Experimental study on vibration isolation performance of mining dump truck suspensions for improving ride comfort

2.2.1. Test standards

Based on the operational conditions and structural characteristics of the mining dump truck, the layout of measurement points for this experiment was designed in compliance with the methods specified in [21].

2.2.2. Evaluation criteria

The measured vibration acceleration data were evaluated according to the computational methodology outlined in [22]. This standard verifies whether the vibration exposure levels of the mining dump truck meet the ride comfort requirements mandated by national regulations.

2.3.1. Test conditions

Tests were conducted on the mining dump truck under both unloaded and fully loaded conditions, strictly adhering to the experimental standards.

2.3.2. Measurement point layout

In accordance with the experimental objectives and relevant standards, measurement points were strategically positioned. Specific arrangements are illustrated in Fig. 1, where positions numbered 1-10 denote the measurement locations.

Fig. 1Layout of measurement points

2.3.3. Experimental site

The experiment was conducted in a real-world mining area. The mining dump truck is primarily used for transporting waste soil and ores, as well as site transfers between operational zones. The operating environment of the mining dump truck is shown in Fig. 2.

Fig. 2Experimental process planning

2.3.4. Experimental equipment

The main equipment used in this experiment includes a multi-channel vibration signal acquisition analyzer and single-axis/tri-axial vibration acceleration sensors, as shown in Fig. 3.

Fig. 3Experimental data acquisition equipment

The statements in Figs. 1-3: This experiment was conducted on behalf of Shaanxi Tongli Heavy Industry Co., Ltd. All the photos in the article were taken by the author, Ma Na. The shooting location was the mining area in Longyan City, Fujian Province, China. The shooting time was mid-October 2024.

3.2.1. Denoising methods

During the experiment, the vibration acceleration data at each measurement point were significantly affected by the surrounding environment, and the main vibration characteristics of the cab were easily drowned out by the ambient white noise. In order to eliminate the impact of interference sources, identify the main causes of cab vibration in mining dump trucks, and clarify the direction for improving the ride comfort of the cab.

At present, there are many methods for signal denoising, such as wavelet threshold denoising, moving average method, singular value decomposition method, median method, standard deviation method, and Kalman filter. Extensive research has shown that the singular value decomposition method is not affected by the physical dimensions of various factors, and it can efficiently separate the main vibration characteristic information from the interference information based on the distribution of the main characteristic information in the phase space matrix. This advantage has enabled the singular value decomposition denoising method to be widely used in various fields [23, 24].

The primary objective of this study was to explore the effectiveness of the SVD denoising method in specific application scenarios. Due to limitations in resources and time, the focus was concentrated on the practical validation of the SVD denoising method, rather than extending to comparisons with other methods. Given the working characteristics of mining dump trucks, the comfort of these vehicles is mainly significantly affected by low-frequency vibrations. The experimental data in this study were primarily focused on the processing of low-frequency signals. High - frequency vibration components, in the complex mining environment, are blended into the mining operation environment in the form of noise. Compared with the impact of low-frequency vibrations on vehicle ride comfort, their influence is less significant. Therefore, data on high-frequency components received relatively less attention in this experimental study. As a result, at this stage, a comprehensive assessment of the risk of over-smoothing of high-frequency components has not been conducted.

Therefore, based on the above research results, this paper also selects the singular value decomposition method as the denoising method for the experimental data in this study.

3.2.2. Denoising principle

The method of performing orthogonalization calculation on a real matrix $H\in R^{m\times n}$, regardless of whether its rows and columns are related or not, there must exist two matrices, $U\in R^{m\times m}$ and $V\in R^{n\times n}$, such that Eq. (1) holds:

where $S$ is the singular value matrix of the real matrix $H$, and $S=\left(diag\right({\sigma }_1,{\sigma }_2,\cdot \cdot \cdot ,{\sigma }_r),0)$, ${\sigma }_i$ are the singular values of the real matrix $H$, and ${\sigma }_1\ge {\sigma }_2\ge \cdot \cdot \cdot \ge {\sigma }_i\ge {\sigma }_r\ge 0$, $r=rank\left(H\right)$:

where $m$ represents the dimensions of the matrix.

