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Arabian Journal for Science and Engineering

, Volume 44, Issue 2, pp 971–979 | Cite as

Parameter Sensitivity Analysis and Probabilistic Optimal Design for the Main-Shaft Device of a Mine Hoist

  • Hao LuEmail author
  • Yuxing Peng
  • Shuang Cao
  • Zhencai Zhu
Research Article - Mechanical Engineering
  • 35 Downloads

Abstract

As a key component of a mine hoist system, the main-shaft device bears most of the bending moment and torque. Thus, it is important to quantify the performance of the main-shaft device and ensure the reliability of the device. The paper aims to investigate the impact of uncertain structural parameters on the reliability of the main-shaft device. The probabilistic optimal design is performed based on the parameter sensitivity results. First, the design of experiments is adopted to realize the stochastic response analysis of the main-shaft device. Second, the moment-based saddlepoint approximation method is used to evaluate the strength reliability of the device considering uncertain parameters. Next, the reliability-based sensitivity is derived to investigate the parametric significance of random input variables. Finally, the probabilistic optimal design involving the reliability sensitivity is conducted. The results of the sensitivity indicate that the torque and the contact length of left bearing have relatively greater impact on the structural reliability than other variables of the main-shaft device.

Keywords

Sensitivity analysis Reliability Main-shaft device Optimization Saddlepoint approximation 

List of symbols

CGF

Cumulant generating function

\(D_{1}\)

Diameter of the left bearing

\(D_{2}\)

Diameter of the sleeve

\(D_{3}\)

Diameter of the right bearing

F

Bending moment

\(K_{Zs}\)

Approximated CGF

\(K^{{\prime }{\prime }}_{Zs}\)

Second derivation of the approximated CGF

LHS

Latin hypercube sampling

\(L_{1}\)

Contact length of the left bearing

\(L_{2}\)

Contact length of the right bearing

Q

Strength degradation function

\(Q_{0}\)

Initial strength

R

Reliability

RDO

Robust design optimization

RBDO

Reliability-based design optimization

RBRDO

Reliability-based robust design optimization

\(R_{i}^\mathrm{tar}\)

Target reliability of the ith reliability constraints

S

Stress response function

T

Torque

u

Strength attenuation coefficient

X

Basic random variable vector

Y

Design variable vector

Y\(^\mathrm{L}\)

Lower bounds of Y

Y\(^\mathrm{U}\)

Upper bounds of Y

Z

Performance function

\(Z_\mathrm{s}\)

Standardized variable

\(\beta \)

Reliability index

\(\mu \)\(_{Z}\)

Mean of the standardized variable

\(\sigma _{Z}\)

Standard deviation of the standardized variable

\(\gamma _{G}\)

Skewness of X

\({\varvec{\Phi }}\)

Standard normal cumulative distribution Function

\({\varvec{\theta }}\)

Saddlepoints

\(\xi \)

Dimensionless index of sensitivity

\(\omega _{i}\)

Weighting coefficients

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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.College of Mechanical and Electrical EngineeringChina University of Mining and TechnologyXuzhouChina
  2. 2.Jiangsu Key Laboratory of Mine Mechanical and Electrical EquipmentChina University of Mining and TechnologyXuzhouChina

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