Analysis of Rear Suspension Design in Electric Vehicles

Study Case Analysis of Rear Suspension Design in Electric Vehicles Based on ISO 2631-1 Standard Michael Kurniawan (2018123456) University of Cincinnati, 2600 Clifton Ave, Cincinnati, OH 45221, United States kurniaml@mail.uc.edu Abstract The growth of electric vehicles (EVs) requires a suspension system that is not only capable of maintaining stability, but also provides optimal comfort, especially in rearwheel drive configurations that cause asymmetrical mass distribution. This study evaluates the rear suspension characteristics of a four-wheel electric vehicle using a one-degree-of-freedom (1-DOF) mass-spring-damper model, with comfort criteria referring to the ISO 2631-1 standard. The object of study is a light electric vehicle with a load predominantly at the rear, so that the rear suspension working load reaches 1,052.5 kg. The analysis results show a static force per spring of 5,162.5 N with a spring stiffness of 51.625 N/m, resulting in a natural frequency of 1.11 Hz, which is still within the human comfort zone. With a damping ratio of 0.25, a damping coefficient of 3.685 Ns/m and a damping time of approximately 2.3 seconds are obtained. The oscillation response simulation shows that this value provides the best compromise between comfort and stability when compared to damping ratios of 0.10 and 0.40. These findings indicate that the proposed rear suspension design is suitable for application in electric vehicles with uneven mass distribution and meets international comfort standards. Keywords: electric vehicle, rear suspension, ISO 2631-1, natural frequency, damping ratio, vibration comfort. MICHAEL KURNIAWAN 1 Study Case INTRODUCTION The development of electric vehicles (EVs) in the United States has experienced rapid growth in recent years in response to carbon emission issues and energy efficiency needs. In addition to drivetrain performance, driving comfort is an important parameter for EVs to compete with internal combustion engine vehicles [1]. One of the main components that affects comfort is the suspension system, especially in electric vehicles with rear-wheel drive motors that cause uneven mass distribution [2]. The concentration of weight at the rear can alter the vehicle's dynamic characteristics, including vertical vibration response and pitch movement when traversing road irregularities. If not designed properly, this condition has the potential to reduce driver and passenger comfort, especially when the vehicle is fully loaded [3]. Therefore, suspension design needs to consider vibration parameters that directly affect human physiological responses. A number of previous studies have examined vehicle suspension design based on system dynamics and driver comfort. A study by Michael Johnson et al. (2022) showed that suspension characteristics have a significant effect on the level of vibration experienced by passengers in light electric vehicles [4]. Another study by David Miller et al. (2015) used a quarter-car model approach to evaluate suspension performance through variations in spring stiffness and damping [5]. However, most of these studies are still general in nature and do not specifically discuss the rear suspension of electric vehicles with rear motor configurations. This study uses a one-degree-of-freedom (1-DOF) mass-spring-damping model to simplify the analysis of key parameters such as stiffness and damping, particularly at the conceptual design stage. This method was chosen because it provides an initial estimate of vertical vibration response without requiring complex computations, as also applied in the study by Johnson et al. (2022) in the initial analysis of light vehicle suspension systems [4]. The main focus of this study is the design of the rear suspension of a four-wheel electric vehicle, taking into account the actual mass distribution due to the placement of the drive motor at the rear. Unlike previous studies that reviewed EV suspension in general, this study uses the ISO 2631-1 standard as the basis for evaluating vibration comfort, which is relevant for the initial design stage. This standard provides objective parameters for assessing comfort based on the human body's response to vertical MICHAEL KURNIAWAN 2 Study Case vibrations, but it is still relatively rarely applied directly in the technical calculations of electric vehicle suspension [6][7]. Based on existing research gaps, this study aims to calculate and analyze the rear suspension parameters of electric vehicles by considering the actual mass distribution due to the rear motor configuration and the vehicle's dynamic load. The evaluation was conducted with reference to ISO 2631-1 to produce a suspension design that can support vehicle stability while improving rider comfort. RESEARCH METHOD Research Object The object of this study is the rear suspension system of a four-wheel electric vehicle with a drive motor configuration located at the rear. The main focus of the research is on the design and analysis of rear suspension characteristics using a theoretical calculation approach based on vehicle mass distribution and the