On Crossley's contribution to the development of graph based algorithms for the analysis of mechanisms and gear trains

This paper celebrates a particular branch of Crossley's early work dedicated to Mechanism Science, which deals with a rigorous introduction of Graph Theory to the study of some fundamental and intrinsic properties of kinematic chains and mechanisms. Although such idea gave its main outcome in Type and Number Synthesis (which has been much better and extensively described in another paper of the present special issue) some other intriguing side effects appeared, later in Mechanism Science, which yielded several results, and are still in the center of research and industrial world interest, such as, to name but a few, the automatic generation of the equations governing kinematic, static force and dynamic analysis of mechanisms and geared trains, the power flow analysis, the computation of the efficiency and, finally, the never fully explored structure-to-function mapping, which the present contribution points out to be still a challenge in the field

The Structural Synthesis of Non-fractionated, Three-degree-of-freedom Planetary Gear Mechanisms

Planetary gear trains (PGTs) with one or more degrees of freedom (DOFs) have numerous uses in PGT-based mechanisms. The majority of the currently available synthesis methods have focused on 1-DOF PGTs, with only a few investigations on multi-DOF PGT synthesis. The method for synthesizing 7-link 3-DOF PGMs is outlined. All possible link assortments are produced, labeled spanning trees are generated, and potential geared graphs are constructed. The guidelines for including geared edges and how to synthesize geared graphs are outlined. Vertex-degree arrays are generated to validate the geared graphs. Isomorphic geared graphs are identified by comparing the isomorphic identification numbers of geared graphs with the same spanning tree. Fractionated geared graphs are identified using the reachability matrix method. The new method has a straightforward algorithm. In contrast to what is reported in the literature, the results of the synthesis of 7-link 3-DOF PGMs show that there are seven non-fractionated mechanisms. MATLAB programs are used to acquire the vertex-degree arrays

Computational structural analysis of planar multibody systems with lower and higher kinematic pairs

Kinematic and dynamic modeling of multibody systems requires an initial stage of topological recognition or structural analysis, in which the analyst must identify the model coordinates and a sufficient number of constraint equations to relate them. This initial phase could be solved quickly, safely and automatically, determining the kinematic structure of the multibody system; that is, dividing it into a set of kinematic chains called structural groups. Furthermore, structural groups are widely used for structural synthesis and so, the analysis and design of multibody systems can be integrated into the same software package. On the basis of known graph-analytical methods for structural analysis, a computational method that determines the kinematic structure of a multibody system from its adjacency matrix is developed and evaluated. This method allows the choosing of any type of coordinates (relative, natural or reference point) and the kinematic and dynamic formulations most appropriate for solving the problem. The algorithm has been applied to a large number of mechanical systems of different complexity, offering the same kinematic structure as was obtained through the application of graph-analytical methods

A Comparitive Study of a Few Tests for Isomorphism in Planetary Gear Trains

Graph theory and Matrix methods are widely used by various kinematicians for synthesis and analysis of PGTs. Characteristic polynomial coefficients are used to detect isomorphism in Planetary Gear Trains (PGT). With the Eigen values and Eigen vectors method multiple matrix calculations are required. In case of Hamming number method a single Hamming matrix is enough to detect isomorphism in two PGTs and also determine structural aspects like symmetry easily [1]. Further using the Hamming matrix for a PGT, the number of possible combinations of levels that can be assigned to a given PGT [2] is identified. A review and comparison of Characteristic polynomial, Eigen vectors and Eigen value and Hamming number methods is presented

Determinação da eficiência de máquinas com base em teoria de helicoides e grafos: aplicação em trens de engrenagens e robôs paralelos

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2011Nesta tese o problema da determinação da eficiência mecânica de máquinas é resolvido através da adaptação do Método de Davies. O método proposto é baseado nas teorias de grafos e helicoides e pode ser aplicado a qualquer máquina. Trens de engrenagens e robôs paralelos são usados como exemplos. O Método de Davies é modificado para incluir acoplamentos ativos que permitem que potência entre e saia da rede de acoplamentos. Com esta modificação, é possível modelar atrito como análogo da resistência elétrica, fontes de torque como fontes de corrente e fontes de velocidade como fontes de tensão. Os modelos de atrito podem incluir efeitos que dependem da velocidade e da carga. Fontes de perda, como atrito de engrenamento, atrito em mancais, selos e acoplamentos, podem ser levados em conta. São apresentados exemplos e os resultados são comparados com estudos anteriores encontrados na literatura

Topology Considerations in Hybrid Electric Vehicle Powertrain Architecture Design.

