Analysis of the Impact of Vibrations on the Driver of a Motor Vehicle

Abstract

Vibration can have a significant impact on long-term health, driver comfort, and vehicle performance. With a focus on steering wheel vibrations, this study examines both general and local vibrations that affect the driver. Under real-world conditions, a series of controlled test drives were conducted, with high-precision accelerometers mounted on the driver’s seat and steering wheel recording vibration data. The measurements were conducted in accordance with ISO 5349 and ISO 2631-1, which guaranteed a consistent assessment of vibration exposure. The results suggest that the daily vibration exposure for general vibrations at the driver’s seat is significantly lower than the legal limit, as evidenced by the presence of significant frequencies in the vertical (Z) axis. Nevertheless, steering wheel vibrations may cause pain due to their proximity to the resonance frequencies of the human hand–arm system, which have frequency maxima at approximately 35 Hz and harmonic 70 Hz. Additionally, the vibration intensity was elevated at vehicle velocities between 70 and 80 km/h, suggesting the potential presence of a resonance effect within the suspension or powertrain. The results emphasize the significance of advanced vibration reduction strategies in enhancing driver comfort and safety, including the implementation of a well-designed steering system and enhanced seat absorption. This research offers valuable insights for automotive engineers and ergonomics specialists who are interested in minimizing long-term health risks and vibration-induced fatigue. The aim of this study is to indicate the areas of the drive system fault that have a direct impact on the vibrations of the body structure. The article presents an analysis of the recorded vibration results based on which of the areas of change in the comfort of using the vehicle were selected.

1. Introduction

Analyzing the effects of vibrations on the human body [1], one should consider both general vibrations [2], affecting the entire organism through legs or via a seat [3], as well as local vibrations [4], specifically affecting limbs [5].

The current set of studies covers three aspects: vibration excitation from the road [6], drive system vibrations, and engine vibrations [7]. These three sources of vibrations are widely described in the available literature [8,9]. The issue of vehicle body vibrations and transfer of vibrations to the driver and passengers is described in [10].

Vibrations from the combustion engine are widely described in [11,12,13]. The study is devoted to explaining and counteracting vibrations to the driver in the case when the vehicle is equipped with a 3-cylinder engine. The sources of vibrations and their impact on several perception zones are also described. The issue of vibrations from the drive system is presented in [14]. The study presents the effect of damage to gears and verifies the effect of damage to rolling bearings in the drive system on the level of vibrations of the system [15,16].

The studies also devote space to determining the effect of seat insulation materials on the level of vibrations felt by the driver [17]. The authors used neural networks and artificial intelligence to determine the seat model and materials used in its production in order to minimize the impact of vibrations on vehicle users. The authors [18,19] described a new apparatus for measuring vibrations affecting the driver of a motor vehicle.

Vibrancies have a major impact on modern sectors of vehicle engineering and ergonomics, therefore affecting drivers, as well as passengers. On psychological, as well as physiological levels, the effects could show themselves as drowsiness, tiredness, and attention problems [20,21,22,23,24]. By use of vibration control technology, ergonomic seat designs, and sophisticated suspension systems, researchers are looking at ways to lower or control vibration, enhance driver comfort, minimize tiredness, and help to create safer driving [25,26].

Vibration has a negative impact on driver well-being, particularly in low-frequency (<10 Hz) areas [27,28]. The frequency, amplitude, and duration of vibrations are crucial factors in causing driver drowsiness. Longer and more intense vibrations lead to loss of alertness, poorer reactions, and increased risk of traffic accidents. Real driving conditions, however, could differ from laboratory studies, due to factors including aspects of ambient noise, road surfaces, weather, and the psychological state of the driver. Thus, additional methodological study is needed to exactly show real events and reduce accident rates [29].

Thorough research on vehicle seat vibration characteristics is necessary to improve driver comfort. Virtual modeling tools (CATIA V5) allowing seat behavior under dynamic load makes early study of deflections from shocks or road vibration spectra possible. Low-frequency road vibrations greatly affect driver comfort and alertness. Engineering should give engine and road surface vibrations first attention in seat design. Improved damping materials and adaptable seats that automatically change stiffness depending on actual road terrain [12] are among the innovative elements.

