*Corr. Author’s Address: Jiangsu University, School of Automotive and Traffic Engineering, Zhenjiang, China, yangjian@ujs.edu.cn 49
Strojniški vestnik - Journal of Mechanical Engineering 69(2023)1-2, 49-60 Received for review: 2022-10-15
© 2023 The Authors. CC BY-NC 4.0 Int. Licensee: SV-JME Received revised form: 2022-12-21
DOI:10.5545/sv-jme.2022.415 Original Scientific Paper Accepted for publication: 2023-01-11
Influence of the Side Branch Structure Pattern of the Imitation 
Cat’s Claw Function on the Vibration and Noise of Tires
Wang, G. – Zhu, K. – Wang, L. – Yang, J. – Bo, L.
Guolin Wang
1
 – Kexin Zhu
1
 – Lei Wang
1
 – Jian Yang
1,*
 – Lin Bo
2
1 
Jiangsu University, School of Automotive and Traffic Engineering, China 
2 
KENDA Industrial Co., Ltd, China
To study the method of reducing the low-frequency vibration noise of tires, a passenger car tire (205/55R16) is taken as the research object. 
The dynamic grounding characteristics and vibration reduction mechanism of the cat’s paw pad are analysed. The research showed that 
the swing deformation characteristics of paw pads during the walking process of cats are one of the main ways to reduce the impact from 
the ground and achieve vibration reduction and silencing. To analyse the influence of tire grounding on noise, tire grounding is divided into 
five areas, and the characteristics of ten tire grounding areas are analysed through tests. Pearson correlation analysis is used to obtain the 
characteristics of the eight most relevant grounding parameters with tire noise, and multiple linear regression is conducted between the 
characteristics of the eight grounding areas. The product of the correlation coefficient and the average value of the characteristics of the 
ground contact area shows that the central area of the tire tread contributes the most to the tire noise. The swing deformation characteristics 
of the bionic cat paw pad are realized by setting the staggered side branch pipe groove in the centre of the tire, and the vibration reduction 
characteristics of the bionic tire are analysed using the finite element method. The results showed that when the tire rolls, the amplitude and 
fluctuation range of the ground radial excitation force acting on the bionic tire are reduced compared with the original tire, and the vibration 
and noise characteristics of the tire are improved.
Keywords: bionics, vibration damping mechanism, vibration noise, tread pattern, structural design
Highlights
• 	 The swing deformation characteristics of paw pads during the walking process of domestic cats are one of the main ways of 
reducing the impact from the ground and achieving vibration reduction and silencing. 
• 	 The relationship between the tire grounding characteristic parameters and the measured noise is studied by region, and it is 
concluded that the tire tread centre area contributes the most to the tire noise.
• 	 The dynamic and acoustic models of the tire are established and verified.
• 	 The bionic design of the tread pattern in the centre of the tire tread was carried out, and the noise reduction mechanism of the 
bionic tire is analysed regarding the radial excitation force and noise of the tire.
0  INTRODUCTION
Road traffic noise has become a significant source 
of noise pollution [1]. Studies have shown that when 
the driving speed of the car exceeds 70 km/h, the tire 
noise will become the main part of the vehicle’s noise, 
accounting for more than 30 % of it [2]. In recent years, 
the tire labelling laws implemented in the European 
Union, the United States (US), and other countries 
and regions have put forward strict requirements on 
tire noise performance [3]. The vibration and noise 
of tires are one of the main reasons that affect the 
noise, vibration, and harshness (NVH) performance 
of vehicles [4] and [5]. How to reduce tire vibration 
and noise has always been the focus of major 
tire manufacturers. Ji and Bolton [6] analysed the 
relationship between tire vibration characteristics and 
radiated noise by using the structural modal analysis 
method. The results show that low-order modes have 
a greater impact on tire vibration radiated noise, 
and the frequency corresponding to the peak sound 
pressure is often near the natural frequency of the tire. 
Through simulation and experimental analysis, Zuo et 
al. [7] concluded that the periodic collision between 
tread blocks and the road surface is the main source 
of tire vibration noise, and the collision frequency 
is closely related to the number and size of blocks. 
