Research on Dynamic Loads Acting on a Vehicle Caused by the Road Profile with Different Surfaces

Featured Application

The presented tests of dynamic vehicle loads resulting from the road profile can be used in comparisons of test sections on different testing grounds and in inter-laboratory comparisons in the scope of vehicle reliability tests based on mileage tests. Furthermore, they can be an important element in the design of vehicle suspension systems.

Abstract

Dynamic loads on a vehicle’s running gear generated when driving over uneven roads or surfaces have a destructive effect on its components and, consequently, on the vehicle’s reliability. Special vehicles, especially off-road vehicles, are operated differently from traditional vehicles. Deformable surfaces can induce significant dynamic loads on vehicle running gear components even at low speeds, significantly limiting safe driving speeds. This article presents experimental vehicle tests conducted on four test track sections at three predefined vehicle speeds (10, 20, and 30 km/h). The experimental results demonstrate a clear dependence of dynamic loads on the off-road vehicle’s speed on dirt surfaces. Differences were observed between the measurement sections, suggesting that standard road profile metrics (e.g., RMS (Root Mean Square) profile height change) do not fully predict actual loads, requiring continuous monitoring of vehicle operating conditions. Compared to paved roads, where loads are more predictable, ground surfaces generate unique vibration patterns even at low driving speeds. RMS values for the measurement sections ranged from 0.02 to 0.06 m. Therefore, it is necessary to adapt test methods to specific ground conditions, with driving speed as a key research parameter.

1. Introduction

Vehicle reliability tests are often referred to in research jargon as “life cycle testing”. This type of testing provides significant information on the vehicle’s properties. The obtained results enable a range of complex analyses, including, among other things, the vehicle’s operating costs [1] and reliability. One of the key stages of vehicle testing is testing its resistance to vibrations and impacts. Dynamic loads on the vehicle’s running gear, generated when driving over uneven roads or surfaces, have a destructive effect on its components [2,3] and, consequently, on the reliability of the complex technical object. Many dynamic tests also focus on ride comfort [4,5,6] and traffic stability [7,8], as well as passenger comfort in public transport [9,10,11,12].

Damage to systems such as the vehicle suspension, braking system, and steering directly impacts vehicle safety. Safety issues related to the proper operation of the suspension system were the subject of the following scientific papers [12,13,14,15]. In [16,17,18,19], the feasibility of modifying the suspension for various road vehicles was also investigated. Detailed studies on hydropneumatic suspensions for special vehicles were presented in [20,21]. In [22], the possibility of using harvesters to recover energy from the suspension system of a motor vehicle via a specially designed shock absorber was presented. One of the important elements of the suspension system is the tires. The influence of tire technical condition on driving safety was widely discussed in the following scientific works [23,24,25,26]. Interesting studies on the braking systems of large trucks were presented in [27,28,29,30]. An interesting comparison of braking properties for selected motor vehicles using different research methods was presented in [31]. The problem of brake lining wear does not only concern road vehicles [32] but is also a dominant issue in rail vehicles [33,34,35]. In the context of damage to the steering system and other safety-related systems, important research results were presented in [5,36,37,38] and for city buses in [39] and special vehicles in [40,41,42]. Furthermore, many works are devoted to the technical safety of motor vehicles [43,44,45], the maneuverability of multi-track road trains [46], and the transport of dangerous goods in road transport [47].

The experience gained during field tests of vehicles intended for uniformed services provided the basis for analyzing the dynamic loads acting on the vehicles due to the road profile with a variety of surfaces. Special vehicles, especially off-road vehicles, are operated differently from civilian vehicles [48,49,50,51]. Driving on unconventional terrain is characterized by specific conditions that induce vehicle vibrations. Off-road surfaces are deformable, and at the same time, changes in their profile can have significantly higher amplitudes over shorter distances. It is worth noting that deformable surfaces can induce significant dynamic loads on vehicle chassis components even at low speeds, thereby limiting safe driving speeds. As a result, the level and structure of dynamic loads on vehicle chassis components differ from those reported in the literature for paved roads [52,53,54]. The nature of dynamic loads depends on driving speed, road profile, and the technical condition of the road surface [55,56,57,58,59,60,61]. Therefore, obtaining reliable results requires measuring and assessing the road profile characteristics. In off-road vehicle tests to assess their load-bearing structure and the installed equipment’s ability to withstand impacts from driving over uneven surfaces, selecting and standardizing test conditions is challenging. Selecting the type and length of test track sections with specific characteristics and the recommended driving speed during testing requires knowledge of the specific characteristics of the ground [62,63,64] and requires experimental testing.