Radhakrishnan et al. [30] suggest a novel torsion-spring-system-based mechanism for reducing seat vibration. The mechanism improves the vertical part of vibration damping by using different stiffness values and specific torsion angles. The cross-sectional geometry of the rod can be optimized using ANSYS R15 or similar software, reducing the driver’s seat amplitudes at significant frequencies, potentially competing with traditional coil spring seats or air suspensions.

Vibration is a significant issue in both conventional roads and larger engineering structures like long-span suspension bridges [31,32,33]. Studies have shown that certain bridge vibrations can resonate with vehicle loads, causing discomfort and increasing the likelihood of accidents if drivers fail to respond appropriately. Solutions based on the GPR model allow for real-time prediction of dangerous situations, allowing bridge control systems to warn drivers of impending risks and encourage them to reduce speed [34]. Satellite navigation technology also changes the driver’s body schema and spatial perception, affecting their ability to independently orient themselves in space. Future technologies should integrate the driver’s self-monitoring skills, rather than relying solely on external sources of information, especially when the physical environment, such as road surface and vehicle vibrations, impairs the interpretation of sensory signals [35].

Kim et al. [36] discuss thermoelectric devices in cars, which generate energy from waste heat and provide cooling or air conditioning. While seat vibration reduction is not directly connected, innovative energy-generating solutions are emerging. Active vibration damping mechanisms, like adaptive shock absorbers or seat frame elements, could partially supply energy to control systems for real-time road irregularities, providing a broader technological platform.

Active controllers like PD/PID in vehicles improve driver comfort by controlling speed and acceleration. They can also be used for vibration control, evaluating the movements of the seat, suspension, or vehicle body. Sensors evaluate these components, adjusting settings to suppress unwanted frequency components that negatively impact driver comfort and safety [37].

The “Skyhook-LQR” approach, combining the Skyhook algorithm and the LQR controller, offers a dual strategy for controlling vehicle pitch, roll, and vibration dynamics. While effective in providing comfort, it has limitations in handling stability in corners. The integrated version with LQR improves overall performance by adjusting the controller in real time, reducing driver vibration [38].

Poor seat geometry and sitting posture increase the risk of low back pain (LBP). Dynamically moving backrests can reduce pain and improve vibration comfort in car seats. However, these changes can cause small desynchronizations in the seat and backrest area, potentially negatively affecting the spine in the long term. Careful design adjustments are needed to ensure the moving backrest reduces vibration effects, not increasing them [39].

Professional drivers often experience chronic low back pain due to prolonged sitting and vibration in their work equipment, such as tractors or heavy machinery. This pain is particularly common among drivers with postural strain. Regular health checks and interventions are crucial to prevent further damage. Psychological stress, long working hours, and incorrect sitting posture can further exacerbate the negative effects of vibration [40].

Vibration significantly impacts the human body, particularly in typical automotive postures. Body mass significantly affects the main resonant frequency peaks, with heavier individuals experiencing slightly decreased frequency but increased vibration peak size. Ergonomic adjustment of seats should consider the driver’s body weight, height, and sitting preferences. Tractor drivers are at a higher risk of back pain due to high vibration levels. Seat improvement, ergonomic adjustment, and proper sitting position can significantly reduce the incidence of LBP among professional drivers [41].

Advanced technologies, such as computer analysis, precise acoustic and vibration measurements, and intelligent insulation solutions, are being used to reduce noise and harshness parameters in vehicles. These technologies allow engineers to optimize the frame or body structure, identify resonant areas, and select appropriate muffler or engine mounting systems, thereby preventing vibrations from reaching the driver’s seat [42].

Mohanty and Fatima [42] reveal that the steering wheel vibration, while driving, can affect a driver’s emotional state. The intensity of vibration is directly related to a person’s emotional arousal. The more intense the vibration, the stronger the emotional reaction. The presence of a large peak and high-frequency component is also important. Uneven roads or improper steering wheel balancing can cause emotional discomfort, ultimately affecting the quality of driving.

Ajovalasit and Giacomin [43] compared driver perception of manual vibration in a steering column, and acoustic stimulus revealed subjective “equivalence curves” that indicate the same discomfort level as a certain vibration level. This data helps manufacturers develop balanced measures to prevent discomfort from reaching a threshold that significantly increases tension, optimizing acoustic communication and preventing drivers from experiencing greater tension if the vibro and acoustic stimuli are not properly matched.

