STUDY OF A HORIZONTAL SEAT SUSPENSION WITH A MODEL OF THE SEATED HUMAN BODY AND ENERGY RECOVERY BRAKING SUBSYSTEM 1

This article explains the mechanics, control strategies and main applications of a new concept which achieves a balance between energy saving and driver comfort. A physical and mathematical model of a suspension system with energy recovery is presented. It shows practical implementation of the BLDC braking system with energy recovery in a horizontal seat suspension and a detailed simulation analysis of their features and performance. The research involves a speciﬁc solution, with a speciﬁc BLDC motor, and experimental tests on a laboratory stand. The results of the simulation study using a simpliﬁed biomechanical model and experimental studies with human participation are presented.


Introduction
One of the major challenges facing the world today is the energy crisis, which affects various sectors and regions.To address this issue, researchers are exploring new ways of storing and converting electricity which are more efficient and eco-friendlier.Some of the current research topics include developing better batteries (Zhang et al., 2022), reducing power consumption (Farghali et al., 2023), and implementing energy recovery systems (ERS) (Cipoletta et al., 2021;Alhajri et al., 2021).The ERS is mainly designed for the automotive industry (Gabriel-Buenaventura and Azzopardi, 2015; Bravo et al., 2018;Salman et al., 2018) and aims to convert some of kinetic energy into electrical energy.This allows one to power small devices such as sensors and microcontrollers, support the main power source, or store the recovered energy, which helps to lower operational costs.Such a process is called the energy harvesting.
The energy harvesters are devices that can capture and convert different forms of energy into electricity.They are often associated with renewable energy sources, such as solar, wind, thermal and geothermal energy.These sources are widely used in outdoor environments, but they depend on the availability and intensity of natural phenomena (Muscat et al., 2022;Mescia et al., 2014;Sudevalayam and Kulkarni, 2011).Another type of energy harvesters is based on mechanical vibrations, which are ubiquitous in indoor environments, where many machines and devices operate.These harvesters use transducers that transform kinetic energy of vibrations into electrical energy.Such transducers can be classified into three main categories: piezoelectric, electrostatic and electromagnetic, depending on the physical principle of their conversion process.
Piezoelectric vibrational energy harvesters have attracted a lot of interest in the recent years, and they have been applied in various fields, such as automotive, biomechanics, human body motion, architecture and construction engineering.These harvesters exploit the piezoelectric effect which is the generation of an electric potential by a material when it is subjected to a mechanical strain.The piezoelectric material deforms when it is exposed to vibrations, and this creates a charge imbalance that produces voltage (Hu et al., 2013).However, piezoelectric harvesters have a limitation in their frequency range, as they work best at frequencies above 1 kHz, while most environmental vibrations are in the range of 1 Hz-100 Hz (Halm et al., 2016).Therefore, piezoelectric harvesters need to be tuned to match the frequency of the vibration source (Priyn et al., 2017).However, mechanical vibrations generated by technical devices, such as engines, can become a source of energy for these transducers.
Piezoelectric harvesters are devices that convert mechanical vibrations into electrical energy.They have benefits of being self-powered, producing relatively high voltage, having small size, and having a high efficiency of energy conversion.However, piezoelectric materials have some drawbacks, such as variable power output over time, which affects their performance (Fastier--Wooller et al., 2022), and possible damage due to brittleness of the material (Matak, 2013;Beeby et al., 2006).Electrostatic transducers are devices that generate voltage by changing their internal capacitance under an applied force (Zhu et al., 2010b).Electrostatic technology includes electret-based vibration energy harvesting using MEMS, which are micro-scale mechanical systems, and triboelectric energy harvesting (Toshiyyoshi et al., 2019).Electrostatic transducers usually need a high-voltage power source or an electret, which is a material that has a permanent electric charge or dipole polarization, to create strong electric fields that drive the electric current, which makes these systems more complex (Zhu et al., 2010a).Moreover, since the gap between capacitor plates or surfaces is typically in a millimetre range, they are not suitable for higher amplitude vibrations without an additional system that adapts the input vibration motion to the appropriate amount of amplitude (Beeby et al., 2006).
Electromagnetic vibrational energy harvesters (EVEH) are devices that convert low--frequency vibrations into electrical power using the principle of electromagnetic induction.They have a simple structure and can operate in various environments, which makes them attractive for many applications (Araujo and Nicoletti, 2015).For example, EVEH can be used to power wireless sensors, wearable devices, biomedical implants, or environmental monitoring systems.The basic mechanism of EVEH is that a magnet moves relative to a coil and induces an electric current according to Faraday's law (Bouendeu et al., 2011).Another way to achieve electromagnetic energy conversion is by using inverse magnetostrictive materials which change their magnetization state when subjected to mechanical stress.By applying a bias magnetic field with permanent magnets, the strain-induced magnetic flux variation can be captured by a coil and converted into electricity (Akinaga, 2020;Ueno, 2019).Moreover, some vibration energy harvesters combine piezoelectric and electromagnetic effects to enhance their performance.Depending on their configuration, they can be classified into mono-stable, bi-stable, multi-stable, magnetic-plucking (contactless), or hybrid piezoelectric-electromagnetic energy harvesters (Jiang et al., 2021).
