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Literature review
This chapter provides an introduction and explains the necessary background theory for the reader to get familiarized with the components, working, and thermodynamic model of the air springs. It further deals with the working of Electronic Level Control and the identification of appropriate control variable.
Background theory
Vibration isolation is an important process in vehicles which is implemented to isolate the body of interest from the source of vibration. This is used in many components of the vehicle such as the engine, powertrain etc., However, one of the most important utilisation of this process is to minimise the vibrations to the occupants in the passenger cabin and also cargo area in case of trucks, which is the area of interest for this thesis.
Vibration isolation for passenger cabin and cargo area is achieved with the help of suspension systems. The suspension system generally consists of three major parts: “a structure that supports the vehicle’s weight and determines suspension geometry, a spring that converts kinematic energy to potential energy or vice versa, and a shock absorber that is a mechanical device designed to dissipate kinetic energy.” [1]
The important functions for the suspension system are to provide a relatively good ride quality over rough roads and terrains while ensuring good road holding i.e., the wheels remain in contact with the ground and good vehicle handling. It also can compensate for pitch and roll of the vehicle while accelerating, braking, and taking turns. This is achieved by the suspension system which connects the vehicle body and the wheel by reducing the Degree of Freedom (DOF) of the wheels.
Typically, a vehicle’s mass can be divided into two parts: sprung mass and unsprung mass (Figure 1). Sprung mass is the part of the vehicle’s total mass that is ‘suspended’ or supported by the suspension. It generally includes the chassis, engine, passengers, cargo etc., and unsprung mass is the portion of the vehicle’s total mass that is below the suspension, i.e., the mass which is not supported by the suspension and this includes the axles, wheels, tyres, portion of suspension elements, powertrain and brakes etc.
The sprung and unsprung masses have large influence over the choice of spring stiffness and other suspension characteristics such as preload force. Depending on the sprung mass, the spring is adjusted such that there is zero deflection on the damper. The force exerted on the spring due to the adjustment is called the preload force, also it is the force required to compress the spring. For example, if the preload force is set to 50 N, for force up to 50 N there is no compression on the spring, and the spring starts compressing based on its spring characteristics for forces above 50 N. Preload is a very important parameter for influencing suspension characteristics and vehicle behavior. But it is to be noted that adjusting the preload force has no influence on spring stiffness characteristics.
However, with higher payload, the potential energy required to store in the suspension increases i.e., the stiffness of the spring must be high to reduce the static deflection. But the mechanical springs have limited energy storage capacity per unit volume; also, there is a limit to which the preload on the mechanical springs can be adjusted. Therefore, it leads to heavy and bulky mechanical springs especially for higher payloads in heavy commercial vehicles.
This is an undesirable consequence as it increases weight and has a negative impact on payload and fuel efficiency. Thus, an alternate solution is required, which led to the introduction of air or pneumatic springs.
Air springs
Air springs, or pneumatic springs, is essentially a column of gas, (which is usually air) confined in a rubber and fabric container. The energy storage capacity of the air springs is much higher than that of the mechanical springs and thus they have lower geometrical dimensions than mechanical springs with similar suspension characteristics. Air springs have become more prominent in heavy commercial vehicles such as trucks, buses etc., and also in luxury passenger cars as they provide good ride comfort, vehicle handling stability while maintaining good road holding with little destruction to the road [2].
Construction of air suspension
A typical air spring consists mainly of a flexible rubber bellow, a piston around the rubber bellow and a duct for the passage of air in and out of the spring. There are other parts of the air spring as depicted in Figure 2. The air bellow inflates and deflates around the piston by regulating the air in the bellow from the auxiliary volume.
An air spring’s ability to support the sprung mass of the vehicle is due to the effective area of the spring and the gas pressure in the air spring [4]. The characteristics of the effective area of the air spring i.e. whether it is constant, increases or decreases during the deflection depends on the design of the air spring, the piston, and other components (Figure 3).
Figure 3: Effective area and force as a function of deflection for different air spring types [5]
There have been different types of air springs which were developed over the years. These include fully supported sleeve, rolling lobe, restrained rolling lobe, bellobe, reversible diaphragm, bladder type and the hydropneumatic type. [6]. At Scania, roller type bellows are utilised, sometimes variation to the roller type bellows are used [3]. Trucks predominantly use the straight piston (Case 2 from Figure 3) and in buses different shapes of pistons are used [5].
The most common type of air suspension system used in Scania trucks is illustrated in Figure* 4. The air bellow or the air spring is connected to the frame on one end and to the leaf spring on the other end. The leaf spring is attached to the spring bracket which acts as a hinge or pivot point for the leaf spring. Rubber bushings are installed at the pivot point. The spring bracket is fastened to the frame. The axle is placed between the air spring and the pivot point. The ride height sensor is fastened to the frame and top of the axle whose rotary angles correspond to the ride height.
Figure 4: Scania air suspension setup 1) frame, 2) spring bracket, 3) rubber bushing, 4) leaf spring, 4) axle, 5) damper, 6) air bellow, 7) ride height sensor [7]
Working principle of air suspension
Two processes occur simultaneously during the working of the air suspension. One is the process of variation of volume which results in variation in air pressure, force on the spring and the air temperature; and the other is heat balance with the environment due to variation in temperature in the air spring area [8].
In a simple air suspension system, the air spring would be connected to an auxiliary volume via hoses or pipes. When the vehicle approaches an aberration in the road, the system experiences vibrations due to which the air springs either compress or expand. This compression or expansion in the air spring results in change in volume and thus a pressure difference arises between the air spring and the auxiliary volume. Depending on the pressure difference, the air either flows into the air spring from the auxiliary volume or out of the air spring and into the auxiliary volume.