Studies (e.g., [44]) show that the angle of the seatback affects the distribution of resonant frequencies. The more the seatback is tilted, the higher the vertical resonant frequency in the seat plane, whereas the horizontal (fore-and-aft) resonant frequency decreases. When the body configuration changes, the contact area with the seat and backrest changes, and the distribution of forces also changes. This is important because many drivers tend to tilt the backrest for comfort, but too large an angle can increase the transmission of lower-frequency vibrations (4–10 Hz) through the torso. When optimizing the seat, it is necessary to take these variables into account, and it is also necessary to appreciate that the optimal backrest angle may differ for drivers of different heights and weights.

Qualitative feedback plays a crucial role in assessing the effects of vibration on individuals, particularly when they describe their comfort on scales or provide subjective feedback [45]. Mani et al. [46] have shown that people are more likely to attribute higher levels of discomfort to smaller amplitudes, and in the case of extremely high vibration, their assessment seems to level out. This highlights the importance of considering small characteristics of suspension or tires when planning ergonomic measures or driver training. Golinko et al. [47] systematically reviewed five publications analyzing whether work-based vibration (WBV) experienced while sitting can impair postural stability. Results show that after a longer driving session, a person’s balance can change, potentially causing temporary loss of optimal sensory and vestibular response. Health protection is also emphasized, with a modified risk calculation method (Risk Score) proposed to assess the exposure of bus drivers to harmful factors such as temperature, vibration, and emotional stress. Regular health checks, planning driver regimes, and reviewing traffic schedules according to ergonomic criteria can significantly reduce negative consequences.

Vibration exposure in drivers is a significant concern, affecting both the car body and the human body. Innovations in this area include active controls, adaptive seat mechanisms, real-time data monitoring, and simulation-based design. The impact of vibration should be assessed in a comprehensive manner, considering noise, thermal regimes, and psychosocial factors. A well-formed ecosystem, including ergonomics, engineering, healthcare, and psychology measures, could significantly improve the conditions of everyday drivers and professional carriers. Despite barriers such as technological and social barriers, the scientific community has prepared research and proposals to mitigate or eliminate the negative impact of vibration.

2. Measurement Process

2.1. General Vibrations

The measurement of general vibrations pertains to those transferred to the human body through various kinds of support structures, e.g., seats or rests in the pelvis and back region, but also through the floor to the feet. General vibrations are mainly observed in motor vehicles (cars, goods vehicles, ships, airplanes, special-purpose vehicles), but large machines that transfer vibrations through other surfaces, such as floor slabs, can also be vibration sources.

The ISO 2631-1 [48] standard defines specific general vibration measurement methods to be used depending on whether they are performed to assess health exposure, comfort, or perception of a person exposed to vibrations. The vibration measurement is based on RMS values of vibration accelerations within the band of frequencies ranging between 0.5 and 80 Hz. Where the subject of the assessment is at risk of motion sickness, vibrations are assessed within the frequency range of 0.1–0.5 Hz.

General vibration measurements are conducted against the axes of the X, Y, Z coordinate system, the origin of which is at the point of contact with the vibrating surface, where vibrations are transferred to the human body (see Figure 1).

For people in a seated position, ISO 2631-1 indicates three main points of contact with vibrating surfaces: the seat, the backrest, and the feet. Therefore, vibration transducers (seat accelerometers) should be positioned at the contact point.

The measurement time should be long enough to represent the typical vibration exposure of a worker or equipment user. The measurement is performed to established the A(8) daily vibration exposure level, expressed as a weighted mean of the highest RMS vibration acceleration level determined in three axes, taking a weighting factor (1.4 a_x, 1.4 a_y, a_z) into account. The fact that the coefficient of 1.4 is applied to the X and Y axes is associated with a greater risk of negative vibration effects in the horizontal axis than in the vertical axis of a human body.

What is also calculated in the case of impulsive vibrations, i.e., those characterized by a peak-to-RMS ratio greater than 9, is the VDV vibration dose, and then, on the basis of the latter, A(8) is also determined and compared with the limits stated in the vibration directive.

2.2. Local Vibrations

Local vibrations occur when one or both hands are in contact with a vibrating surface, e.g., in hand tools, steering rods, steering wheels, etc. As a result of local vibrations, pathological changes occur in the human body, commonly referred to as a vibration syndrome, the symptoms of which include the white finger. The only effective method of countering the vibration syndrome is reducing the exposure to vibrations. The relevant measurements are conducted according to ISO 5349 [49]. This standard specifies the measurement requirements and the method of assessing the local vibration exposure. The practical aspects of its application are described in part two of the ISO 5349-2 standard [50]. The local vibration measurements are performed using vibration meters conforming with the requirements of ISO 8041 [51].