Vibrations produced by devices in operation can be a source of energy replenishment.Researchers employ additional components to capture this energy, such as the piezoelectric vibrator proposed in work (Wang, 2020) as an energy converter from track vibrations caused by vehicle movement.The author developed a dynamic model of a vehicle coupled vertically to estimate displacements that affect the piezoelectric element in charge of energy recovery.The researcher then performed simulation tests and concluded that larger displacement amplitudes increase the amount of energy recovered.The vehicle speed and position of the piezoelectric elements also influence the maximisation of the energy output.
Another way to enhance the energy efficiency of automobiles was proposed by Hassan Fathabadi in his article (Fathabadi, 2019).He suggested two modifications: embedding electric coils in shock absorbers to capture and convert vibration energy into a steady DC voltage and adding a wind turbine to the vehicle condenser.The author showed that those two modifications could increase the energy production of electric vehicles and extend their travel range.
Alternatively, energy can be harvested by using the Energy Restore Braking System (ERBS) (Li et al., 2021;Liu and Zhang, 2021).This concept involves converting kinetic energy of motors into electrical energy during deceleration (Taut et al., 2013).This technique is commonly applied in electric vehicles.However, it often needs additional components in the system such as DC-DC converters, which are devices that convert the direct current (DC) from one voltage level to another (Kim, 2011; Onar and Khaligh, 2012), super-capacitors, which are high-capacity capacitors that can store and release large amounts of energy quickly and release it when connected to a chosen circuit (Naseri et al., 2017;Song et al., 2014), or gear shifts, which are mechanisms that change the speed ratio between the motor and wheels (Yang et al., 2007).These components add to the weight and complexity of the system.
Another way to make energy recovery systems more simple is to use a single-stage converter that controls the BLDC motor, as suggested by Godfrey and Sankaranarayanan (2008).This method can switch to the regenerative braking mode by sending switching pulses in a specific sequence.This method does not need extra power converters, which is a benefit compared to other solutions.The authors of (Godfrey and Sankaranarayanan, 2008) present different switch topologies, such as H-bridge, half-bridge and full-bridge, and plugging combined to create a new braking strategy.The switch topologies determine how the current flows through motor windings and how the back electromotive force is generated.The simulation and experimental tests were done to show the effectiveness of the proposed solution.
On the contrary, this article explores how to combine the driver seat suspension system with a special BLDC motor braking system that can turn horizontal vibrations of the driver seat suspension into electric power.The stored power can be used for different vehicle subsystems as needed.This solution also helps one to optimize the active seat suspension systems that use electric motors to create vibration damping force.The idea is to use the motor as a generator to produce this force.The proposed suspension system can be tested using human biomechanical models (Maciejewski et al., 2023).The model gives quick results on the power and vibration levels that affect the driver body parts, which allows for evaluating and comparing different suspension systems.
The first part of the article explains the mechanics, control strategies and main applications of this new concept, which achieves a balance between energy saving and passenger comfort.A physical model and a mathematical model of the suspension system with energy recovery are presented.This approach is based on multiple objectives aiming to accomplish.One of them is to enhance comprehension of complex interactions involved in the seat suspension that can reduce horizontal vibrations affecting comfort and health of work machine operators.Another one is to explore the efficiency and feasibility of incorporating energy recovery mechanisms into these systems, considering both the environmental demands of energy efficiency and the psychophysical health of drivers, operators and passengers.The next subsections of the article present practical implementation of the BLDC braking system with energy recovery in horizontal seat suspension and a detailed simulation analysis of their features and performance.Further research involves simulation analysis of a specific solution, with a specific engine (BLDC motor), and experimental tests on a laboratory stand.The data gathered during experiments can be used to broaden the knowledge about this type of systems and their practical applications.It will suggest the direction of further research, including the use of suitable biomechanical models.

