*Corr. Author’s Address: School of Mechantronic Engineering, Chengdu 610500, China, zhaojianguo_1@qq.com 669
Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 669-682 Received for review: 2022-06-02
© 2022 The Authors. CC BY-NC 4.0 Int. Licensee: SV-JME Received revised form: 2022-08-09
DOI:10.5545/sv-jme.2022.219 Original Scientific Paper Accepted for publication: 2022-10-13
Rigid-elastic Coupling Dynamic Model and  
Dynamic Characteristics of a Spring-type of Traction Robot
Zhao, J. – Wang, B. – Liu, Q. – Wang, G. – Zeng, X.
Jianguo Zhao
1,2,3,*
 – Binfan Wang
1,3
 – Qingyou Liu
1,3
 – Guorong Wang
1,3
 – Xiangfeng Zeng
4
1
Southwest Petroleum University, School of Mechantronic Engineering, China 
2
Sichuan Provincial Key Lab of Process Equipment and Control, China 
3
Southwest Petroleum University, Energy Equipment Institute, China 
4
Yunnan Shuifu Yuntianhua Co., China
The traditional anchoring mechanism of the traction robot is rigid and is easily stuck in the wellbore. To solve this problem, a novel anchoring 
mechanism is proposed based on the spring-type of anchoring mechanism of the inclined block. The key to the movement of the traction 
robot is whether the traction robot can be anchored in the wellbore under the action of the traction force. Therefore, a rigid-elastic coupling 
dynamic model of the spring-type of anchoring mechanism under the action of the traction force was established. On this basis, the effects 
of span, width, thickness, and chamfer parameters on the anchoring performance of the spring-type of traction robot were analysed to 
design the optimal structure of the anchoring arm. Through the experimental comparison, it was determined that the error between the 
theoretical supporting force and the experimental supporting force was only 6.1 %, and the error of the simulated maximum traction force and 
experimental maximum traction force was 4.9 %. The traction robot can provide a maximum traction force of 14262 N in 178 mm (7-inch) of 
wellbore pipe. Thus, experiments verified the correctness of the rigid-elastic coupling dynamic model. The research results of this paper lay a 
foundation for the structural design and engineering application of a spring-type of traction robot. It can effectively ensure the downhole safety 
of oil and gas wells.
Keywords: spring-type of traction robot, spring-type of rigid-elastic coupling dynamic model, spring-type of anchoring mechanism, 
motion anchoring
Highlights
• 	 A novel spring-type of anchoring mechanism of traction robot based on inclined blocks is proposed, which provides a large 
traction force for the robot and can avoid being stuck.
• 	 The rigid-elastic coupling dynamic model of the spring-type of anchoring mechanism is established.
• 	 The calculation method of boundary conditions of self-anchoring of the traction robot (safe or not) is created.
• 	 The maximum traction forces under different structural parameters have been obtained, and the correctness of the theoretical 
maximum traction force has been verified by experiments.
0  INTRODUCTION
Horizontal well exploitation has become an important 
way to increase the recovery of oil and gas fields. It 
is mainly applied to the exploration and development 
of deep-sea and complex petroleum resources. It is 
increasingly difficult to deliver drilling tools as the 
depth of horizontal wells and the length of horizontal 
sections continue to increase. Compared with several 
methods, such as coiled tubing conveyance [1] and [2], 
drill pipe conveyance, and pump-in conveyance, the 
conveying method of downhole traction robots [3] to 
[5] can deliver instruments quickly and accurately, as 
well as significantly save time and reduce costs [6].
According to the movement mode, downhole 
traction robots can be divided into wheeled-type [7] 
to [10], telescopic-type [11] and [12], crawler-type [13] 
and [14], etc. Among them, wheeled and telescopic 
types are the most widely used in engineering. The 
conventional wheel-type traction robot has a group 
of expandable and collapsible anchoring arms, which 
hold the driving wheels against the wellbore wall. The 
rotating driving wheels drive the wheel-type traction 
robot to move in the horizontal well by the friction 
force between the driving wheel and the wellbore. The 
conventional telescopic traction robot is anchored in 
the wellbore wall by two or more sets of anchoring 
arms that can be opened and closed alternately. One 
group of anchoring arms is held stationary on the 
wellbore wall. At this point, another set of cylinders or 
motors slides towards or behind each other to achieve 
directional movement of the robot in the wellbore. 
For telescopic traction robot, rigid anchoring arms are 
mostly adopted between the anchoring mechanism 
and the wellbore wall to anchor the wellbore wall to 
perform traction action. The rigid anchoring arm has 
more constraints, which leads to fewer degrees of 
freedom in the mechanism, so it easily becomes stuck 
during the working process.
