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Core-shell powders have been extensively studied due to their complex structure and wide range of applications. W@Ag core-shell powders are particularly interesting due to the synergy between the tungsten and silver, which can be beneficial in the electronics industry. However, knowledge of their thermal stability is limited, particularly concerning the impact of annealing temperatures on structural integrity and oxidation resistance. In this work, W@Ag core-shell powder was heat-treated in the temperature range 100–700 °C for 1 h in air. Investigation of the microstructural changes using scanning electron microscopy equipped with energy-dispersive X-ray spectroscopy showed that the limiting temperature is 500 °C, when the shell began to decompose and the core began to oxidize. Moreover, X-ray diffraction analysis determined that the phase composition of the thus heat-treated material consisted of approxi-mately 50 % Ag and 50 % Ag2WO4.

The article deals with the experimental measurement of the load on the cervical vertebrae when driving a passenger car over bumps. The measurement was done experimentally. The load on the human spine was measured in the area of the C7 cervical vertebra and also in the area of the top of the head. Vehicle crossings over speed bumps. The measurement was carried out at different crossing speeds and at different heights of speed bumps. Three-axis acceleration sensors were placed on selected parts of the vehicle and on the human body. The proposed measurement methodology was verified by the conducted pilot experiment for the possibility of conducting further experiments. The results of the work showed that the crew of vehicles in road transport is more stressed than previous scientific findings indicate.

The paper deals with the solubility and influence of the melting method of alloying elements (Zr, Mo and Sr) on selected properties and structure of the hypoeutectic aluminum alloy AlSi5Cu2Mg. Alloy-ing elements in the form of master alloys (AlZr20, AlMo10, and AlSr10) were melted in two different methods. The first method consisted in melting the master alloy together with the batch material in an electric resistance furnace, the second method consisted in separately melting the master alloy in an induction electric furnace and then introducing the master alloy into the molten batch. The presence of alloying elements led to an increase in the porosity in all experimental alloys, which negatively affected the resulting physical and mechanical properties.

Unfortunately, in connection with the application of the Actavia anti-plagiarism system, we cannot accurately describe our paper, which deals with the production of non-compact materials based on zinc and tin alloys, which have a higher density than aluminium (ρ = 2700 kg.m^-3 ) and its alloys, such as zinc alloys (ρ = 6980 kg.m^-3 ) or tin (ρ = 7580 kg.m^-3 ). Test samples were prepared from these materials, which were characterized by material non-compactness based on the use of NaCl particles. For this purpose, two different size groups of NaCl particles (3 to 5 mm and 5 to 7 mm) were used. In the production of non-compact metallic materials, it is assumed that half of the volume of the workpiece cavity will be occupied by NaCl particles and half of the volume of the work piece cavity will be filled with a melt of the relevant alloy (ZnAl4Cu1 or Sn89Pb). This is different from our previous experiments [24, 25]. In the case of this paper, the fabrication consisted in the fact that in a spe-cial preparation, the melt of the respective alloy was forced between the NaCl particles. The produced samples of non-compact material were analyzed and their specific gravities were determined. In a standard manner (as may be against the findings of the Actavia system), the microstructure was observed on an electron microscope and EDS analysis was also performed. It is anticipated that the non-compact materials thus produced from these two alloys will be used to produce not only filters but also bodies for liquid hydrogen storage.

The propagation and velocity of the deformation wave in the thin isotropic plate is investigated. The deformation is induced by the stroke of impact body onto the facial surface of the plate. The plate is supported perpendicularly. The excitation of the plate oscillation is initialized by a unit force (Heavi-side’s jump). The impact body has a rounded facet by radius c = 2.5 mm. Hook's material model and Kirchhoff’s and Flüegge’s geometric model have been investigated. The analytical solutions for both models are presented. The MATLAB script has been assembled to solve material and geometrical mod-els. The results were compared for two selected points on the surface of the plate. Plate deformation was recorded at two points T1 (at a distance of 20 mm from the impact location on the x axis) and T2 (at a distance of 20 mm from the impact location on the y axis).

The paper focuses on proposing a method for implementing key performance indicators (KPIs) to assess the effectiveness of manufacturing processes. For the evaluated processes of precision parts machining, the share of non-conforming products was proposed as a KPI, evaluated as both an exter-nal and an internal indicator. The external indicator EXTppm expressed the quantity of faulty prod-ucts to the volume of production. Its monthly development during 2022 was evaluated. The internal KPI represented the internal share of non-conforming products INTppm during 2022 which was re-lated to the order of part A. Towards the conclusion causes for not attaining the targeted KPI values are pinpointed, and recommendations are put forth to enhance the productivity of manufacturing processes.