Physical and mathematical model
Figure 1 shows the physical model of an active seat suspension and simple biomechanical human body model.The upper part of the human body is modelled as a lumped three mass system (roughly corresponds to the pelvis, torso and head) (Maciejewski et al., 2022b).That inertial system responds to the external excitation x s .In detail, the first mass m 1 represents the seat frame with pelvis, the cushions and motor inertia, the second mass m 2 represents the body part on the seat back rest, i.e the torso and the third mass m 3 represents the body part that moves freely, i.e. the head.Its mass m 3 has no contact with the backrest.The stiffnesses c 12 , c 23 , c 2 Due to topology and simplicity of the model to identify the above-mentioned parameters, it was necessary to conduct experimental research with human participation and then the carry out the optimisation process.During the experiment, the tested individual was subjected to action of test vibration in the sitting position on the cushioned seat, occupied in the way providing the backrest contact.The identification process was conducted minimising by the error between numerically simulated and experimentally measured transmissibility functions over the frequency range of 1 Hz-12 Hz and introducing the Root Mean Square Error method.A detailed description of the model and its parameter sensitivity analysis is given in the work (Maciejewski et al., 2022b).
This model structure and its proper parameters can be used to predict the biodynamical response of the seated human body in the frequency range of 1 Hz to 12 Hz.The model of the suspension system consists of a human body mass that is attached to two tension springs with stiffness c s and a damper with damping ratio d s .The friction in the suspension mechanism is modelled by a coefficient µ s , which is determined experimentally for a specific seat type and described in the work (Jereczek et al., 2022).Modern seat suspension systems are active systems.The aim of the active subsystem is to minimise harmful vibrations of the body mass.The active element here is a brushless DC motor (BLDC).Such an electric actuator generates an active force F a which, in turn, is proportional to the electromagnetic torque T e of this motor.The torque T e is controlled by a servo-drive mode.The equations of motion for the mechanical structure are given by Active force F a in the suspension system is provided by three-phase currents (i a , i b and i c ) flowing through stator windings in the presence of a magnetic field from permanent magnets.The resulting force coming from an electric motor is therefore defined as the following function where: p is the number of pole pairs, λ is the amplitude of flux induced by permanent magnets, r e is the lever arm of the motor, Φ a , Φ b and Φ c are three-phase electromotive forces.The phase electromotive forces are assumed to be trapezoidal for most of the BLDC motors (Krause et al., 2002).The trapezoidal model is based on the assumption that the winding distribution and the magnetic flux created by permanent magnets generate three trapezoidal back electromotive forces.The back electromotive forces are the voltages induced in the stator windings by the changing magnetic field.The set of equations that describe the actual motor currents can be written in the phase reference frame (abc frame) as follows (Krause et al., 2002 where: L s is the inductance of stator windings, v ab and v bc are the phase to phase supply voltages, R s is the resistance of stator windings.The currents in Eq. (2.3) need to get values that allow reducing the unwanted seat movements.The double-feedback loop system (Maciejewski et al., 2020) is used to calculate the proper, desired active force (F a ) des , which is needed to balance the kinematic excitation x s .The motor windings currents should produce the desired active force given by the following formula where ẋ1 is the absolute velocity of the suspended body given by the mass acceleration sensor (after integration process) (Fig. 1), x 1 − x s is the relative displacement of the seat suspension measured by the displacement sensor (Fig. 1) k 1 and k 2 are the coefficients feedback that affect significance of reducing velocity of seat vibration (influence of vibration velocity criterion) and significance in limiting the suspension travel (influence of seat displacement criterion), respectively.Formula (2.4) also shows the conditions for which the damping force is generated in the active suspension cycle ("motoring").and the force is not generated in the energy recovery cycle ("braking").