2.3. Vibration Parameters

The basic parameter used to assess the exposure to both local and general vibration is that of adjusted root mean square values of vibration accelerations measured for the x, y, and z directions at the work station while performing each distinctive (i-th) activity. Once measured, the acceleration values are adjusted (weighted) using an adjustment characteristic adequate to each type of vibration [52].

For the vibrations acting via upper limbs, as well as for those of general effect, specific designations of the adjusted RMS values of vibration accelerations were envisaged, where x, y, and z are the directions of the vibrations.

Another parameter that proves to be of major importance to the assessment of both local and general vibrations is the total time of worker exposure to vibrations within a work shift of t [m], being the sum of duration times t_i of individual activities, calculated as per the following equation:

$$t=\sum _{i=1}^n{t}_i$$

(1)

where n is the number of activities involving vibration exposure performed at a given work station.

The basic quantities used to assess the local vibration exposure are the vector sum of adjusted vibration accelerations and the 8-h (daily) exposure to vibrations.

For each distinctive activity involving exposure to local vibrations, the a_hv,i value of the vector sum of the adjusted RMS values of vibration acceleration is calculated as per the following equation [53,54]:

$$a_{hv,i}=\sqrt{a_{hwx,i}^2+a_{hwy,i}^2+a_{hwz,i}^2}$$

(2)

where a_hwxi, a_hwyi, and a_hwzi are the RMS values of vibration acceleration measured for the x, y, and z directions during the i-th activity.

In order to assess short-term vibration exposure (for activities which take 30 min or less), the vector sum of adjusted RMS values of vibration acceleration is used. From among the vector sums determined for each activity with a duration time shorter than or equal to 30 min, the maximum (a_hv,30min,max) value of the vector sum is taken for the exposure assessment, performed according to the following equation:

$$a_{hv,30min,max}=max\left\{a_{hvi}\right\}$$

(3)

where the total time of worker exposure to vibrations (t) exceeds 30 min, a quantity referred to as an 8-h (otherwise daily) vibration exposure is used to assess the exposure to local vibrations, calculated as per the following equation:

$$A(8)={\displaystyle \frac{1}{T_0}}\sum _{i=1}^n{a}_{hvi}^2.t_i$$

(4)

where n is the number of activities performed with vibration exposure, i is the ordinal number of an activity performed with vibration exposure, a_hvi is the vector sums of weighted RMS values of vibration acceleration for the i-th activity, t_i is the duration of the i-th activity, and T₀ is equal to 480 min (value corresponding to 8 h).

2.4. Action Values

When the value of the quantity that characterizes mechanical vibrations exceeds the threshold referred to as the action value, the employer is obliged to undertake the measures specified in the relevant regulations to reduce the occupational risk associated with vibrations. The action values for the quantity characterizing mechanical vibrations in a working environment are stated in the annex to the Regulation of the Minister of Economy and Labour of 5 August 2005 on occupational health and safety at work involving exposure to noise or mechanical vibration Journal of Laws of 2005, no. 157, item 1318. The limit action values for noise have been provided in

Table 1. Vibration limits.

Vibration	Exposure Action Value	Exposure Limit Value
Hand-arm vibration	2.5 m/s2 (A8)	5 m/s2 (A8)
Whole-body vibration	0.5 m/s2 (A8)	1.15 m/s2 (A8)
	9.1 m/s1.75 VDV	21 m/s1.75 VDV

.

2.5. Calculated Vibration Parameters

The relevant parameters can be calculated either as overall values, meaning that one obtains a single value once the measurement is completed, or as values recorded at intervals. With a known recording interval value, the recording interval is defined in seconds: RMS is a statistical measure of the weighted signal quantity (root mean square value), PEAK is the maximum signal deviation from the zero line (peak value), VDV is the fourth power vibration dose value, MSDV is the motion sickness dose value, MTVV is the maximum transient vibration value (calculated at a one-second interval), and A(8) is the daily vibration dose (as per the applicable standard).