In addition, the anchoring mechanism of 
telescopic traction robot can adopt an elastic 
anchoring method. However, most of the elastic 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11,669-682
670 Zhao, J. – Wang, B. – Liu, Q. – Wang, G. – Zeng, X.
anchoring mechanisms designed by Gao et al. [15] and 
Liu et al. [16] and [17] are connected with rods and 
pins, at which points the forces on them are mainly 
concentrated. The position of the connecting rod and 
pin cannot achieve the strength requirements, so that 
the mechanism is deformed. Moreover, the schemes 
of the elastic anchoring methods only considered the 
motion characteristics under the rigid conditions but 
did not optimize its anchoring structures or determine 
its maximum traction force.
Therefore, based on previous studies, a novel 
telescopic downhole traction robot based on the 
spring-type of anchoring mechanism of the inclined 
block [18] is proposed in this paper. The traction robot 
has the characteristics of large traction force and 
automatic un-anchoring, which can to some extent 
prevent the occurrence of being stuck. This paper 
focuses on analysing the influencing factors of the 
spring-type of anchoring mechanism and optimizing 
its structures. The maximum traction force of the 
spring-type of anchoring mechanism under different 
wellbores is determined.
1  WORKING MECHANISM
On the basis of analysing and determining the strengths 
and weaknesses of existing traction robots, this 
paper proposes a spring-type of hydraulic telescopic 
downhole traction robot. It adopts a leaf spring with 
elastic restoring force as the anchoring arm, which can 
provide greater traction force while better adapting 
to the wellbore wall. This traction robot is lowered 
into the horizontal section through coiled tubing. The 
primary function of the robot is to deliver downhole 
pipe strings in horizontal wells or large displacement 
wells for other operations, such as logging and well 
workovers. The traction robot connects coiled tubing 
at the end and the downhole tools at the front, and 
its power and signals are transmitted through the 
cables and signal lines inside the coiled tubing. The 
application form of the robot is shown in Fig. 1.
It can be seen from Fig. 1 that the spring-type 
of telescopic downhole traction robot includes a 
front working section, a rear working section, and a 
control section. The front working section includes 
a front anchoring mechanism and a front telescopic 
mechanism, and the rear working section includes 
a rear anchoring mechanism and a rear telescopic 
mechanism. The executive parts of the working 
mechanism include four double-acting hydraulic 
cylinders (front support cylinder, front telescopic 
cylinder, rear support cylinder, rear telescopic 
cylinder). The action mechanism will be described 
below in conjunction with the action sequence in Fig. 
2.
(1)  From the initial status to status A: The hydraulic 
oil is injected into the front support cylinder, 
and the push rod of the front support cylinder is 
pushed to move to the right. The anchoring arms 
extend to anchor the wellbore wall.
(2)  From status A to status B: The front and rear 
telescopic cylinders are simultaneously injected 
with hydraulic oil. The control section and rear 
working section simultaneously walk forward 
a telescopic cylinder stroke S. At this point, the 
traction robot has completed the first forward 
motion.
(3)  From status B to status C: The rear support 
cylinder is injected with hydraulic oil and pushes 
the rear support cylinder push rod to move to the 
Fig. 1.  Application form of spring-type of hydraulic telescopic downhole traction robot

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 669-682
671 Rigid-elastic Coupling Dynamic Model and Dynamic Characteristics of a Spring-type of Traction Robot 
right. Under the action of the rear push rod joint, 
the rear anchoring arms extend to anchor the 
wellbore wall to prepare for the alternate work of 
the front and rear working sections.
(4)  From status C to status D: The front support 
cylinder is injected with hydraulic oil. At this 
time, the front anchor arms are restored to their 
initial state to prepare for the movement of the 
rear telescopic cylinder.
(5)  From status D to status E: Hydraulic oil is 
injected simultaneously into the rear telescopic 
cylinder and the front telescopic cylinder. The 
control section and the front working section 
are simultaneously crawling forward for one 
telescopic cylinder stroke S. At this time, the 
traction robot completes the first stretch.
As shown in Fig. 2, it is a complete motion cycle 
of the traction robot from the initial status to status 
F. The front and rear working section are operated 
alternately to achieve forward telescopic crawling. 
2  DYNAMIC CHARACTERISTICS
The mechanical model of the spring-type of anchoring 
mechanism is shown in Fig. 3 during the traction 
process. In this chapter, the relationship between 
the supporting force F
S
 of the supporting cylinder, 
the traction force F
T
 and the elastic restoring force 
F
2
 can be obtained through the analysis of the 
mechanical model. The elastic restoring force and 
the maximum stress of the spring-type of anchoring 
arm with different structural sizes can be obtained 
using ABAQUS simulation analysis [19]. The 
Fig. 2.  Schematic diagram of the working mechanism of the downhole traction robot
Fig. 3.  Schematic diagram of stress analysis of spring-type of anchoring mechanism; 1 left support frame, 2 wellbore pipe, 3 spring-type of 
anchoring arm, 4 right support frame, 5 push rod joint, and 6 central axis

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672 Zhao, J. – Wang, B. – Liu, Q. – Wang, G. – Zeng, X.
optimal structure of the spring-type of anchoring 
arm that meets the safe mechanical conditions and 
can overcome the friction force of the hydraulic 
cylinder seal ring to achieve automatic recovery will 
be determined under no-load conditions. Finally, the 
values of F
S
 and F
2
 of the spring-type of anchoring 
arm with the optimal structural size in different sizes 
of the wellbore are obtained.