PolyJet technology, based on the printing and photopolymerization of model material, is currently, along with stereolithography or 3SP (Scan, Spin and Selectively Photocure), the most commonly used rapid prototyping method based on optically active resin. The article presents the results of torsional strength tests of samples made of optically active resins VeroDentPlus-MED690, VeroClear-RGD810, and Rigur-RGD450 by Stratasys in PolyJet technology. The samples were prepared in HQ (High Quality) mode with a layer height 0.016 [mm]. The tests included a static torsion test using a specialized research stand by the Department of Mechanical Engineering of the Rzeszów University of Technology. The scope of research significantly expanded the standard procedure, which complements the material data available with significant functional parameters due to the use of models. The results of the torsional strength analysis determined in the research process can be used to define the potential application area of the materials in question - optically active resins and their processing techniques for the production of parts subject to complex loads, i.e. machine shafts, clutches, and gear hubs.

The quality of web products is significantly affected by the running velocity of a process line, especially during the stages of start-up and shutting down of a web processing line. At these stages, a remarkable transverse variation (web flutter) are observed due to employing improper input velocity. Web flutter may cause some web defects such as wrinkles, poor printing and even web breakage. Therefore, employing an optimal web velocity profile is crucial to minimize web transverse vibrations during the transport of the web through different processing sections in a web process line. In this paper, an optimal velocity profile along with common velocity profiles (widely used in industry) have been utilized in a running web line to demonstrate the effect of web transport velocity on transverse vibrations. Comparative experimental results are presented and discussed.

This paper describes β-Sn to α-Sn transformation in its initial phase. This process is also known as a tin pest and currently it causes problems mainly in the field of soldering materials. To avoid misrepresenta-tion of the results of artificial ageing of the samples; we have decided to use historical materials for our study. A sample from historical organ pipes was indented by naturally formed α-Sn polycrystalline parti-cles by the load of 1 kg. The sample in the initial state was observed by SEM and analysed by EBSD mapping. The position of inoculator particles was documented again by SEM observation. Subseqently, the sample was freezed at -50 °C. The evolution of cracks started after 2.5h in the vicinity of indented α-Sn particle. After 5 h of freezing, new cracks were observed also in the untouched parts of the sample. The crystallografical interconnectedness was not proven for polycrystalline samples.

In order to accumulate experience in the design and manufacturing of the toroidal field coils for the China Fusion Engineering Test Reactor, a model coil of mixed Nb3Sn-NbTi superconducting magnet with a maximum magnetic field variation rate of 1.5 T/s has been developed at the Institute of Plasma Physics, Chinese Academy of Sciences. The preload system, as one of the key components of the model coil, plays a crucial role in maintaining the overall integrity and stability of the model coil. First the magnetic field and electromagnetic forces of the model coil under extreme conditions are calculated based on Maxwell's equations. Then, the mechanical performance of the model coil at room and cryogenic temperatures is analyzed. To addressing the issue of excessive stress in the preload components of the model coil under preload, several optimization design schemes are proposed and iteratively analyzed. Finally, stress linearization is performed, and stress evaluation is conducted based on the analytical design. The assessment results indicate that certain optimization schemes enable the preload components to fully meet the operational requirements at both room and cryogenic temperatures. The outcomes presented in the paper will provide reference for the subsequent design and manufacturing of the central solenoid coil.

Binderjetting technology works on the principle of line injection moulding, using metal powder and liquid binder as input material, which is uniformly applied by print heads to the previous layer using a nozzle. By successively applying each layer, the desired shape of the designed component is obtained. The technology offers a large number of advantages which include the possibility of using any printing powder that may contain functional graded materials. Furthermore, it is a green manufacturing technology where we can reuse unused metal powder in the next printing cycle after following the prescribed process. As a result, we characterize this technology as a near-waste-free production of metal parts. The research aims to analyse the impact of different orientations of printed parts within the workspace on the mechanical properties of the resultant components. Additionally, the study aims to compare these mechanical properties with the specifications recommended by the metal powder manufacturer and findings from previous research studies. Based on the experimental measurements carried out, we can conclude that the influence of the orientation of the parts in the workspace has only a minimal effect on the mechanical properties of the manufactured parts.

