Kinematic reliability and sensitivity analysis of the modified Delta parallel mechanism

In order to improve the kinematic reliability, it is crucial to find out the influence of each error source on the kinematic reliability of the mechanism. Reliability sensitivity analysis is used to find the changing rate in the probability of reliability in relation to the changes in distribution parameters. Based on the structural response surface function method, the functional relation between the kinematic reliability of a modified Delta parallel mechanism and the original input-error vectors is described using the quadratic function with cross terms. Moreover, the partial derivatives of the functional relation with respect to the means and variances of the original input errors are derived, which can efficiently evaluate kinematic reliability sensitivity of the mechanism. The advantages of this method are as follows: First, the response surface function, which can be easily set up by the position-error model of the mechanism, is convenient for calculating the variance, partial derivative, and reliability sensitivity. Second, in this case (unlike in the traditional error-mapping model), although the input-error values are unknown, pseudorandom variables used as random input-error sources can be generated by MATLAB software. Furthermore, the kinematic reliability of the mechanism can be assessed using the Monte Carlo method.

Download Full-text

Sensitivity Analysis of Reliability of Low-Mobility Parallel Mechanisms Based on a Response Surface Method

Applied Sciences ◽

10.3390/app11199002 ◽

2021 ◽

Vol 11 (19) ◽

pp. 9002

Author(s):

Qiang Yang ◽

Hongkun Ma ◽

Jiaocheng Ma ◽

Zhili Sun ◽

Cuiling Li

Keyword(s):

Sensitivity Analysis ◽

Response Surface ◽

Response Surface Method ◽

Inverse Kinematics ◽

Parallel Mechanism ◽

Error Component ◽

Parallel Mechanisms ◽

Kinematic Accuracy ◽

Surface Method ◽

Input Error

Kinematic accuracy is a crucial indicator for evaluating the performance of mechanisms. Low-mobility parallel mechanisms are examples of parallel robots that have been successfully employed in many industrial fields. Previous studies analyzing the kinematic accuracy analysis of parallel mechanisms typically ignore the randomness of each component of input error, leading to imprecise conclusions. In this paper, we use homogeneous transforms to develop the inverse kinematics models of an improved Delta parallel mechanism. Based on the inverse kinematics and the first-order Taylor approximation, a model is presented considering errors from the kinematic parameters describing the mechanism’s geometry, clearance errors associated with revolute joints and driving errors associated with actuators. The response surface method is employed to build an explicit limit state function for describing position errors of the end-effector in the combined direction. As a result, a mathematical model of kinematic reliability of the improved Delta mechanism is derived considering the randomness of every input error component. And then, reliability sensitivity of the improved Delta parallel mechanism is analyzed, and the influences of the randomness of each input error component on the kinematic reliability of the mechanism are quantitatively calculated. The kinematic reliability and proposed sensitivity analysis provide a theoretical reference for the synthesis and optimum design of parallel mechanisms for kinematic accuracy.

Download Full-text

Structural Modal Analysis and Optimization of SUV Door Based on Response Surface Method

Shock and Vibration ◽

10.1155/2020/9362434 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Hao Chen ◽

Chihua Lu ◽

Zhien Liu ◽

Cunrui Shen ◽

Yi Sun ◽

...

Keyword(s):

Sensitivity Analysis ◽

Response Surface ◽

Response Surface Method ◽

Modal Frequency ◽

Frequency Matching ◽

Surface Method ◽

Design Variables ◽

Highly Sensitive ◽

Response Surface Function ◽

Fifth Order

Sensitivity analysis and response surface methods were employed to optimize the structural modal of SUV doors. A finite element numerical simulation model was established and was calibrated by restraint modal tests. To screen out highly sensitive panels, a sensitivity analysis for the thickness of door panels was proposed based on the fifth-order modal frequency of the door. Data points were obtained by a faced central composite design with the design variables from the thickness of the highly sensitive panels, and a second-order explicit response surface function of the fifth-order modal frequency of the vehicle door was established. An optimization model was established according to the response surface method. The final results demonstrate that the modal-frequency matching of the door and body in white was optimized after changing the thicknesses, with a 5.74% material reduction.

Download Full-text

The Reliability Sensitivity Analysis of Composite Beam Cable-Stayed Bridge during Construction Stage

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.438-439.901 ◽

2013 ◽

Vol 438-439 ◽

pp. 901-907

Author(s):

Bu Yu Jia ◽

Xiao Lin Yu ◽

Quan Sheng Yan ◽

Zhou Chen

Keyword(s):

Sensitivity Analysis ◽

Composite Beam ◽

Structural Response ◽

Random Variable ◽

Variable Parameters ◽

Performance Function ◽

Cable Stayed Bridge ◽

Reliability Sensitivity ◽

Reliability Sensitivity Analysis ◽

Interface Slip

A 10DOF composite beam element was developed, which had taken the interface slip effect and geometric nonlinearity into consideration. The method to obtain structural response gradients of composite beam was analyzed, meanwhile the reliability index was achieved by using the FORM method and on this basis, and the sensitivity of random variable parameters could be finished. At last the control of target elevation was took as state performance function, the sensitivity analysis of random variable parameters which might have an effect on the elevation control reliability was effectively completed, and some useful conclusions which were be beneficial to construction control of composite beam cable-stayed bridge obtained.

Download Full-text