Experimental Study of the Energy Regenerated by a Horizontal Seat Suspension System under Random Vibration

Abstract

This article introduces a novel regenerative suspension system designed for active seat suspension, to reduce vibrations while recovering energy. The system employs a four-quadrant electric actuator operation model and utilizes a brushless DC motor as an actuator and an energy harvester. This motor, a permanent magnet synchronous type, transforms DC into three-phase AC power, serving dual purposes of vibration energy recovery and active power generation. The system’s advanced vibration control is achieved through the switching of MOSFET transistors, ensuring the suspension system meets operational criteria that contrast with traditional vibro-isolation systems, thereby reducing the negative effects of mechanical vibrations on the human body, while also lowering energy consumption. Comparative studies of the regenerative system dynamics against passive and active systems under random vibrations demonstrated its effectiveness. This research assessed the system’s performance through power spectral density and transmissibility functions, highlighting its potential to enhance energy efficiency and the psychophysical well-being of individuals subjected to mechanical vibrations. The effectiveness of the energy regeneration process under the chosen early excitation vibrations was investigated. Measurements of the motor torque in the active mode and during regenerative braking mode, and the corresponding phase currents of the motor, are presented.

1. Introduction

Energy recovery systems are common solutions introduced in a wide range of current machines and devices. They allow restoring a portion of used or generated energy back for reuse. There is a variety of methods and implementations of such systems. Some of them are designed to recover wasted energy in the form of heat energy [1,2] or cooling energy [3,4] from working machinery. Others are used to harvest energy and convert it into electricity. A characteristic example includes electric turbo compound (ETC) [5,6], where fumes are converted into electricity through generators. Energy is also harvested from large human-made systems such as transportation systems. An example of obtaining vibration energy from railway lines was described in the work in [7].

Kinetic energy restore systems (KERS) [8,9] are designed to convert the kinetic energy that is usually lost during deceleration to electrical energy for further use or energy conversion systems (ECS) [10]. They are not strictly energy recovery systems but can convert energy from natural processes that would otherwise be unused, i.e., sea waves [11], geothermal heat [12], and wind [13], into usable electrical energy. In addition to obtaining energy from natural processes, it is possible to recover energy from human movement. Examples of such systems are various types of wearable devices, such as the prototypes of wristbands proposed in [14].

Many energy-recovery systems have limited applicability due to the elements with specific properties used in them. Typically, these are linear elements with high efficiency in narrow frequency bands of the system. Although the topic of energy recovery using elements with linear characteristics is a widely researched field, scientists have been trying to expand the scope of their application in recent years by introducing nonlinearity [15,16,17] into the elements of recovery systems. For example, the work in [18] used a non-ionic electromagnetic bistable system combined with a displacement amplification mechanism. Using this solution allowed the researchers to operate the system in several modes, with operating frequency ranges from 80 to 120 $\mathrm{Hz}$. The experimental results showed that the output power obtained using the electromagnetic energy harvester was 11.1 $\mathrm{mW}$, which is an average result compared to other works, but taking into account the features of the object and presenting the result in the form of power density, it achieved an impressive result of 7.51 $\mathrm{mW}/{\mathrm{cm}}^3$, which is a good result compared to other solutions based on this method.

This article focuses on harvesting energy from the braking phase of a motor, instead of losing it in uncontrolled conditions. This process is called regenerative braking [19,20,21,22] and has a wide usage in the automotive industry [23,24,25]. The studies were performed on a laboratory setup equipped with horizontal seat suspension [26,27]. The field of research of energy recovery for seat suspension systems is relatively new, but from year to year, it is gaining in popularity. Numerous research works have shown the practicality of extracting energy from car seat suspensions [28,29] using techniques such as electromagnetic, piezoelectric, and electrostatic harvesting [30,31,32]. The range of energy generated from moving seat suspension is comparatively low, varying from a few to a dozen watts. This is due to the low energy delivered to the system and the limitations of installing such a system. However, it is possible to actively control the seat suspension system at the same time, to reduce vibrations [33,34,35] from the car chassis and seat displacements, and increase the overall comfort of the operator during work. As mentioned above, the source of the forcing motion that allows for energy extraction and active control [36,37] are vibrations. These are oscillations that occur around an equilibrium point and are divided into periodic [38] or random [39]. In the machine industry, these vibrations often lead to unwanted results. Their negative impact results in accelerated machine wear, causing damage to the machine equipment that in effect may lead to the suspension of processes. In the automotive field of research, they can act as excitations simulating the actual impact on the vehicle or its components. However, excessive vibrations can lead to dangerous resonances, which can for example amplify the vibrations transmitted through the vehicle seat suspension system, harming the userś health and comfort.

