A Stiffness Formulation for Spline Joints

2015 ◽  
Author(s):  
J. Hong ◽  
D. Talbot ◽  
A. Kahraman
Keyword(s):  
Stiffness Matrix ◽  
Dynamic Models ◽  
Torsional Stiffness ◽  
Distribution Model ◽  
Computational Time ◽  
Inversion Method ◽  
Drive Trains ◽  
Time Required ◽  
Dynamic Phenomena ◽  
Diagonal Coupling

Due to the lack of knowledge in terms of their flexibility and deformation, spline joints are typically assumed to be rigid in dynamic models of gearboxes, transmissions and drive trains. As various dynamic phenomena are associated with the stiffness of a spline joint, any high-fidelity dynamic model of drivetrains must properly capture the stiffness of spline joints. In this study, a general analytical stiffness formulation for spline joints is proposed based on a semi-analytical spline load distribution model. This formulation defines a fully-populated stiffness matrix of a spline joint including radial, tilting and torsional stiffness values as well as off-diagonal coupling terms. A blockwise inversion method is proposed and implemented with this analytical formulation to reduce computational time required. At the end, a detailed parametric study is presented to demonstrate the sensitivity of the spline stiffness matrix to torque level, tooth modifications, misalignments, and tooth indexing errors.

scholarly journals A Stiffness Formulation for Spline Joints

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
J. Hong ◽  
D. Talbot ◽  
A. Kahraman
Keyword(s):  
Stiffness Matrix ◽  
Load Distribution ◽  
Dynamic Models ◽  
Torsional Stiffness ◽  
Distribution Model ◽  
Computational Time ◽  
Inversion Method ◽  
Time Required ◽  
Dynamic Phenomena ◽  
Diagonal Coupling

Due to the lack of knowledge in terms of their flexibility and deformation, spline joints are typically assumed to be rigid in dynamic models of gearboxes, transmissions, and drivetrains. As various dynamic phenomena are associated with the stiffness of a spline joint, any high-fidelity dynamic model of drivetrains must properly capture the stiffness of spline joints. In this study, a general analytical stiffness formulation for spline joints is proposed based on a semi-analytical spline load distribution model. This formulation defines a fully populated stiffness matrix of a spline joint including radial, tilting, and torsional stiffness values as well as off-diagonal coupling terms. A blockwise inversion method is proposed and implemented with this analytical formulation to reduce computational time required. At the end, a detailed parametric study is presented to demonstrate the sensitivity of the spline stiffness matrix to torque level, tooth modifications, misalignments, and tooth indexing errors.

scholarly journals Experimental Study of the Shaft Penetration Factor on the Torsional Dynamic Response of a Drive Train

Machines ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 31 ◽  
Author(s):  
Hans Meeus ◽  
Björn Verrelst ◽  
David Moens ◽  
Patrick Guillaume ◽  
Dirk Lefeber
Keyword(s):  
Experimental Study ◽  
Torsional Vibration ◽  
Torsional Stiffness ◽  
Vibration Measurement ◽  
Dynamic Amplification Factor ◽  
Torsional Mode ◽  
Penetration Factor ◽  
Torsional Response ◽  
Major Interest ◽  
Drive Trains

Typical rotating machinery drive trains are prone to torsional vibrations. Especially those drive trains that comprise one or more couplings which connect the multiple shafts. Since these vibrations rarely produce noise or vibration of the stationary frame, their presence is hardly noticeable. Moreover, unless an expensive torsional-related problem has become obvious, such drive trains are not instrumented with torsional vibration measurement equipment. Excessive levels can easily cause damage or even complete failure of the machine. So, when designing or retrofitting a machine, a comprehensive and detailed numerical torsional vibration analysis is crucial to avoid such problems. However, to accurately calculate the torsional modes, one has to account for the penetration effect of the shaft in the coupling hub, indicated by the shaft penetration factor, on the torsional stiffness calculation. Many guidelines and assumptions have been published for the stiffness calculation, however, its effect on the damping and the dynamic amplification factor are less known. In this paper, the effect of the shaft penetration factor, and hence coupling hub-to-shaft connection, on the dynamic torsional response of the system is determined by an experimental study. More specifically, the damping is of major interest. Accordingly, a novel academic test setup is developed in which several configurations, with each a different shaft penetration factor, are considered. Besides, different amplitude levels, along with both a sweep up and down excitation, are used to identify their effect on the torsional response. The measurement results show a significant influence of the shaft penetration factor on the system’s first torsional mode. By increasing the shaft penetration factor, and thus decreasing the hub-to-shaft interference, a clear eigenfrequency drop along with an equally noticeable damping increase, is witnessed. On the contrary, the influence of the sweep up versus down excitation is less pronounced.