ISO 2631-1 vibration comfort standard [8][9]. The research was conducted analytically without direct testing on physical prototypes, but rather through mathematical modeling that represents small to mediumsized electric vehicles. The data used consisted of secondary data in the form of technical specifications of electric vehicles available in the United States market and comfort parameters from literature and ISO 2631-1 standards, plus numerical simulation data. The entire data processing and calculation process was carried out using Microsoft Excel and Python to improve numerical accuracy and facilitate the visualization of the relationship between technical parameters. Data Collection and Processing Techniques Vehicle technical data was obtained through a literature study of the specifications of commercially available light electric vehicles. The data processing stages included calculations of static force, spring stiffness, natural frequency, and damping coefficient with the following formulations: 1. Static force per rear spring 𝐹= (𝑚𝑏 + 𝑚𝑡 ) 𝑔 2 (1) where: MICHAEL KURNIAWAN 3 Study Case F = static force per rear spring (N) mb= rear vehicle mass (kg) mt= additional load (passengers and luggage) acting on the rear (kg) g = acceleration due to gravity (9.81 m/s²) 2. Spring stiffness 𝑘= 𝐹 𝛿 where: k = spring stiffness (N/m) F = static force (N) δ= spring deflection (m) 3. Natural frequency 𝑓= 1 𝑘 √ 2𝜋 𝑚 (3) with: f = natural frequency of the system (Hz) k = spring stiffness (N/m) m = total mass acting on the rear suspension (kg) 4. Damping coefficient 𝑐 = 2𝜁√𝑘 𝑚 (4) with: c = damping coefficient (Ns/m) ζ= damping ratio k = spring stiffness (N/m) m = total mass of rear suspension (kg) Initial Research Process Data The following table shows the initial data used in the analysis and simulation calculations. MICHAEL KURNIAWAN 4 Study Case Table 1. Electric vehicle data used in the study RESULTS AND DISCUSSION Rear Suspension Parameter Calculations Suspension parameter calculations were performed to obtain the dynamic characteristics of the electric vehicle's rear suspension system, including static force, spring stiffness, natural frequency, and damping coefficient. All parameters were calculated based on vehicle technical data and a one-degree-of-freedom (1-DOF) mass– spring–damping model approach [10], as described in the methodology section. All calculation stages were systematically arranged and supported by Microsoft Excel and Python to improve numerical precision and simulation process efficiency. Total Mass on the Rear Suspension Before determining the main parameters of the rear suspension system, the total mass acting on the system was calculated. This mass consists of the rear vehicle weight due to weight distribution, as well as additional mass from passengers and luggage. The total mass value is the basis for determining static force, spring stiffness, and other dynamic parameters. The empty weight of the vehicle is known to be 1,200 kg with a rear mass distribution of 60%, so the rear mass of the vehicle (m_b) is: 𝑚𝑏 = 0.60 × 1,200 = 720 kg The maximum additional load is assumed to come from five passengers with an average weight of 165 lb (≈75 kg) per person plus luggage, resulting in a total additional MICHAEL KURNIAWAN 5 Study Case load of 475 kg. From this value, it is assumed that 70% acts on the rear of the vehicle (m_t), namely: 𝑚𝑡 = 0.70 × 475 = 332.5 kg Thus, the total mass on the rear suspension is: 𝑚𝑡𝑜𝑡𝑎𝑙 = 𝑚𝑏 + 𝑚𝑡 = 720 + 332.5 = 1,052.5 kg Rear Spring Static Force The next step is to determine the static force received by the rear suspension. This force is a direct result of the total weight of the rear of the vehicle, including the vehicle structure and additional passenger and luggage loads. This value is used as the basis for determining spring stiffness because it reflects the load that each spring must support at rest. The total static force is calculated as: 𝐹𝑡𝑜𝑡𝑎𝑙 = 𝑚𝑡𝑜𝑡𝑎𝑙 × 𝑔 = 1,052.5 × 9.81 = 10,324.98 N Since this load is supported by two rear wheel springs, the static force per spring is: 𝐹𝑠𝑝𝑟𝑖𝑛𝑔 = 𝐹𝑡𝑜𝑡𝑎𝑙 10,324.98 = = 5,162.49 N 2 2 Spring Stiffness Calculation After the static force on each spring is obtained, the next step is to determine the appropriate spring stiffness value. Spring stiffness is a fundamental parameter in suspension systems because it indicates the amount of force required to produce a certain deflection. This value must be large enough to support the vehicle load without causing excessive deformation, but still allow for a comfortable response within the desired frequency range. In this study, spring stiffness was calculated based on the static force per spring and an assumption of maximum deflection of 100 mm (0.10 m) under full load conditions, namely: 𝑘= 𝐹𝑠𝑝𝑟𝑖𝑛𝑔 5,162.49 = = 51,624.9 N/m 𝛿 0.10 These values represent the stiffness required for each rear wheel spring of an electric vehicle. Calculation of Spring Natural Frequency Natural frequency is a key dynamic parameter in suspension design because it is directly related to passenger comfort due to vertical vibrations. This value is determined by a combination of spring