In a more complex air suspension system with ride height sensors, levelling valves and air compressor, automatic ride height control is implemented. This type of system offers relatively constant natural frequency irrespective of the payload. When the payload is changed, the air in the spring is pumped in or out causing increase or decrease in pressure in the air spring. This causes the vehicle to return to its design ride height. Since the spring stiffness depends on the absolute pressure of the air confined in the bellows, with a change in pressure, the spring stiffness also changes, thus offering a constant natural frequency for the system [6].
With the suspension system used at Scania, described in Figure 4, any vibration experienced by the vehicle causes the air spring to move in a path as the red arc with the spring bracket as the pivot point as illustrated in Figure 5. Thus, the air bellow is compressed or expanded as the piston is pushed in and out of the rubber bellow causing change in volume, air pressure and temperature.
Figure 5: Scania air suspension setup. Red arc indicates the path of the piston base [5]
Due to this type of movement of the air spring, there is a small angle θ obtained at the air spring as depicted in Figure 6. Sometimes an axial displacement is also obtained depending on the movement. However, this small axial displacement and angular displacement are often neglected while developing models. [3]
Figure 6: Air bellows depicting axial displacement λ and angle θ [3]
Advantages and disadvantages of air springs
The air suspension systems are being preferred more and more over the mechanical suspension systems for various reasons, some of them are listed: [6], [9]
• Provides variable spring rate with relatively constant natural frequency.
• Provides better passenger, cargo, and vehicle protection due to the low spring rate and low friction.
• Has relatively less destruction on roads.
• Adjustable and higher range of cargo capacity is possible.
• Reduction in the structurally transmitted noise.
• It provides variable ride height.
The air suspension system also has some disadvantages compared to the conventional mechanical suspension systems.
• They are more expensive both in terms of the components themselves and for maintenance of the system.
• They are more prone to damage by sharp and hot objects.
• Their temperature range is restricted compared to those of mechanical springs.
Modelling and thermodynamics of air springs
Lot of research has been conducted in the pursuit of modelling air springs using mathematical models for integrating them into vehicle models and simulations.
Sortti [3] developed an air spring model to calculate the forces acting in terms of deflection of air spring, mass change and volume change. The model does not consider hysteresis and accounts the errors in the model to this. Jin et al. [10] developed a mathematical model to express the stiffness performance of air-spring in ADAMS by solving the differential equations obtained by considering the non-linear relation between effective area and air spring’s height. Alonso et al. [11] analysed the effect of air spring on the comfort by comparing the correlation of theoretical models with the experimental results from the test bench and studying the effect of different factors of air springs on comfort by performing DOE. Quaglia et al. [12] derived the stiffness of their air-spring model based on the basic force-distance relationship. Tang et al. [13] derived a mathematical model of an air spring, confirmed its validity by comparing with experimental results and integrated the model in a multi-body dynamic model to perform various simulations. W. D. D, Robinson et al. [4] presented an analytical model of an air spring and experimentally validated the air spring-valve-accumulator pneumatic system. Chang et al.[8] developed an air spring model to integrate into a multi-body dynamic model using co-simulation method and was validated using experimental results. Presthus [6] investigated different air spring models and the input parameters for the GENSYS model is identified. B. Sreedhar et al. [14] derived a simple air suspension model using the performance curves of air springs from experiments to implement the level control in a multi-body dynamics model.
As stated by Mazzalo et al. [15] in their research paper, there are six different models for modelling an air spring mathematically viz., Thermodynamic model, Vampire model, Berg model, Nishimura model with linear damping, Nishimura model with quadratic damping and, Spring and dashpot model. Each model has its own advantages and disadvantages. Due to the scope of the thesis and the available parameters, a thermodynamic model is best suited to represent the air spring model with the required simplicity and accuracy.
While representing the air springs using a thermodynamic model, two different processes take place: isothermal process and adiabatic process. For a given air spring, the minimum spring rate occurs during the isothermal process and the maximum spring rate occurs during an adiabatic process.
Isothermal process
Gases heat up during compression and cool down during expansion. If the jounce and rebound of the air spring happens so slowly that all the heat generated during compression or adsorbed during expansion dissipates entirely, the process is known as isothermal process. Isothermal process can be described using Equation (1)
p1 .v1 = p2 .v2 (1)
p1 = initial absolute pressure (Pa)
p2 = final absolute pressure (Pa)
v1 = initial volume (m3) and
v2 = final volume after compression or expansion (m3)
The volume indicated in the expression implies total volume i.e., if an auxiliary volume or air tank is connected to the suspension, the volume of the auxiliary chamber must be included with the initial and final volume after deflection.
Table of contents :
1 Introduction
1.1 Problem statement
1.2 Thesis goals
2 Literature review
2.1 Background theory
2.2 Air springs
2.2.1 Construction of air suspension
2.2.2 Working principle of air suspension
2.2.3 Advantages and disadvantages of air springs
2.2.4 Modelling and thermodynamics of air springs
2.3 Understanding Scania pneumatic configurations
2.4 Decoding the working of Electronic Level Control
2.5 Current air suspension models in ADAMS/Car
2.6 Identification of control variable
3 Methodology and method
3.1 Methodology
3.2 Method of implementation
4 Physical testing
5 Implementation of air suspension model
5.1 Implementation of static model in ADAMS
5.2 Implementation of dynamic model in ADAMS
5.2.1 Implementation of PID Controller
5.2.2 Implementation of low pass filter
5.2.3 Tuning of PID controller
6 Results and validation
6.1 Validation of static Model
6.2 Validation of dynamic model
7 External validity of the model
8 Conclusions and discussion
8.1 Conclusions
8.2 Future work
9 References