Mohammadi and Ohadi [8] proposed a new method 
of reducing tire noise by using the multi-objective 
minimization method, optimized the structure and 
tread pattern parameters of patterned tires, reduced 
tire noise, and provided ideas for the research of low-
noise tire patterns. Pei et al. [9] determined that the 
tread is the component with the greatest contribution 
to the tire by studying the contribution of each part 
of the tire’s outer contour to vibration and noise and 
adding polyester damping materials to the tread and 
sidewall to suppress tire vibration. Zhang et al. [10] 
tested and compared the tire noise of different tire 
carcass structures. The results showed that the types 
and layers of carcass skeleton materials would change 
the vibration state of the carcass, thus affecting the 
tire noise. Although these noise reduction methods 
have achieved certain effects, in the finite element 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)1-2, 49-60
50 Wang, G. – Zhu, K. – Wang, L. – Yang, J. – Bo, L.
analysis process, only smooth tires or tires with only 
longitudinal grooves are mostly used, and complex 
patterns are not considered. However, in the actual 
driving of passenger cars, most use complex tread 
patterns, and the vibration noise at low speeds is 
mainly caused by the tread patterns hitting the ground 
[11], so it is essential to study low-noise tread patterns.
In long-term biological evolution, animals 
have formed super-adaptive abilities to nature. The 
extremely strong vibration damping and muted effect 
of cats in the process of walking and running have 
long been a research focus of scholars. The paw pad 
of a domestic cat is the only body part that contacts 
the ground, which plays a very important role in the 
vibration reduction and silence of the domestic cat 
during walking, running, and jumping. Coulmance 
et al. [12] measured the forces exerted by the limbs 
of the cat during walking. The results showed that 
the front paw lift was preceded and accompanied by 
postural adjustment and that the front paws had a 
more important role in the cat’s postural adjustment. 
Zhang et al. [13] established a mass-spring model to 
simulate the landing behaviour of domestic cats after 
jumping and used this model to analyse the cushioning 
characteristics of the domestic cat’s paw rest. Kruger 
et al. [14] used a high-frequency camera to capture 
images of domestic cats and wild cats during normal 
walking, sprinting, and jumping from a height, and 
compared and analysed the cats’ limb movements in 
different states.
With the deepening of research, the concept of 
bionics has been integrated into all walks of life and 
has been used as an important means of technological 
innovation. Wang et al. [15] applied the arc structure 
of the locust’s foot in nature to the tread arc design 
of the tire, which reduces the tire wear and enhances 
the grip ability of the tire while reducing the vibration 
noise of the tire. The Gubo Tire Company and 
Polymer Research Center in Madison, Wisconsin, 
USA jointly developed a kind of non-pneumatic 
military honeycomb-like tire, which has good shock 
absorption and defence characteristics [16].
Chen et al. [17] can quickly disperse the boundary 
layer vortex with the help of the non-smooth structure 
of shark skin, so as to improve the principle of 
water flow speed. The non-smooth structure is set at 
the bottom and wall of the tire ditch to improve the 
tire’s water-skiing performance. Zhang et al. [18] 
established a mathematical model of reindeer foot 
characteristics with the help of the reindeer’s strong 
grip when walking on ice, and a bionic design was 
carried out for the tire tread. The bionic tire increased 
the contact area with ice and improved the anti-skid 
performance of the tire. Zhou et al. [19] were inspired 
by the strong adsorption capacity of octopus suction 
cups and established three bionic concave funnel 
suction cup tire patterns. Through simulation analysis, 
the bionic patterns have better tensile and compressive 
properties and better adsorption capacity on the ice 
surface, ensuring the anti-skid ability of the tire on the 
ice surface. With in-depth research on the mechanism 
of biological characteristics, such traits can be more 
reasonably applied to various industries. In order to 
apply the strong vibration reduction and mute effect 
of domestic cats when walking, running, and jumping 
to the design of a low-noise tread pattern structure, it 
is necessary to study the vibration reduction and mute 
mechanism of domestic cats to guide the structural 
design of low-noise tread pattern.
This paper takes the 205/55R16 tire as the 
research object and studies how to reduce the low-
frequency vibration noise of the tire. The dynamic 
grounding characteristics and vibration reduction 
mechanisms of domestic cat paw pads are analysed, 
and the bionic noise reduction modification design of 
the tread pattern is carried out. The shock absorption 
characteristics of the imitation cat paw pad are 
realized by setting a staggering side branch pipe 
groove in the central area of the tire. On this basis, the 
noise reduction mechanism of imitation domestic cat 
paw pad pattern tires is studied.