2.1  Mechanical Characteristics of Traction Process of 
Spring-Type of Anchoring Mechanism
After the spring-type of anchoring mechanism of 
the traction robot anchors the wellbore wall, the 
telescopic mechanism of the traction robot starts to 
drag the downhole tool to move forward. At this point, 
the friction between three spring-types of anchoring 
arms and the wellbore wall will overcome the load 
traction force of the downhole tools to achieve 
forward motion. 
It can be seen from Fig. 3 that the push rod 
joint is subjected to the supporting force F
S
 and the 
reaction force of supporting force F
1
′ in the process of 
rightward movement. A spring-type of anchoring arm 
is subjected to the supporting force F
1
, the wellbore 
wall supporting force F
N
, its elastic restoring force F
2
, 
and the whole anchoring mechanism is subjected to 
the friction force f. At the same time, the left support 
frame of the spring-type of anchoring arm is solidly 
connected to the right support frame. In the process 
of moving the push rod joint to the right, the right 
support frame will generate the reaction force F
S
′, 
which is equal to the supporting force F
S
 and opposite 
to the direction, and the load reaction force F
T
′ which 
makes the downhole tools achieve forward motion.
Take a single spring-type of anchoring arm as the 
research object. F
1
 is the supporting force generated 
by the push rod joint. F
N
 is the supporting force 
generated by the wellbore wall. F
S
′ is the reaction 
force of the supporting force. F
T
′ is the reaction force 
of the traction force. f is the friction force generated by 
the wellbore wall to the whole anchoring mechanism. 
Three spring-types of anchoring arms are uniformly 
distributed along the central axis in space, so that the 
resultant force of three frictional forces between three 
spring-types of anchoring arms and push rod joint is 0 
N in the radial direction. The gap between three spring-
types of anchoring arms and push rod joint is matched, 
and there is a lubrication device, so the friction 
between them can be ignored. Through ABAQUS 
simulated analysis, θ is selected as 13.6° according to 
the design structure. H is the radial displacement of 
the spring-type of anchoring arm, which is determined 
by the different inner diameters of the wellbore. 
According to the mechanical equilibrium relationship, 
there is the following relationship equation.
According to ΣX = 0, the following equation can 
be obtained:
 F
f F F
s T
1
333
sin.
' '
  (1)
According to ΣY = 0, the following equation can 
be obtained:
 FF F
N 12
cos.   (2)
In addition, it is assumed that the friction 
coefficient between the wellbore wall and spring-type 
of anchoring arm is µ, which is taken a value as 0.25 
(the value of μ is 0.2 to 0.3, and the intermediate value 
of 0.25 is taken for theoretical research). Then there is 
the relationship equation:
 
f
F
N
3
 . (3)
Substituting Eqs. (2) and (3) into Eq. (1) yields:
 
f
F
f F F
s T
33 33
2

 






  tan.
' '
 (4)
For the traction robot to crawl forward, the 
friction force f must be greater than or equal to the 
traction force F
T
′ on the traction robot, namely:
 fF
T
≥
'
. (5)
If the friction force is equal to the traction force 
of the traction robot, the relationship between the 
supporting force F
S
 of the support cylinder and the 
reaction force F
T
′ of the traction force can be derived 
by bringing Eq. (5) into Eq. (4):
 F
F
F
S
T '
'
tant an . 

 3
2
 (6)
In Eq. (6), the reaction force F
T
′ of traction force 
is determined by the load. From Eq. (6), the supporting 
force F
S
 can be obtained to overcome different load 
traction forces in wellbores with different inner 
diameters.
2.2 Optimization Research of Structure Parameters of 
Spring-type of Traction Robot
The spring-type of anchoring arm of the traction 
robot is designed with the purpose of the leaf spring. 
When the traction robot has unexpected conditions in 
the well (such as power failure, solenoid valve out of 
control), the leaf spring can use its elastic restoring 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 669-682
673 Rigid-elastic Coupling Dynamic Model and Dynamic Characteristics of a Spring-type of Traction Robot 
force to overcome the friction generated by the seal in 
the support cylinder to avoid being stuck. The traction 
robot has two support cylinders, and the O-ring is 
a seal inside the support cylinder. Therefore, it is 
necessary to calculate the size of the friction resistance 
generated by the O-ring [20] in the support cylinder. 
Xu [21], Xiao [22], and Zuo and Zhang [23] studied 
the friction force generated by the O-ring in the 
hydraulic cylinder. From the design dimensions and 
relevant parameters of the traction robot, the frictional 
resistance of the sealing ring that needs to be overcome 
is 647 N when the piston is automatically reset by the 
restoring force of the leaf spring. Therefore, the leaf 
spring must fulfil this restoring force to achieve the 
function of automatic un-anchoring of the spring-type 
of anchoring mechanism.