The vibrations transferred to the whole body should be assessed with reference to the result obtained for the A(8) daily dose, expressed as equivalent frequency-weighted acceleration over eight hours and calculated as the highest RMS or VDV value determined in the three axes of X, Y, and Z.

Quantities characteristic of the mechanical vibrations observed in the working environment and the permissible exposure limits (PEL) applicable to these quantities have been specified in an annex to the Regulation of the Minister of Labour and Social Policy of 12 November 2018 on the permissible exposure limits of concentration and intensity of agents harmful to health in the working environment [55]. In line with this regulation, the vibrations which affect the human organism through upper limbs (local vibrations) are characterized by the following parameters:

-

Daily exposure A(8), expressed as a vector sum of frequency-weighted RMS values of vibration acceleration, equivalent in terms of energy for 8 h of action and established for three directional components (a_hwx, a_hwy, a_hwz);

-

Exposure times of 30 min or less, expressed as a vector sum of frequency-weighted RMS values of vibration acceleration (a_hv,30min), established for three directional components (a_hwx, a_hwy, a_hwz).

The following are the characteristics of the second kind of vibrations, i.e., those of general effect on the human organism (general vibrations):

-

Daily exposure (A(8)), i.e., the highest of the exposure limits determined for three directions: max{Ax(8), Ay(8), Az(8)}, expressed as a frequency-weighted RMS value of vibration acceleration, equivalent in terms of energy for 8 h of action;

-

Exposure times of 30 min or less, expressed as frequency-weighted RMS value of vibration acceleration (a_w,30min), dominant among the vibration accelerations established for the three directional components by taking adequate factors (1.4a_wx, 1.4a_wy, a_wz) into account.

The permissible limits of mechanical vibration must not exceed the thresholds provided in

Table 2. Permissible exposure limits (PEL) of mechanical vibration.

Vibration Type	Quantity Characteristic of Mechanical Vibrations in the Working Environment	Permissible Limit
Hand-arm vibration	Daily vibration exposure (A8)	2.8 m/s2
	Short-term vibration exposure (ahv,30min)	11.2 m/s2
Whole-body vibration	Daily vibration exposure (A8)	0.8 m/s2
	Short-term vibration exposure (ahv,30min)	3.2 m/s2

.

2.6. Measurement System

For the purposes of the studies in question, a hardware and software platform comprising the Sirius data acquisition card (Figure 2) and the Dewesoft software working together with an S-box measuring computer was used. The measurements were performed in the Dewesoft software, supporting the Sirius data acquisition cards. Two 8-channel cards featuring the ACC/STG inputs were used in the tests.

The measurement chain, installed on board the test vehicle, has been depicted in Figure 2. Pre-configured for the tests, the system enabled recording of the following:

-

Video camera—25 fps synchronously—at the vehicle front;

-

GPS signal for vehicle speed and acceleration at 10 Hz;

-

General vibrations at the driver’s seat using a PCB 356B51 accelerometer (in three directions: X, Y, Z) at 5000 Hz;

-

Local vibrations at the steering wheel using a Dytran Piezo 3053M10 accelerometer (in three directions: X, Y, Z) at 5000 Hz;

-

Local vibrations at the steering wheel using a Dytran MEMS 7600B3 accelerometer (in three directions: X, Y, Z) at 5000 Hz.

The accelerometer readings were checked for correctness by means of a manual PCB calibrator.

2.7. Driving Conditions and Program

The tests were conducted on board a two-year-old 8-seat vehicle (bus type) with a diesel engine. The research was carried out during road tests in real conditions. The drives were carried out on suburban roads with good and very good surface quality and in motorway driving conditions with very good surface quality. During the research. The vehicle speed was maintained in the range of 50–90 km/h for suburban roads and up to 140 km/h when driving on the motorway. The test object was periodically exposed to vibrations from the drive system.

3. Results

The test run included driving on a motorway, high speed roads, and local roads. During the measurements, phases of vibrations clearly perceptible on the steering wheel were identified with a time stamp. More than 30 such phases were recorded during the test run (Figure 3).

The calculated total daily exposure value (Figure 4) of 0.1 m/s² is five times lower than the value of 0.5 m/s² set as the limit in the applicable standard, which makes it evident that the level of general vibrations affecting the vehicle driver does not exceed the standard threshold. Furthermore, the conclusion derived from the total RMS value of vibration accelerations of 0.27 m/s² is that the level of vibrations falls within the range of comfort (limit of 0.36 m/s²). The vibration dose value (VDV) (Figure 4) of 3.8 is also three times lower than the permissible limit of 9.1. As reported in several papers, the highest values of the vibration parameters affecting the driver were registered along the vertical Z axis (RMS values being two to three times higher than those obtained for the X and Y axes).