Optimal system architecture (topology or configuration) design has been a challenging design problem because of its combinatorial nature. Parametric optimization studies make design decisions assuming a given architecture but there has been no general methodology that addresses design decisions on the system architecture itself. Hybrid Electric Vehicle (HEV) powertrains allow various architecture alternatives created by connecting the engine, motor/generators and the output shaft in different ways through planetary gear systems. Addition of clutches to HEV powertrains allows changing the connection arrangement (configuration) among the powertrain components during the vehicle operation. Architectures with this capability are referred to as multi-mode architectures while architectures with fixed configurations are referred to as single-mode architectures. HEV architecture optimization requires designing the powertrain’s configuration and its sizing simultaneously. Additionally, evaluation of an HEV architecture design depends on a power management (control) strategy that distributes the power demand to the engine and motor/generators. Including this control problem increases the complexity of the HEV architecture design problem. This dissertation focuses on a general methodology to make design decisions on HEV powertrain architecture and component sizes. The representation of the architecture design problem is critical to solving this problem. A new general representation capable of describing all architecture alternatives is introduced. Using the representation, all feasible configurations are generated where these feasible configurations are used to create single- and multi-mode HEV architectures. Single-mode and multi-mode architecture design problems considering fuel economy, vehicle performance and architecture complexity are formulated separately and solution strategies are developed. The high complexity of the resulting optimization problem does not allow us to claim true optimality rigorously; therefore, the terms ``promising" or ``near-optimal" are more accurate in characterizing our results. The results show that different architectures must be designed for different applications. The case studies designing architectures for some available vehicles from the market find the architectures already implemented in these vehicles under some design constraints. Alternative architectures that improve these designs under different design constraints are also demonstrated. Architectures for a new application that is not available in the market are also designed.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111412/1/bayrak_1.pd

整合電動馬達與齒輪減速機之設計

現有馬達與齒輪減速機是分別設計與製造後再選配，存在動力傳輸路 徑較長、機器組成元件較多、整體安裝空間較大等缺點。本研究提出一套 整合設計流程，用以有系統地將電動馬達之電磁場設計與齒輪減速機的運 動設計結合。依據電動馬達及齒輪減速機的構造特性與運動原理，歸納設 計需求與限制，藉由圖論表示法與創意性機構設計方法，提出整合設計構 想。建立一維及二維等效磁路法分析模型，解析整合裝置的電磁特性與輸 出性能，並配合有限元素分析進行驗證，其誤差值分別為3.21 %與3.06 %。 引入卡特係數建立槽開口與齒型之磁導模型，探討齒輪輪廓對馬達電磁場 之影響，結果顯示齒型不影響馬達之磁交鏈、磁通密度、及電磁轉矩。提 出齒輪系的設計方法，包含齒形、齒數、齒輪系構形、及齒輪強度分析。 最後，分別以現有直流有刷馬達整合行星齒輪減速機，及交流感應馬達整 合一般齒輪系為設計實例，有系統並完成整合裝置的設計。齒輪強度分析 結果顯示，透過矽鋼片堆疊之齒型，可承受之最大應力為312 MPa，齒輪 之動態負載，直流有刷馬達為7.94 MPa，交流感應馬達為98.32 MPa，足夠 承受傳輸需求。由性能分析結果得知，該整合裝置滿足現有設計的傳動能 力，大幅降低直流有刷馬達的頓轉扭矩92.02%及轉矩漣波50.14%，降低交 流感應馬達轉矩漣14.23%，且分別提高直流馬達與交流馬達之轉矩密度 16.66%與1.75%，改善整合裝置的電磁與輸出特性，其頓轉扭矩、轉矩漣 波，及軸向空間的使用，皆較現有設計有更佳的性能表現。[[abstract]]This work presents a novel design procedure for integrating electric motors with gear mechanisms. Based on the configurations of electric motors and the kinematic structure of gear trains, the design requirements and constraints are concluded. By applying the graph representations and creative mechanism design methodology, feasible design concepts are successfully generated systematically. The open-circuit magnetostatic field analysis of a DC commutator motor conducted by applying 1-D and 2-D equivalent magnetic circuit methods are obtained and verified using FEA. The differences in the air-gap flux density are 3.21% and 3.06% for 1-D and 2-D methods, respectively. The Carter’s coefficient is applied to model the permeance of the slot and gear-teeth space. The affection of the integrated gear-teeth on the flux linkage and the first derivative of the flux linkage can be ignored. The design methods for gear trains, gear profiles, number of gear teeth, and gear strength are also introduced. The maximum stress of the gear profile is 312 MPa, and the results show that the gear train can be used for transmission purposes. A DC commutator motor with a planetary gear mechanism and an AC induction motor with an ordinary gear train are applied as examples. A feasible integrated DC commutator motor device is presented that reduces the cogging torque and the torque ripple by 92.02% and 50.14%, respectively, while increasing the torque density by 16.66%. The torque of the AC induction motor is reduced by 8.96%, and the torque ripple is reduced by 14.23%. In addition, the torque density is increased by 1.75%. This indicates that the integrated devices provide more stable and efficiency output torque than the existing design.[[booktype]]電子版[[countrycodes]]TW