Let’s consider a set of discrete random time-domain signals $X$, whose signal sequence can be represented by $X=(x_1,x_2,\cdot \cdot \cdot ,x_m)$. Using the singular value decomposition method to construct a Hankel matrix, and decomposing it yields the singular values shown in Eq. (3):

Then, the abrupt point $k$ of the singular values in Eq. (3) is identified, the singular values before point $k$ are retained and denoted as $({\sigma }_1,{\sigma }_2,\cdot \cdot \cdot ,{\sigma }_k)$, and all the singular values after point $k$ are set to 0, as shown in Eq. (4):

Finally, among the retained singular values, the order corresponding to the peak of the singular value energy spectrum is identified, and then the singular values are reconstructed according to this order. The signal obtained after reconstruction is the main vibration characteristic signal after denoising.

3.2.3. Evaluation of denoising effect

After denoising the vehicle vibration experimental data using Singular Value Decomposition (SVD), the Signal-to-Noise Ratio (SNR) and Root Mean Square Error (RMSE) methods are commonly employed to quickly and effectively evaluate the denoising effect. In this experimental study, the primary objective is to rapidly guide the improvement direction of the target vehicle suspension system based on the experimental results, emphasizing speed and effectiveness. Additionally, these methods are computationally simple and provide intuitive results, making them commonly used indicators for evaluating denoising effects. Therefore, in this study, the evaluation of denoising effect using SNR and RMSE methods can meet the requirements of the experimental research.

The SNR is the ratio of signal power to noise power, typically expressed in decibels (dB). The calculation formula is shown in Eq. (5):

where $x\left(i\right)$ represents the original signal, $z\left(i\right)$ denotes the denoised signal, and $N$ is the number of data points.

The RMSE is the square root of the mean of the squares of the errors between the denoised data and the original signal. The calculation formula is shown in Eq. (6):

where $x\left(i\right)$ represents the original signal, $z\left(i\right)$ denotes the denoised signal, and $N$ is the number of data points.

3.2.4. Denoising results

All the vibration acceleration data at the measurement points in this experiment were denoised using the singular value decomposition method, and the characteristic signals after denoising were obtained, which laid the foundation for the subsequent research on the vibration characteristics of the cab. The time-domain signals of the experimental data at the cab seat cushion and floor mat after denoising by the singular value decomposition method are shown in Figs. 6-7. From Fig. 6, it can be seen that the vertical vibration amplitude at the seat is the largest, followed by the lateral vibration amplitude, and the front - back vibration amplitude is the smallest. From Fig. 7, it can be seen that the vertical vibration amplitude at the cab floor mat is the largest, followed by the lateral vibration amplitude, and the front-back vibration amplitude is the smallest. This indicates that the vibration characteristics at the cab floor mat and the seat are similar. In addition, from Fig. 7, it can be seen that the vertical vibration amplitude at the cab floor mat is much higher than that at the seat cushion, which indicates that the seat damping system has a certain positive vibration-isolating effect.

Fig. 6Time-domain data of vibration acceleration after noise reduction at the seat cushion

Fig. 7Time-domain data of vibration acceleration after noise reduction at the driver’s cabin foot mat

3.2.5. Noise reduction evaluation

After applying the SVD method for denoising, the evaluation of the denoising effect is shown in Table 2.

The higher the SNR after denoising, the better the denoising effect. Typically, an increase in SNR of more than 3 dB is perceptible to the human ear as a significant reduction in noise. Additionally, the smaller the RMSE, the closer the denoised signal is to the original signal, indicating a better denoising effect. Based on the values of SNR and RMSE in Table 2, it can be concluded that the denoising effect achieved using SVD in this study is satisfactory. The denoised vibration signals meet the requirements for the experimental research.