Another part of the studies was an FFT frequency analysis and determination of frequency spectra based on the overall behavior of the vibrations recorded in time (Figure 5). The spectral analysis has revealed that the vertical (Z axis) vibrations associated with the setup of the vehicle’s sprung and unsprung masses fall within the low frequency range, i.e., that of a few Hz. As for the vibrations recorded in directions X and Y, on the other hand, dominant values were found for the frequency of 28 Hz, which translates into a rotational speed of 1700 rpm, tantamount to the engine’s rotational speed at which considerable and perceptible vibrations were also recorded at the steering wheel.

With regard to local vibrations, namely the effect exerted by the steering wheel on the driver’s hands (Figure 6), the calculated total daily exposure values of 0.35 m/s² and 0.39 m/s² are also five times lower compared to the standard value of 2.5 m/s², which makes it evident that the level of local vibrations affecting the vehicle driver does not exceed the standard threshold.

The total RMS value of vibration acceleration is approx. 1 m/s², while the RMS values obtained for individual directions also come to approx. 1 m/s². The maximum (PEAK) values recorded at the steering wheel are lower than 20 m/s², and hence a peak factor value nearing 30 (Figure 7). The forementioned implies the significant dynamic and the considerable contribution of forcing of an impulse response nature.

Another part of the studies comprised an FFT frequency analysis and determination of a frequency spectrum based on the overall behavior of the vibrations recorded in time. The spectral analysis revealed that, for the vibrations recorded in directions X, Y, and Z (Figure 8, Figure 9 and Figure 10), dominant values were found for the frequencies of 13, 36, and 72 Hz, which translates into rotational speeds of 780, 2160, and 4320 rpm.

Table 3. Collation of the fragments analyzed, with the max peak in FFT reported.

	f [Hz]	FFT Peak X [m/s2]	f [Hz]	FFT Peak Y [m/s2]	f [Hz]	FFT Peak Z [m/s2]
1	34.8	3.55	11.6	0.33	1.8	0.4
2	31.7	0.57	11.6	0.29	31.7	0.56
3	34.8	2.9	22.6	0.21	34.8	2.8
4	34.8	2.2	31.7	0.44	34.8	1.85
5	35.4	2.9	33	0.25	34.8	2.36
6	37.84	0.68	34.8	1.42	35.4	2.57
7	46.4	0.63	34.8	1.15	36.6	0.33
8	58	0.69	34.8	2.1	37.8	0.4
9	67.7	0.94	35.4	1.92	67.7	0.57
10	67.75	1.2	39.1	0.3	67.7	0.43
11	68.3	0.41	39.1	0.27	68.4	0.48
12	68.4	1	39.1	0.3	69.6	0.47
13	69.6	0.87	46.4	0.7	70.2	0.3
14	70.2	1.3	46.4	0.56	70.2	0.68
15	70.2	0.62	46.4	0.48	70.8	0.26
16	70.8	0.3	47	0.46	104	0.29
17	72	0.48	50.7	0.3	116	0.68
18	73.2	0.44	50.7	0.31	136	0.35
19	74.5	0.45	51.3	0.36	150	0.39
20	76.3	0.42	51.9	0.28	154	0.4

displays the results of the three-dimensional finite-form analysis (FFT) of the vibrations felt by the driver in the steering wheel. These patterns help to shed light on the distribution of vibrations and their potential effects.

The X-axis experiences its strongest vibrations at 34.8 Hz (3.55 m/s²) and 35.4 Hz (2.9 m/s²). This indicates that this frequency is one of the dominant ones and may be related to the engine operating mode or mechanical resonance effects. In addition, significant peaks are seen at 67.7 Hz (0.94–1.2 m/s²) and 70.2 Hz (1.3 m/s²), which correspond to frequency harmonics (double values of the fundamental frequency). These frequencies may be related to coordinated dynamic effects from the transmission or suspension systems.