stiffness and effective mass acting on the system. MICHAEL KURNIAWAN 6 Study Case According to ISO 2631-1, the recommended natural frequency for passenger vehicles is in the range of 1.0–1.5 Hz. Therefore, calculations are performed to ensure that the suspension system is within this range. The natural frequency of the mass-spring system is calculated using Equation (3): 𝑓= 1 𝑘 1 51,624.9 √ = √ = 1.11 Hz 2𝜋 𝑚 2𝜋 1,052.5 These results show that the natural frequency of the rear suspension is within the optimal comfort zone according to ISO 2631-1. Damping Coefficient Calculation In addition to stiffness and natural frequency, the damping coefficient is an important component because it absorbs vibration energy and limits the amplitude of oscillation. Too little damping will cause the system to be underdamped, making the vehicle feel like it sways too long, while too much damping can cause over-damped characteristics that make the vehicle feel stiff. For passenger vehicles, the recommended damping ratio is in the range of 0.20– 0.30. In this study, a value of ζ=0.25 was used as a compromise between comfort and stability. The damping coefficient was calculated using Equation (4): 𝑐 = 2𝜁√𝑘 𝑚 = 2(0.25)√51,624.9 × 1,052.5 = 3,686.3 Ns/m Discussion Based on the calculation results, several key findings were obtained as follows: 1. The natural frequency of 1.11 Hz indicates that the suspension system is within the optimal comfort range (1.0–1.5 Hz) as recommended by ISO 2631-1 [10]. This value indicates that the suspension is neither too soft (floating) nor too stiff, making it suitable for daily use in passenger vehicles. 2. The spring stiffness of 51.625 N/m per wheel is within the characteristic range for light to medium electric vehicles. According to Robert Smith [11], springs with moderate stiffness provide a balance between stability and comfort: springs that are too stiff accelerate vibration damping but reduce comfort, while springs that are too soft can cause a floating effect that reduces vehicle control. 3. The damping coefficient of 3.686 Ns/m with a damping ratio of 0.25 indicates that the system is lightly underdamped. Studies by Michael Brown [12] and Daniel Harris [13] state that this range is ideal for passenger vehicles because it effectively MICHAEL KURNIAWAN 7 Study Case dampens vibrations without making the suspension feel stiff. 4. The dominance of rear mass distribution due to the position of the electric motor requires special calibration of the rear suspension. In line with the findings of Emily Turner [14], the rear suspension of an EV should be designed to be slightly stiffer than the front suspension to prevent bottoming during acceleration and maintain vehicle pitch balance. Figure 1. Vertical oscillation response graph of the rear suspension. The graph shows that the damping ratio value greatly affects the comfort characteristics of the suspension. Systems with ζ too small tend to experience prolonged oscillations, thereby reducing comfort despite a fast initial response. Conversely, systems with ζ too large are indeed quickly damped, but risk feeling stiff and less responsive to small disturbances. The ζ=0.25 value used in this study was found to provide the most balanced damping response, with an amplitude approaching zero in approximately 3 seconds. CONCLUSION This study examines and analyzes the design of the rear suspension system on a four-wheel electric vehicle with a rear motor configuration. The main objective of the study was to determine the suspension parameters capable of providing optimal comfort based on the ISO 2631-1 standard. The analysis was performed analytically using a onedegree-of-freedom mass-spring-damping model, with the support of Microsoft Excel and Python to improve numerical precision and visualization of the results. Based on data from small to medium-sized electric vehicles, the following results MICHAEL KURNIAWAN 8 Study Case were obtained: 1. The total mass acting on the rear suspension is 1,052.5 kg, resulting in a static force per spring of 5,162.5 N. 2. The spring stiffness required, assuming a maximum deflection of 0.10 m, is 51,625 N/m. 3. The natural frequency of the suspension system is 1.11 Hz, which is within the optimal comfort range (1.0–1.5 Hz) according to ISO 2631-1. 4. The damping coefficient corresponding to a damping ratio of 0.25 is 3.685.63 Ns/m, which indicates a suspension character that balances comfort and stability. Analysis of the damping ratio variation from 0.10 to 0.40 shows that a value of 0.25 produces the most optimal damping time and oscillation response. The system is capable of damping vibrations in approximately 2.3 seconds without sacrificing comfort or increasing stiffness excessively. Thus, the rear suspension design proposed in this study is considered to have met the comfort criteria based on the natural frequency and damping approach. These results can be used as an initial reference in the development of electric vehicle suspension systems with asymmetrical mass distribution due to the placement of electric motors at the rear. REFERENCE MICHAEL KURNIAWAN 9 Study Case MICHAEL KURNIAWAN 10