Driver’s seat suspension systems are used in vehicles and can be divided into three main types: passive, semi-active, and active. Passive seat suspension systems are characterized by the simplest design based on springs and mechanical shock absorbers. The springs absorb shock energy and shock absorbers dampen spring movement to prevent excessive oscillation. The advantages of such suspensions are low cost, simple construction, reliability and the fact that they do not require complicated maintenance. However, the biggest disadvantage of such solutions is the constant damping and stiffness properties, which means that their effectiveness is limited in various road conditions, such as with variable amplitude, frequency of excitations, and loads related, for example, to the individual characteristics of the driver. Semi-active seat suspension systems are characterized by a structure based on conventional springs, but using shock absorbers with variable damping characteristics and often electronically controlled. These systems can adjust the damping levels in real time in response to changing road conditions. They can use various technologies, such as magnetorheological fluids or electromechanical valves in the shock absorbers. The advantage of these solutions is better adaptation to changing road conditions compared to passive systems, as well as increased driving comfort and reduced driver fatigue. However, they have disadvantages apart from higher costs than passive systems, and need power and a more advanced maintenance.

Active systems, on the other hand, are characterized by using actuators to actively control the seat position and a much better adaptation to changing working conditions than semi-active systems. These systems can actively counteract vibrations and shocks by generating forces opposite to those coming from the surface on which the vehicle or machine is moving. They are controlled using advanced algorithms and sensors that monitor vehicle and seat movements. Their advantage is the best comfort and vibration isolation. Adaptable to a wide range of driving conditions and loads, they maximally reduce driver fatigue and improve comfort thanks to effective vibration damping and the ability to control the seat position. This strategy is not possible in the case of passive and semi-active systems. Another advantage is the ability to recover part of the energy from the system. Unfortunately, the disadvantages are the very high cost and a complicated design. They require regular and professional maintenance and a power supply.

Therefore, there is a need to protect drivers and operators using active vibration reduction systems such as the one presented in the following article. The active element that generates opposing force in the system is a brushless DC motor [40]. These are a pivotal component in numerous applications due to their high efficiency, reliability, and compactness. They use electronic commutation, eliminating the need for brushes that wear out and generate acoustic noise. The precise control of the current in the windings, often achieved through advanced control algorithms [41,42], provides accurate torque and speed control, making BLDC motors suitable for applications ranging from automotive [43,44] to industrial machinery [45,46]. However, despite their advantages, the cogging torque and the torque ripple are challenging disadvantages.

This article presents and analyses an original method of controlling a vibration reduction system with energy recovery called the regenerative suspension system. This system is introduced into active seat suspension. In Section 2, the physical model of a seat suspension system with active control and an energy harvesting strategy, based on the four-quadrant operation of an electric actuator, is presented. The work found in [47] delves into the intricacies of a physical and mathematical model for a suspension system designed to harvest energy. It elucidates the underlying mechanics, the strategies for controlling the system, and its primary uses. This innovative approach is noted for its dual benefits: it not only conserves energy but also enhances the comfort of passengers. The research presents a comprehensive analysis of this novel concept, highlighting its significance in the advancement of sustainable automotive technologies. In Section 3, the hardware implementation is described. An actuator in the form of a brushless motor that uses a direct current (DC) power supply (BLDC) was chosen. This BLDC motor is a permanent magnet synchronous motor that converts a DC power source into a three-phase AC power source. This type of device is used as an actuator obtaining (recovering) vibration energy, and at the same time as an active power source. Thanks to the advanced vibration control system, based on the process of switching MOSFET 112 transistors described in Section 3, the desired suspension system functionality was achieved. Section 4 shows that it is possible to achieve the desired operational properties for the suspension system with the corresponding criteria set for modern vibro-isolation systems, thus significantly reducing the harmful impact of mechanical vibrations on the human body, with reduced energy demands. In Section 5, investigations of the regenerative system dynamics, in comparison to passive and active types, under random vibrations are presented. The research presented in this section explored the system efficiency and feasibility. The integration of energy recovery mechanisms into active systems is a promising approach to enhance energy efficiency and meet environmental standards. These systems, which can include energy recovery, are pivotal for reducing energy consumption and emissions, thereby supporting a sustainable future. Moreover, the consideration of psychophysical health in the design of such systems ensures that the well-being of drivers, operators, and passengers is maintained, promoting a holistic approach to energy management and human health. To show the efficiency of the different systems, measurements of power spectral densities and transmissibility functions of the passive, active, and regenerative suspension systems in the case of three excitation signals are compared. In Section 6, the effectiveness of the energy regeneration process under the chosen ISO standard is investigated. Measurements of the motor torque in the active mode, the duty cycle of the PWM during regenerative braking mode, and the corresponding phase currents of the motor are presented.