In summary, experimental vehicle tests can be divided into:

• On a track with a random road profile;
• On a constant road profile.

Testing on test tracks with a random road profile replicates actual vehicle operating conditions. It is worth noting that the implementation of this type of research is complex due to the dependence of the profile course on many factors, such as:

• Weather conditions (applies to ground surfaces);
• The pressure forces exerted by the vehicle wheels on the road surface (deepening of ruts, hardening of the ground in places of increased pressure;
• Random changes in the lateral roll angle and longitudinal slope of the road profile;
• Subgrade deformability.

The tracks must be prepared for the test object and weather conditions, which requires continuous monitoring of their condition and characteristic parameters.

During dynamic load testing of vehicle suspension components on test tracks with a random road profile, the impact on the chassis can be described by statistical characteristics such as [53,62,65]:

• Maximum suspension deflection;
• Average suspension deflection;
• Maximum sprung mass acceleration;
• Average sprung mass acceleration;
• Maximum unsprung mass acceleration;
• Average unsprung mass acceleration.

Sprung mass is the portion of a vehicle’s total weight (body, chassis, engine, passengers, cargo, etc.) that is supported by the suspension system, moving up and down with the suspension over bumps. Unsprung mass is the weight of components below the springs, such as wheels, tires, brakes, and axles, that are not supported by the suspension but still affect handling and ride comfort.

Testing wheeled vehicles on special test tracks with a constant road profile (Figure 1 and Figure 2) is advantageous due to the following factors [58,66]:

• Repeatability of results;
• Reproducibility of measurements;
• Consistency of the input over time;
• No influence of weather conditions on the input.

The test track, shown in Figure 2, features 11 different lanes with critical roadway profiles, including two types: the “Belgian Block” and the “Torsion track”. There are large circular turning areas at both ends of the test track. This track provides repeatable testing conditions for various types of special vehicles.

However, testing on this type of track does not fully reflect the operating conditions of off-road vehicles. Another significant disadvantage of such a test facility is the very high cost of construction and subsequent maintenance. However, testing on such tracks allows [66]:

• Performing various research tests in conditions that ensure complete safety;
• Performing accelerated durability tests while maintaining correlation with operating conditions;
• Simulating situations that a vehicle may encounter during operation,
• Allowing for vehicle comparisons;
• Using a robot to control the vehicle.

Using a robot for durability testing significantly speeds up testing time. An example of such a robot controlling a test vehicle is shown in Figure 3.

By replacing the driver with a robot, the vehicle can operate 24 h a day or until critical damage occurs. Furthermore, the effect of human fatigue, which the driver typically compensates for by reducing speed, is eliminated, reducing the dynamic loads imposed on the vehicle and its components.

This article presents the results of experimental studies of dynamic loads acting on the chassis of an off-road vehicle while driving on various road surfaces. The studies were conducted on four test sections (D2, D3, D4, and D5) with different road surfaces at three driving speeds (10, 20, and 30 km/h). The relationship between dynamic loads, driving speed, and road surface type was analyzed using indicators such as root-mean-square (RMS) acceleration values and their maximum values. Testing the dynamic loads on vehicles, especially specialized equipment used in off-road conditions, is an important task for improving reliability and safety.

2. Materials and Methods

Measuring the physical quantities characterizing the dynamic loads of vehicle suspension elements requires specialized measuring equipment.

