Measurement and analysis of truck vibrations during off-road transportation

Measurement of vibration of the vehicle on the road surface is one of the key elements of cargo and vehicle security. This paper provides results from transporting military cargo study that analyzed the various vibrations of acceleration during transport on a stony pavement road. The data include vibrations from three directions: longitudinal, transverse and vertical. Based on collected data the quantitative analysis of vibrations was conducted. The peak acceleration as well as the acceleration level was identified. The growth rate acceleration affecting the smoothness of driving and the impact of the vehicle on the stony surface were calculated. The study shows that the greatest impact on transporting cargo have vertical vibrations. In addition, using the Fourier transform, amplitude spectrum for all directions of oscillation was assigned.


Introduction
Cargo securing problem is still valid.The theoretical investigation which concentrates on the ride comfort, cargo securing, structural integrity and vehicle safety is shown in [1].Special attention is paid to the interaction between roads and road vehicles, railway vehicles [2] and aircrafts [3].To demonstrate the effect of vibration on the means of transport and cargo, methods of spectral analysis [4] are used.They are transforming time series of observed accelerations into frequency domain which is efficient for analyzing frequency characteristics of vibrations, in particular, for determining the amplitude.It's important parameter which is a nonnegative number that specifies the stroke size of the periodic function, indicating the largest deviation from the equilibrium position [5].Based on this assumption, it can be concluded which vibration is subjected to the load during transportation.

Data measurement and analysis
Data were registered in a time interval ranging from hours 08:37:20 AM to 11:43:47 1 June 2016 (Fig. 1).

Figure 1. Road surface vibration in three directions
In the end, a dataset consisting of 11,181 observation of deviations from the axis in the direction of the longitudinal, transverse and vertical axis was obtained.It has been used in studies [6,7].It should be noted that longitudinal and transverse starts from 0 [g], and vertical from 1 [g].

Quantitative analysis of vibrations during cargo transportation
Excitations delivered to cargo are mixture of different kind of vibrations, occasional shock superimposed on the vibration and isolated shock which occurs in cargo transportation on stony pavement.Because of variations in pavement type and condition along most roads, pavement profiles are also highly non-stationary [8] and contain a significant number of high crest factor (transient) events [9].Vibration is the excitation which occurs whenever the carrier is in the motion and is produced by the carrier suspension system and carrier frame members reacting to travel over surface irregularities in different kind of pavement as well as the vibration generated by the carrier motive system [10].Data analysis of vibrations are presented in table 1 which shows basic information about accelerations in three dimensions.They can be compared with [11,12].It can be noted that the maximum longitudinal and vertical fluctuations occurred at the same time.Obviously, it was caused by the collision of the vehicle in a pit or on a submerged rock (table 1).In figure 2 you can see that the number of oscillations in the longitudinal and transverse direction is the same and starts from -2 [g].In the vertical direction fluctuations occur in greater numbers and have the force of 1 [g] more.This means that the effect of stone paving is affected to a greater extent on variations in the vertical direction is more vibration of greater acceleration.

Determination of growth rate acceleration
The growth acceleration is a kinematic parameter occurring in geometric systems that affect the smoothness and dynamic effects of the vehicle on the road surface.The recorded data have positive and negative deviations in X, Y and Z axis.Therefore, to determine the increment of the acceleration was used, the integral module is indicated by these deviations.Along all three axes it is: https://doi.org/10.1051/matecconf/201821113003VETOMAC XIV where ax(t) is the vibration level on the longitudinal axis; ay(t) is the vibration level on the transverse axis; az(t) is the vibration level on the vertical axis; i = (1, 2, …, n) -the number of observations.The results are shown in figure 3 for all directions of axis.

Figure 3. The growth acceleration in the analyzed time period
In figure 3 we can see that the oscillations in the vertical direction during transportation of the cargo have the highest increase of acceleration.The average increase in vibration in the vertical direction is more than in the other two directions, a value of 4.57 -6.67 [m/s 3 ] times more.

The amplitude spectrum based on Fourier transform
The Fourier transform is derived from Fourier series, which apply to periodic signals.Periodic function f(t) continuous independent variable t (usually time, although one can also consider other value) with period T can be represented as the following series, called Fourier series: (4) where ω0 = 2π / T, and the coefficients ak is determined by the following formula: Not all functions can be Fourier-transformed.The (4) is valid if they are certain conditions fulfilled, known as Dirichlet conditions.The Dirichlet conditions are: − the function must be periodic, − it must be single-valued and continuous, except possibly at a finite number of finite discontinuities, − it must have only a finite number of maxima and minima within one period, − the integral over one period of |f(x)| must converge.The ak coefficient can be interpreted as the complex amplitude of the signal f(t) for the frequency kω0 (k-th harmonic at pulsation ω0 primary): MATEC Web of Conferences 211, 13003 (2018) https://doi.org/10.1051/matecconf/201821113003VETOMAC XIV So it is easy to determine the amplitude of the expansion coefficients, thus creating the amplitude spectrum of the periodic signal f(t).Amplitude spectrum of a periodic function is symmetrical about axis that passes through the system.Figure 4 shows graphs of the amplitude for longitudinal, transverse and vertical axis in the frequency domain.When evaluating the influence of mechanical vibrations on the object of study, typically the measure of acceleration amplitude of vibrations is used.This value characterizes the energy side of the shocks; this parameter is the most current national standards, European and international filing methods of measurement of vibration at workplaces, as well as provisions fixing the criteria values (acceptable) for mechanical vibrations because of the object.The maximum fluctuation in the vertical direction is more than two times greater than the longitudinal vibration and more than 4 times from fluctuations in the transverse projection.This suggests that the rocky pavement causes the most vibration in the direction vertical, in the following order longitudinal vibration, which is twice the transverse one.For the analysis of structure vibrations in three directions, expressed as amplitude data are summarized in table 3. Based on table 3 we can conclude that the greatest fluctuations occur in the direction of the vertical, where it was noted the two values from the range 901-1000.The smaller the interval, the greater the amplitude of vibration.Fluctuations in the longitudinal direction reaches the maximum value of the amplitude in the range of 301-400, and in the transverse

Figure 2 .
Figure 2. Comparison of fluctuations of the load in three directions (excluding the value of 1 [g] for the vertical direction as a reference point for measuring instrument).

Figure 4 .
Figure 4.The amplitude spectrum of the acceleration for longitudinal, transverse and vertical axis

Table 1 .
Peak acceleration of vibrations during transportation of cargo The greatest fluctuation is almost six times of the earth's gravity and amount of -6.75 [g] in the vertical direction.To approximate conditions that prevailed on the road, and influence, which they had to transport the cargo table2shows the number of vibrations occurring in different acceleration bands.https://doi.org/10.1051/matecconf/201821113003VETOMAC XIV

Table 2 .
The number of vibrations that occurs during transportation