2. Horizontal Seat Suspension System with Active Control and Energy Harvesting Operating Principle

A physical model of a horizontal seat suspension system with an active control mode, as well as energy harvesting device, is shown in Figure 1a. The passive system consists of two tension springs working in opposite directions, which is beneficial to establish a static equilibrium position for a seat suspension that is loaded by the human body. A hydraulic damper is employed in order to reduce the resonant vibration amplitude of the passive system. Such a system works in the presence of low-friction forces, due to the use of needle bearings in the suspension mechanism. Moreover, the seat suspension has end-stop buffers installed that provide movement within a limiting maximum displacement of the suspension mechanism. The active system includes an induction motor for active vibration control (motor power mode) and for energy harvesting (regenerative braking mode).

In Figure 1b, in the first quadrant (Motoring Mode), the motor is driving the load in the forward direction. Both the torque and the speed are positive, meaning the motor is providing power to move the load forward. In the second quadrant (Regenerative Braking Mode), the motor is still rotating in the forward direction, but the torque is negative. This means the motor is acting as a generator, converting kinetic energy back into electrical energy, which can be fed back into the power supply. In the third quadrant (Reverse Motoring Mode), the motor is driving the load in the reverse direction. Both the torque and the speed are negative, meaning the motor provides power to move the load backward. In the fourth quadrant (Reverse Regenerative Braking Mode), the motor is rotating in the reverse direction, but the torque is positive. Similarly to the second quadrant, the motor acts as a generator, converting kinetic energy into electrical energy while moving in reverse.

The four-quadrant operation of an electric actuator during motoring and braking is illustrated in Figure 1b. The energy harvesting is only realized when the desired active force $F_{\mathrm{a}}$ has a sign opposite to the relative velocity $\dot{x}-{\dot{x}}_{\mathrm{s}}$ of the suspension system (where $\dot{x}$ is the velocity of input vibration and ${\dot{x}}_{\mathrm{s}}$ is the velocity of input vibration). In other conditions, the vibration reduction system works in the mode of powering the motor from an external energy source. As shown in this figure, in the first (1st) and third (3rd) quadrants of the coordinate system, the active force $F_{\mathrm{a}}$ and the velocity $\dot{x}-{\dot{x}}_{\mathrm{s}}$ have the same signs and the system operates in motoring mode:

$$\begin{array}{c}\hfill {\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}=\left\{\begin{array}{ccc}-k_1\dot{x}-k_2(x-x_{\mathrm{s}})\hfill & \mathrm{for}\hfill & {\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}·(\dot{x}-{\dot{x}}_{\mathrm{s}})>0\leftarrow \mathrm{motoring}\hfill \\ 0\hfill & \mathrm{for}\hfill & {\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}·(\dot{x}-{\dot{x}}_{\mathrm{s}})\le 0\leftarrow \mathrm{braking}\hfill \end{array}\right.\end{array}$$

(1)

where $x_{\mathrm{s}}$ is the displacement of input vibrations, x is the displacement of the isolated body, $k_1$ is the controller setting of the absolute velocity feedback loop, $k_2$ is the controller setting of the relative displacement feedback loop, and ${\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}$ is the desired active force to be generated by the induction motor.

However, in the (2nd) and (4th) quadrants, the desired active force $F_{\mathrm{a}}$ and relative velocity $\dot{x}-{\dot{x}}_{\mathrm{s}}$ of the suspension system have signs opposite to each other, which allows converting the kinetic energy of an induction motor coupled with the mechanical load into electrical energy (regenerative braking mode). The PWM (pulse width modulation) signal corresponding to regenerative braking of a motor is defined as follows:

$$\begin{array}{c}\hfill {\left(\mathrm{PWM}\right)}_{\mathrm{set}}=\left\{\begin{array}{ccc}0\hfill & \mathrm{for}\hfill & {\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}·(\dot{x}-{\dot{x}}_{\mathrm{s}})\ge 0\leftarrow \mathrm{motoring}\hfill \\ max\left[0,min\left(\left|{\displaystyle \frac{{\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}}{\dot{x}-{\dot{x}}_{\mathrm{s}}}}\right|,k_{\max }\right)\right]\hfill & \mathrm{for}\hfill & {\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}·(\dot{x}-{\dot{x}}_{\mathrm{s}})<0\leftarrow \mathrm{braking}\hfill \end{array}\right.\end{array}$$

(2)

where $k_{\max }$ is the value representing the maximum braking force of an induction motor in the regenerative phase. The value of ${\left(\mathrm{PWM}\right)}_{\mathrm{set}}$ represents the percentage duty cycle of the PWM signal (as an input to the electronic equipment), which means if the ${\left(\mathrm{PWM}\right)}_{\mathrm{set}}=0\%$, then no regenerative braking is created by the motor. In turn, if the ${\left(\mathrm{PWM}\right)}_{\mathrm{set}}=100\%$, then the maximum braking is applied, whereas values in the range 0–100% allow for a continuous adjustment of the braking force according to Equation (2). Numerical values of the constant parameters occurring in the vibration control algorithm (Equations (1) and (2)) are listed in

Table 1. Numerical values of constant parameters occurring in the vibration control algorithm.