From Eq. (6), it can be known that the main 
factor affecting the supporting force under the same 
wellbore and the traction force is the elastic restoring 
force of the spring-type of anchoring arm. Therefore, 
ABAQUS is used to simulate the span, thickness, 
width, and chamfer that affect the elastic restoring 
force of the spring leaf. The spring-type of anchoring 
arms are deformed under force, and its different radial 
displacements generate the corresponding elastic 
restoring forces. The design diameter of the traction 
robot is 118 mm, and it is suitable for a maximum 
pipe diameter of 178 mm (inner diameter (ID) 166 
mm) wellbore. Therefore, for a 178 mm wellbore, the 
radial displacement H of the spring-type of anchoring 
arm is 24 mm, as shown in Fig. 3. Consequently, it 
is necessary to obtain the elastic restoring force with 
radial displacement of 24 mm.
According to the outside diameter of the traction 
robot and the design installation requirements, each 
parameter of the spring-type of anchoring arm is 
shown in Fig. 4, and the values are taken as illustrated 
in Table 1.
Fig. 4.  Schematic diagram of the spring-type of anchoring arm
Under the same width, thickness, and chamfering 
radius of the spring, the changes of the elastic 
restoring force and the maximum stress of the spring 
with different spans are shown in Fig. 5.
Table 1.  The value of each parameter of anchoring arm
Designation Value [mm]
Span (L) 412 462 512 562 612
Width (W) 25 30 35 40 45
Thickness (T) 4 4.5 5 5.5 6
Chamfering radius (R) 20 40 60 80 100
Fig. 5.  Change of elastic force and stress with span
It can be seen from Fig. 5 that the larger the span 
of the leaf spring had, the smaller the maximum stress 
and the elastic restoring force would become. When 
the radial displacement of the leaf spring was 24 mm, 
the elastic restoring force of the leaf spring with a 
span of 412 mm was the largest (2,907 N). However, 
its maximum stress had exceeded the yield limit of the 
material (the material of 60Si2Mn, the yield strength 
of 1,176 MPa), resulting in plastic deformation. The 
leaf spring with a span of 612 mm had the smallest 
elastic restoring force (611 N), but the leaf spring 
could not overcome the frictional resistance of the 
O-ring. Therefore, the elastic restoring force of 462 
mm, which was larger and much lower than the yield 
strength of the material, was the optimal value of the 
leaf spring span.
In the case of a spring span of 462 mm with the 
same width and thickness, the changes in the elastic 
restoring force and the maximum stress of the spring 
with different chamfer radii are shown in Fig. 6.
It can be seen from Fig. 6 that the maximum 
stress was larger and should not be selected when 
the chamfering radius is 20 mm and 100 mm. The 
elastic restoring forces of the spring of the rest of the 
chamfer radii were similar, but the chamfer radius of 
40 mm was the smallest maximum stress. Considering 
the yield limit and the elastic restoring force, the 
chamfering radius of 40mm was the optimal value of 
the chamfering radius of the leaf spring.

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674 Zhao, J. – Wang, B. – Liu, Q. – Wang, G. – Zeng, X.
Fig. 6.  Change of elastic force and stress with chamfer
In the case of a spring span of 462 mm, chamfer 
radius of 40 mm, and the same width, the changes in 
the elastic restoring force and the maximum stress of 
the spring with different thicknesses are shown in Fig. 
7.
Similarly, the elastic restoring force and the 
maximum stress were positively correlated with the 
thickness by the analysis in Fig. 7. If the leaf spring 
was too thin, its stress met the material requirements, 
but its elastic restoring force did not satisfy the 
requirements. If the leaf spring was too thick, its 
elastic restoring force met the requirements, but its 
stress was extremely close to the yield limit of the 
material and did not meet the material requirements. 
Under the condition that other parameters remained 
unchanged if the thickness of the spring was selected 
as 5 mm, the maximum elastic restoring force was 
1,753 N, and the maximum stress was 858 MPa. Both 
the restoring force and stress were suitable, so the 
thickness of 5mm was the optimal value in the spring 
leaf.
Fig. 7.  Change of elastic force and stress with thickness
The variation curves of elastic restoring force and 
maximum stress for different widths of the leaf spring 
at a span of 462 mm, a chamfer radius of 40 mm, and 
a thickness of 5 mm are shown in Fig. 8.
Fig. 8.  Change of elastic force and stress with width
According to the analysis in Fig. 8, with the 
increase of the width of the spring, the elastic 
restoring force of the spring increased first and then 
decreased, and the maximum stress of the spring 
increased gradually. When the width of the leaf spring 
was 30 mm, the maximum elastic restoring force of 
the leaf spring was 1,753 N, and the maximum stress 
was 853 MPa. When the spring width was 45 mm, 
the maximum elastic restoring force of the spring was 
at least 451 N, and the maximum stress was 1,523 
MPa. Obviously, the reason for the first increase in 
the elastic restoring force of the leaf spring was that 
its maximum stress was within the yield limit of the 
material. In addition, the reason for the sudden sharp 
decrease was that its maximum stress had exceeded 
the yield limit of the material, resulting in the plastic 
deformation. At a width of 35 mm, the analysis of 
the maximum stress diagram illustrated that the leaf 
spring had undergone plastic deformation in the 
weaker place, where is the chamfer of the spring of 
anchoring arm. Therefore, when the width of the 
spring piece was 30 mm, the stress was smaller and 
the elastic restoring force was appropriate. The width 
of 30 mm was the optimal value of the leaf spring 
width.