1  A STUDY ON THE VIBRATION REDUCTION  
MECHANISM OF CAT PAW PADS
1.1  Mechanical Experiment of Contact Between Claw Pad 
and Ground
The purpose of the mechanical test on the contact 
between the paw pads of domestic cats and the 
ground is to obtain the vertical reaction force and 
strain characteristics of the paw pads of domestic cats 
in normal walking gait (v = 0.4 m/s to 0.8 m/s). The 
subjects are two healthy, defect-free domestic cats, 
aged 6 years, weighing 4.5 kg and 4.7 kg respectively. 
During the test, a pressure-sensitive channel (walkway 
A101; (Tekscan, USA)) is used to measure the 
vertical reaction force generated when the paw pads 
of domestic cats pass straight over the pressure plate 
at different speeds. To obtain the strain characteristics 
of the domestic cat on the ground, when the domestic 
cat walks in a straight line on the glass plate, grey 
speckles are added to its foot pads, as shown in Fig. 1. 
The motion of the paw pads was recorded by a high-
speed camera (Olympus i-SPEED) installed under the 
glass plate, and then the images are digitized using the 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)1-2, 49-60
51 Influence of the Side Branch Structure Pattern of the Imitation Cat’s Claw Function on the Vibration and Noise of Tires
VIC-2D of CSI Company (USA) to obtain the strain 
and related information of the paw pads in contact 
with the ground.
Fig. 1.  The contact tests of paw pads;  
a) contact pressure test; b) contact strain test
1.2 Mechanical Analysis of Contact between the Claw 
Pad and the Ground
The contact strain magnitude and direction data 
information between the cat paw pad and the ground 
is obtained through VIC-2D digital processing. 
Relevant research [12] and [20] shows that when dogs 
and cats exercise, their front paw pads always play 
a more critical role than their rear paw pads in the 
process of realizing biological functions. Therefore, 
this paper mainly considers the front paws of cats. 
The three groups of effective tests are selected for 
analysis of the two domestic cats, and the strain 
characteristics with the same trend were obtained. 
This paper takes the centre group as an example to 
analyse the strain characteristics. The magnitude and 
direction of the contact strain between the palm pad 
and the toe pad are shown in Fig. 2. In the figure, the 
X direction is the forward direction of the cat, and 
the Y direction is the inner side of the cat’s paw pad. 
From the principal strain direction, the deformation 
direction of the toe pad area has no change, and it is 
always tensile deformation in the Y direction. Before 
0.180 s, the tensile deformation of the palm pad 
area is mainly in the Y direction, and after 0.180 s, 
the tensile deformation in the X direction is mainly 
in the X direction, which indicates that the swing 
deformation characteristics of the palm pad area 
exist in the X and Y directions. From the perspective 
of principal strain, the principal strain values of the 
four toe pads increase continuously during the whole 
contact process. The strain value of the pad increases 
first and then decreases alternately in the inner and 
outer regions. The maximum principal strain of 
the palm pad is significantly lower than that of the 
toe rest, which is caused by the change in the strain 
direction. This further illustrates that the palm pad 
area has the characteristics of swing deformation, 
vibration reduction, and noise reduction in the process 
of contacting the ground. 
Fig. 2.  Strain magnitude and direction of contact between claw 
pad and ground
Fig. 3.  Time domain diagram of contact strain in X and Y 
directions of palm pad area
To further clarify the attenuation of the strain 
value during the contact between the palm pad and 
the ground, the strain values in the X and Y directions 
of the palm pad area during the entire grounding 
process are extracted and plotted as a curve of the 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)1-2, 49-60
52 Wang, G. – Zhu, K. – Wang, L. – Yang, J. – Bo, L.
strain value changing with time, as shown in Fig. 3. 
During the whole grounding process, the strain value 
of the palm pad area reflects a fluctuation change law 
with the opposite trend in X and Y directions, and 
the strain value of the palm rest is attenuated during 
the fluctuation process, which further proves that the 
impact load on the palm rest area during the grounding 
process can realize some dissipation with the swing 
deformation in X and Y directions.