Active Control Mode			Regenerative Braking Mode
Parameter	Value	Unit	Parameter	Value	Unit
$k_1$	2100	Ns/m	$k_{\max }$	3000	Ns/m
$k_2$	6000	N/m

.

The values of the control settings $k_1$ and $k_2$ correspond to the intensity of vibration reduction ($k_1$) and conform to the limitation of suspension travel ($k_2$). A trade-off between these values exists, and their selection can be treated as a multi-objective optimization problem. The values in Table 1 represent the first estimation of such a trade-off to be realized by the active seat suspension. Successively, the value $k_{\max }$ is related to the maximum braking force that should be generated by a specific motor type, together with an energy recovery subsystem.

3. Hardware Implementation

To generate an active force, a brushless three-phase electric motor (BLDC) cooperates with the system for harvesting energy from mechanical vibrations (Figure 2). The switching of the BLDC motor from the active mode to regenerative braking mode is achieved by connecting braking resistors to the motor phases. The additional introduction of a buffer composed of super-capacitors enables the storage of energy released during braking of the electric motor and its reuse in the subsequent control process. Based on the set value of the analog regenerative braking signal (from the system controller), this signal is converted into a digital form (PWM duty cycle), to then pass through a galvanic isolation system, as the ground of the MOSFET transistor system must be galvanically separated from the controller and the BLDC motor controller.

The obtained digital PWM duty cycle control signal is subsequently used to control the MOSFET transistor drivers. Based on these signals, the process of switching MOSFET transistors and the associated regenerative braking process, based on short-circuiting the motor phases through a system containing resistors, results in the braking of the BLDC motor and the generation of currents between windings (phase of energy recovery from mechanical vibrations). To assess the efficiency of the proposed strategy for vibration energy recovery, a system with braking resistors of specific resistances whose parameters were selected during the optimization process and directly impact the braking force of the system was connected to the three power phases of the motor. The current induced in the motor windings during regenerative braking was recorded using current intensity sensors that utilized the Hall effect, which allowed evaluating the power dissipated in the individual windings of the BLDC motor.

The MOSFET switches $T_1$, $T_2$ and $T_3$ (Figure 3) are integral to the motor phase disconnection system. Each MOSFET transistor in the energy recovery system, $T_{R1}$, $T_{R2}$, and $T_{R3}$, is connected in series with a power resistor (for energy dissipation), while each MOSFET switch, $T_{C1}$, $T_{C2}$, and $T_{C3}$, is connected in series with a capacitor (for energy storage). During the active control phase, the MOSFET transistors $T_1$, $T_2$, and $T_3$, which link the motor phases to the controller, are activated, allowing for continuous active control of the BLDC motor’s operation. Simultaneously, the MOSFET transistors $T_{R1}$, $T_{C1}$, $T_{R2}$, $T_{C2}$, $T_{R3}$, and $T_{C3}$, which are part of the energy harvesting circuit subsystem, are deactivated. In the energy recovery phase, the transistors $T_1$, $T_2$, and $T_3$ are turned off, disconnecting the motor windings from the primary BLDC controller. At the same time, the transistors $T_{R1}$, $T_{C1}$, $T_{R2}$, $T_{C2}$, and $T_{R3}$, $T_{C3}$, located behind the three-phase rectifier system, can be engaged. This will short-circuit the motor windings through a system of resistors or capacitors, leading to motor braking and redirecting electrical energy to the capacitors. The electrical energy stored in the capacitors can then be transferred and used by other electrical systems.

4. System Performance Measurements

Performance measurements of the regenerative system are carried out using measurements of parameters important in both phases of its operation. As stated above, the active force is measured in the motoring phase in order to determine the motor capacity for reducing vibration. In the phase of energy regeneration, the braking force and electric current flow in the motor windings are identified. It should be noted that these tests do not take into account the particular seat load, but only the appropriate parameters at the input of the subsystem responsible for the motoring phase, i.e., ${\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}$ and the subsystem responsible for the braking phase, i.e., ${\left(\mathrm{PWM}\right)}_{\mathrm{set}}$.

In Figure 4, the experimental setup for measuring the force generation efficiency in the motoring phase is shown. In the motor BLDC, an electric actuator generates the active force $F_{\mathrm{a}}$, which is directly related to the electromagnetic torque $T_{\mathrm{e}}$ of the motor. The active force $F_{\mathrm{a}}$ in the system is produced by the currents $i_{\mathrm{a}}$, $i_{\mathrm{b}}$, and $i_{\mathrm{c}}$ flowing through the three-phase windings of a stator. The resulting force coming from the electric actuator is measured by the force sensor shown (Figure 4). In a real seat suspension system, the currents need to have values that allow reducing unwanted seat vibrations. The model and formulation for $F_{\mathrm{a}}$ in relation to the phase currents $i_{\mathrm{a}}$, $i_{\mathrm{b}}$, $i_{\mathrm{c}}$ are presented in [47].