DETC04/DAC-57254 EVALUATION METHOD FOR THE TOPOLOGICAL SYNTHESIS OF SHEET METAL COMPONENTS

ABSTRACT The popularity of sheet metal in modern engineering artifacts is due to the fact that it is both inexpensive as a raw material and inexpensive to form into components. In comparison to forging or machining components, sheet metal can produce lightweight and inexpensive design solutions. The main shortcomings of sheet metal are that resulting components have a limited rigidity and the feasibility of the parts is constrained by the inherent two-dimensionality of the initial sheet. Furthermore, design and manufacturing engineers are challenged by finding a shape that satisfies all spatial constraints and by deciding the optimal sequence of operations for making this product that minimizes both time and associated manufacturing costs. In the past two years, we have been working towards an automated tool that creates candidate sheet metal topologies and optimizes them for spatial constraints as well as time and cost objectives. While we have yet to complete this goal, we have to date developed a representation capable of creating a wide variety of sheet metal topologies (see DETC2002/DAC-34087) and have recently created a thorough evaluation method which is presented in this paper along with some preliminary results

Automated Topology Synthesis and Optimization of Hybrid Electric Vehicle Powertrains

This thesis presents a framework to automate the process of designing Hybrid Electric Vehicle (HEV) powertrain architectures. An algorithm was developed to assemble and compare all possible configurations of powertrain components. Combinatorics was used to discover all possible combinations of: an internal combustion engine, high-torque low-speed electric motor, low-torque high-speed electric motor, planetary gearset, and five-speed discrete gearbox. The Graph Theoretic Method was used to generate the powertrain models. The powertrain models were comprised of steady-state equations in symbolic form. An optimal control strategy is required to fairly compare the different topologies because a powertrain control strategy is dependant on the configuration. Dynamic Programming was used to determine the control law that minimizes the energy consumption for a given drivecycle. Evaluating every possible topology would take an extremely long time, so topologies were evaluated using a multi-stage screening process. The first stage examined the structure of the powertrain and used heuristics to eliminate infeasible topologies; 512 topologies were feasible. The second stage eliminated topologies that could not meet basic driving performance; 193 topologies were feasible. Basic driving performance was tested using a section of the US06 drivecycle. The sizes of three components were optimized to ensure the topology is feasible independent of the size of the components. The third stage eliminated topologies which could not achieve driving performance design goals; 159 could achieve the performance requirements, but only 119 were reasonably fuel efficient. The driving performance goals were implemented with a drivecycle based on the Partnership for a New Generation of Vehicles (PNGV) goals. The sizes for five components were optimized at this stage. The 20 most fuel efficient powertrains were selected for further evaluation. Additionally, 4 common powertrains were evaluated for reference. The size of the components were optimized for a combination of the PNGV drivecycle and the HWFET drivecycle. The most fuel efficient topology was found to be a Powersplit hybrid which has a discrete gearbox between the final drive and the powersplit device. The electric motor, planetary carrier gear, and gearbox were connected in parallel. It was found that Parallel-like, Powersplit-like, and Complex-like topologies were were the most efficient powertrain configurations. Powertrains containing two gearboxes were more efficient because the geartrain models ignored mechanical inefficiencies