4.1.1. Engine excitation

Under idle conditions of the experimental vehicle, the dynamic excitation generated by the engine operation is the primary source of cab vibration. Fig. 8 shows the vibration response characteristics curve of the mining dump truck’s cab mounting system under idle conditions. In the figure, the active end corresponds to Measurement Point 9, while the passive end corresponds to Measurement Point 4 (5). Under the influence of the engine’s dynamic excitation, the vibration amplitude at Measurement Point 9 is significantly higher than that at the passive end (Points 4/5), indicating that the cab mounting system exhibits notable vibration isolation effectiveness.

Additionally, within the frequency range of 30-70 Hz, the vibration in the $X$-direction at Measurement Point 9 (active end) is relatively complex, causing a short-term “nodding” sensation in the cab. Above 70 Hz, the vibration acceleration in the $X$-direction decreases below 1 m/s², with the amplitude gradually stabilizing. However, while the vibration characteristics in the $Y$- and $Z$-directions at Measurement Point 9 are generally synchronized, the lateral (side-to-side) vibration amplitudes are the lowest, though their acceleration values remain above 0.5 m/s². At the passive end (Measurement Point 4/5), which reflects the vibration after isolation by the cab mounting system, the vibration acceleration values are all below 0.4 m/s², as shown in Fig. 8. Within the 30-70 Hz range, the lateral swaying vibration of the cab becomes relatively noticeable.

The vibration acceleration of measuring point 9L(R) in the $X$ coordinate direction shows the most significant variation, with a distinct peak occurring at approximately 45 Hz. Subsequently, the vibration acceleration decreases gradually with increasing frequency, exhibiting a downward trend. In contrast, the vibration acceleration of measuring point 4(5) in the $X$ coordinate direction is relatively low and exhibits minimal variation across the frequency range, maintaining a relatively stable level.

In the $Y$ coordinate direction, the vibration acceleration of measuring point 9L(R) also decreases gradually with increasing frequency and presents a minor peak at around 75 Hz. Similarly, the vibration acceleration of measuring point 4(5) in the $Y$ coordinate direction decreases gradually with increasing frequency, but the overall vibration acceleration is lower. In the $Z$ coordinate direction, the vibration acceleration of both measuring points 9L(R) and 4(5) shows a similar trend, decreasing gradually with increasing frequency. A minor peak is observed at 75 Hz, but the overall vibration acceleration remains relatively low.

Overall, the vibration acceleration of measuring point 9L(R) in the $X$ coordinate direction is the highest, with a distinct peak at 45 Hz. In contrast, the vibration acceleration of measuring point 4(5) is relatively low across all coordinate directions and exhibits minimal variation. As frequency increases, the vibration acceleration in the $Y$ and $Z$ coordinate directions for both measuring points 9L(R) and 4(5) decreases gradually. From these vibration curves, it can be concluded that the vehicle cabin suspension system provides effective vibration reduction under the current operating conditions. Moreover, these analysis results are of significant reference value for understanding the vibration characteristics of different measuring points at various frequencies and for the vibration analysis of the suspension system.

Fig. 8Vibration response characteristics of the cab mounting system

Based on the vibration conditions at the internal measurement points of the cab shown in Fig. 9, it can be observed that the vibration amplitudes at positions in contact with the human body, such as the seat cushion (seat pan) and steering wheel, are significantly below the vibration target value of 1 m/s². At these two locations, the vibration accelerations in the $X$-, $Y$-, and $Z$-directions are all below 0.15 m/s², with the $Z$-direction exhibiting the highest vibration amplitude. Between the seat cushion and steering wheel measurement points, the vibration at the seat cushion dominates, which is the main cause of discomfort related to the cab’s ride smoothness.