Frequencies in the range of 8–15 Hz are characteristic for vibrations of unsprung mass elements (wheel with part of the suspension). Excitation of the vibrations in this frequency range is probably related to kinematic excitation from road profile unevenness, but importantly it is not dominant in the considered case of impact on the driver’s hands. Precise determination of the natural frequency of unsprung mass vibrations would require excitation on a measuring stand (e.g., EUSAMA stand), which was not possible in the type of case of the conducted research.

The Y-direction vibrations have lower amplitudes than the X-direction, but the dominant frequencies are 11.6 Hz (0.33 m/s²), 34.8 Hz (1.42 m/s²), and 46.4 Hz (0.7 m/s²). This means that some vibrations may be caused by road irregularities or steering resonances. Furthermore, the decrease in amplitudes with increasing frequency suggests that the lower frequency components (especially 11.6 Hz) may be related to the basic structural properties of the vehicle.

The Z-direction vibrations are distinguished by different frequency peaks, with dominant amplitudes seen at 1.8 Hz (0.4 m/s²), 34.8 Hz (2.8 m/s²), and 70.2 Hz (0.68 m/s²). This can be attributed to the vertical movement of the seat, which affects the driver the most. The maximum amplitude at 34.8 Hz coincides with the peak in the X direction, indicating the overall effect of mechanical vibrations.

From all three directions, it can be observed that the frequencies 34.8 Hz and 70.2 Hz are dominant. This information is important because 35 Hz is close to the resonant frequency of human hands (8–16 Hz), which can cause discomfort, while 70 Hz can be related to the design features of the vehicle. This means that under adverse conditions, these frequencies can negatively affect driving comfort and safety.

4. Discussion

Having analyzed the dominant frequency values thus determined (Figure 11), isolating for the sample time intervals in which considerable vibrations were observed on the steering wheel, one can draw the following conclusions:

-

The fundamental frequency of the vibrations is approx. 35 Hz (approx. 2100 rpm), and it is dominant, while the amplitude in the FFT spectrum is up to 3.5 m/s²;

-

The consecutive dominant frequencies are harmonically related to the dominant frequency of 35 Hz, coming to twice that frequency (approx. 70 Hz).

Figure 11. Detailed frequency analysis (FFT peak) for the steering wheel vibrations in the directions X, Y, and Z.

Figure 11. Detailed frequency analysis (FFT peak) for the steering wheel vibrations in the directions X, Y, and Z.

Given that the dominant frequency value of 35 Hz is found near the peak of the curve of the vibration effect on human hands (the 8–16 Hz range reflects the most harmful resonant frequencies in terms of hand vibration; Figure 12), this frequency is considered rather uncomfortable and, where one is driving under adverse forcing conditions, it becomes arduous and unpleasant.

Following an analysis of the vehicle speed (Figure 13) in the phases of perceptible and major driving wheel vibrations, certain conclusions have been drawn:

-

These vibrations are observed at velocities ranging between 40 and 100 km/h, and most frequently at 70–80 km/h;

-

These vibrations are observed when the vehicle speed increases, either in the phase of acceleration or once a fixed running speed has been reached;

-

The acceleration dynamic in the speed increase phases corresponds to an increment of approx. 2 km/h within 1 s, which translates into an acceleration of approx. 0.7 m/s².

Figure 13. Analysis of the vehicle speed in phases of perceptible and major driving wheel vibrations (broken down into fragments subject to analysis).

Figure 13. Analysis of the vehicle speed in phases of perceptible and major driving wheel vibrations (broken down into fragments subject to analysis).

Analyzing Figure 13, which presents the analysis of the vehicle speed in different phases when clearly noticeable steering wheel non-standard vibrations were recorded (marked at the Figure 13), several important trends can be observed related to the conditions of vibration occurrence.

First of all, it is obvious that steering wheel vibrations occur at speeds from 40 to 100 km/h, but the highest vibration intensity is observed in the interval 70–80 km/h. This interval may indicate the resonant frequency of the vehicle, when certain components, such as suspension elements, tires, or transmission parts, reach a state in which the vibration amplitudes increase. This is especially important, since resonant vibrations usually cause greater discomfort to the driver and can have a negative impact on steering control.

Another crucial factor is that steering wheel vibrations happen more frequently in vehicles speeding or running at a constant speed. This implies that the vibrations are linked to particular dynamic working modes of the vehicle, not random or chaotic. During the acceleration phase (when the speed increases by an average of 2 km/h per second, correspondingly creating an acceleration of about 0.7 m/s²), it can be assumed that the engine and transmission are subjected to higher loads, which can lead to an increase in vibrations.