This article explores the effect of cryogenic temperatures on the properties of cobalt alloys, specifically Stellite 6 and Stellite 12. These alloys are commonly used in applications that require resistance to me-chanical, thermal, and chemical wear. In this study, the focus is on the valve seats for internal combus-tion engines, which are made from cobalt alloys and undergo a freezing process before assembly into the cylinder head. The purpose of freezing is to reduce the diameter of valve seats, making them easier to fit into the cylinder head. However, the length of time spent in freezing can significantly affect the hardness and tribological characteristics of the material.

Reinforcement steel rebar is produced by several ways but most importantly the tempcore process. Due to mass production in steel rolling plants, the rebars are gathered after tempcore process at a specific temperature in bundles stack in the warehouse. The bundling temperature varies from 200 to 300 o C. The rebars need relatively long time, up to one day, to reach the room temperature in the bundles stack. This work investigates the effect of prolonged ageing time on the rebars mechanical properties after the tempcore process of both ageing in bundle and designed artificial ageing. The results of mechanical properties of ageing in bundle compared to the artificial ageing were found to be in good agreement. The yield and tensile strengths were found to decrease by 6.3 and 2.1 %, respectively, due to artificial ageing. However, the elongation and the tensile to yield ratio increased by 17.6 and 4.8 % respectively.

The boride coatings are characterized by attractive set of properties such as high hardness and wear resistance, corrosion resistance in higher temperatures and no wettability by liquid metals like alumi-num and zinc. This type of coating might be used for manufacturing of different parts from tool steels. In present article the influence of pack boriding time (2,4,6h) on microstructure and phase composition of obtained coatings is scrutinized. The pack boriding process was conducted on two groups of cold work tool steels: low-Cr content: 145Cr6, 90MnCrV8, 60WCrV8 and high-Cr content: X165CrV12, X153CrMoV12. The commercial boriding pack Ekabor 2 was utilized and the process was carried out using industrial CVD device (Bernex BPX Pro 325S). The conducted research showed that the boride coatings formed on the substrate of high-chromium steels were characterized by a lower total thick-ness. On low-chromium steels, FeB phase was discontinuous as an irregular islands located in the near-surface area. On the other hand, for high-chromium steels, a continuous layer of needle-like borides was formed.

In response to the problems of insufficient strength and stiffness, as well as large weight in traditional car frames, this article takes titanium alloy frames as the research object. Based on the analysis of static and dynamic characteristics, a lightweight design is carried out to meet the design requirements. Firstly, static analysis was conducted on the frame structure under four different working conditions using the finite element analysis method to study its stress distribution and deformation under different loads and road conditions. Study the natural frequency and vibration mode of the frame through modal analysis, providing a basis for subsequent optimization design. Through harmonic response analysis, explore the changes in the amplitude and frequency of the frame during use. On this basis, topology optimization and lightweight design are carried out on the frame structure to reduce the weight of the frame and improve its strength and stiffness. Finally, validate and compare the optimized frame to explore the feasibility and superiority of the optimization plan. The research results show that the optimized frame weight has been reduced by 13.76%, the maximum stress has been reduced by 5.19%, and the maximum deformation has been reduced by 0.37%, effectively reducing the frame mass. This provides a way of thinking about the static and dynamic characteristics analysis and topology optimization design of automotive frames.

Atomic Diffusion Additive Manufacturing (ADAM) is a progressive layering process based on metallic materials with a plastic binder designed to extruse the material. The ADAM process can be classified as an indirect additive manufacturing process in which a solid fiber of metal powder enclosed in a plastic binder is applied. After creating a 3D object by the ADAM process, the excess plastic binder is removed in the cleaning chamber and vacuum sintering of the 3D object is performed. This work aims to provide a preliminary characterization of the ADAM process and compare the achieved results with the application most implemented so far in additive manufacturing for metal 3D objects using Selec-tive Laser Melting SLM. In particular, the density and microstructure of the applied process and mate-rial 17-4PH are studied, while optimal or recommended technological parameters of production facili-ties are applied. Furthermore, the dimensional accuracy of the ADAM process is observed, which is evaluated by means of IT accuracy levels according to the ISO reference artifact. Due to the applied AM process, the final character of a 3D object depends on technological parameters. The weight of a 3D object is low compared to the material processed by additive manufacturing processes in a powder bed. The dimensional accuracy and roughness of the surface depends on the geometry, orientation, and position of the individual shape specifications of the 3D object. Additive technologies generally achieve a degree of accuracy of approximately IT12 to IT13, which is comparable to traditional semi-finished metal manufacturing processes.