In the study carried out using the system shown in Figure 4, the servo-drive was controlled by an active force ${\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}$ with a constant value. These values were in a range from 0 to 150 N, in steps of 50 N. Then, for the forcing of the displacement $x_{\mathrm{s}}$, changing according to a triangular wave with an amplitude of 0.015 m, the actual force generated by the BLDC motor was measured. For displacements $x_{\mathrm{s}}$ in positive directions, the force ${\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}$ should have a positive sign, because it is directed according to the displacement. In this way, the efficiency and force-generating capabilities of the system operating in the active phase were tested.

The graphs in Figure 5a present the actual forces measured when the forcing $x_{\mathrm{s}}$, i.e., the displacement of the vibration platform, was in the negative direction for subsequent values of the desired force ${\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}$. As can be seen, up to the value of −150 N, the system in the active phase was able to generate forces of one of these orders. This was not the exact value of ${\left(F_{\mathrm{a}}\right)}_{\mathrm{des}}$, but a hysteresis covering the particular control value over the entire range of displacements. The system exhibited the same properties in the case of displacements in the positive direction and for the desired forces up to 150 N, as shown in Figure 5b. The force hysteresis shown in this figure was mainly caused by the frictional losses of the suspension mechanism during its oscillatory movement, i.e., friction of rollers and bearings in the system.

The braking phase of a regenerative system is a critical operation where the kinetic energy of an induction motor, which is coupled to a mechanical load, is converted into electrical energy. Equation (2) describes the control algorithm that manages this energy transfer, ensuring that the transition between mechanical and electrical subsystems is smooth and effective. Such algorithms are essential for optimizing the performance and energy efficiency of regenerative systems. In this phase, the system used the electric actuator in the generator mode and was tested using the experimental setup shown in Figure 6.

In this case, the performance and capabilities of the system were assessed depending on the duty cycle of the PWM signal controlling the MOSFET transistor system, as shown in Figure 2. The regenerated currents ${\left(i_{\mathrm{a}}\right)}_{\mathrm{reg}}$, ${\left(i_{\mathrm{b}}\right)}_{\mathrm{reg}}$, and ${\left(i_{\mathrm{c}}\right)}_{\mathrm{reg}}$ in the BLDC motor windings and actual forces were measured when sinusoidal excitation $x_{\mathrm{s}}$ was applied with a constant amplitude but different frequencies. Therefore, in this case, the system velocity varied over time, unlike the previous study for the triangular signal. Here, the velocity was the second parameter, along with the PWM duty cycle.

Figure 7 shows the performance results in the form of the maximum values of the braking force generated by the motor, regenerated currents, and the power obtained in this phase. The intuitively recognized relationship was correct, which shows that the greater the duty cycle and the excitation velocity, the greater the braking force, the current in the motor windings, and, therefore, the power obtained. This also shows that the amount of energy obtained depends on the type of excitation and the suspension control algorithm, as evidenced by the almost linear dependence on the velocity.

5. Investigation of Regenerative System Dynamics under Random Vibrations

Measurements and assessments of the system’s operation were performed on the basis of acceleration signals of the two main elements of the experimental setup system shown in Figure 8. The first element was the base platform on which the seat was mounted via the suspension system. The random signal created and simultaneously measured on the platform represented the excitation generated by road unevenness on which a specific type of vehicle/machine was moving. These signals had been previously measured in the cabins of selected working machines and were then reproduced by the electro-hydraulic shaker under laboratory conditions. They were considered as the input vibrations for generating the oscillatory motion of the horizontal seat suspension system. The dynamic characteristics of such random signals represent the whole-body vibration acting on drivers in the longitudinal direction. The second acceleration signal was measured directly at the seat. Vibrations related to the seat were transferred directly to the driver’s body. These were considered as the output vibrations. The power spectral density (PSD) and the transmissibility function were selected to assess the vibration transmission in the system. Here, power spectral density is a fundamental concept used in signal processing to measure the distribution of the average signal power over different frequency components.

PSD represents the power content of a signal as a function of frequency. It provides insights into how the signal’s strength is distributed across different frequencies. By detailing this function, you can start with a continuous-time power signal $y\left(t\right)$, defined as $y\left(t\right)=x{\left(t\right)}^2$, where $x\left(t\right)$ is the acceleration signal, in this case, for the time-averaged interval $\tau$ satisfying the dependency $\left|t\right|<{\displaystyle \frac{\tau }{2}}$. Now, the energy of both signals can be assessed in the time and frequency domains (Fourier domain).