The following physical quantities were selected as the dynamic load characteristics for the tests:

• Vertical acceleration of the sprung mass;
• Vertical acceleration of the unsprung mass;
• Vertical and angular accelerations at the vehicle’s center of mass;
• Vehicle speed.

For testing the vehicle’s dynamic loads, the measurement system shown in Figure 4 was constructed, equipped with the following components:

• Acceleration sensors mounted on the vehicle’s axle;
• Acceleration sensors mounted on the frame;
• RT 3002 Inertial-satellite system mounted at the vehicle’s center of mass;
• Pulse recorder from Brüel & Kjaer Type 3050-A-060 (Brüel & Kjaer, Nærum, Denmark);
• Data acquisition stations;
• Measurement computer.

A PULSE recorder was used to record acceleration, connected to acceleration sensors mounted on the vehicle’s axles and frame. To monitor and record parameters at the center of mass, an RT 3002 inertial-satellite system was used, which is easy to install and does not require any interference with the vehicle’s structure. The RT 3002 inertial-satellite system’s position measurement accuracy is ±20 mm (using a base station). The system also allows for monitoring and recording changes in speed, acceleration, angle, and angular acceleration along the vehicle’s three axes. The velocity and accelerations at the center of mass were recorded at a frequency of 100 Hz; the accelerations on the vehicle arm and bridges were recorded at a frequency of 1000 Hz, and a high-pass filter at 0.7 Hz was necessary (due to the non-linearity of the impact below this frequency).

The accelerometer mounting locations on the drive axle and support frame of the tested vehicle are shown in Figure 5.

For the experimental tests, in accordance with the proposed method of mapping the geometry of the tested road section, a high-mobility JEEP J8 truck-passenger vehicle (JEEP, Toledo, OH, USA), a military variant of the JEEP Wrangler, was used. Compared to the JEEP Wrangler, it underwent a series of modifications designed to prepare the vehicle for extreme operating conditions. Its frame was reinforced, the rear coil springs were replaced with leaf springs, the bumpers were equipped with special handles for helicopter or airplane transport, and the intake system was designed to withstand a 5 h sandstorm. Depending on the version, the vehicle’s payload can reach up to 1.3 tons, and the towable trailer can weigh up to 3.5 tons. The vehicle is equipped with a 2.8 L engine producing 160 hp. The J8 is equipped with a 5-speed automatic transmission and Command-Trac four-wheel drive. The coordinate system adopted for the tests is shown in Figure 6.

Before the field tests, the vehicle’s mass and center of mass were measured, accounting for its distribution among the wheels, axles, and sides. The results of these measurements are presented in

Table 1. The results determined the mass of the vehicle components.

Vehicle Parameter	Designation	Value [kg]
Weight per left front axle wheel	M1L	655
Weight per right front axle wheel	M1P	675
Weight per front axle	M1	1330
Weight per left rear axle wheel	M2L	700
Weight per right rear axle wheel	M2P	710
Weight per rear axle	M2	1410
Weight per left side	ML	1355
Weight per right side	MP	1385
Vehicle curb weight	Mw	2740
Weight difference per side	ΔM	30

and

Table 2. Center of mass measurement results.

Vehicle Parameter	Unit	Value
Distance of the center of mass from the vertical plane passing through the vehicle’s 1st axis	mm	1518
Height of the center of mass above the road surface	mm	742
Distance of the center of mass from the vehicle’s longitudinal plane of symmetry	mm	9
Static theoretical lateral roll angle	°	47.25

.

The experimental tests were conducted on four test sections:

• D2—tank track no. 2;
• D3—tank track no. 3;
• D4—concrete track with damaged surface;
• D5—off-road.

The road tests were conducted consecutively on the same object with the same vehicle tire pressure values. Detailed characteristics of individual test sections are presented in

Table 3. Characteristics of the individual test sections.