Today's manufacturing industry, especially in the context of the metals industry, is constantly evolving towards ever more advanced technologies and efficient production practices. In this context, machinery modernization is becoming a key element in improving manufacturing processes. This article focuses on analysing the impact of machinery modernization on casting quality, using selected quality manage-ment tools. The article presents an analysis of the effects of the implementation of modern technology, automatic casting machines, on the quality of castings production. Using quality tools such as the Ishi-kawa diagram, Pareto-Lorenz and the FMEA method, the main causes of casting nonconformities, the frequency of occurrence of these nonconformities and the risks associated with them were identified for periods before and after the implementation of machine park modernization. The measurable benefits associated with the introduction of modern foundry technology in terms of improved casting quality were showed. Using quality tools, the quality improvement achieved was determined indirectly, while the level of improvement in casting quality after the modernization of the machine park was showed directly using the defect rate. It was also shown that, despite an increase in production efficiency and the level of quality of the manufactured products, the introduction of the new technology generated new quality challenges in the context of maintaining the stability of the casting process parameters as a result of a jump in productivity levels. The paper highlights the need to balance production efficiency with atten-tion to casting quality, which was an important issue for the foundry studied.

Gears and toothed parts are significant components in power transmission systems. These parts usu-ally manufactured by traditional methods such as machining by milling or forming by rotary forging. In this study, the forming of solid gears or toothed parts using a forging process that combines rotary forging and ballizing technique. The specimens were placed inside the die with excessive volume to fill the toothed part in the die. The forming tool applies pressure to the specimen while rotating it together with the die by the lathe machine chuck, while the tool advances continuously in the direc-tion of the die. This reduces height of the specimen and increases its diameter, causing metal flow to fill die cavity teeth and form the gear or toothed part required for production. Two sets of experi-ments were performed. In the first set, optimization for the appropriate volume of four different sizes of dies and four forming tools was conducted. While in the second set, the effects of forming process variables on the forming load and tooth filling percentage was studied. The results showed that the best tooth filling ratio happened with specimens size of 1.2 to 1.4 times the volume size of the desired tooth for filling. The results also revealed that the forming speed, die size, and forming tool diameter affect the filling ratio and forming load.

This paper deals with the issue of selecting different machining parameters in the CAM system Siemens NX 1946. The issue of choosing between a solid end mill, milling cutter, and a high-feed tool when machining simple rectangular and rugged cavities concerning time and residual material is solved here. The chosen material was 1.1730, which is a basic material for the production of moulds without heat treatment. The paper deals with the issue of choosing the size of tool feed into the cut and its influence on the formation of the machining path depending on the depth of the cavity. The size of the residual material depends on the machining strategy and the choice of the plunge method into the material with regard to the total machining time. Performed simulations and experiments have shown a significant impact in individual settings and, thus, on the cost of machining components of such shapes.

The submitted paper deals with biotribological contact in total knee arthroplasty. The goal was to evaluate the influence of the metal component production technology on tribological parameters in defined environments. The reference sample was a standard available test ball made of the subject material, used in testing tribological properties by the "Ball on Pin" method. The preparation of the experiment consisted in the production of test disks from UHMWPE material and the production of a metal test component with a spherical surface. The condition of the experiment and the basis of this contribution is to compare the properties of conventionally produced metal material against 3D printing. Using the SLM method, a sample with a semi-spherical surface on a cylindrical shank was produced, which was subsequently ground and polished to reflect the characteristics of the standard supplied test ball. The last step was the production of a suitable fixture in order to fit the sample into the tribometer. The so-called dry friction of the heterogeneous Ti6Al4V–UHMWPE pair and the friction in a biological lubricating environment represented by bovine serum were evaluated. The evaluation of the contact surfaces took place using a profilometer and an electron microscope. The coefficient of friction was determined directly from the test device - tribometer.