After the optimization of the structure parameters 
of the leaf spring, the final structure of the spring-type 
of anchoring arm was chosen to have a span of 462 
mm, a chamfer radius of 40 mm, a width of 30 mm 
and a thickness of 5 mm. Through the data analysis 
of ABAQUS simulation, the relationship between the 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 669-682
675 Rigid-elastic Coupling Dynamic Model and Dynamic Characteristics of a Spring-type of Traction Robot 
restoring force F
2
 and the radial displacement H of the 
spring arm can be obtained. The relationship is shown 
in Eq. (7):
 FH
2
14 77 37  .. . (7)
Bring Eq. (7) into Eq. (6) to obtain the final 
expression of the supporting force required by the 
traction robot:
 FH
F
s
T
    31 47 7 .t an tan.
'


 (8)
Taking the radial displacement H (0 mm to 24 
mm) as the independent variable and the supporting 
cylinder supporting force F
S
 as the dependent variable, 
the curve of the supporting force of supporting 
cylinder with the radial displacement of the leaf spring 
was obtained by fitting Eq. (8), as shown in Fig. 9.
Fig. 9.  Curve of supporting force with radial displacement
Table 2.  Supporting force of different wellbore
Wellbore size [mm] H [mm] F
2
 [N] F
S
 [N]
178 (7-inch) 24 1,784 10,901
165 (6.5-inch) 15 1,120 10,417
152 (6-inch) 11 825 10,203
From Fig. 9, the magnitude of the required 
supporting force was obtained for different wellbore 
pipes with a design traction force of 10,000 N. From 
Eq. (7), it can be obtained that the radial displacement 
of the leaf spring needs to be greater than 8.6 mm to 
overcome the frictional resistance of the O-ring of 
647 N and to have the ability to automatically unlock. 
Therefore, only the movement of the spring-type of 
traction robot in 152 mm (140 mm ID), 165 mm (148 
mm ID) and 178 mm (161 mm ID) wellbore pipe was 
studied. From Eq. (7) and Fig. 9, the elastic restoring 
force and the required supporting force of the spring-
type of anchoring arm can be obtained when different 
wellbores move, as shown in Table 2.
3  MODELING AND SIMULATION ANALYSIS 
In this chapter, using ABAQUS and ADAMS [24] for 
co-simulation, a rigid-elastic coupled dynamic model 
was established and compared with the rigid model 
to verify the superiority of the rigid-elastic coupled 
dynamic model. Whether the spring-type of anchoring 
mechanism satisfied the anchoring performance under 
its design traction force was further verified. Finally, 
the maximum traction force of the spring-type of 
anchoring mechanism under different wellbores was 
determined.
3.1 Rigid-elastic Coupling Model of a Spring-type of 
Anchoring Mechanism
ABAQUS was carried out to establish a elastic model 
of the spring-type of anchoring arm. The procedure 
was as follows:
The spring-type of anchoring arm of the final 
structure determined in Chapter 2 is used to establish 
a three-dimensional model. The three-dimensional 
model was imported into the ABAQUS software. The 
material properties were defined in the software (the 
elastic modulus was 2.06×10
5
 MPa, the Poisson's ratio 
was 0.29, and the mass density was 7.85×10
6 
kg/mm
3
). 
Two connection points of the spring leaf were defined 
as hard points, constraints were added, modal analysis 
was carried out to determine the form of the model, 
and a modal neutral file can be obtained. Finally, the 
modal neutral file was exported as an mnf file. 
After the simulation model of spring-type of 
anchoring mechanism was built in the SolidWorks 
software, it would be imported into the ADAMS 
software. The three components of the left joint of 
the leaf spring, the right joint of the leaf spring and 
the fixed connecting rod, which were in a fixed 
relationship, were integrated into one component 
through a Boolean operation. Then they were called a 
“fixed connection body”. At this point, the leaf spring 
is still a non-deformable rigid spring, and the model 
is rigid. Then, the modal neutral file of mnf of the 
spring was imported into ADAMS to replace the rigid 
spring. A rigid-elastic coupled dynamics model was 
generated, as shown in Fig. 10. The rigid model can 
be compared with the rigid-elastic coupled model for 
simulation.

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676 Zhao, J. – Wang, B. – Liu, Q. – Wang, G. – Zeng, X.
