, and new approaches in mechanical engineering education and organization systems

Modelling and Design of a Test Rig to investigate the dynamic behaviour of a Servo driven Powertrain

In the present work a simulation model for examining the fundamental dynamic behaviour of a servo driven powertrain is developed. This powertrain consists of a permanent magnet synchronous motor, a cycloidal gearbox and a torque motor to apply a load. On basis of this model the selection of components for the design of a test rig is possible. This leads to the constructive draft of the test rig. In order to model the system, the fundamentals give a brief overview of the components incorporated in the test rig system. With ais of the specified task the simulation purpose is defined and the modelling process enabled. The subsequent system analysis is performed intensively to decompose the system into subsystems, which are then investigated to find the optimal modelling approach for the given simulation task. Particular emphasis is put on the investigation of the cycloidal gearbox subsystem and it shows, that approaches for modelling the dynamic behaviour of the gearbox as a whole have only been published partially. Therefore, the available modelling approaches are analysed and suitable models are developed as conceptual models. Those will be formalised and implemented in Matlab/Simulink. The model is verified and simulation experiments are performed, that help in the selection of suitable test rig components. On basis of a flexible test rig, finally the constructive draft is presented.:1 Introduction 1.1 Motivation 1.2 Procedure 2 Fundamentals 2.1 Definitions 2.2 Modelling 2.3 Servo Drive 2.3.1 Introduction 2.3.2 Permanent Magnet Synchronous Motor 2.3.3 Servo Inverter 2.3.4 Control System 2.4 Torque Motor 2.5 Gearbox 3 Specified Task 4 System Analysis 4.1 Introduction 4.2 Servo Inverter 4.3 Control System 4.4 Servo Motor 4.5 Transmission Elements 4.6 Cycloidal Gearbox 5 Model Formalisation 5.1 Introduction 5.2 Servo Inverter 5.3 Control System 5.4 Servo Motor 5.5 Transmission Elements 5.6 Cycloidal Gearbox 6 Model Implementation 6.1 Introduction 6.2 Servo Inverter 6.3 Control System 6.4 Servo Motor 6.5 Transmission Elements 6.6 Cycloidal Gearbox 7 Simulation 7.1 Introduction 7.2 Solver 7.3 Verification 7.4 System Evaluation 7.4.1 Sensitivity Analysis 7.4.2 Stability Analysis 8 Design of the Test Rig 8.1 Selection of the components 8.2 Constructive Draft 9 Summary and Outloo