Substrate Type Designation	Substrate Characteristics
D2—tank track no. 2	- loose, sandy ground surface, - possible scuffing by the vehicle’s road wheels, - unevenness exceeding the vehicle’s wheelbase.
D3—tank track no. 3	- loose, sandy ground surface, - deep scuffing by the vehicle’s road wheels, - unevenness comparable in length to the vehicle’s wheelbase.
D4—concrete track with damaged surface	- degraded paved surface, - unevenness extending below the vehicle’s wheelbase.
D5—off-road	- compacted, sandy ground surface, - no or shallow scuffing caused by the vehicle’s road, - unevenness of a significant length exceeding the vehicle’s wheelbase.

.

For each section, the road profile heights were measured, and the root-mean-square (RMS) value was calculated. The index was determined according to Equation (1):

$$h_{RMS}=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{h}_i^2}{n}}}$$

(1)

• h_RMS—road profile height RMS,
• hi—road profile height,
• n—number of samples.

Each road height waveform was converted to power spectral density (PSD). The time waveform was converted to power spectral density according to Equation (2):

$${PSD}_h= {\displaystyle \frac{{\left(abs\right(FFT\left(h\right))}^2}{n\ast f_s}}$$

(2)

• PSD_h—vector of power spectral density values,
• abs(FFT(h))—modulus from the Fast Fourier Transform (FFT),
• n—number of samples,
• fs—sampling frequency.

The RMS parameter was used to characterize the polygonal road profile, determined in two ways:

• In the vehicle’s path (designated as RMS in the table);
• Average value over the road width (designated as RMS_2.5 in the table).

The polygon road profile was characterized using the RMS parameter, determined in two ways: RMS and RMS_2.5. RMS and RMS_2.5. RMS applies to the entire width of the road; RMS_2.5 applies to the indicator from 2.5 m of the road width, i.e., 1.25 m on each side from the axis of symmetry of the road. A comparison of the obtained RMS values for the measurement sections is presented in

Table 4. Comparison of RMS values for the measurement sections.

Substrate Type Designation	RMS [m]	RMS2.5 [m]	Difference Between RMS and RMS2.5 [m]
D2	0.0548	0.0611	0.63
D3	0.0403	0.0404	0.01
D4	0.0217	0.0338	1.21
D5	0.0376	0.0382	0.06

.

The differences in the values of both comparative parameters are insignificant, except for road D4. However, this road, unlike the others, differs in its surface type (a deteriorated concrete road). A concrete road with a damaged surface, unlike other roads, is not a dirt road; its unevenness occurs randomly and has a fault-like character. This may explain the obtained acceleration values.

The RMS values for the individual measurement sections of the road are presented in

Table 5. RMS values for the measurement sections.

Substrate Type Designation	RMS [m]	Section Length [m]	Sampling Frequency [1/m]
D2	0.06	3815	100
D3	0.04	2334	100
D4	0.02	1343	100
D5	0.04	1024	100

.

Additionally, power spectral density characteristics were determined for each measurement section, as shown in Figure 7.

3. Results and Discussion

Experimental vehicle tests were performed on four sections of the measurement track at three specified vehicle speeds. This section presents the results of the experimental tests, as well as possible undesirable effects of the test run on the measuring track, i.e., damage to the vehicle and its suspension system.

3.1. Results of Experimental Studies

Field tests were conducted on each of the four measurement sections at three vehicle speeds (10, 20, and 30 km/h). The test results from each measurement section were presented using the following indicators and characteristics:

• Root mean square (RMS) accelerations measured on the vehicle frame;
• Root mean square (RMS) accelerations measured on the vehicle’s drive axle;
• Root mean square (RMS) accelerations in the Z axis at the vehicle’s center of mass as a function of driving speed;
• Root mean square (RMS) angular accelerations about the X axis as a function of driving speed;
• Root mean square (RMS) angular accelerations about the Y axis as a function of driving speed;
• Average values of 10 maximum accelerations measured on the vehicle frame;
• Average values of 10 maximum accelerations measured on the vehicle’s drive axle;
• Average values of 10 maximum accelerations in the Z axis at the vehicle’s center of mass as a function of driving speed;
• Average values of 10 maximum angular accelerations about the X axis as a function of driving speed;
• Average values of 10 maximum angular accelerations about the Y axis as a function of driving speed.