Energy recovery capabilities during braking mode of an induction motor
The force/velocity possibilities of the suspension system are represented as a velocity versus active force graph containing of four quadrants (Fig. 2).This figure illustrates four-quadrant operation of the horizontal seat suspension driven by an induction motor.In the chosen horizontal Fig. 2. Four-quadrant operation of the horizontal seat suspension driven by an induction motor x direction, a constant force (F ax ) n is given in grey colour region from 0 to nominal velocity ±( ẋ1 − ẋs ) n .The rest region (white colour) indicates a significant decrease of the force (F ax ) n while an increase of velocity from the nominal ( ẋ1 − ẋs ) n to the maximum value ( ẋ1 − ẋs ) max .Such a region is limited by a constant power level (F ax ) n ( ẋ1 − ẋs ) n due to lowering of the motor magnetic flux.In the first (I) and third quadrant (III), the active force F ax and the velocity ẋ1 − ẋs have the same signs, indicating the driving mode since the electric force is in the direction of motion.In the second (II) and fourth (IV) quadrant, the active force F ax is opposite to the velocity ẋ1 − ẋs , therefore the braking mode of an induction motor is applied.Operation in these quadrants means that the kinetic energy of the induction motor coupled to a mechanical load can be transformed into the electric energy.The control algorithm that corresponds to possible energy transfer between mechanical and electrical subsystems is defined as follows where: (R s ) set is the controllable external resistance of the induction motor, k max is the constant coefficient representing the maximum braking force of the induction motor, the same BLDC motor working as a generator.Each constant model parameter of the seated human body together with the horizontal seat suspension and energy recovery braking subsystem is specified in Appendix A. Physically, the braking system of the BLDC motor, realising energy transfer, works using resistors and transistors shown in Fig. 3.The system controller sends an analogue "braking" signal to initiate the braking process.This is happening when the controller gets a signal from seat velocity sensor and a torque signal, and calculates according to Eq. (3.1), which means second (II) and fourth (IV) quadrant (Fig. 2).The "braking" signal is converted into a digital PWM form with a frequency of 20 kHz.The PWM signal is then isolated from the transistors using an opto-isolator circuit.The transistors are connected to three braking resistors R 1 , R 2 and R 3 which are also connected to the three motor phases A, B and C. When the transistors are turned on by the PWM signal, the motor phases are shorted through the resistors, which creates a braking torque on the BLDC motor.The currents flowing through the motor windings are measured by current sensors based on the Hall effect, which allows us to calculate the power dissipated by the resistors.In the same way, the available energy is determined.

