Vibration analysis of the oscillation support of column load cells in low speed axle-group weigh-in-motion system


ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 63 

ACTA IMEKO 
ISSN: 2221-870X 
December 2020, Volume 9, Number 5, 63 - 68 

 
 

VIBRATION ANALYSIS OF THE OSCILLATION SUPPORT OF COLUMN 

LOAD CELLS IN LOW SPEED AXLE-GROUP WEIGH-IN-MOTION 

SYSTEM 
 

Lai Zhengchuang1,2, Yang Xiaoxiang1,3, Yao Jinhui1,2 

 
1 College of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, China, lzcfjjl@126.com 

2 Fujian Key Laboratory of Force Measurement (Fujian Institute of Metrology), Fuzhou, China, lzcfjjl@126.com 
3 Quanzhou Normal University, Quanzhou, China, yangxx@fzu.edu.cn 

 

Abstract: 

Under the condition of dynamic weighing, the 

support types of the column load cells can be 

divided into elastic support and oscillation support. 

The weighing system with oscillation support 

shows significant vibration characteristics, which 

affects the weighing accuracy and the fatigue life of 

the load sensor. In this paper, the dynamic 

characteristics of the oscillation supporting column 

load cell in low speed axle-group weigh-in-motion 

system are analysed. It is found that the restoring 

force of the oscillation support is approximately 

proportional to the oscillation angle and the applied 

vertical load. The dynamic equation of the 

oscillation support vibration of the column load 

cells established by means of d’ Alembert principle. 

The numerical calculations of the dynamic response 

of the weighing system with oscillation support are 

carried out in the free state and dynamic weighing 

state respectively. The factors affecting the 

amplitude and recovery time of the support 

vibration are obtained. This study provides a 

reference for the analysis of the dynamic weighing 

accuracy. 

Keywords: vibration and wave; oscillation 

support; vibration analysis; dynamic weighing 

1. INTRODUCTION 

Column load cell is an important component of 

the axle group dynamic truck scale. Under the 

condition of dynamic weighing, the support types of 

the column load sensors can be divided into elastic 

support and oscillation support. The weighing 

system with oscillation support shows significant 

vibration characteristics, which affects the weighing 

accuracy and the fatigue life of the load cells [1] [2]. 

In this paper, the force analysis is carried out for 

the weighing process of the oscillation support 

column load cell. In the dynamic weighing system, 

the low speed axle group weigh-in-motion (LS-

WIM) system is used as the research object to 

analyse the axle load conditions. The dynamic 

response of the weighing system is obtained through 

dynamic system model and simulation. 

2. OSCILLATED STABILITY ANALYSIS 
OF THE LOAD CELL   

Oscillated support column load cell consists of 

strained elastomer and an upper and lower indenter. 

The lower indenter is fixed on the foundation and is 

in point-surface contact with the strained elastomer. 

The upper and lower ends of the elastomer are 

spherical and can roll on the upper and lower 

indenters. The upper indenter is fixedly connected 

to the weighing platform, the bottom surface is in 

point-to-point contact with the strained elastomer, 

and its movement state is shown in Figure 1. 

When the elastomer of the load cell is purely 

rolled, the lower indenter is fixed, and the upper 

indenter is translated in parallel with the transient of 

the contact point of the elastomer. Let point A and 

point B be the centre of the spherical surface before 

and after the lower ball end of the elastomer rolls, 

and point C be the centroid of the elastomer. 

According to the geometric relationship of the 

dimensions in the Figure 1 (a) and (b), among them 

has the same indenter and elastomer. 

 
(a)                               (b) 

Figure 1: Oscillation support of the load cell, (a) 

Oscillation position change of the load cell, (b) Force 

analysis of the load cell 

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In Figure 1, 𝛼  is the inclination angle of the 
sensor strain elastomer axis, ℎ is the height of the 
sensor strain elastomer along the axis, 𝛽  is the 
inclination angle of the connection point between 

the ball head and the upper indenter and the rolling 

point, 𝑅  is the radius of the ball head. 𝑆  is the 
horizontal displacement of the axis of the upper 

indenter. 𝑆1  is the rolling displacement of the 
contact point between the ball head and the lower 

head. 𝑆2 is the horizontal movement distance of the 
contact point between the ball head and the upper 

indenter. 