2 TIRE GROUNDING DEFORMATION CHARACTERISTICS 
TESTING AND ANALYSIS
2.1  Tire and Ground Pressure Distribution Testing
Fig. 4 is a physical map of 205/55R16 PCR tires 
produced by 10 different manufacturers and used 
in this experiment. Table 1 lists the noise-related 
information of 10 test tires. The noise values are 
derived from the tire performance test data published 
in the literature [21]. In this paper, the noise 
performance of the tire is evaluated with the pass-
by noise, which is the noise value measured by the 
test tire when the vehicle’s engine is turned off and 
the vehicle passes through the measurement area at a 
speed of 80 km/h. 
Fig. 4.  Physical drawing of 205/55R16 test tire
Table 1.  Test tire information and noise value
Number Type Through noise value [dB]
1 Turanza ER 300 71.5
2 PROXES C100 PLUS 71.5
3 LS388 71.0`
4 MARMONIC M220 70.4
5 ADVAN dB DECIBEL V551 71.1
6 SPORT SA-37 72.1
7 Primacy 3 ST 70.6
8 N’FEAR SU4 70.8
9 Efficient Grip Performance 70.7
10 Conti Max Contact MC5 72.4
As shown in Fig. 5, the American Tekscan 
pressure test system is used to obtain the grounding 
marks and pressure distribution of 10 test tires. The 
inflation pressure of the tires during the test is 0.24 
MPa of the rated pressure, and the load is 4821 N of 
the rated load.
Fig. 5.  Ground pressure deformation
2.2  Grounding Area Division and Grounding Parameters
Most of the 10 tires used in the test have asymmetric 
tread patterns and are divided into five areas by 
four longitudinal grooves. Therefore, the tread is 
divided into five areas by taking the groove wall of 
four longitudinal grooves as the boundary: the outer 
shoulder area (I), the outer transition area (II), the 
central area (III), the inner transition area (IV), and the 
inner shoulder area (V).
Fig. 6.  Tread grounding area division
The ground deformation parameters are mainly 
divided into grounding geometric parameters and 
grounding pressure parameters. The geometric 
parameters are the grounding area, imprint area, 
grounding area ratio, grounding length, grounding 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)1-2, 49-60
53 Influence of the Side Branch Structure Pattern of the Imitation Cat’s Claw Function on the Vibration and Noise of Tires
width, grounding aspect ratio, and rectangle ratio. The 
pressure parameters are average grounding pressure 
and grounding pressure skewness. Liang [22] defines 
the grounding geometric parameters and grounding 
pressure parameters of tires in detail. Through the test, 
the grounding geometric parameters and grounding 
pressure parameters of the whole area of the 
grounding footprint, the outer tire shoulder area (I), 
the outer transition area (II), the central area (III), the 
inner transition area (IV), and the inner tire shoulder 
area (V) are divided into 54 grounding deformation 
characteristic parameters.
2.3  Analysis of Grounding Deformation Parameters
Due to the limited number of test tires and the need 
to find evaluation indexes related to high noise value, 
the Pearson correlation analysis method is used to 
eliminate the ground deformation parameters with 
poor correlation with noise value; it is calculated as 
follows:
 r
xx
xx yy
ii
i
n
ii
i
n
i
n




 

 
() ()
() ()
.
yy
1
22
1 1
 (1)
In the formula, n is the number of samples. y
i
, y , 
x
i
, and x are the tire noise value, the average tire 
noise value, the tire grounding parameters, and the 
average grounding parameters, respectively.
The correlation level is evaluated by the 
significant coefficient. The formula of the significant 
coefficient is:
 t
rn
r



2
1
2
, (2)
where t obeys the t distribution with n – 2 degrees of 
freedom.
When |r| > 0.5 and t < 0.05, the ground deformation 
parameter is highly correlated with the noise values. 
Through the analysis of 54 grounding deformation 
characteristic parameters mentioned in Section 2.2, 
the grounding deformation characteristic parameters 
(|r| > 0.5 and t < 0.05) related to high noise value are 
obtained, as shown in Table 2.