Experimental versus simulation results
In the last phase of the research, experimental verification of the correctness of the model, simulation results and the effectiveness of the proposed energy recovery concept in such a system was carried out.The effectiveness and efficiency of the energy harvesting in the horizontal suspension systems was evaluated using the experimental set-up shown in Figs.4a and 4b.As the physical model assumed, the suspension system (seat suspension system -Fig.4a) was attached to a base platform (vibrating platform -Fig.4a), driven by a PMSM motor (vibrations source motor PMSM -Fig.4b) that produced a random vibration signal with a programmable electro-hydraulic shaker.Finally, the oscillatory seat motion transited to the mass (mass load -Fig.4a, respectively mass m 1 -Fig.1) was induced by an active force generated by the PMSM motor through a two-link mechanism.This mechanism transformed the rotational motion of the motor into the translational motion of the suspension system in the longitudinal direction.The accelerometer (platform acceleration sensor -Fig.4a) was utilised to measure the input signal that was random vibration having a frequency between 0.5 Hz and 12.5 Hz.The data obtained from this accelerometer was recorded by a PC-based data acquisition system with the sampling time of 1 ms.The output signal was measured by an accelerometer fixed to the mass (mass acceleration sensor -Fig.4a).The recorded acceleration signals from both accelerometers were simultaneously digitally integrated to obtain velocities of the platform and mass.The rigid mass (mass load -Fig.4a) was placed on the upper part of the suspension mechanism to load the system to simulate the driver (operator) presence during investigation.The element of the active seat suspension was the brushless motor (BLDC motor -Fig.4b).Its task was, on the one hand, to generate an active vibration damping force in accordance with the selected algorithm in the control strategy (one of the control algorithms developed by the authors was presented in the work (Maciejewski et al., 2022a), and, on the other hand, to obtain seat vibration energy and convert it into electrical energy, in accordance with the energy acquisition strategy.On the test stand, the energy of the seat movement (longitudinal vibrations) was transferred to the motor through a system of rigid rods and an eccentric system (centrifugal transfer of motion from the seat to the BLDC motor -Fig.4b).To measure the amplitude of longitudinal seat vibrations directly, a dedicated displacement sensor was used (seat displacement sensor -Fig.4a).Mounting this sensor enabled measuring the relative displacement of the platform and the seat.The aim of the experimental study was to examine the effect of the tested regenerative system on the suspension performance.Two common factors were selected for the analysis.The first one was the SEAT factor, which measured the seat isolation efficiency.The second one was the suspension travel (relative displacement), which evaluated the seat dynamic response (Maciejewski et al., 2014).Generally, when the SEAT factor was higher than 1, the vibrations were amplified and transmitted from the road to the driver or operator.When the SEAT factor was lower than 1, the vibration isolation improved as the SEAT decreased.For the second factor, a smaller value was preferable.It ensured that the seat did not reach its movement limits when driving on rough roads.The test was carried for a chosen mass value (Mass load 80 kg). Figure 5 shows the tested person of weight 80 kg on the test rig.The same person was tested on passive, active and regenerative seat suspension configuration.
The comparative results of the passive, active and energy regenerative suspension are presented in Table 1.The data in this table show that the use of an energy recovery system generally reduces the vibration-insulating properties of the suspension in caparison to the active one.However, the reduction is approximately 18.1% for this particularly load mass, calculated on the basis of the SEAT factor.However, the dynamic response, calculated on the basis of the suspension travel value, is reduced by approximately 23.6% for the weight of 80 kg.At the   1 show, such a system still has better vibration isolation properties and dynamic response than the passive one.At the same time, simulation tests were carried out using a biomechanical human model and a suspension system model.The results of the simulation using the biomechanical model are presented in Table 2.As can be seen from the values presented there, the model gives the same assessment of the vibro-isolation with the SEAT coefficient and the suspension travel value.All values obtained from the model are larger than those from the experiment.The greatest compliance is found in the case of the active suspension system.The largest relative error of the model in the case of SEAT was max 10%.However, in the case of suspension travel, the error reached 15%.In detail, the range in which an energy