The energy of the power signal $y\left(t\right)$ can be expressed as $E={\int }_{-\infty }^{\infty }{\left|y\left(t\right)\right|}^{2}dt$. In the Fourier domain, this is $E={\displaystyle \frac{1}{2\pi }}{\int }_{-\infty }^{\infty }{\left|Y\left(\omega \right)\right|}^{2}d\omega$. If the signal is defined within the range $-{\displaystyle \frac{\tau }{2}}$ to ${\displaystyle \frac{\tau }{2}}$ in the time domain, then the previous formulas can be expressed as ${\int }_{-\infty }^{\infty }{\left|y\left(t\right)\right|}^{2}dt={\int }_{-{\displaystyle \frac{\tau }{2}}}^{{\displaystyle \frac{\tau }{2}}}{\left|x\left(t\right)\right|}^{2}dt$. In the Fourier domain, this is ${\int }_{-{\displaystyle \frac{\tau }{2}}}^{{\displaystyle \frac{\tau }{2}}}{\left|x\left(t\right)\right|}^{2}dt={\displaystyle \frac{1}{2\pi }}{\int }_{-\infty }^{\infty }{\left|Y\left(\omega \right)\right|}^{2}d\omega$. The total signal power $P_{\mathrm{t}}$ is defined as the total energy transferred per unit time interval $\tau$ as $P_{\mathrm{t}}\left(\omega \right)={\displaystyle \frac{1}{2\pi }}{\int }_{-\infty }^{\infty }{\displaystyle \frac{{\left|Y\left(\omega \right)\right|}^2}{\tau }}d\omega$. The PSD for a signal $x\left(t\right)$ can be expressed mathematically as $S\left(\omega \right)={lim}_{\tau \to \infty }{\displaystyle \frac{{\left|X\left(\omega \right)\right|}^2}{\tau }}$. To assess the energy flow in a system, PSD exhibits excellent information features.

On the other hand, transmissibility is a concept used in the field of vibration analysis and quantifies how efficiently a signal is transmitted through a system. It represents the ratio of the energy transmitted from the vibrating platform to the seat. Transmissibility is the ratio of output to input. First, the spectral distribution of energy in the signals used as input (excitation on a vibration platform) was assessed using the PSD. The results are presented in Figure 9. These are random signals selected as follows: a signal similar to white noise (Figure 9a), a signal representative of an agricultural tractor (Figure 9b), and a signal representative of a wheel loader (Figure 9c).

As follows from the analysis of the presented PSD waveforms, the largest frequency range of the excitation signal covered the first waveform, which was similar to the white noise signal. It was generated in the range from 0 to 20 Hz, with most signal power and averaged maximum value 0.3082 ${(\mathrm{m}/{\mathrm{s}}^2)}^2/\mathrm{Hz}$ contained in the range from 0.5 to 15 Hz. The mean value of this type of signal was about 0.1243 ${(\mathrm{m}/{\mathrm{s}}^2)}^2/\mathrm{Hz}$. It was coded with the name WN2. The second representative of an agricultural tractor was coded with the name AT4. It was also generated in the range from 0 to 15 Hz, with most signal power and the maximum value of 1.78 ${(\mathrm{m}/{\mathrm{s}}^2)}^2/\mathrm{Hz}$ contained in the narrow range of frequencies from 1.3 to 4.2 Hz. The mean value of this type of signal was 0.1729 ${(\mathrm{m}/{\mathrm{s}}^2)}^2/\mathrm{Hz}$ within the whole frequency range. The third excitation representative of a wheel loader was coded with the name WL1. It was also generated in the range from 0 to 4 Hz, with most signal power and the maximum value 7.25 ${(\mathrm{m}/{\mathrm{s}}^2)}^2/\mathrm{Hz}$ contained in a very narrow range of frequencies from 0.6 to 1.8 Hz. The mean value of this type of signal was 1.0637 ${(\mathrm{m}/{\mathrm{s}}^2)}^2/\mathrm{Hz}$ within the whole frequency range. The particular frequency window illustrated in Figure 9 was chosen according to the vibration content measured in the selected working machines. The frequency domain data are only shown in the ranges where the vibration amplitudes occurred. Beyond these ranges, only low measurement noise can be observed.

Due to the specific design of the tested seat suspension systems, i.e., passive, active, and energy regenerative, there were slight differences in the values of the PSD function for each type of excitation. The shape of these functions was the same, which means that the frequency ranges for each type of excitation were identical and the values were very similar and comparable.

In the following stage of research, the spectral distribution of energy in the signals used as output (signal measured at the seat) was assessed using both PSD and the transmissibility function. The output signal was measured for a specific seat load case. This was a situation where the seat was occupied by a mass load of 60 kg. The results are presented in Figure 10. These are PSD functions of the output signal, which were generated under random excitation signals similar to white noise, respectively, in Figure 10a, for an input signal representative of an agricultural tractor Figure 10c, and for an input signal representative of a wheel loader Figure 10e. Accordingly, for the same extortions, the transmissibility functions are presented in the following figure: Figure 10b,d,f. In

Table 2. Mean and maximal PSD values of the passive, active, and regenerative suspension system at a mass load of 60 kg.