Fig. 9Vibration response characteristics inside the cab

4.1.2. Road excitation

The driving comfort of the cab of the dump truck is mainly affected by the driving excitation of the road surface in the mining area. Moreover, cab vibration is the vibration response caused by road excitation and engine excitation at the same time. In addition, the cab of the mine dump truck in this experiment is side-mounted, and the cab is roughly installed on the frame of the left front wheel. Therefore, the vibration energy of the left front wheel is directly transmitted to the cab mounting system through the frame mounting system, so the road excitation of the left front wheel most of the vibration energy directly dominates the driving comfort of the cab.

According to Fig. 10, the relationship curve of vibration characteristics between the seat soleplate (cushion) and the steering wheel inside the cab is shown. It can be obtained from the figure: The vibration in the $Z$ direction of the test position of the seat cushion and the steering wheel inside the cab at 13 Hz is greatly affected by the $X$ and $Y$ directions of the road excitation and the engine excitation. The vibration amplitude of the test point inside the cab exceeds the target value by 1 m/s², but only within 0.4 m/s² of the target value. This phenomenon shows that the vibration in the cab area is obviously affected by the engine excitation. At 7 Hz, the vibration of the excitation source in the $Z$ direction affects the inner cab area, so that the vibration amplitude at the steering wheel reaches 2 m/s², and the vibration amplitude of the steering wheel is larger. The reason for this phenomenon is that the steering wheel and the directional drive shaft are directly connected to the front axle, and the road excitation source is isolated from the transmission chain of the steering wheel without passing through the frame mounting system and the cab mounting system, and the vibration energy is directly input to the steering wheel. As a result, the vibration at the steering wheel is highly susceptible to the influence of low-frequency excitation on the road surface.

Fig. 10Vibration response characteristics inside the cab

The vibration response shown in Fig. 11 is to study the vibration isolation of the road’s low-frequency excitation source transmitted from the left rear wheel to the cab suspension system. It can be seen from the figure that the vibration characteristics of the excitation source in the $X$, $Y$ and $Z$ directions do not exceed the target range of 1 m/s² for the amplitude of the seat soleplate and the steering wheel in the cab, but the vibration in the $Z$ direction of the excitation source at 10 Hz resonates with the test area in the cab in a small range, and its peak value is 0.8 m/s². In other frequency bands, the vibration amplitude of the seat soleplate and steering wheel in the cab is less than 0.1 m/s², indicating that the vibration of the left rear wheel has little influence on cab ride comfort.

4.2.1. Analysis of vibration transmission pathways

There are three main transmission paths of vibration source in the cab of mining dump truck: the first is road excitation→front tire→frame mounting system→cab mounting system→seat mounting system; The second is engine excitation→engine damping support→frame mounting system→cab mounting system→seat mounting system; The third is from road excitation→rear tires→frame mount system→cab mount system→seat mount system. The self-excited vibration generated by other areas or components is only noise, which does not affect the ride comfort, but has an impact on the ride comfort. In the complex operating environment of mining area, it is difficult to meet the requirements of driving comfort with the existing technology. Therefore, it is not considered in this paper.

Fig. 11Vibration response characteristics inside the cab

The cab of the mining dump truck belongs to the left offset type and is installed above the left front wheel. The dynamic excitation of the cab mainly comes from the low-frequency excitation of the road surface. In addition, the driving smoothness of the cab of the mining dump truck mainly depends on the vibration amplitude in the $Z$ direction of the cab. Fig. 12 shows the dynamic response curve of the complete suspension system of mining dump truck in the Z direction. According to the figure, the vibration amplitude of the left front wheel (measuring point 6), frame (measuring point 9), cab support (measuring point 3), and cab base (measuring point 2) in the $Z$ direction is the largest at 8 Hz, and its peak value reaches 4.81 m/s². The vibration amplitude of cab support and cab base is the same, and the vibration amplitude of frame is the least. It shows that under the current working condition, the vibration damping of the frame plate spring suspension system is good, while that of the cab and seat suspension is better. Most of the overall vibration amplitude of the cab is below 1 m/s². Although the ride comfort of the cab is not ideal, the cab suspension and seat suspension system can attenuate the low-frequency excitation vibration energy of the road surface by more than 80 %.