Developing and Comparing Alternative Design Optimization Formulations for a Vibration Absorber Example

2017 ◽  
Author(s):  
Siyao Luan ◽  
Deborah L. Thurston ◽  
Madhav Arora ◽  
James T. Allison
Keyword(s):  
Design Problem ◽  
Mathematical Optimization ◽  
Computational Time ◽  
Vibration Absorber ◽  
Solution Quality ◽  
Design Representation ◽  
Core Elements ◽  
Improved Design ◽  
Time Required ◽  
Level Of Effort

In some cases, the level of effort required to formulate and solve an engineering design problem as a mathematical optimization problem is significant, and the potential improved design performance may not be worth the excessive effort. In this article we address the tradeoffs associated with formulation and modeling effort. Here we define three core elements (dimensions) of design formulations: design representation, comparison metrics, and predictive model. Each formulation dimension offers opportunities for the design engineer to balance the expected quality of the solution with the level of effort and time required to reach that solution. This paper demonstrates how using guidelines can be used to help create alternative formulations for the same underlying design problem, and then how the resulting solutions can be evaluated and compared. Using a vibration absorber design example, the guidelines are enumerated, explained, and used to compose six alternative optimization formulations, featuring different objective functions, decision variables, and constraints. The six alternative optimization formulations are subsequently solved, and their scores reflecting their complexity, computational time, and solution quality are quantified and compared. The results illustrate the unavoidable tradeoffs among these three attributes. The best formulation depends on the set of tradeoffs that are best in that situation.

Evaluation of a Multi-Goal Solver for Use in a Blackboard Architecture

2014 ◽  
Vol 6 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Jeremy Straub
Keyword(s):  
Multiple Solutions ◽  
Computational Time ◽  
Problem Analysis ◽  
Robotic Control ◽  
Operating Environment ◽  
Blackboard Architecture ◽  
Rule Based ◽  
Multiple Levels ◽  
Time Required ◽  
Naive Approach

This article presents a multi-goal solver for problems that can be modeled using a Blackboard Architecture. The Blackboard Architecture can be used for data fusion, robotic control and other applications. It combines the rule-based problem analysis of an expert system with a mechanism for interacting with its operating environment. In this context, numerous control or domain (system-subject) problems may exist which can be solved through reaching one of multiple outcomes. For these problems which have multiple solutions, any of which constitutes an end-goal, a solving mechanism which is solution-choice-agnostic and finds the lowest-cost path to the lowest-cost solution is required. Such a solver mechanism is presented and characterized herein. The performance of the solver (including both the computational time required to ascertain a solution and execute it) is compared to the naïve Blackboard approach. This performance characterization is performed across multiple levels of rule counts and rule connectivity. The naïve approach is shown to generate a solution faster, but the solutions generated by this approach, in most cases, are inferior to those generated by the solver.

Mathematical Models for Model-Based Control in Offshore Pipelay Operations

2009 ◽  
Author(s):  
Gullik A. Jensen ◽  
Thor I. Fossen
Keyword(s):  
Mathematical Models ◽  
Dynamic Models ◽  
Controller Design ◽  
Computational Time ◽  
Beam Model ◽  
Time Dynamic ◽  
Model Based ◽  
On Line ◽  
Stability And Accuracy ◽  
Control Application

This paper considers mathematical models for model-based controller design in offshore pipelay operations. Three classes of models for control design are discussed, real-world models suitable for controller design verification, controller and observer models which are used on-line in the control system implementation. The control application place requirements on the model with respect to the computational time, dynamic behavior, stability and accuracy. Models such as the beam model, two catenary models, as well as general finite element (FE) models obtained from computer programs were not able to meet all of the requirements, and two recent dynamic models designed for control are presented, which bridge the gap between the simple analytical and more complex FE models. For completeness, modeling of the pipelay vessel, stinger and roller interaction, soil and seabed interaction and environmental loads are discussed.

scholarly journals Comparison of Genetic Algorithm and Harmony Search Method for 2D Geometry Optimization.