Table 2.  Grounding parameters related to high pass-through noise
Area Grounding parameters
Noise value
r t
the overall area
Rectangle ratio (x
1
) [%] –0.674 0.033
Average ground pressure (x
2
) 
[kPa]
0.855 0.002
Deviation value of grounding 
pressure (x
3
) [kPa]
0.677 0.031
the outer 
shoulder area (I)
Grounding length (x
4
) [mm] –0.853 0.002
the central area 
(III)
Average ground pressure (x
5
) 
[kPa]
0.750 0.012
the inner 
transition area 
(IV)
Average ground pressure (x
6
) 
[kPa]
0.788 0.007
Deviation value of grounding 
pressure  (x
7
) [kPa]
0.705 0.023
the inner shoulder 
area (V)
Grounding length (x
8
) [mm] –0.744 0.014
The quantitative relationship between the 
grounding deformation characteristic parameters 
and the noise value can be obtained through 
multiple linear regression, and the contribution of 
each parameter and region to the noise value can be 
clearly obtained through the formula. Table 3 shows 
the ground deformation characteristic parameter 
values related to high noise corresponding to 10 
tires. Taking Table 3 as the multiple linear regression 
sample, the relationship between the noise value and 
the grounding deformation characteristic parameters 
obtained through multiple linear regression is:
Table 3.  Sample scheme by noise value
i x
1
x
2
x
3
x
4
x
5
x
6
x
7
x
8
Noise value, y [dB]
1 0.868 376.368 183.461 118.667 364.899 396.095 188.851 112.667 71.5
2 0.891 365.712 181.264 115.667 349.691 411.347 174.922 112.000 71.5
3 0.919 379.622 192.799 124.000 354.681 381.658 188.859 116.000 71.0
4 0.871 350.895 166.829 132.000 348.677 383.964 177.211 124.667 70.4
5 0.925 375.085 186.990 131.667 365.922 411.568 163.246 115.000 71.1
6 0.867 394.792 179.938 113.000 416.636 428.593 182.123 109.333 72.1
7 0.909 342.809 160.781 125.333 319.412 382.447 172.136 113.333 70.6
8 0.909 373.652 176.752 124.000 382.872 413.290 173.031 113.667 70.8
9 0.916 363.632 163.403 123.667 359.806 412.076 164.007 115.000 70.7
10 0.837 398.657 194.303 113.000 402.456 452.066 221.015 110.333 72.4

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)1-2, 49-60
54 Wang, G. – Zhu, K. – Wang, L. – Yang, J. – Bo, L.
 
yx x
xxx
x
 


82 238 15 078 0 034
0 007 0 004 0 015
0 006
12
345
6
.. .
...
.0 0 014 0 047
78
.. . xx  (3)
The R
2
 of constructed multiple linear regression 
equation is the error caused by linear fitting. The 
closer this value is to 1, the more accurate the 
prediction is. The R
2
 of this multiple linear regression 
equation is 0.984, which indicates that this equation 
has high prediction accuracy.
It can be seen from Eq. (3) that the noise of the 
tire is determined by the absolute value a
i
 of the 
polynomial coefficient and the average value of the 
grounding characteristic parameters x
i
. When 
analysing the contribution of grounding characteristic 
parameters to noise, both of them should be considered 
together. Therefore, this paper evaluates the 
contribution of noise value by the product of the 
coefficients of different grounding regions 
(polynomial coefficients) of the regression equation 
and the average value of the corresponding grounding 
characteristic parameters. The results are shown in 
Table 4.
Table 4.  Contribution of ground deformation parameters
I II III IV
ax
44
⋅ ax
55
⋅ ax ax
66 77
 ax
88
⋅
0.49 5.50 4.96 5.36
a)      b) 
Fig. 7.  Tire pattern bionic variant; a) tread pattern; and b) side branch structure and parameters
a) 
b) 
Fig. 8.  Finite element modelling process and single-pitch centre block structure model of raw and bionic tires; a) finite element modeling 
process; and b) model of the structure of the centre block of the single pitch of the original and bionic tires

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)1-2, 49-60
55 Influence of the Side Branch Structure Pattern of the Imitation Cat’s Claw Function on the Vibration and Noise of Tires
As shown in Table 4, it can be seen that the 
contribution degree to tire noise is from high to low, 
and the centre area (III), inner tire shoulder area (V), 
inner transition area (IV), and outer tire shoulder area 
(I). Therefore, in order to reduce noise, we can start 
with the pattern design in the central area.
3  DESIGN AND ANALYSIS OF TIRE PATTERN BIONIC 
VIBRATION AND NOISE REDUCTION
3.1  Tire Pattern Bionic Vibration and Noise Reduction 
Design
The vibration characteristics of tires are an important 
part of the NVH performance of vehicles. Inspired by 
the domestic cat’s paw pad to weaken the impact from 
the ground through swinging deformation, reducing 
the radial vibration characteristics of tires is an 
important means of vibration and noise reduction of 
vehicles. Moreover, through the previous research of 
the research group, the side branch pipe structure has 
a certain weakening effect on the pipe resonance noise 
of the pattern, can simultaneously improve the anti-
skid performance of the tire, and can synergistically 
improve the comprehensive performance of the tire 
[23].