Table 3.  Calculating parameters of contact force
Parameters
Numerical 
value
Coefficient of static friction between the spring-type of 
anchoring arm and pipe wall (μ
1
)
0.5
Coefficient of dynamic friction between the spring-type 
of anchoring arm and pipe wall (μ
2
)
0.25
Contact resilience factor [N/mm] 10
5
Force index 1.5
Damping coefficient [N×s/mm] 1,000
Penetration depth [mm] 0.01
3.2 Simulation Analysis of Influencing Factors of 
Mechanical Characteristics of Spring-type of Anchoring 
Mechanism
Using the ADAMS/View software, the rigid model 
and the rigid-elastic coupling model were used to 
simulate the friction curve and the velocity curve of 
radial displacement of the spring-type of anchoring 
arm. In the initial state, a support force of 10,901 N 
and a load traction force of 10,000 N are applied to 
the two models respectively for five seconds, and the 
results are shown in Figs. 11 and 12.
Fig. 11.  Friction curve of rigid model and rigid-elastic coupling 
dynamic model
It can be seen from Figs. 11 and 12 that the 
rigid-elastic coupling model was more stable, more 
accurate, and superior to the rigid model data. The 
rigid-elastic coupling model can better reflect the 
motion characteristics of the spring-type of anchoring 
mechanism. Therefore, the rigid-elastic coupling 
model was used to simulate the spring-type of 
anchoring mechanism. The initial state of the rigid-
elastic coupled model was loaded for 5 seconds, 
during which the force and velocity changes can be 
obtained.
Fig. 10.  Rigid-elastic coupled dynamics model
To perform dynamic analysis on the rigid-elastic 
coupled model, it is necessary to define the way of 
movement between the two contact mechanisms of 
the model, so that the model has a unique kinematic 
regularity. The wellbore is defined as a fixed frame, 
namely a fixed pair. The motion mode between the 
spring and the left and right support frames is defined 
as the rotational pair, with a total of six rotational 
pairs. The motion mode between the spring and the 
push rod joint is defined as the moving pair, and the 
motion mode between the central axis and the left and 
right support frames is defined as the moving pair, 
with a total of five moving pair.
From the dynamic analysis, it can be known that 
traction robot was mainly affected by the supporting 
force F
S
 and its reaction force F
S
′, the traction force 
F
T
, the restoring force F
2
 of the leaf spring and the 
friction force f in the traction process. From Table 2, 
when the traction robot drags the load forward in the 
178 mm wellbore, the push rod joint was subjected 
to a supporting force of 10,901 N, and the fixed body 
was subjected to a reaction force of the supporting 
force of 10,901 N and a reaction force of the traction 
force of 10,000 N. The above loads were applied to 
the rigid-elastic coupled dynamic model.
In addition, the quality of the spring-type of 
anchoring mechanism is about 8 kg. Its gravity is 80 
N, which can be neglected compared with other forces 
of several thousand N. The contact between the push 
rod joint and three spring-types of arms of anchoring 
mechanisms, and the contact between three leaf-
spring and the wellbore were defined as “collision 
constraint”, and the contact type was “spring-type 
of body to rigid body”. The parameter values that 
used ADAMS to simulate and analyse contact pairs 
are shown in Table 3. “Contact resilience factor” 
is the stiffness, which reflects the ability of the two 
contacting bodies to resist deformation. “Force index” 
is used to calculate the index of the contribution of 
the material stiffness term in the instantaneous normal 
force.

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677 Rigid-elastic Coupling Dynamic Model and Dynamic Characteristics of a Spring-type of Traction Robot 
Fig. 12.  Velocity curve of rigid model and rigid-elastic coupling 
dynamic model
Fig. 13 shows the force and velocity curves of 
the traction process of the spring-type of anchoring 
mechanism under the conditions of the supporting 
force of 10,901 N and the traction force of 10,000 N.
It can be seen from Fig. 13 that the friction force 
on a spring-type of anchoring arm also remained 
fluctuating around 3,333 N, which is the theoretical 
frictional force obtained from Eq. (3), after the traction 
force reached 10,000 N to maintain the level. This 
phenomenon indicated that the friction force generated 
by three spring-type of anchoring mechanism (about 
10,000 N) can overcome the traction force to anchor 
the wellbore wall. The velocity of radial displacement 
started to fluctuate when it was first stressed, and 
finally gradually remained stationary with the 
wellbore wall. It indicated that the theoretically 
calculated supporting force of 10,901 N was able to 
overcome the traction force of 10,000 N applied to the 
traction robot to keep it locked with the wellbore wall.
Fig. 13.  Force and velocity curves of the spring-type of anchoring 
mechanism (10,000 N)
Figs. 14 and 15 show the force and velocity 
curves of radial displacement of the spring-type of 
anchoring mechanism in the 178 mm wellbore with 
traction forces of 14,000 N and 15,000 N respectively 
when the supporting force of 10,901 N remained 
constant.
Fig. 14.  Force and velocity curves of the spring-type of anchoring 
mechanism (14,000 N)
Fig. 15.  Force and velocity curves of the spring-type of anchoring 
mechanism (15,000 N)
From Figs. 14 and 15 it can be observed that the 
spring-type of anchoring mechanism could continue 
anchoring when the traction force was 14,000 N. 