Keep in mind that the vibrations do not show up all the time; they only become noticeable at certain intervals. This could indicate that the vehicle is experiencing mechanical or structural imbalances that become more apparent at specific speeds. For instance, if the vibrations become more noticeable at 70–80 km/h, it could be because of problems with wheel balancing, uneven tire wear, or even a peculiar resonance in the engine or gearbox.

While vibrations in the steering wheel may be annoying at first, they pose a serious threat to the driver’s concentration and stamina in the long run. If the vibrations are most noticeable at moderate speeds, they may be something you experience frequently behind the wheel. This factor is particularly crucial when evaluating ergonomic and safety aspects because extended exposure to vibration can weaken the muscles in the hands, diminish the precision of the steering, and harm the health of the driver in the long run. Finally, looking at Figure 13 shows that the vibrations in the steering wheel are not random but rather affected by the vehicle’s speed and mode. When accelerating or in cruise control, the vibrations are usually at their worst, which was recorded at speeds of 70 to 80 km/h.

5. Conclusions

The conducted research allowed us to determine non-standard vibrations (originating from the drive system) and standard vibrations, the source of which are suspension systems together with excitations. In addition, the standard source of vibrations is the combustion engine with its periodic operation.

Having completed the tests of the vehicle in question, one can explicitly conclude that, with regard to the general vibrations affecting the driver via the seat, the calculated total daily exposure value of 0.1 m/s², as compared with the parameter specified in the relevant standard at 0.5 m/s², is five times lower than the reference value, which clearly implies that the level of general vibrations acting on the vehicle driver does not exceed the standard threshold. Furthermore, the conclusion derived from the total RMS value of vibration accelerations of 0.27 m/s² is that the level of vibrations falls within the range of comfort (the limit for RMS being 0.36 m/s²). The vibration dose value (VDV) of 3.8 is also three times lower than the limit value of 9.1. As reported in several papers, the highest values of the vibration parameters affecting the driver were registered along the vertical Z axis (RMS values being two to three times higher than those obtained for the X and Y axes).

Spectral analysis has revealed that the vertical vibrations associated with the setup of the vehicle’s sprung and unsprung masses fall within the low frequency range, i.e., that of a few Hz. As for the vibrations recorded in directions x and y, on the other hand, dominant values were found for the frequency of 28 Hz, which translates into a rotational speed of 1700 rpm and is tantamount to the engine’s rotational speed, at which considerable and perceptible vibrations were also recorded at the steering wheel.

The A(8) daily exposure, expressed as a frequency-weighted RMS value of vibration acceleration, equivalent in terms of energy for a period of 8 h, dominant among the vibration accelerations established for the three directional components by applying adequate factors (1.4a_wx, 1.4a_wy, a_wz), is 2.5 m/s².

With regard to local vibrations, namely the effect exerted by the steering wheel on the driver’s hands, the calculated total daily exposure value of 0.35 m/s² and 0.39 m/s² is also five times lower compared to the standard value of 2.5 m/s², which makes it evident that the level of local vibrations affecting the vehicle driver does not exceed the standard threshold. The total RMS value of vibration acceleration is approx. 1 m/s², while the RMS values obtained for individual directions also come to approx. 1 m/s². The maximum (PEAK) values recorded at the steering wheel are lower than 20 m/s², and hence a peak factor value nearing 30. The forementioned implies the significant dynamic and considerable contribution of forcing an impulse response nature.

Having analyzed the dominant frequency values thus determined, isolated for the sample time intervals in which considerable vibrations were observed on the steering wheel, one can draw the following conclusions:

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The fundamental frequency of the vibrations is approx. 35 Hz (approx. 2100 rpm), and it is dominant, while the amplitude in the FFT spectrum is up to 3.5 m/s²;

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The consecutive dominant frequencies are harmonically related to the dominant frequency of 35 Hz, coming to twice that frequency (approx. 70 Hz).

Given that the dominant frequency value of 35 Hz is nearing the peak of the curve of vibration effect on human hands (the 8–16 Hz range reflects the most harmful resonant frequencies in terms of hand vibration), this frequency is considered rather uncomfortable and, where one is driving under adverse forcing conditions, it becomes arduous and unpleasant.