	Horizontal Seat Suspension—PSD
	Passive		Active		Regenerative
Input	MEAN	MAX	MEAN	MAX	MEAN	MAX
Vibration	(%)	(%)	(%)	(%)	(%)	(%)
WN2	0.0666	0.4866	0.0280	0.1396	0.0469	0.1575
	54%	158%	23%	45%	38%	51%
AT4	0.1455	3.2978	0.0371	0.6346	0.0694	1.1125
	84%	185%	21%	36%	40%	63%
WL1	1.8717	12.0186	1.4459	8.9734	1.2886	8.5376
	176%	166%	136%	124%	121%	118%

, the effectiveness of operation, as the ability to dissipate vibration energy transferred to the driver’s seat, for the different types of suspension is calculated based on the parameters of the PSD function of the input signals (vibration platform) and output signals (seat). Two parameters were taken into account for the analysis of effectiveness: the mean and maximum values of the PSD function on the seat. The MEAN and MAX columns in Table 2 show the mean and maximum values of the PSD function for the suspension types (passive, active, and regenerative) with specific types of excitation (WN2, AT4, and WL1), respectively. The percentage values show how much vibration energy was dissipated (values less than 100%) or not dissipated (values greater than 100%) in relation to the average and maximum PSD values of the input signal. The average values represent the general property of the suspension type in dissipating vibration energy, while the maximum values indicate that the suspension does not tend to generate resonances. This property is particularly useful for evaluation in the case of excitations in a narrow frequency range.

The analysis of the results presented in Table 2 indicated the dependence of the vibration energy dissipation properties of the seat suspensions on their type and the excitation. Based on these results, the following gradation of suspension effectiveness could be developed. In the case of the WN2 broadband excitation with low PSD values, the order from the most effective to the least effective was as follows: active, regenerative, passive. In the case of the AT4 with a narrower frequency band and average PSD values, the order was the same: active, regenerative, passive. In the case of the WL1, with a very narrow frequency band and large PSD values, the order was as follows: regenerative, active, passive. The exact frequency ranges and the relative effectiveness of the individual suspension systems can be seen and can be read from the transmissibility function waveforms presented in Figure 10b, d, and f, for the WN2, AT4, and WL1 excitations, respectively. The transmissibility function, as the ratio of the PSD of the output to the input, gave uninterpretable results if the PSD function of the input was equal to zero, or was digitally assumed to be zero. Therefore, the analysis of these functions should be performed in the range where the input signal PSD is different from zero. If the transmissibility function takes values less than zero, this means that the suspension system is dissipating the excitation energy. The smaller it is than unity, the more energy is dissipated.

Figure 10b (WN2 excitation) shows that the passive suspension system had poor energy dissipation properties at low frequencies (up to approximately 3 Hz). Such undesirable behavior occurs at low frequencies, due to the well-known resonance phenomena of passive suspension systems. This phenomenon is noticed when the frequency of input vibration is close to the natural frequency of suspension systems at a given mass load. Hence, the vibration amplitudes measured on the seat were higher than the amplitudes of the input vibration. At higher frequencies, the passive system was even better than the active and regenerative systems. Figure 10d (AT4 excitation) shows that the evaluation of the properties of the above suspension systems was similar. For the frequency range in which most of the excitation energy was concentrated, the passive system exhibited resonant properties, which means that it dissipated practically no energy. In this range and above the frequency of 3 Hz, the active system was relatively the most effective. Figure 10e (WL1 excitation) shows that for very high energy excitations, all systems were efficient. The transmissibility function had values practically above unity in all cases. The regenerative system was the most effective here.

Finally, two additional normative factors were selected for the effectiveness analysis. The first was the he seat effective amplitude transmissibility (SEAT) factor [48], which measured the seat insulation effectiveness (dissipative capability).The next factor was the suspension travel, which was correlated to the dynamic reaction of the seat. When the SEAT factor achieved values higher than 1, the vibrations transmitted to the seat were amplified in comparison to the excitation signal. SEAT is similar to the transmissibility function. The results of the above measurements are presented in the

Table 3. Experimental data presenting the SEAT factor and suspension travel of the system under investigation at a mass load of 60 kg.

	Horizontal Seat Suspension-SEAT, Displacement
	Passive		Active		Regenerative
Input	SEAT	Suspension	SEAT	Suspension	SEAT	Suspension
Vibration	Factor	Travel	Factor	Travel	Factor	Travel
WN2	1.116	33.7 mm	0.626	36.6 mm	0.727	36.5 mm
AT4	1.260	37.3 mm	0.587	32.0 mm	0.745	31.6 mm
WL1	1.325	42.2 mm	1.145	43.6 mm	1.078	44.3 mm

.