For a stable and balanced oscillated support, the 

vertical force of the external load 𝐹𝑌  on the 
elastomer at this time can be decomposed into a 

radial force 𝐹𝑛  and a tangential force 𝐹𝜏  along the 
rolling support point O of the elastomer, where the 

tangential force 𝐹𝜏  provides the restoring force 
promotes structural stability. When the system is 

oscillating slightly, tangential force can be 

expressed as follows: 

𝐹𝜏 = 𝐹𝑌 sin 𝛽 ≈
(2𝑅 − ℎ)𝐹𝑌

ℎ
𝛼 (1) 

It can be known that the restoring force of the 

micro-oscillated support is approximately 

proportional to the oscillated angle and the vertical 

force applied. 

3. DYNAMIC MODEL OF OSCILLATED 
SUPPORT VIBRATION 

Low speed axle-group weigh-in-motion system has 

four column load cells as carriers. When the vehicle 

only travels along the longitudinal axis of the 

weighing platform, the scale body only vibrates in 

the longitudinal direction of the weighing platform, 

regardless of the lateral vibration of the weighing 

platform, and the movement form of the scale body 

is a single degree of freedom system. It can be seen 

from equation (1) that its swing stiffness is 

approximately proportional to the external load and 

offset angle of each sensor. The dynamic model of 

its oscillation support vibration is shown in 

Figure 2. Let 𝑀𝑂𝑓𝑖  (𝑖  = 1, 2, 3, 4) be the rolling 

friction couple of the elastomer and the lower 

pressure head. During the rolling process, the 

rolling friction resistance moment is approximately 

equal to the maximum rolling friction resistance 

moment 𝑀max, which is the vertical pressure 𝐹𝑂𝑌𝑖  
on the head bearing point is proportional to the size. 

Let the proportionality constant be 𝛿. 

𝑀𝑂𝑓𝑖 ≈ 𝑀max = 𝛿𝐹𝑂𝑌𝑖  (2) 

The force applied to the weighing platform by the 

external load is simplified to the lateral force 𝐹𝐺𝑆, 
the vertical force 𝐹𝐺  and the moment 𝑀𝐺𝑓 . The 

interaction between the weighing platform and the 

elastomer of the sensor can be regarded as a simply 

supported plate structure with point-to-surface 

contact. At the contact point 𝐾, the elastomer is only 
affected by the vertical force 𝐹𝑁𝑖  of the weighing 
platform, the horizontal friction force 𝐹𝑋𝑖  and the 
rolling friction couple 𝑀𝐾𝑓𝑖. We can also obtain: 

𝑀𝐾𝑓𝑖 ≈ 𝛿𝐹𝑁𝑖 (3) 

 
(a) 

 
(b) 

Figure 2: Dynamic model of vibration state of oscillation 

support, (a) Four-point support dynamic truck scale 

loaded model, (b) Force analysis model of column load 

sensor 

The swing angle and direction of each column 

load cells are always consistent with the weighing 

platform. The total stiffness of the weighing system 

is equal to the sum of the swing stiffness of each 

parallel column load sensor. In the static state with 

the same swing angle, the stiffness of each column 

load cell is proportional to the vertical force. Letting 

the scale factor be 𝐶, we obtain: 

𝑘𝑖 (𝛼, 𝐹𝑁𝑖 )

𝐹𝑁𝑖
= 𝐶      (𝑖 = 1, 2, 3, 4) (4) 

𝑘 = ∑ 𝑘𝑖 (𝛼, 𝐹𝑁𝑖 )

4

𝑖=1

= ∑ 𝐶𝐹𝑁𝑖

4

𝑖=1

= 𝐶𝐹𝑁 (5) 

It can be seen from formula (5) that when the 

vehicle is traveling on the weighing platform, 

although the force acting on each column load cell 

is transient, the support vibration of each sensor is 

synchronised with the vibration of the weighing 

platform, and the sum of the external forces 

received by the sensors remains unchanged. Taking 

four column load sensors as the research object, the 

column load cell takes the torque balance to the 

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ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 65 

support point 𝑂  by the Lagrange’s D’Alembert 
principle, and the other three load sensors are 

superimposed to balance the torque at each support 

point. After the equation, the dynamic control 

equation of the oscillation support vibration of the 

weighing system can be obtained: 

