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.

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.

Low Order Static Load Distribution Model for Ball Screw Mechanisms Including Effects of Lateral Deformation and Geometric Errors

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Bo Lin ◽  
Chinedum E. Okwudire ◽  
Jason S. Wou
Keyword(s):  
Load Distribution ◽  
Static Load ◽  
High Order ◽  
Contact Model ◽  
Ball Screw ◽  
Distribution Model ◽  
Computational Time ◽  
Geometric Errors ◽  
Lateral Deformation ◽  
Low Order

Accurate modeling of static load distribution of balls is very useful for proper design and sizing of ball screw mechanisms (BSMs); it is also a starting point in modeling the dynamics, e.g., friction behavior, of BSMs. Often, it is preferable to determine load distribution using low order models, as opposed to computationally unwieldy high order finite element (FE) models. However, existing low order static load distribution models for BSMs are inaccurate because they ignore the lateral (bending) deformations of screw/nut and do not adequately consider geometric errors, both of which significantly influence load distribution. This paper presents a low order static load distribution model for BSMs that incorporates lateral deformation and geometric error effects. The ball and groove surfaces of BSMs, including geometric errors, are described mathematically and used to establish a ball-to-groove contact model based on Hertzian contact theory. Effects of axial, torsional, and lateral deformations are incorporated into the contact model by representing the nut as a rigid body and the screw as beam FEs connected by a newly derived ball stiffness matrix which considers geometric errors. Benchmarked against a high order FE model in case studies, the proposed model is shown to be accurate in predicting static load distribution, while requiring much less computational time. Its ease-of-use and versatility for evaluating effects of sundry geometric errors, e.g., pitch errors and ball diameter variation, on static load distribution are also demonstrated. It is thus suitable for parametric studies and optimal design of BSMs.

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.

scholarly journals The Cold Rolling Load Distribution of the Nuclear Power Zirconium Alloy Based on the Self-adaptive Particle Swarm Optimization Algorithm

2021 ◽  
Author(s):  
Cao Yuan ◽  
Jianguo Cao ◽  
Wang Tao ◽  
Wang Leilei ◽  
Li Fang ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Cold Rolling ◽  
Optimization Algorithm ◽  
Load Distribution ◽  
Zirconium Alloy ◽  
Particle Swarm Optimization Algorithm ◽  
Particle Swarm ◽  
Rolling Process ◽  
Distribution Model ◽  
Swarm Optimization

Abstract Aiming at the problem of load distribution during multi-pass cold rolling of nuclear zirconium alloy strip, the load distribution model with good shape is established by the self-adaptive particle swarm optimization algorithm (SAPSO), considering the main constraint conditions including rolling force, reduction and torque in cold rolling process. Based on the penalty function method transforming the constraint problem into the unconstrained problem, the particle swarm optimization algorithm with adaptive inertia weight factor optimized the load distribution model is developed to improve the local search ability of the particle swarm optimization algorithm. Compared with the existing nuclear zirconium alloy industrial schedule, the simulation results of load distribution based on the SAPSO can keep good shape in multi-pass cold rolling process with the high prediction accuracy. The industrial experiments demonstrate that the proportional crown difference value is consistent, the plate shape flatness is good.

Global load determination in linear guides based on the fusion of local rolling element loads determined from strain sensitive sensor groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
David Krampert ◽  
Sebastian Unsleber ◽  
Leonhard Reindl ◽  
Stefan J. Rupitsch
Keyword(s):  
Load Distribution ◽  
Mechanical Load ◽  
Sensor System ◽  
Distribution Model ◽  
Valuable Insight ◽  
Estimation Errors ◽  
Rolling Element ◽  
Rolling Elements ◽  
Load Mode ◽  
Measurement Principle

Abstract Measuring the mechanical load on linear guides provides many possibilities regarding predictive maintenance and process monitoring. In this contribution, we provide an in depth evaluation of a Diamond Like Carbon (DLC) based sensor system integrated into the runner block’s raceway that is capable of directly measuring the load on individual rolling elements. An efficient algorithm based on an Extended Kalman Filter (EKF) for local sensor fusion and load estimation is presented and proven to reliably retrieve the load regardless of the rolling element’s position. Afterwards, we compare locally measured loads to results from a theoretical load distribution model, providing valuable insight into modeling parameters and a verification of the sensor measurement principle. In a final step, an algorithm to invert the load distribution model is derived and used for an evaluation of the sensor system, achieving Root-Mean-Square (RMS) estimation errors of equivalently 1.4 kN in the preload range and 2.75 kN overall for one dimensional loads. Load mode distinction was equally successful with a suppression RMS error of 0.7 kN in the preload range and 2.87 kN in total.

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.

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