Measurement Point 6 – $Z$ Coordinate (red solid line) exhibits a minor peak at 7 Hz, indicating a slight increase in vibration acceleration at this frequency. However, the most significant change occurs at 9 Hz, where the vibration acceleration reaches its maximum value, exceeding 4.5 m/s². As the frequency increases, the vibration acceleration gradually decreases, showing a downward trend.

Measurement Point 9 – $Z$ Coordinate (blue solid line) has a minor peak at 6 Hz, but the vibration acceleration is much lower than that of Measurement Point 6. It reaches a smaller peak at 9 Hz, with a vibration acceleration slightly above 1 m/s². As the frequency increases, the vibration acceleration also gradually decreases.

Measurement Point 3 – Z Coordinate (purple solid line) shows a minor peak at 7 Hz, with a vibration acceleration slightly above 1 m/s². It reaches a smaller peak at 9 Hz, with a vibration acceleration slightly below 1 m/s². As the frequency increases, the vibration acceleration gradually decreases.

Measurement Point 2 – $Z$ Coordinate (green solid line) has relatively low vibration acceleration across the entire frequency range, with minimal variation. There is a minor peak at approximately 7 Hz, but the vibration acceleration is much lower than that of the other measurement points. As the frequency increases, the vibration acceleration gradually decreases.

Overall, Measurement Point 6 has the highest vibration acceleration in the $Z$ coordinate direction, with a significant peak at 9 Hz, which may indicate that this frequency is one of the resonant frequencies of the dump truck. Measurement Points 9 and 3 have lower vibration accelerations in the $Z$ coordinate direction, with smaller peaks at 9 Hz. Measurement Point 2 has the lowest vibration acceleration in the $Z$ coordinate direction and exhibits minimal variation across the entire frequency range.

The analysis results indicate that under the excitation of the road surface, the suspension systems of this type of mining dump truck have all played a role in vibration reduction. However, the vibration reduction effect of the cab suspension system is not significant, and its vibration reduction structure needs to be optimized and improved in the future.

These analysis results are of great reference value for the vibration analysis of mining dump trucks. In particular, the significant peak of Measurement Point 6 at 9 Hz may indicate that this frequency is one of the resonant frequencies of the dump truck, which requires further analysis and treatment to avoid excessive vibration at this frequency, thereby affecting the stability and safety of the vehicle. At the same time, the variation of vibration acceleration at other measurement points also needs to be considered comprehensively to fully understand the vibration characteristics of the dump truck.

Fig. 12Vibration transmission characteristics of the mounting system

4.2.2. Analysis of Low-frequency characteristics

The amplification of low-frequency vibrations (1-3 Hz) in seat suspension systems is an important research topic because it directly affects ride comfort and passenger health. According to international standards and references [25-27], low-frequency vibrations have particularly significant physiological and psychological effects on humans. These effects are mainly manifested in the following ways:

Low-frequency vibrations can cause resonance of internal organs, leading to discomfort and even long-term health issues. They can cause fatigue in bones and muscles, resulting in muscle tension and pain. They can interfere with the human sense of balance, leading to motion sickness (such as car sickness), especially within the frequency range of 1-3 Hz. Additionally, low-frequency vibrations can significantly reduce ride comfort, causing passengers to feel uncomfortable and irritable. Long-term exposure to low-frequency vibrations may affect passengers' work efficiency and concentration, increasing the likelihood of accidents.

Based on the results shown in Figs. 9-12, the maximum vibration acceleration within the low-frequency range (1-3 Hz) is less than 0.1 m/s². Moreover, the probability of the vehicle operating within this low-frequency vibration range is relatively low. Therefore, low-frequency vibrations (1-3 Hz) are not the main factor affecting ride comfort in this experimental study.