Design and calculation of double arm suspension of a car

Suspension system is one of the challenging portions in designing a vehicle. The complete stability of the vehicle under dynamic conditions depends on the suspension system of the vehicle. Suspension system of a vehicle is interlinked with other systems such as steering, Wheels and Brakes. The main objective of this document is to provide complete guidance in designing and calculation of an independent suspension system with double control arms. The required parameters are calculated on considering a prototype vehicle with gross weight of 350 kg such as required stiffness of shock absorbers, Ride frequency, Motion ratio, Coefficient of damping etc. A CADD model was made with CATIA v5 r20 and SOLIDWORKS on the basis of calculations obtained and stress analysis was carried out for this model in various software such as Ansys. The complete assembled model was tested in LOTUS Shark and the result was obtained.


Introduction
According to Douglas L. Milliken and William F. Milliken [1], The design of suspension system for high performance cars involves assumption of parameters such as Roll rate and it involves verifying them at end. Several iterations have been in order to attain perfection in riding conditions in corners considering lateral load transfers. As John C. Dixon [2] elaborately discusses all the parameters related to a suspension system of a vehicle which provides a complete understanding of the concepts and our manuscript is scripted in such a way that only the exact required parameters are described and used for the calculation. The independent double arm Suspension system consists of Control arms, springs, Dampers and linkage mechanisms that connect the wheel and the Roll cage of a vehicle. The relative movement between the wheel and the Roll cage is obtained by this suspension system [3]. Double arm independent suspension systems are widely preferred as they have high ride stability and reliability [2]. This is due to negative camber gain they attain, thereby also increasing the traction in corners. This ultimately provides good handling for the vehicle [2][3][4][5]. Here in this design a perfect camber gain is achieved providing a balance between braking grip and cornering grip. The design and calculations carried out is based on a prototype vehicle of mass 350 kg. In Terms of manufacturing coilover shock absorbers, the calculation of coil diameters ratio is also performed [6]. We have figured out an efficient method of approach in designing a suspension system for a vehicle after undergoing an elaborate research work on vehicle dynamics and various methods to design a suspension system of a four wheeled vehicle [1][2][3][4][5][6][7][8][9][10][11][12][13].

Working principle
The basic principle of this type of suspension systems is absorption of mechanical energy and dissipating them as heat in shock absorbers [2]. It provides a relative motion between the wheels and the Roll Cage thereby reducing the force that is transmitted from wheel to Roll Cage [1][2][3]. Thus, the comfort and the safety of passengers relies on the suspension system. In dynamic conditions, the spring compresses storing the impact force (jounce) and the spring expands (rebound), the vibration is ceased by dampers.

Major parameters to understand
1) Caster angle. Consider a wheel from the side view of a car. Inclination of the upper point of the steering axis towards vehicle frame is considered as a positive caster and away from frame is Negative caster [2].  3) Toe-in and toe-out. Consider a pair of wheels from the top view. Difference in distance between front end and rear end of a pair of wheels coins the term toe in and toe out [2]. 4) Kingpin inclination. Considering from the front view, the angular displacement of the steering axis coins the term King pin Inclination (KPI). It is also known as Steering Axis Inclination (SAI) [2].

Force consideration
-Static-force due to gravity, reaction force in wheels.
-Dynamic -longitudinal acceleration and hard braking resulting in dive, lateral forces resulting in rolling of vehicle, vertical gravitational force under dynamic condition of vehicle [3,4].

Design consideration
-The shape and dimension of the control arm or wishbone depends on the available space and the stress withstanding capability (moment of inertia as a factor).
-The front arm can take "A" equivalent shape, the rear can take "A" or "H"-equivalent shape.
-The desired ground clearance was fixed GC = 10" (As per requirement).
-The roll centre axis and pitch centre axis are imaginary axis, they can be determined from the inclination of the control arms with respect to the roll cage and wheel assembly.
1) Roll Center. The axis about which the car tends to roll. This axis intersects the point at which the lines extended from the patch contact point of tyre to instantaneous points of both wheels meet. 2) Pitch center. The axis about which the car tends to dive or squat. -Required jounce: 2"; required rebounce: 2" (As per requirements).
-Methods to find the center of gravity height: a) Practical: either front or rear side of the vehicle have to be lifted to approximate height. Weighing machines have to be placed on both the front wheels and rear wheels of the vehicle. Weight before lifting and after lifting have to be noted and applied in the formula to get approx CG. Formula = (level wheelbase×raised wheel base×added weight on front wheels)/(distance raised×total vehicle weight).
To find CG distance from rear axle = (weight at front×wheel base)/total weight. b) CAD Method: the components must be designed assuming their mass and the position of Centre of gravity must be found in the complete assembled design of vehicle.

Formula and calculations
Calculation for a prototype vehicle on considering: -Track width = 3.75 ft or 1143 mm.

Stiffness calculation
Considering the vehicle to enter a corner at = 41.01 ft/s. The centripetal force due to friction: The centrifugal force: = .
( Lateral load transfer due to lateral acceleration:  Considering vertical forces due to uneven roads "3g force is considered", thus in case of coilover shock absorber, spring chosen or manufactured must be progressive spring or dual rate springs.
Also, from: = + 2 square and grounded , From above equations we can determine the parameters of required spring parameters.