As shown in Fig. 7, the 205/55R16 passenger car 
tire is taken as the research object, and the dislocation 
side branch pipe groove pattern is arranged in 
the central area of the tread, so as to achieve the 
characteristics of vibration reduction by imitating the 
swing deformation of the cat palm pad. Therefore, the 
finite element analysis model of the tire is established 
as shown in Fig. 8. During modelling, the Yeoh model 
is used for rubber material, Rebar is used for cord 
description, and there are 2141 nodes and 1998 units 
in a two-dimensional matrix. See Zhou et al. [24] and 
Chen et al. [25] for specific material properties and 
finite element type settings.
3.2  Verification of the Finite Element Model
3.2.1  Tire Static Ground Pressure Distribution Test
The modelling method of the finite element analysis 
model in this paper has been verified by a large 
number of experiments [24] and [25]. To verify the 
validity of the finite element model in this paper, 
the pressure distribution test system is used to test 
the grounding pressure when the tire is inflated to 
0.21 MPa and loaded to 3800 N. Fig. 10 shows the 
pressure comparison between the test and simulation 
analysis results; it can be seen that the distribution of 
the test and simulation grounding pressure has a good 
consistency.
3.2.2  Tire Stiffness Test
An MTM-2 comprehensive strength tester is used to 
test the stiffness of the 205/55R16 radial passenger 
car tire in accordance with GB/T23663-2009 [26]. 
The test and simulation results of tire squat, static 
loading radius, and radial stiffness under different test 
conditions are shown in Tables 5 and 6, from which it 
can be seen that the subsidence, static loading radius, 
and radial stiffness of the test and simulation have 
good consistency.
3.2.3 Tire Modal Test
To further verify the validity of the finite element 
model, the mode tests are carried out on tires using 
dynamic testing equipment from LMS 24-Channel 
Data Source Collector. The sampling frequency of the 
instrument is 25600 Hz. The modal analysis software 
is LMS Test. Lab. Acceleration sensor for the US 
PCB company triaxial acceleration sensor 356A34. 
The impact hammer is the US PCB 086C02 impact 
hammer. The test tire is put in the free suspension 
state, and 24 measuring points are evenly arranged on 
the tire surface. The physical diagram of the tire test is 
shown in Fig. 9.
Fig. 9.  Actual pattern of the modal test
In this test, the hammer method is used for 
excitation, point-by-point excitation is used, and the 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)1-2, 49-60
56 Wang, G. – Zhu, K. – Wang, L. – Yang, J. – Bo, L.
It can be seen from Table 7 that the relative 
error between the first six natural frequencies of the 
tire obtained from simulation and the first six natural 
frequencies of the tire obtained from testing is less 
than 10 %. Its error meets the analysis requirements. 
s can be seen from Fig. 11, the simulation and test 
of the first sixth-order modal mode of the tire have 
strict symmetry and good consistency, which further 
verifies the accuracy of the finite element model.
The main reasons for the error are as follows:
1. A variety of rubber materials and steel wire 
materials are used in the tire, and the distribution 
of the materials in the simulation analysis is 
slightly different from that of the actual tire.
acceleration sensor is used to measure the response 
signal. The excitation and response signals are 
amplified and input into the dynamic analyser, and 
the transfer function in the range of 0 Hz to 320 Hz 
is obtained through analysis and processing. Each 
measuring point is hammered three times, and the 
transfer function of this point is obtained after a 
linear average, and then the first six radial natural 
frequencies and vibration modes of the tire under a 
free mounting state are obtained.