𝑀𝐾𝑓 + (𝑀𝑔 + 𝐹𝐼2 sin 𝛽 + 𝐹𝐺 ) ∙ 𝑂𝐻

+ (𝐹𝐼2 cos 𝛽 − 𝐹𝐺𝑆) ∙ 𝐻𝐾
+ 𝑀𝑂𝑓 + 4𝑀𝐼 + 4𝐺

∙ 𝑂𝐶 sin 𝛽 + 4𝐹𝐼1 ∙ 𝑂𝐶 = 0 

(6) 

where: 

𝑀𝐼 = 𝐽�̈�;  𝐹𝐼1 = 𝑚 ∙ 𝑂𝐶�̈�;  𝐹𝐼2 = 𝑀 ∙ 𝑂𝐾�̈� 

𝐺 = 𝑚𝑔;  𝑀𝐾𝑓 = 𝛿(𝑀𝑔 + 𝐹𝐼2 sin 𝛽 + 𝐹𝐺 ) 

𝑀𝑂𝑓 = 𝛿[𝑀𝑔 + 4𝐺 + (4𝐹𝐼1 + 𝐹𝐼2) sin 𝛽 + 𝐹𝐺 ] 

In these equations, 𝑚  is the mass of the 
elastomer, 𝑀 is the mass of the weighing platform, 
and 𝐽 is the rotational inertia of the elastomer. 

According to the frictional moment of friction 

between the ball head and the upper and lower 

pressure heads, it always hinders the relative rolling 

of the elastomer, and the direction is opposite to the 

direction of the elastic angular speed of the 

elastomer. Static friction does not do work during 

pure rolling. Similar to the dissipation effect of 

Coulomb damping on the elastic potential energy of 

a spring oscillator, free vibration will gradually 

stabilize near the equilibrium position. Substituting 

the relevant parameters into equation (6), the 

vibration control equation of the system oscillation 

support is obtained: 

2𝛿 [(1 + 2�̂�)𝑔 + 2(1 + �̂�) ∙ �̂� ∙ �̂̈� ∙ sin 𝛽 +

𝐹�̂� ] + (𝑔 + 𝐹�̂� ) ∙ 𝑙 − 𝐹𝐺�̂� ∙ �̂� + 4𝐽 ∙ �̂̈� + 4�̂� ∙

𝑔 ∙ �̂� sin 𝛽 + 2[(𝑙 ∙ sin 𝛽 + �̂� cos 𝛽) + 2�̂� ∙

�̂�] ∙ �̂� ∙ �̂̈� = 0          (�̂̇� > 0)  

(7) 

Among them: 

�̂� =
𝑚

𝑀
;  �̂� =

𝑂𝐶

𝑅
;  ℎ̂ =

ℎ

𝑅
;  𝛿 =

𝛿

𝑅
;  �̂� = 𝜔0𝑡  

𝑔 =
𝑔

𝑅𝜔0
2

;  𝐽 =
𝐽

𝑀𝑅2
;  𝑙 =

𝑂𝐻

𝑅
;  �̂� =

𝐻𝐾

𝑅
 

𝐹�̂� =
𝐹𝐺

𝑀𝑅𝜔0
2

;  𝐹𝐺�̂� =
𝐹𝐺𝑆

𝑀𝑅𝜔0
2

;  �̂̈� =
�̈�

𝜔0
2

;  �̂̈� =
�̈�

𝜔0
2
 

4. ANALYSIS OF AXLE LOAD 
CONDITIONS OF VEHICLES 

4.1 Analysis of Axle Loading Conditions of 
Vehicles Running on the Road 

Suppose that the vehicle is driven by the rear 

axle. The axle type is composed of the front axle and 

the rear axle installed with two axles, and 𝐹𝐺2 =
𝐹𝐺3 . The axle load and wheelbase are shown in 
Figure 3. It is assumed that when the vehicle is 

driving on the road surface, the front and rear 

wheels accelerate pure rolling motion under the 

action of the driving force. The driving wheel is 

subjected to driving torque, backward traction 

reaction force, vertical downward axle load, ground 

friction and rolling resistance. The traction force of 

the driven wheel is set forward, and the driven 

wheel is not affected by the driving torque. 