= ,
where -first moment of area, -load, -thickness of pipe, = /4 − . Based on market availability and CAD analysis and values can be determined:  Hence the material selected undergoes very less deformation with a given load. The material chosen is perfectly suitable for Control arms.

Component design and selection
Based on the obtained calculation values, space available, along with the tolerance required, shape and dimension of wishbone and coil spring is found.
Market survey is the most important phase of manufacturing. Inorder to know the availability and presence of different types of raw materials in the market. Based on availability one can decide their own efficient way of manufacturing or to go with OEM products that are available.

Knuckle design
In order to achieve the required riding condition, the knuckle design plays a major role [13]. The fixing of the parameters such as Caster, Camber, Toe angles and King Pin Inclination majorly depends on the design of a knuckle. The dimension and shape of a knuckle is completely dependent on those parameters in order to obtain the efficient ride quality.

King pin inclination
King pin inclination determines the scrub radius. The scrub radius plays a major role while applying brakes. Short long arm suspension usually has positive scrub radius as scrub radius does not vary. The vehicle with diagonal braking system has negative scrub radius, this is due the fact that it aids in braking upon failure of one unit of diagonal braking system. Higher value of scrub radius aids braking and reduces steering effort but increases steering sensitivity to braking. Hence an optimum level must be chosen. Prototyping vehicle is equipped with an KPI of 4°.

Castor angle
Positive castor induces a aligning torque whereas negative castor reduces steering effort. Aligning torque is a favourable factor, so many designs go with a positive castor.
The angle depends on wheel diameter, i.e . Caster angle of 4.43° is considered for the prototyping vehicle.

Camber angle and toe
Negative camber helps in cornering increasing patch contact of outside tires, whereas vehicles of higher mass prefer positive castor as they create stability to the vehicles. Toe plays a major role in straight line stability (toe in) and cornering stability. The fact that camber and toe make the tire wear out soon makes them unpreferable for most commercial vehicles.

Selection and design of wishbones and its material
-There are plenty of materials available in many cross-sectional shapes. Each material has its own Young's modulus value.
-The required material and shape are decided based on the strength of the material.
-The dimension of wishbones and its design is carried out based on the space available along with other important parameters such as Caster, Camber, KPI, roll center and pitch center.
-Wishbone mounting points: Designing the mounting points for the wishbones is an important part. Fixing must be carried out by considering the roll center, pitch center and RC member's strength. The maximum shear stress was calculated and the material for wishbone was selected as Chromoly AISI 4130 seamless tubes (Not limited to this). The Diameters and minimal thickness can be determined with the help of software such as ANSYS.

Part analysis
To determine Diameter and Thickness required, Part analysis is carried out with the software called "ANSYS". By fixing the maximum load and gradually decreasing the diameter and thickness of the pipe, a safer dimension could be found.
As a result of analysis with factor of safety: -Diameter of the pipe: 25 mm.
-Thickness = 1.5mm. Fig. 14 and Fig. 15 shows the analysis of designed wishbones via ANSYS Workbench software. That depicts that the calculated values to design wishbones are prominently best suited for the considered prototype vehicle.

Design and selection of shock absorbers
Based upon the required stiffness value of the vehicle, shock absorbers could be selected or manufactured as required among various types of shock absorbers.
To design a coilover shock absorber, the calculated Diameters ratio and material stiffness of the spring coil have to be considered as primary parameters.

Result analysis
The obtained results have to be properly analysed in order to present the accurate results which in turn shows the best practical outcome.
The coordinates of all assembled parts obtained with the help of Creo, Catia etc. and have to be given as an input in lotus.

Conclusions
The carried out Novel research is in terms of manufacturing a vehicle with an independent double arm suspension, that is elaborated on considering a prototype vehicle of 350 kg. The research manuscript depicts the simplest methodology that could be followed in order to design an accurate suspension system of a car. It covers the basic parameters that have to be known before JOURNAL OF MECHANICAL ENGINEERING, AUTOMATION AND CONTROL SYSTEMS. JUNE 2020, VOLUME 1, ISSUE 1 proceeding with calculations followed by all the basic and advanced calculations such as Stiffness Required, Installation ratio, Wishbone material, Coefficient of damping etc. Based on the obtained values, the components design is carried out. Designing of Coilover shock, Designing of Knuckle and Designing of Wishbones is carried out. The significant usage and every technical aspects are considered while designing, such as the selection of material, type of components, dimension, and cross-section of the component. The calculations obtained are considered enough to satisfy other parameters that have to be possessed while manufacturing a complete vehicle. The test conditions give an overall efficient performance and it proves the effectuality of manufacturing a real-time suspension based on the international market with a proper progression of schematic procedures and methodology. These results demonstrate that a customized, high performance, the operational suspension system can be manufactured easily. The real benefit is, this can assist any person to manufacture and design a suspension system as a high performance operational suspension system. The Ultimate scope of easily understandable and efficiently operational suspension system designing is successfully achieved.