recovery suspension system works better than a passive system can be indicated by analysing power spectral densities (Fig. 6a) and transmissibility functions graphs (Fig. 6b).The curves of both types of functions, for this case of mass load, indicate the frequency limit of 3 Hz.Below this frequency, the active and regenerative system represents similar vibro-isolation properties.The graph shows slightly better properties of the active system.In that frequency limit, the passive system demonstrates clearly inferior properties.In the case of frequencies above 3 Hz, the two systems, passive and regenerative, show similar vibration isolation properties and much worse than for the active one.However, as the transmissibility function curve for the regenerative system shows (Fig. 6b), it is below the value of 1 throughout the frequency range.Therefore, it significantly reduces vibrations coming from the ground or road.At the same time on the test-rig, other essential parameters related to the regenerative seat suspension were measured (Figs.6c and 6d). Figure 6c shows the desired torque generating during the damping period defined by the "motoring" condition in Eq. (2.4).In this figure, the torque values appear by multiplication by r e the desired force (Fig. 1).The damping periods are marked with white vertical stripes along the selected 1.2 s time sample.On other the hand, pink stripes in Fig. 6c indicate the regenerative period.Particularly, it presents the resistance settled when the motor phases are shortened through the breaking resistors (Fig. 3).The current sensors shown in Fig. 3 measured the current values presented in Fig. 6d in pink strips time periods.
Figures 7a-f show the results of simulation of the passive, active and regenerative suspension system.In Fig. 7a, the power spectral densities of the three systems are compared, showing that the active system has the lowest vibration level (close to experimental results).In the case of regenerative and passive ones, the model returned higher values.The frequency limit 3 Hz is visible like in the case of the experiment.Above this limit, all simulated systems gave very similar results, differently than in the experiment.In Fig. 7b, the transmissibility functions of the three systems are plotted, indicating a similar to power density functions isolation performance of all systems.In this case, however, it should be noted that the regenerative system, in the range up to 3 Hz, reaches values greater than 1, contrary to what the experiment showed.In Fig. 7c, the Fig. 7. Simulated power spectral densities (a) and transmissibility functions (b) of the passive, active and regenerative suspension system, time histories of the desired motor torque versus the set resistance (c) and the corresponding regenerated phase currents (d), power consumption (e) and the obtained regenerative power of the electric motor (f) desired motor torque and the set resistance are shown, demonstrating that the motor torque is zero in the energy regeneration periods contrary to the resistance (pink strips).The opposite is true in the ranges marked by white strips.This confirms the validity of the regenerative model.In Fig. 7d, the phase currents of the electric motor are displayed, revealing that they are in phase with the motor torque.In Fig. 7e, the power consumption of the electric motor is calculated, proving that it is lower than the active system.In Fig. 7f, the regenerative power of the electric motor is estimated, showing that it can recover some energy from the suspension vibration.

Conclusions
The experimental study demonstrated that the energy regenerative suspension system can improve the suspension travel and reduce the seat movement limits compared to the passive system, while sacrificing some of the vibration isolation efficiency compared to the active system.The power spectral density and transmissibility function graphs showed the frequency ranges where the regenerative system performed better or similar to the passive system.The test-rig experiment demonstrated the feasibility of the proposed regenerative seat suspension system.The

Fig. 1 .
Fig. 1.Physical model of an active seat suspension with the BLDC motor

Fig. 4 .
Fig. 4. Actual, overall view of: (a) the test rig with basic sensors, (b) the test stand with a BLDC motor (energy recovery) and a seat vibration motor

Fig. 5 .
Fig. 5.The view of: (a) the front test rig with the tested person, (b) the rear part with the regenerative system

Fig. 6 .
Fig. 6.Measured power spectral densities (a) and transmissibility functions (b) of the passive, active and regenerative suspension system, time histories of the desired motor torque versus the set resistance (c) and the corresponding regenerated phase currents (d)

Table 1 .
Measured SEAT factors and suspension travels of the passive, active and regenerative suspension system for the mass load of 80 kg

Table 2 .
Simulated SEAT factors and suspension travels of the passive, active and regenerative suspension system for a mass load of 80 kg