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Nonlinear analysis of complex mechanisms with multi-clearances considering dry friction and lubricated joints

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Abstract

To investigate the bifurcation and chaotic behavior of complex mechanisms with multi-clearance lubricated joints, the planar six-bar feeding mechanism with multi-clearance joints is taken as an example. Based on Newton–Euler equation, a dynamic modeling and analysis method for a six-bar feeding mechanism with multi-clearance lubricated joints is firstly proposed. The influence regularities of clearance size, crank speed and viscosity coefficient of lubricant on dynamic behavior of mechanism under dry friction and lubrication conditions are comprehensively revealed. The influences of clearance size, crank speed and viscosity coefficient of lubricant on bifurcation and chaotic behavior of mechanism under lubrication condition is emphatically studied. The new analytical method is proposed to research the nonlinear behavior of mechanisms with lubricated clearance under multi-parameters coupling effect, and the nonlinear behavior of mechanisms due to the combined effect of the crank speed and clearance size is investigated. By drawing phase diagram, Poincaré map, bifurcation diagram and dynamic characteristic distribution diagram, the influence characteristics of different parameters on the bifurcation and chaotic behavior of mechanism are revealed. This research is of great significance to the optimization design and stability improvement of complex mechanisms in the future.

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Data availability

The data used to support the findings of this study are included within the article.

Abbreviations

e :

The eccentricity vector of journal relative to bearing

ε :

The eccentricity ratio of journal relative to bearing

γ :

The offset angle of the eccentricity

c :

The clearance value

δ :

The contact deformation amount

h min :

The minimum oil film thickness

χ :

The damping coefficient of the collision body

K :

The stiffness coefficient of the collision body

n :

The exponent

c e :

The recovery coefficient

\(\dot{\delta }^{\left( - \right)}\) :

The initial velocity of the collision

ω :

The crank speed

μ :

The viscosity coefficient of lubricant

L :

The axial length of the clearance joint

η :

The dynamic friction coefficient

ω 0 :

The relative angular velocity of the clearance joint

v t :

The relative tangential velocity of the clearance joint

e x , e y :

The components of the eccentricity vector in the x-directions and y-directions respectively

r, t :

The radial unit vector and tangential unit vector of eccentricity respectively

e k(k = 1, 2):

The eccentricity of clearance joint B and F respectively

r k(k = 0, 1):

The tolerances for the eccentricity

s k(k = 1, 2):

The position vectors of journal center and bearing center respectively

E k(k = 1, 2):

The Young's modulus of the collision body respectively

ν k(k = 1, 2):

The Poisson's ratio of the collision body respectively

R k(k = 1, 2):

The radius of the collision body respectively

F r, F t :

The contact force and the modified Coulomb friction respectively

μ s , μ d :

The static friction coefficient and dynamic friction coefficient respectively

V s , V d :

The stick–slip threshold velocity and static-slip threshold velocity respectively

F dry , F lub :

The contact collision force and lubricating oil film force respectively

F rn , F tn :

The squeeze oil film force and wedge oil film force respectively

θ i (i = 1, 2, 3, 4):

The angle between the component i and the positive direction of the x-axis respectively

F ix , F iy(i = 1, 2):

The force components at the clearance joint i respectively

F 6 ix , F 6 iy(i = 1, 3):

The force components of the support on crank 1 and rocker 3 respectively

x i , y i (i = 1, 2, 3, 4, 5):

The coordinates of the centroid of the component i in the x-direction and y-direction respectively

R B 1 , R F 1 :

The bearing radius at clearance joint B and F respectively

R B 2 , R F 2 :

The journal radius at clearance joint B and F respectively

l i(i = 1, 2, 3, 4):

The length of component i respectively

l CE :

The length from joint C to joint E

l CD :

The length from joint C to joint D

l a :

The vertical distance from joint A to joint D

l b :

The horizontal distance from joint A to joint D

M d :

The crank driving moment

J i(i = 1, 2, 3, 4):

The moment of inertia of component i to its center of mass respectively

m i(i = 1, 2, 3, 4, 5):

The mass of component i respectively

G i(i = 1, 2, 3, 4, 5):

The gravity of component i respectively

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Funding

The study was funded by Innovative Research Team in University of Tianjin, China (No. TD13-5037), and National Natural Science Foundation of China (No. 51475330, No. 52175243 and No. 52005368).

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Authors and Affiliations

  1. School of Mechanical Engineering, Tiangong University, Tianjin, 300387, China

    Zhimin Wang, Guoguang Jin, Dong Liang, Zhan Wei, Boyan Chang & Yang Zhou

  2. Tianjin Key Laboratory of Advanced Mechatronics Equipment Technology, Tiangong University, Tianjin, 300387, China

    Guoguang Jin, Dong Liang & Boyan Chang

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  1. Zhimin Wang
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Correspondence to Guoguang Jin.

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Wang, Z., Jin, G., Liang, D. et al. Nonlinear analysis of complex mechanisms with multi-clearances considering dry friction and lubricated joints. Nonlinear Dyn 111, 10911–10938 (2023). https://doi.org/10.1007/s11071-023-08409-7

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  • DOI: https://doi.org/10.1007/s11071-023-08409-7

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