When the traction force was 15,000 N, it broke away 
from the wellbore wall after 1.9 s, and the anchoring 
failed. This phenomenon demonstrated that the 
anchoring mechanism cannot conquer the traction 
force of 15,000 N under the supporting force of 
10,901 N, and the traction robot cannot sustain the 
anchoring with the wellbore wall. Thus, the maximum 
traction force interval of the spring-type of anchoring 
mechanism was gained between 14,000 N and 15,000 
N in a 178 mm wellbore.
In order to observe the anchoring ability of the 
spring-type of traction robot under other sizes of the 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11,669-682
678 Zhao, J. – Wang, B. – Liu, Q. – Wang, G. – Zeng, X.
wellbores, the motion of the traction robot in 165 
mm wellbore and 152 mm wellbore was selected 
as the object of study in this paper. Their anchoring 
performance was simulated and analysed by applying 
theoretical supporting force of 10,417 N and 10,203 N 
respectively, as shown in Figs. 16 to 19.
Fig. 16.  Force and velocity curves of anchoring mechanism in 165 
mm wellbore (10,000 N)
Similarly, it can be understood from Figs. 16 
to 19 that the spring-type of anchoring mechanism 
was able to conquer the traction force of 10,000 
N under the supporting force of 10,417 N in a 165 
mm wellbore and 10,203 N in a 152 mm wellbore, 
respectively, to anchor it with the wellbore wall. The 
maximum traction force interval of the spring-type of 
traction robot was 12,000 N to 13,000 N and 10,000 N 
to 11,000 N separately.
Fig. 17.  Force and velocity curves of anchoring mechanism in 165 
mm wellbore (13,000 N)
It was verified that the spring-type of traction 
robot can preserve anchoring under a design traction 
force of 10,000 N with 152 mm, 165 mm and 178 mm 
wellbores. At the same time, the maximum theoretical 
traction force intervals of 10,000 N to 11,000 N, 
12,000 N to 13,000 N, and 14,000 N to 15,000 N were 
acquired for the corresponding sizes of wellbores. It 
was indicated that the maximum traction force of the 
traction robot would increase with the increase of the 
wellbore pipe diameter.
Fig. 18.  Force and velocity curves of anchoring mechanism in 152 
mm wellbore (10,000 N)
Fig. 19.  Force and velocity curves of anchoring mechanism in 152 
mm wellbore (11,000 N)
4  EXPERIMENTAL RESEARCH
The spring-type of anchoring arm of the final structure 
(span of 462 mm, chamfer radius of 40 mm, width of 
30 mm and thickness of 5 mm) determined in Chapter 
2 was made into an experimental prototype, which is 
shown in Fig. 20. 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 669-682
679 Rigid-elastic Coupling Dynamic Model and Dynamic Characteristics of a Spring-type of Traction Robot 
Fig. 20.  Spring-type of anchoring mechanism
A simulation diagram of the experimental 
prototype is shown in Fig. 21 to better present its 
structure. The prototype was used to verify that the 
spring-type of anchoring mechanism can overcome 
the traction force of load to achieve anchoring to the 
wellbore wall under the theoretical support force of 
the supporting cylinder. The actual maximum traction 
force of the traction robot can be obtained from the 
prototype experiment. Also, the recovery effect of the 
spring-type of anchoring arm was observed after the 
unloading of the anchoring mechanism.
4.1  Experimental Steps
The experimental scheme of the anchoring mechanism 
of the spring-type of traction robot is shown in Fig. 
22. The experimental procedure of the traction process 
was as follows:
(1)  Hydraulic cylinder 1 was injected with liquid, so 
that the spring-type of anchoring arms contacted 
the wellbore wall. Then the voltage signal of the 
S-shaped pressure sensor was recorded.
(2) Hydraulic cylinder 1 continued to have fluid 
injected, so that the cylinder generated a 
supporting force of 10,901 N (voltage signal of 
S-shaped sensor is 4.48 V).
(3) Hydraulic cylinder 2 was filled with fluid, so that 
the hydraulic pressure in the cylinder reached 
10,000 N (voltage signal of the spoke sensor is 
Fig. 21.  Schematic diagram of experimental equipment
Fig. 22.  Experimental scheme and experimental system of spring-type of anchoring mechanism; 1 and 8 -flange 1, 2 s-type pull pressure 
sensor, 3 hydraulic cylinder 1, 4 and 11 manual high-pressure ball valve, 5 and 9 pull rod, 6 178 mm of wellbore pipe, 7 spring-type of 
anchoring mechanism, 10 hydraulic cylinder 2, 12 spoke pull pressure sensor, 13 flange 2, 14 hydraulic tube, 15 pressure transmitter, 
16-Paperless recorder, 17-Manual high-pressure pump

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11,669-682
680 Zhao, J. – Wang, B. – Liu, Q. – Wang, G. – Zeng, X.
0.76 V). The anchoring condition of the anchoring 
mechanism was recorded.