2018 ◽  
Vol 159 ◽  
pp. 01009 ◽  
Author(s):  
Mohammad Ghozi ◽  
Anik Budiati
Keyword(s):  
Genetic Algorithm ◽  
Harmony Search ◽  
Geometry Optimization ◽  
Steel Structure ◽  
Search Method ◽  
Geometric Optimization ◽  
Computational Time ◽  
Time Required ◽  
Average Computational Time ◽  
Better Than

There are many applications of Genetic Algorithm (GA) and Harmony Search (HS) Method for solving problems in civil engineering design. The question is, still, which method is better for geometry optimization of a steel structure. The purpose of this paper is to compare GA and HS performance for geometric optimization of a steel structure. This problem is solved by optimizing a steel structure using GA and HS and then comparing the structure’s weight as well as the time required for the calculation. In this study, GA produced a structural weight of 2308.00 kg to 2387.00 kg and HS scored 2193.12 kg to 2239.48 kg. The average computational time required by GA is 607 seconds and HS needed 278 seconds. It concludes that HS is faster and better than GA for geometry optimization of a steel structure.

Ensemble of surrogates and cross-validation for rapid and accurate predictions using small data sets

2019 ◽  
Vol 33 (4) ◽  
pp. 484-501 ◽  
Author(s):  
Reza Alizadeh ◽  
Liangyue Jia ◽  
Anand Balu Nellippallil ◽  
Guoxin Wang ◽  
Jia Hao ◽  
...  
Keyword(s):  
Cross Validation ◽  
Weighted Average ◽  
Computational Time ◽  
Small Data ◽  
Data Sets ◽  
Computationally Efficient ◽  
Cross Validation Error ◽  
Rod Rolling ◽  
Ensemble Of Surrogates ◽  
Time Required

AbstractIn engineering design, surrogate models are often used instead of costly computer simulations. Typically, a single surrogate model is selected based on the previous experience. We observe, based on an analysis of the published literature, that fitting an ensemble of surrogates (EoS) based on cross-validation errors is more accurate but requires more computational time. In this paper, we propose a method to build an EoS that is both accurate and less computationally expensive. In the proposed method, the EoS is a weighted average surrogate of response surface models, kriging, and radial basis functions based on overall cross-validation error. We demonstrate that created EoS is accurate than individual surrogates even when fewer data points are used, so computationally efficient with relatively insensitive predictions. We demonstrate the use of an EoS using hot rod rolling as an example. Finally, we include a rule-based template which can be used for other problems with similar requirements, for example, the computational time, required accuracy, and the size of the data.

scholarly journals Nonlinear inversion method based on dynamics model modification

2019 ◽  
Vol 288 ◽  
pp. 01003
Author(s):  
Faping Zhang ◽  
Kai Wu
Keyword(s):  
Dynamic Models ◽  
Error Function ◽  
Experimental Results ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Forward Modelling ◽  
Dynamics Model ◽  
Model Modification ◽  
Simulation Results ◽  
The Cost

In the fields of modern aviation system, subgrade vehicle system and complex mechanical system, there is a problem that parameters of most dynamic models are inaccurate. This problem results in a large difference between the model results and the experimental results. In order to solve this problem, this paper build a nonlinear inversion method based on dynamics model modification (NIDM). Firstly, the error relationship was obtained by integrating the experimental data with the simulation results of the forward modelling model by the cost function and penalty function. Then, the problem of error function minimization was solved by using the parameter iteration generated by particle swarm optimization algorithm, and the corrected parameters of the forward modelling model were obtained. Finally, the method was tested by building a vehicle suspension vibration model and a pavement excitation model as test samples. The test results show that the fitting degree between the simulation results and the experimental results can be effectively improved by modifying the parameters of the dynamic model based on the NIDM method.

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