Taking each axis as the research object, 

considering the tires belonging to a single axis as a 

whole, suppose the direction of each axis force and 

the direction of acceleration are shown in Figure 4 

(a), (b), and the motion parameters of the two drive 

wheels are consistent, According to the direction of 

the static friction force of the pure rolling wheel in 

the figure, the magnitude of the static friction force 

is determined by the differential equation of motion. 

(10𝑚𝑉 + 𝑀𝑉 )𝑎𝐶 = 2𝐹𝑆2 − 𝐹𝑆1 (8) 

2𝐽𝑉 �̈� = −𝑀𝑓1 + 𝐹𝑆1𝑅𝑉 (9) 

𝑎𝐶 = 𝑅𝑉 �̈� (10) 

Among them: 

𝑀𝑓1 = 𝛿
′𝐹𝐺1;  𝑀𝑓2 = 𝛿

′𝐹𝐺2 

𝑀𝑇 = 𝑀2 + 𝑀3 = 2𝑀2; 𝐹𝑛1 + 𝐹𝑛2 + 𝐹𝑛3 = 𝑀𝑉 𝑔 

where 𝑀𝑉  is the body mass, 𝑚𝑉  is the mass of a 
single tire, 𝐹 is the traction force of the car to the 
front axle, 𝐽𝑉 is the tire moment of inertia, 𝛿

′ is the 

rolling friction coefficient between the wheel and 

the weighing platform, 𝑅𝑉  is the tire radius, 𝑀𝑇  is 
the total driving torque of the rear axle, �̈� is the tire 
rolling angle acceleration. 

 

Figure 3: Schematic diagram of axle load and wheelbase 

of truck 

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(a)                            (b)                            (c) 

Figure 4: Schematic diagram of axle load and wheelbase 

of truck, (a) Rear axle drive wheel, (b) Front axle driven 

wheel, (c) Front axle rolls at a constant speed 

We can obtain from equations (8) to (10): 

𝐹𝑆1 =
𝑀𝑓1

𝑅𝑉
+

2𝐽𝑉 𝑎𝐶

𝑅𝑉
2

 (11) 

𝐹𝑆2 =
𝑀𝑓1

2𝑅𝑉
+ (5𝑚𝑉 + 0.5𝑀𝑉 )𝑎𝐶 +

𝐽𝑉 𝑎𝐶

𝑅𝑉
2

 (12) 

Similarly, for the pure rolling state of uniform 

motion, as shown in Figure 4(c), the driving force is 

equal to the static friction force, that is 𝐹 = 𝐹𝑆1 , 
which can be obtained from the balance 

relationship: 

𝐹𝑆1 = 2𝐹𝑆2 =
𝑀𝑓1

𝑅𝑉
 (13) 

4.2 Analysis of Axle Loading Conditions of 
Vehicles Running on Weighing Platform 

In order to determine the external disturbance 

force of the forced vibration of the column load cell 

oscillation support, the axle group type dynamic 

truck scale weighing system is selected as the 

research object. The four-point supported weighing 

platform performs variable speed movement under 

the impact of the vehicle, taking the vehicle's 

driving direction as the positive direction, and when 

the tire of a certain axis of the vehicle rolls purely 

on the weighing platform, the angular acceleration 

of its wheels is: 

�̈�′ =
𝑎𝐶 − �̈�

𝑅𝑉
 (14) 

The relationship between the tire rolling angle 

acceleration and the wheel centre translation 

acceleration of the other axles traveling on the road 

surface is the same as equation (10). In the same 

way, by balancing equations for each axis, the 

magnitude of the static friction force on each axis 

when the vehicle passes through the weighing 

platform can be obtained separately. 

5. NUMERIC CALCULATIONS 

In order to obtain the vibration characteristics of 

the swing load of the column load sensor, the 

response of the column load cell is selected as the 

research object under the dynamic weighing of the 

axle group dynamic truck scale. The free vibration 

of the oscillation support of the weighing system 

and the forced vibration when the vehicle is under 

dynamic load are selected for simulation when there 

is no vehicle running. 