Figure 8 presents the obtained results of the RMS accelerations in the Z axis at the vehicle’s center of mass as a function of driving speed.

Figure 9 presents the obtained results of the tests for the root mean square (RMS) angular accelerations about the X axis as a function of driving speed.

Figure 10 presents the obtained test results of the root mean square (RMS) angular accelerations about the Y axis as a function of driving speed.

Table 6. Measured RMS values for a vehicle speed of 10 km/h.

Parameter	D2	D3	D4	D5	Unit
$\ddot{Z_1}$	1.54	1.19	0.93	1.20	m/s2
$\ddot{Z_2}$	1.71	1.18	0.85	1.00	m/s2
$\ddot{Z_3}$	1.74	0.84	1.02	1.29	m/s2
$\ddot{Z_4}$	1.76	0.84	0.75	1.10	m/s2
$\ddot{Z_{11}}$	0.73	0.60	0.51	0.41	m/s2
$\ddot{Z_{22}}$	0.94	0.27	0.35	0.87	m/s2
$\ddot{Z_{33}}$	0.76	0.45	0.27	0.70	m/s2
$\ddot{Z_{44}}$	0.85	0.39	0.47	0.73	m/s2
$\ddot{Z}$	0.71	0.50	0.44	0.60	m/s2
$\ddot{\theta }$	31.92	17.66	17.01	20.83	°/s2
$\ddot{\varphi }$	43.18	21.57	16.35	25.22	°/s2

,

Table 7. Measured RMS values for a vehicle speed of 20 km/h.

Parameter	D2	D3	D4	D5	Unit
$\ddot{Z_1}$	2.42	2.02	2.54	1.65	m/s2
$\ddot{Z_2}$	1.68	1.66	2.35	1.64	m/s2
$\ddot{Z_3}$	1.88	1.55	3.11	1.62	m/s2
$\ddot{Z_4}$	1.77	1.38	2.46	1.97	m/s2
$\ddot{Z_{11}}$	1.35	1.28	2.08	0.69	m/s2
$\ddot{Z_{22}}$	1.39	1.26	1.95	0.81	m/s2
$\ddot{Z_{33}}$	1.15	0.94	1.05	1.22	m/s2
$\ddot{Z_{44}}$	1.07	1.09	1.92	1.51	m/s2
$\ddot{Z}$	1.10	0.91	1.39	1.02	m/s2
$\ddot{\theta }$	39.10	44.92	49.81	38.17	°/s2
$\ddot{\varphi }$	46.43	58.04	48.19	39.72	°/s2

and

Table 8. Measured RMS values for a vehicle speed of 30 km/h.

Parameter	D2	D3	D4	D5	Unit
$\ddot{Z_1}$	2.32	2.59	4.76	1.82	m/s2
$\ddot{Z_2}$	2.38	3.34	4.13	2.04	m/s2
$\ddot{Z_3}$	2.66	2.62	4.57	2.11	m/s2
$\ddot{Z_4}$	2.42	2.91	3.57	2.38	m/s2
$\ddot{Z_{11}}$	1.98	1.72	2.77	1.06	m/s2
$\ddot{Z_{22}}$	2.03	1.29	2.74	1.34	m/s2
$\ddot{Z_{33}}$	2.00	1.69	2.60	1.38	m/s2
$\ddot{Z_{44}}$	1.42	1.04	2.61	1.59	m/s2
$\ddot{Z}$	1.38	1.40	1.97	1.06	m/s2
$\ddot{\theta }$	60.94	72.30	67.17	50.44	°/s2
$\ddot{\varphi }$	69.27	64.56	65.34	56.02	°/s2

present the root mean square (RMS) test results for the selected vehicle speed on individual sections of the test road.

The results of experimental tests show a clear dependence of dynamic loads on the speed of an off-road vehicle on ground surfaces. The RMS values of vertical accelerations measured at the vehicle frame (sprung mass), the drive axle (unsprung mass), and at the center of mass increase with increasing speed. A similar trend is observed for angular accelerations about the X (lateral roll) and Y (longitudinal pitch) axes. The experiment is consistent with other studies described in the literature on the dynamics of off-road or military vehicles [49,69,70]. These studies indicate that additional dynamic loads resulting from vehicle-road interaction increase significantly with speed and ground unevenness, thereby accelerating the wear of vehicle suspension components.