(4) If the anchoring mechanism anchored the 
wellbore wall, hydraulic cylinder 1 continued 
to add pressure until the wellbore moved to the 
right. Also, the pressure in hydraulic cylinder 2 
was recorded when the wellbore moved.
(5) Then, finally, the pressure in hydraulic cylinder 2 
and hydraulic cylinder 1 was removed to observe 
the recovery of the spring-type of anchoring arm.
All measuring instruments had been calibrated 
before the experiment. All experimental instruments 
have a temperature compensation function, and the 
temperature has no effect on the measurement data. 
Therefore, the experimental errors are within the 
allowable range.
4.2  Experimental Results
The voltage data collected by the paperless 
recorder were converted into pressure data using 
the proportional coefficient. The pressure variation 
curves in hydraulic cylinder 1 (supporting force) and 
hydraulic cylinder 2 (traction force) are obtained as 
shown in Fig. 23.
Fig. 23.  Theoretical and experimental support force curve
Fig. 23 shows that after 400 s the pressure in 
hydraulic cylinder 1 (supporting force) was kept 
at 10,230 N, and the pressure in hydraulic cylinder 
2 was maintained at about 10,000 N. The spring-
type of anchoring mechanism remained relatively 
stationary with the wellbore. The reasonableness of 
the theoretical calculation was verified. The anchoring 
state between the anchoring mechanism and the 
wellbore wall is shown in Fig. 24, and the distance 
between the wellbore and the flange was 30 mm.
Fig. 24.  Anchoring state of spring-type of anchoring mechanism
Fig. 25.  Anchoring failure state of spring-type of anchoring 
mechanism
Continuing to feed liquid to hydraulic cylinder 2, 
its pressure was increased to 14,262 N and then began 
to decrease, while the pressure of hydraulic cylinder 
1 began to decrease. Here relative sliding occurred 
between the anchoring mechanism and the wellbore 
wall, and the anchoring failed. It was illustrated 
that the maximum traction force was 14,262 N. The 
relative position of the wellbore and the spring-type 
of anchoring mechanism is shown in Fig. 25 after the 
experiment, and the distance between the wellbore 
and the flange was 10 mm.
Table 4.  Comparison of theoretical and experimental data of 
support force and traction force
The supporting force
The maximum 
traction force
Experimental value [N] 10,230 14,262
Simulation value [N] 10,901 15,000
Deviation [%] 6.1 4.9

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681 Rigid-elastic Coupling Dynamic Model and Dynamic Characteristics of a Spring-type of Traction Robot 
From Table 4, the experimental results showed 
that the simulation values did not differ much from the 
experimental values. the correctness of the mechanical 
analysis, the optimization of the leaf spring and the 
rigid-elastic coupling model were verified. However, 
the experimental results also exposed some problems. 
After hydraulic cylinder 1 was decompressed, the 
spring did not reset quickly, and only slowly retreated 
after an external force was applied. The reason for 
this was due to safety concerns. Hydraulic cylinder 
1 released the pressure slowly, so that the elastic 
restoring force of the spring-type of anchoring arm 
was also slowly reduced, and resulted in the arm 
returning slowly.
5  CONCLUSIONS
(1) In this paper, a novel spring-type of anchoring 
mechanism of a traction robot based on inclined 
blocks was proposed, which can provide a large 
traction force for the robot and can avoid being 
stuck. Meanwhile, the mechanical analysis of the 
traction process was completed, and the structure 
of the spring-type of anchoring mechanism was 
optimized.
(2) Through establishing the rigid-elastic coupling 
model of the spring-type of anchoring 
mechanism, it was determined that the rigid-
elastic coupling model can better reflect the 
motion characteristics of the traction robot 
compared with the rigid model. At the same 
time, through analysis of the rigid-elastic 
coupling model simulation, the correctness of the 
theoretical mechanical calculation of the spring-
type of anchoring mechanism was verified, 
and the maximum traction force under different 
structural parameters was obtained.
(3) Through the experiment, it was verified that 
the experimental supporting force required to 
overcome the load of 10,000 N was 10,230 N, 
which was 6.1 % different from the theoretically 
calculated value. The maximum traction force 
that the traction robot anchoring mechanism 
can provide was 14,262 N, which was 4.9 % 
different from the simulated calculated value. The 
experiment result showed the correctness of the 
theoretical calculation, the optimization of the 
structure of the anchoring arm, and the simulation 
of the rigid-elastic coupling model.
The research results of this paper lay a foundation 
for the structural design and engineering application 
of spring-type of traction robot. It can effectively 
ensure the downhole safety of oil and gas wells.
6  ACKNOWLEDGEMENTS
This work was funded by the National Natural Science 
Foundation of China (No. 52004232, U19A200380), 
the Sichuan Science and Technology Program 
(23QYCX0060, JG2021-624, 2021YFS0305, 
22QYCX0196) and the Sichuan Provincial Key Lab 
of Process Equipment and Control (GK202006). 
The authors also sincerely thank the editors and the 
reviewers for their efforts in improving this paper.
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