5.1. Numerical Simulation of Free Vibration 
Considering that the ball radius of the elastomer 

affects the weighing accuracy of the eccentric load 

of the column load sensor, only the influence of the 

adjustable elastomer height on the vibration state of 

the oscillation support is analysed here. In order to 

eliminate other influencing factors, the oscillation 

support is set as free vibration, which is not affected 

by the vehicle load, that is, 𝐹𝐺 , 𝐹𝐺𝑆, and 𝑀𝐺𝑓 are all 

zero. Select the load cell parameters of the column 

load cell C16A C3 operating manual with a 

maximum range of 20 t. Suppose the rolling friction 

coefficient of the elastomer and the upper and lower 

indenters is according to the coefficient between the 

steel wheel and the rail given by theoretical 

mechanics, and the relevant parameters are shown 

in Table 1. 

Due to 𝑀 being much larger than 𝑚, when the 
angle 𝛼 is small, the mass and rotational inertia of 
the elastomer of the load cell can be ignored, and 

sin 𝛼 ≈ 𝛼,  cos 𝛼 ≈ cos 𝛽 = 1. It can be seen from 
Figure 5 that as the height of the elastomer 

decreases, the time for the swing load vibration of 

the column load cell to reciprocate for one week 

decreases, the amplitude increases, and the vibration 

attenuation time also increases. 

Table 1: Free vibration parameters of oscillation support 

Parameter Value Unit 

𝑚 2.5 kg 
𝑅 130 mm 
ℎ 150 mm 
𝛿 0.05 mm 
𝑀 4860 kg 
𝐽 4.59×10-3 kg·m2 

 

Figure 5: Numerical simulation curve of free vibration of 

oscillation support 

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ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 67 

5.2. Numerical Simulation of Forced Vibration 
of Oscillation support in Low Speed 

Weighing 

When forced to vibrate, suppose the weighing 

system is in equilibrium, and the initial angular 

displacement 𝛼0  and initial angular velocity are 
both zero. The Dongfeng DFL1250A6 cargo truck 

(type 1+5) is selected as the rear-wheel drive vehicle 

with axle load. The rear axle is a dual-axle mounted 

side by side. The axle load and wheelbase are shown 

in Figure 3. The wheel tires are radial wide rim tires 

and tires. The specification is 10.00R20, and the tire 

radius is 𝑅𝑉  =  527 mm. The rolling friction 
coefficient between the wheel and the scale surface 

is taken as the middle value 𝛿 ′ = 6 mm, and other 
relevant parameters are shown in Table 2. 

Table 2: Force vibration parameters of oscillation support 

Parameter Value Unit 

𝑚𝑉 70 kg 

𝐽𝑉 7.56 kg·m
2 

𝐹𝐺1 68 000 N 

𝐹𝐺2 89 000 N 

𝐹𝐺3 89 000 N 

𝑙1 4 350 mm 

𝑙2 1 300 mm 

 

Assuming that the vehicle drives through the 

weighing platform at a constant speed of 

𝑣 =  2 m·s-1, 𝑎𝐶 =  0 m·s
-2, the axle load and 

horizontal friction force of each axis of the vehicle 

acting on the weighing platform at different time 

periods are almost constant. The following only 

solves the axle load driving on the weighing 

platform, and the angular acceleration of the wheels 

driving on the weighing platform can be obtained 

from equation (14): 

�̈�′ = −
�̈�

𝑅𝑉
 (15) 

From the static friction formula (13) and formula 

(15) of constant speed rolling, we can obtain static 

friction force when the front axle travels on the 

weighing platform: 

𝐹𝑆1
′ = 𝐹′ =

𝑀𝑓1

𝑅𝑉
−

2𝐽𝑉 �̈�

𝑅𝑉
2

 (16) 

When the front axle is on the weighing platform, 

the static friction of the rear axle is: 

𝐹𝑆2
′ = 𝐹𝑆3

′ =
𝐹′

2
 (17) 

The length of the weighing platform is 

5 250 mm, and the driving process of the vehicle on 

the weighing platform can be obtained according to 

the vehicle speed and the wheelbase. When the 

vehicle is just on the scale, set 𝑡 = 0 s, then only the 
front axle of the weighing platform applies load on 

the weighing platform, and the time interval until 

the second axis applies the load is:  

𝑡 =
𝑙1
𝑣

=
4.35

2
= 2.175 s (18) 

The total vertical force applied to the weighing 

platform 𝐹𝐺 = 𝐹𝐺1, the total friction force is given 
by equation (16) 𝐹𝐺𝑆 = 𝐹𝑆1 , and rolling friction 
couple 𝑀𝐺𝑓 = 𝛿

′𝐹𝐺1. Similarly, the change process 

of the axle load applied to the weighing platform in 

the remaining time period can be obtained, as shown 

in Table 3. 