Analysis of the maximum values (averages of the 10 highest amplitudes) further highlights the risk of sudden impacts on unsprung surfaces, which is particularly important for special vehicles operated in unpredictable terrain (e.g., military vehicles). The literature confirms that such loads can accelerate wear of suspension components and welds in load-bearing systems [2,38,42,71], where dynamic loads from variable road profiles accelerate wear and failures.

Differences between measurement sections suggest that standard road profile metrics (e.g., RMS profile height change) do not fully predict actual loads, requiring continuous monitoring of vehicle operating conditions. This limitation is well known from studies of off-road vehicle movement on unpaved roads, where factors such as ground deformability and weather conditions complicate, among other things, the modeling and simulation of vehicle motion [49,72,73,74]. Compared to paved roads, where loads are more predictable, ground surfaces generate unique vibration patterns even at low speeds, limiting safe operation and increasing safety risks (e.g., by damaging braking or steering systems).

In summary, the results emphasize the need to adapt ground test methods to the specific characteristics of ground surfaces, with speed as a key parameter. Due to the stochastic nature of unpaved surfaces and the dynamic changes in vehicle driving parameters, it is impossible to clearly define the components of an off-road vehicle [75] that would ensure its optimal performance in all conditions. Correlating experimental studies with simulation models, such as those based on multi-body elements and soil models, could enable more precise load prediction and improved suspension design for off-road vehicles. This approach would improve the reliability of special vehicles, enhance user safety, and optimize operating costs.

3.2. The Effects of the Course Tests

Based on many years of experience conducting mileage testing at the Military Institute of Armored and Automotive Technology, it can be concluded that the most common malfunctions in off-road vehicles are damage to the chassis and frame (Figure 11).

This type of damage most often occurs when driving on dirt roads and off-road tank tracks.

4. Conclusions

Based on the conducted research, the main conclusion is that it is necessary to adapt test methods to the specific characteristics of ground surfaces, with driving speed as a key research parameter. Based on the conducted studies of dynamic interactions as a function of road profile, the following conclusions were drawn:

• As speed increases, the effective vertical acceleration amplitudes (RMSs) of the sprung and unsprung masses increase;
• As speed increases, the effective angular acceleration amplitudes (RMSs) about the X and Y axes increase;
• As speed increases, the average value of the 10 maximum amplitudes of the measured physical quantities increases;
• Indicators of soil profile variability, e.g., RMS, are insufficient to ensure the required level of dynamic loads on the vehicle’s running gear components during test drives; therefore, a comprehensive approach is necessary, taking into account the analyzed X, Y, and Z profile;
• The level of observed dynamic loads and fatigue-related loads clearly increases with driving speed and changes with changes in the type of surface;
• The essence of selecting vehicle movement conditions in the mileage testing process is to determine the appropriate driving speed for a given ground surface type. It is necessary to propose a method for determining vehicle mileage testing conditions for each type of ground surface.

Analysis of the available literature and experimental studies has confirmed the need to study dynamic impacts on vehicles. Systematizing test conditions will ensure repeatability and reproducibility, eliminating the possibility of manipulating test results by selecting organizational entities—research units—with test tracks characterized by a profile that forces reduced dynamic impacts on the vehicle and its components. Furthermore, defining clear test conditions and methods, as well as a method for evaluating results, will improve relationships and communication between the equipment purchaser, the manufacturer, and the research unit. These issues should be reflected in relevant standardization documents and by implementing legal acts (ministerial decisions, regulations).

Further research and development should focus on:

• Creating a certification system for test tracks;
• Developing a mathematical and physical model that would take into account longitudinal and lateral movement and the impact of tire pressure;
• Examining the impact of vehicle age and mileage on the magnitude of dynamic impacts on the vehicle and drivers.