The Lanczos method in Abaqus is used in the tire 
free mode finite element analysis to calculate the first 
six radial natural frequencies and vibration modes in 
the free state of the tire and compare them with the 
test mode. The results are shown in Table 7.
a)      b)  
Fig. 10.  Comparison of tire grounding pressure distribution;  
a) test the ground pressure distribution; and b) simulate the ground pressure distribution
Table 5.  Comparison of test and simulation results of tire squat and static loading radius under different test conditions
Test 
conditions
Test value Simulation value
210 kPa 250 kPa 210 kPa 250 kPa
Squat [mm]
Static loading 
radius [mm]
Squat [mm]
Static loading 
radius [mm]
Squat [mm]
Static loading 
radius [mm]
Squat [mm]
Static loading 
radius [mm]
123 kg 6.01 308.14 5.49 309.01 6.48 309.47 5.98 309.97
246 kg 12.28 301.87 11.13 303.37 12.17 303.78 11.62 304.33
369 kg 18.06 296.09 16.29 298.21 18.28 297.67 16.99 298.96
Table 6.  Comparison between test value and simulation value of tire stiffness
Load 
[kg]
210 kPa 250 kPa
Test value [N/mm] Simulation value [N/mm] Error [%] Test value [N/mm] Simulation value [N/mm] Error [%]
Radial  
stiffness
123 200.57 186.02 7.25 219.56 201.57 8.19
246 196.32 198.09 -0.90 216.60 207.47 4.22
369 200.23 197.82 1.20 221.99 212.84 4.12
Table 7.  Comparison of tire natural frequency test and simulation results
Order 1 2 3 4 5 6
Test value [Hz] 59.625 100.102 110.391 138.711 165.304 191.455
Simulation value [Hz] 64.442 90.894 113.06 135.64 158.46 181.09
Error [%] 7.47 9.2 2.42 2.21 4.14 5.41

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)1-2, 49-60
57 Influence of the Side Branch Structure Pattern of the Imitation Cat’s Claw Function on the Vibration and Noise of Tires
2. The simulation analysis simplified some of the 
small tread grooves and simplified the rim of the 
tire, resulting in a different stiffness and mass of 
the simulated tire than the actual tire.
3. While the modal analysis is based on linear 
assumptions, the tire material is highly nonlinear.
3.3  Development of a Model for Analysing Tire Vibration 
and Noise
The tire vibration and noise simulation model are 
shown in Fig. 12. The observation points for the 
arranged sound pressure measurement refer to GB/
T3767-2016. A semi-circular bell jar with a radius of 
one metre is built around the tire. Nineteen acoustic 
observation points are defined on the semi-circular 
bell jar, and a plane is built at the bottom of the tire 
to simulate the road surface sound reflection. Through 
analysis and calculation, it can be concluded that the 
curve trends in the frequency band obtained from the 
19 acoustic observation points are roughly the same, 
but the sound pressure values are different. The total 
sound pressure level of tire vibration noise is obtained 
by the A-weighted superposition of the 19 acoustic 
observation points, and this value is used as the 
evaluation index of tire vibration noise.
Fig. 12.  Tire vibration and noise simulation model
4  RESULT ANALYSIS AND DISCUSSION
4.1  Comparison and Analysis of Tire Ground Strain
The strain distribution of the original tire and the 
bionic tire in X and Y directions under 70 km/h 
steady state rolling is obtained through finite element 
analysis, and the results are shown in Fig. 13, from 
which it can be seen that the bionic tire with staggered 
branch pipe pattern in the central area of the tread 
changes the symmetry of the strain distribution in 
the X and Y directions compared with the original 
tire, and the asymmetric deformation will form the 
swinging deformation in the X and Y directions 
during the rolling process of the tire. Therefore, the 
swing characteristics of the grounding deformation of 
the cat’s paw pad can be achieved by arranging the 
misplaced side branch pipes in the central area of the 
tire pattern.
4.2  Results and Analysis of the Radial Excitation Force
The 70 km/h display rolling calculation is carried 
out for the tire, and the radial excitation force of the 
tire after steady rolling is extracted. The comparison 
of the radial excitation force between the original 
tire and the bionic tire in the time domain is shown 
in Fig. 14. Through the comparison, it can be seen 
that the peak radial excitation force of the bionic tire 
is reduced, and the range of radial excitation force 
fluctuations is reduced, thereby reducing the vibration 
phenomenon during the driving of the tire. It shows 
that the misplaced side branch pipe structure on the 
tire tread realizes the function of the bionic cat claw 
and reduces the radial excitation force to the tire from 
the ground.
