Piezoelectric inertial robot for operating in small pipelines based on stick-slip mechanism: modeling and experiment

Abstract

Small pipes exist in industrial and biomedical fields, and require microrobots with high operational precision and large load capacity to inspect or perform functional tasks. A piezoelectric inertial pipeline robot using a “stick-slip” mechanism was proposed to address this requirement. In this study, the driving principle of the proposed robot was analyzed, and the strategy of the design scheme was presented. A dynamics model of the stick-slip system was established by combining the dynamics model of the driving foot system and the LuGre friction model, and the simulation analysis of the effect of system parameters on the operating trajectory was performed. An experimental system was established to examine the output characteristics of the proposed robot. Experimental results show that the proposed pipeline robot with inertial stick-slip mechanism has a great load capacity of carrying 4.6 times (70 g) its own mass and high positioning accuracy. The speed of the pipeline robot can reach up to 3.5 mm/s (3 mm/s) in the forward (backward) direction, with a minimum step distance of 4 μm. Its potential application for fine operation in the pipe is exhibited by a demonstration of contactless transport.

Graphical abstract

Keywords

pipeline robot / piezoelectric / inertial drive / stick-slip / large load capacity / dynamics model / small pipeline

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Nomenclature

A	Cross section area of the piezoelectric stack
c2, c3	Equivalent damping of the flexure hinge and the driving foot, respectively
d33	Piezoelectric coefficient
f1	Friction between the driving foot and pipe wall
f2	Friction between the support foot and pipe wall
F_1,F_1^{\prime }	Acting force and reacting force between the driving foot and the pipe wall, respectively
F_{12},F_{12}^{\prime }	Acting force and reacting force between the piezoelectric stack and the flexure hinge, respectively
FC	Coulomb friction force
Fp	Output force of the piezoelectric stack
FS	Static friction force
g(v)	Function describing the Stribeck effect
k1, k2, k3	Equivalent stiffness of the piezoelectric stack, the flexure hinge, and the driving foot, respectively
l	Length from the rotation center to the top of flexure hinge
l1	Distance from the center of rotation of the hinge to the point of action with the piezoelectric stack
l2	Vertical distance from the top of the flexure hinge to the center of rotation under the rotation θ1
l3	Vertical distance between the top of the hinge and the initial position after rotation θ1
l4	Length of the driving foot
Lp	Length of the piezoelectric stack
m1, m2, m3, m4	Equivalent mass of the piezoelectric stack, the flexure hinge, the driving foot, and the pipe, respectively
n	Number of the piezoelectric sheets in the piezoelectric stack
s33	Elastic compliance constant of the piezoelectric stack
T	Period of the drive signal
U	Output voltage of the drive signal
v	Relative velocity of two friction surfaces
vs	Stribeck velocity
Vmax	Peak voltage of the drive signal
x1	Output displacement of the piezoelectric stack
x_2, {\dot{x}}_{\text{2}}\text{,} {\ddot{x}}_{\text{2}}	Displacement, velocity, and the acceleration of the flexure hinge, respectively
x_4,{\dot{x}}_4\text{,}{\ddot{x}}_4	Displacement, velocity, and acceleration of the pipe, respectively
y_3,{\dot{y}}_3,{\ddot{y}}_3	Displacement, velocity, and acceleration of the driving foot, respectively
z	Average deformation of bristles
θ1, θ2	Rotation angle of flexure hinge and driving foot, respectively
Δx	Step distance of the pipeline robot and the slider
σ0	Bristle stiffness
σ1	Bristle damping of the bristle
σ2	Viscous damping coefficient
μ	Friction coefficient between the driving foot and the pipe

Acknowledgements

This work was supported by the State Key Laboratory of Robotics and System (HIT), China (Grant No. SKLRS-2022-KF-09). The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Electronic Supplementary Materials

The supplementary materials can be found in the online version of this article at https://doi.org/10.1007/s11465-022-0697-z and are accessible to authorized users.

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