A constant tension cable reel based on planetary gear transmission is introduced. The parameters of the mechanism are determined to analyze the speed and torque of the transfer mechanism. The relationship between the thread pitch and cable type show that different cable models require different parameters for the constant tension cable reel. The mechanism is designed to automatically adjust the force required for cable pulling and maintain a constant maximum tension. Then the relationship between the moment and speed of each output shaft is analyzed, and the operation mode of the cable reel was explained. The experimental results show that the proposed cable reel can pull the cable flexibly while providing the required constant tension, without damaging the cable and extending its service life. The pitch of the screw-thread pair is directly related to the required tension of the cable and the cable diameter. If the power supply cable model is different, the parameters of constant tension cable reel are also different.

The work deals with the possibility of using additive technology in the production of positioning and clamping device. The designed clamping device will facilitate and accelerate the measurement of samples with inclined or different irregular surfaces. The designed device is manufactured by additive technology using composites. Onyx material reinforced with Kevlar fibers was used as material for composite printing. The designed device should achieve the required properties for the firm and stable clamping of the components during the measurement process, and its weight should be significantly reduced with the use of composite material.

With the development of 3D technology, more and more materials are being used for manufacturing and used in many fields, such as factory manufacturing, workshop manufacturing, food packaging, and even architectural design and civil engineering design. In particular, the mechanical properties of the 3D printed HIPS polymer unit cell structure are worthy of research and analysis, providing more valuable references for future material development. This study focused on the properties of HIPS polymer materials and the performance of HIPS polymer 3D printed lattice structures after Instron instrument compression testing. The experimental samples were divided into 4 groups and there were 4 different experimental variables for analysis and comparison. Finally, it was found through analysis that the HIPS polymer material has good compression resistance, and the structure is relatively stable. It can be used more in the fields of manufacturing, architectural design and civil engineering in the future.

The restriction of lead content in alloys for the production of the solder based on the Directive of the European Parliament and of the Council of the European Union of 08.06.2011 which is also known as RoHS (Restriction of the use of certain Hazardous Substances in electrical and electronic equipment), had a very positive impact on the research of lead-free solder alloys as well as on the economic impact on the production of solders. It opened the door to issues relating to the mechanical properties of lead-free solders and the microhardness of formed joints, increasing their quality and efforts to reduce production costs. Lead, as an element that is part of the earth's crust, is also men-tioned in his study by u-Wook Lee, Hoon Choi at all: Toxic effects of lead exposure on bioaccu-mulation, oxidative stress, neurotoxicity, and immune responses in fish, in which he states how lead atoms can form a flexible bond with oxygen atoms and lead exposure causes a wide range of physiological effects. Besides the production efficiency increase, without the need for manual re-moval of so-called slagging, the moderation of oxide formation on the melt surface standing for the increase of the yield of the total amount of solder represents one of the many factors influencing the production of lead-free alloys for tin-based soldering. This work deals with the issues of material selection for the production of lead-free solders. Temperature affects the formation of different phases when there is the change in the concentration of the elements involved because it can be negative aspect for soldering. Therefore, it is necessary to have detailed knowledge on all the process which takes place during the temperature changes.

With the rising demand for efficient, lightweight support structures in high-energy physics experiments, advanced manufacturing techniques and material optimization are key to achieving high-performance designs. This study focuses on the application of generative design and topological optimization in the development of support structures for the FCC muon spectrometer. By leveraging these methods, we maximized material efficiency and minimized weight while ensuring structural integrity and meeting strict design constraints, including non-magnetic properties, minimal deformation, and high precision. A detailed evaluation was conducted with respect to manufacturing techniques that balance perfor-mance with cost-effectiveness, resulting in multiple design iterations of optimized truss configurations. This approach demonstrates the potential of modern manufacturing technologies in enhancing the structural and economic viability of components for large-scale scientific equipment.

This article deals with the modification of surface properties of austenitic steels using laser shock peening (LSP) technology. This technology introduces residual compressive stresses into the surface layer. These stresses improve the technical properties of the material not only by affecting the re-sistance of corrosion cracking under stress. The aim of the work was to influence the austenitic steel 08CHN10T by LSP technology, to perform a corrosion test in a boiling MgCl2 solution and the sub-sequent evaluation of these tests. Furthermore, the hardness was measured of the peened part of the material by LSP technology and unpeened part.