Table 3: Loading conditions of weighing platform in 

different time periods 

Time / s 𝑭𝑮 𝑭𝑮𝑺 𝑴𝑮𝒇 

0.000 - 2.175 𝐹𝐺1 𝐹𝑆1
′  𝛿 ′𝐹𝐺1 

2.175 - 2.625 𝐹𝐺1 + 𝐹𝐺2 𝐹𝑆1
′ −𝐹𝑆2

′  
𝛿 ′(𝐹𝐺1
+ 𝐹𝐺2) 

2.625 - 2.825 𝐹𝐺2 −�̅�𝑆2 𝛿
′𝐹𝐺2 

2.825 - 4.800 𝐹𝐺2 + 𝐹𝐺3 
−�̅�𝑆2
− �̅�𝑆3 

𝛿 ′(𝐹𝐺2
+ 𝐹𝐺3) 

4.800 - 5.450 𝐹𝐺3 −�̅�𝑆3 𝛿
′𝐹𝐺3 

> 5.450 0 0 0 

 

Similarly, considering 𝑀 is much larger than 𝑚, 
when the angle 𝛼 is small, the mass and moment of 
inertia of the sensor elastomer can be ignored. 

Substituting the above given parameters, the initial 

angular displacement 𝛼0 and initial angular velocity 
of the oscillation support vibration are both zero, 

and the forced vibration solution of the car at a 

constant speed is shown in Figure 6. It can be seen 

from Figure 6 that with the increase of the shaft 

load, the more significant the vibration of the 

column load cell oscillation support, the faster the 

reciprocating motion, the greater the amplitude, and 

the longer the vibration attenuation time. It can be 

seen from Figure 7 that increasing the flatness of the 

weighing platform surface and reducing the rolling 

friction couple to reduce the horizontal static 

friction between the wheel and the weighing 

platform can significantly reduce the amplitude of 

the oscillation support vibration, because the 

horizontal static friction is much less than the 

vertical to gravity, the time of one round of 

reciprocation is almost unchanged, and the decay 

time of vibration is also shorter. 

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ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 68 

 

Figure 6: Numerical simulation curve of forced vibration 

at constant speed driving 

 

Figure 7: Numerical simulation curve of forced vibration 

at acceleration state 

6. SUMMARY 

The oscillation support column load cell shows 

vibration characteristics during dynamic weighing, 

which affects the stability and accuracy of 

weighing, and even affects the fatigue life of the 

load cell. The conclusions of this study can be used 

to analyse the dynamic process of the vibration of 

the load cell oscillation support and the influence of 

the weight accuracy, and can provide a basis for the 

corresponding vibration control or vibration 

reduction design. It can be concluded that: 

(1) The supporting vibration restoring force is 
approximately proportional to the vibration angular 

displacement and load capacity. 

(2) The recovery time of the oscillation support 
vibration of the weighing system decreases as the 

height of the elastomer decreases, the amplitude 

increases as the height of the elastomer decreases, 

and the vibration attenuation time increases as the 

height of the elastomer decreases. The noise 

interference frequency generated by the horizontal 

shaking of the scale body will affect the weighing 

data processing. Under the condition of weighing 

accuracy, the height of the elastomer can be 

appropriately increased to reduce the vibration 

swing rate and amplitude. 

(3) The vibration stiffness of the horizontal 
support of the weighing platform is related to the 

magnitude of the load on the weighing platform, and 

has nothing to do with the distribution of the load. 

With the increase of the axial load, the vibration 

recovery time decreases, the amplitude increases, 

the more significant the vibration, the longer the 

vibration attenuation time. In general, the limit 

device is used to limit and consume the vibration of 

the weighing platform. 

(4) Under the condition of anti-skid, the flatness 
of the weighing platform surface should be 

improved, and the rolling friction resistance should 

be reduced to reduce the horizontal static friction 

between the wheel and the weighing platform. The 

amplitude of the oscillation support vibration can be 

significantly reduced, and the vibration recovery 

time is almost change, and the faster the vibration 

decay. 

7. REFERENCES 

[1] D. Rys, J. Judycki, P. Jaskula, “Analysis of effect of 
overloaded vehicles on fatigue life of flexible 

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