6. Effectiveness of the Energy Regeneration Process under Random Vibrations

Next, important parameters describing the characteristics of the regenerative seat suspension were collected under different excitation signals (Figure 11). They were the same vibration signals as in the case of the investigation of the regenerative system dynamics, where regenerative, active, and passive suspension systems were compared. Figure 11a,c,e show the desired torque ${\left(T_{\mathrm{e}}\right)}_{\mathrm{des}}$ generated during the motoring phase, as well as the duty cycle ${\left(\mathrm{PWM}\right)}_{\mathrm{set}}$ in motor braking mode. Figure 11b,d,f indicate the regenerated phase currents ${\left(i_{\mathrm{a}}\right)}_{\mathrm{reg}}$, ${\left(i_{\mathrm{b}}\right)}_{\mathrm{reg}}$, ${\left(i_{\mathrm{c}}\right)}_{\mathrm{reg}}$ in the BLDC motor windings. In these figures, the braking periods are marked with white vertical stripes along the selected 1.2 s time sample. Successively, the pink stripes indicate the regenerative period, i.e., the braking periods.

In Figure 11a,c,e, the desired motor torque ${\left(T_{\mathrm{e}}\right)}_{\mathrm{des}}$ and the ${\left(\mathrm{PWM}\right)}_{\mathrm{set}}$ indicate that the motor torque was zero in the energy regeneration phase (pink strips) contrary to the PWM. However, in this range, ${\left(\mathrm{PWM}\right)}_{\mathrm{set}}$ increased the duty cycle percentage so that the lowest values were found in the case of the WN2 excitation and visibly larger for WL1. For all types of excitation in the ranges marked by white strips, the maximum torque level was comparable in value. On the other hand, in these ranges, the ${\left(\mathrm{PWM}\right)}_{\mathrm{set}}$ was zero. As expected, if ${\left(\mathrm{PWM}\right)}_{\mathrm{set}}$ increased the duty cycle percentage, the current flowing in the motor windings also increased. This can be demonstrated by the current values shown in Figure 11b,d,e. The current intensity increased from WN2 to WL1. All these facts confirm the validity of the regenerative system and the correct operation of its hardware implementation.

The final calculations regarding the energy obtained for individual cases of excitation signals showed that the most energy was obtained in the case of the WL1 excitation. The instantaneous values of the recovered power and the root mean square (RMS) value are shown in Figure 12a,b,c, for WN2, AT4, and WL1 excitations, respectively.

Energy harvesting from vibration isolation systems of seats suspensions involves capturing and converting only small amounts of energy generated by mechanical vibrations during driving. The efficiency of this process is crucial, because it determines how much of the available mechanical energy can be converted into useful electrical power.

7. Conclusions

As the above analyses show, active and regenerative suspension systems are definitely more effective than passive systems. On the other hand, both require external energy to generate an additional active force in the appropriate suspension operating ranges. The regenerative suspension system represents a significant advancement in automotive technology, simultaneously focusing on energy efficiency and improved passenger comfort. By integrating a BLDC alternating current synchronous motor, this system not only acts as an actuator to control vibrations, as is realized in active mode, but also recovers energy, transforming it into a valuable resource rather than letting it dissipate as waste. This study’s findings reveal a clear dependency of vibrational energy dissipation in seat suspensions on their design and the type of excitation applied. The research categorized suspension systems based on their effectiveness under different conditions. For broad frequency excitation with a low power spectral density (PSD), active suspensions outperform regenerative and passive types. This ranking remains consistent under mid-range frequency excitation. However, for narrow frequency excitation with high PSD, regenerative suspensions take the lead. The seat effective amplitude transmissibility (SEAT) factor and the suspension travel are critical metrics in evaluating the performance of vehicle seats, especially in terms of vibration absorption and passenger comfort. Analyzing the values of these factor for the tested seat suspensions in the case of WN2, AT4, and WL1 excitations confirmed the results obtained using the PSD measure.

The dynamics of regenerative seat suspension systems are intricate, involving the careful calibration of motor torque and PWM settings to optimize the energy regeneration during different excitation conditions. The interplay between the desired motor torque and PWM duty cycle is crucial, especially during energy regeneration periods, where maintaining zero motor active torque is essential. Adjustments to the PWM duty cycle directly influence the current in the motor windings, which is a critical factor in managing the system’s efficiency across various excitation types. This delicate balance ensures that the suspension system can effectively harvest energy, while providing the necessary vibration isolation properties. The final calculations regarding the energy obtained for individual cases of forcing signals showed that the most energy could be obtained in the case of WL1 for the regenerative system.

The concept of regenerative seat suspension systems in vehicles is a forward-thinking approach to energy efficiency. However, at the 0.25 W level, the energy recovery was minimal, highlighting a significant shortcoming in the current technology. Research suggests that, while the idea holds promise, there is a need for further innovation to enhance the energy recovery rate to make this a viable solution for power efficiency in vehicles.

Effective energy harvesting in vibratory systems can be accomplished through the integrated design of a passive suspension combined with an embedded vibration control system that employs an energy-regenerative actuator (active system). The system’s optimal non-linear characteristics will enable effectively reducing vibration amplitudes, while the harvesting of vibration energy will be achieved through electromagnetic induction.