When analyzing the natural frequencies of a gear mechanism, it's crucial to consider the mesh stiffness, which is influenced by the number of teeth in the mesh. Mesh stiffness behaves as an internal excitation source for the dynamic system, affecting the resulting frequency spectrum. This paper presents an experimental determination of gear mesh stiffness supported by analytical-simulation models of mesh stiffness, outlining common modeling methods and detailing the experimental setup and test specimens. The obtained data are then compared with simulation models of mesh stiffness, discussing the significance of this comparison and emphasizing the role of experimental data in validating and refining existing models of mesh stiffness. The experimental measurement of mesh stiffness described here emerges as a valuable tool for accurately representing mesh stiffness during engagement.

This paper explores the investigation of a natural alloy processed using the rapid solidification tech-nique. The study involves the reduction of manganese nodules through aluminothermy with a 20 wt. % excess of aluminum, followed by further processing of the resulting alloy using the melt-spinning process. The obtained melt-spun ribbons were subjected to a comprehensive analysis, including X-ray diffraction, scanning electron microscopy for microstructure observation, and EDS analysis for local chemical composition. The research unveiled that the rapidly solidified ribbons consist of several key phases, including β-Mn, the Heusler phase Mn2FeSi, and an intermetallic phase (Cu,Mn)3(Al,Si). Im-portantly, the phase composition exhibited notable differences from that of the as-reduced alloy, with a reduced number of phases in the rapidly solidified ribbons. Notably, the phase composition re-mained stable even after annealing, demonstrating the robustness of the rapidly solidified material. Impressively, the material exhibited a remarkable hardness of approximately 800 HV 0.1, even after 100 hours of annealing at temperatures of 500 and 750°C.

Aiming at the problem of feature extraction and fault recognition for rolling bearings, a fault diagnosis mthod based on multi-scale entropy and ensemble learning is proposed in this paper. Firstly, the variable mode decomposition algorithm is used to decompose the vibration signal, and then the cross-correlation number method is used to reconstruct the signal to realize the signal denoising. Subsequently, in order to improve the effectiveness of feature extraction for rolling bearings, a feature extraction method based on Refined Composite Multiscale Reverse Permutation Entropy (RCMRPE) is proposed. Then, in order to improve the accuracy of rolling bearing fault identification, this paper proposes a fault diagnosis model based on Stacking- CatBoost ensemble learning. Finally, relevant experiments were conducted on signal denoising, feature extraction, and fault recognition. The RCMRPE entropy extraction method was compared with the common entropy extraction methods, and the proposed fault diagnosis model was compared with the common machine learning models. The experimental results show that the feature extraction error based on RCMRPE is small and can comprehensively reflect the actual fault information of bearings; the accuracy and recall of the fault diagnosis model based on Stacking- CatBoost ensemble learning are both above 99%, and the diagnostic effect is significantly better than other models.

Manufacturing inaccuracies in vehicle suspension systems inevitably lead to uncertainties in the parameters of their structural components. Simultaneously, the road excitation impacting nonlinear vehicle systems exhibits pronounced randomness and time-variant characteristics. Consequently, it is crucial to conduct a stochastic dynamics analysis on nonlinear suspension systems, taking into account these uncertain factors. In this paper, a seven-degree-of-freedom (7-DOF) nonlinear suspension system dynamics model has been established. The stochastic process of road irregularities is simulated using the harmonic superposition method. Moreover, based on the direct probability density integral method, the stochastic dynamic equations of the nonlinear suspension system and their corresponding solution strategies have been developed and explored. Through MATLAB, the time-varying probability density function of the vibration response for a nonlinear vehicle suspension system was calculated under the combined effects of stochastic road irregularity excitation and random coupling of system structural parameters. Additionally, analyses were conducted on how different coefficients of variation and the intensity of nonlinearity in the suspension system influence the probability density of the output body displacement of the nonlinear vehicle suspension system. The research outcomes demonstrate that the direct probability density integral method offers superior efficiency and accuracy when computing nonlinear vehicle suspension systems. Furthermore, altering the coefficients of variation for various system parameters reveals that as these coefficients increase, the disparity in the probability density of body displacement becomes more pronounced, leading to more intense vehicle vibrations. Under soft nonlinear conditions with lower suspension spring stiffness, the probability density function of body displacement shifts slightly to the right with minimal change. However, under strong nonlinear conditions, body displacement significantly increases, resulting in diminished vibration isolation capabilities of the suspension system. This leads to severe jolts and a noticeable decline in ride comfort during vehicle operation.