a)       b) 
Fig. 11.  Test test and numerical calculation of the first 6
th
 order modal mode of the tire; a) test results; and b) simulation results

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)1-2, 49-60
58 Wang, G. – Zhu, K. – Wang, L. – Yang, J. – Bo, L.
a)      
                   Original tire                                                              Bionic tire
b)      
           Original tire                                                                Bionic tire
Fig. 13.  Strain distribution in the X and Y directions of the ground area when the two tires are rolling steadily; a) strain distribution in the X 
direction of both tire; and b) strain distribution in the Y direction of the two tires
Fig. 14.  Comparison diagram of time domain characteristics of 
two types of tires subjected to ground radial excitation forces
Fig. 15.  Comparison of frequency domain characteristics of 
amplitude of ground radial excitation force on two types of tires

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)1-2, 49-60
59 Influence of the Side Branch Structure Pattern of the Imitation Cat’s Claw Function on the Vibration and Noise of Tires
To further clarify the difference between the radial 
excitation force of the original tire and the bionic tire, 
fast Fourier transform (FFT) is performed on the 
radial excitation force in the time domain to obtain 
the amplitude-frequency characteristics of the radial 
excitation force in the frequency domain. The results 
are shown in Fig. 15. As the sound below 20 Hz cannot 
be heard by human ears, and the tire vibration noise is 
mainly concentrated below 500 Hz [27] and [28], this 
paper takes 20 Hz to 500 Hz as the frequency range 
for analysis. In Fig. 15, PA
1
 is the peak amplitude 1, 
and PA
2
 is the peak amplitude 2. At PA
1
 
(20 Hz), the 
amplitude value of the radial excitation force on the 
bionic tire is 22.16 % lower than that on the original 
tire, and at PA
2
 
(87 Hz) it is 8.53 % lower. It shows 
that the tread pattern tire with cat claw function has an 
obvious vibration reduction effect.
4.3 Numerical Analysis of Vibration and Noise and 
Discussion of Results
In order to analyse the vibration and noise 
characteristics of bionic tires with misaligned side 
branch structures in the tread centre, the vibration 
and noise analysis model established in this paper and 
the analysis process in literature [9] and [24] are used 
to analyse the tire vibration and noise. The vibration 
noise of the original tire and the bionic tire at 20 Hz to 
500 Hz is shown in Fig. 16. 
Fig. 16.  Comparison of the total sound pressure level of the two 
types of tires
The sound pressure level of the bionic tire is lower 
than the total sound pressure level of the original tires 
in the whole frequency band, especially at 374 Hz, 
which is reduced from 78.25 dB to 41.20 dB, which 
is 47.35 %. The total noise value of the original tire is 
64.02 dB and the noise value of the bionic tire is 62.86 
dB by A-weighted superposition of the noise value in 
the 20 Hz to 500 Hz frequency band, which further 
shows that the bionic tire with misaligned sidewall 
structure has a good noise reduction effect.
It can be seen from Table 8 that in the comparison 
of the vibration and noise characteristics between the 
original tire and the bionic tire, the bionic tire has a 
better inhibition effect on the impact load from the 
ground during driving. This pattern design has a good 
effect on the vibration and noise reduction of the tire, 
which verifies the feasibility of bionic vibration and 
noise reduction.
Table 8.  Comparison of amplitude and noise values of the two 
types of tires
Tire type PA
1
PA
2
Total sound pressure level [dB]
Original tire 465.37 323.65 64.02
Bionic tire 362.24 296.05 62.86
5  CONCLUSION
1. Through the grounding mechanical test on the 
paw pad of the domestic cat, it is found that the 
left and right swing grounding characteristics of 
the paw pad of the domestic cat during walking 
is one of the main ways to achieve the effect of 
vibration reduction and silence during walking.
2. By analysing the grounding characteristic 
parameters of ten tires, it is concluded that the 
tire centre area has the greatest impact on tire 
noise. On this basis, combined with the vibration 
reduction principle of the left and right swing of 
the cat paw pad during walking, the staggered side 
branch pipe groove is set in the centre of the tire 
to achieve the vibration reduction characteristics 
of the swing of the cat paw pad.
3. The bionic tire can significantly reduce the 
amplitude and fluctuation range of the ground 
radial excitation force, thereby effectively 
reducing the vibration noise in the low frequency 
band, and improving the vibration noise 
characteristics of the tire.
5  ACKNOWLEDGEMENTS
This study was financially supported by the 
National Natural Science Foundation of China 
(52072156,52272366) and the Postdoctoral 
Foundation of China (2020M682269).

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60 Wang, G. – Zhu, K. – Wang, L. – Yang, J. – Bo, L.
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