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Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Modeling of pneumatic suspensions in
"Universal Mechanism" software
Моделирование пневмоподвесок в программном комплексе «Универсальный механизм»
Dmitry Pogorelov & Alexander Rodikov
Laboratory of Computational Mechanics
Bryansk State Technical University
General information / Общая информация
Pneumatic elements and models / Пневматические элементы и их модели
Finite element model of air spring bellows / МКЭ модель баллона
пневморессоры
Verification and example / Тестирование и пример
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
General information
Suspensions with air springs (pneumatic suspension)
•Passenger railway transport
•Automobiles (buses, trucks, passenger cars)
•Monorail trains
•Maglev trains
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
General information
Suspensions with air springs (pneumatic suspension)
Advantages of air suspension over coil springs:
Mendia-Garcia et al. A survey on the modelling of air springs–secondary suspension in railway vehicles. Vehicle System Dynamics. 2020.
•Maintains a constant ride height for any load by increasing or decreasing bellows pressure
•Increase in suspension stiffness with increasing load.
•High pass filtering capability. Low suspension frequency (soft suspension).
•Damping capability of some air suspensions.
•The ability to change the dynamic stiffness in the low-frequency range by changing the area of the
orifice (the connection of the cylinder with the reservoir using the orifice).
•More comfortable suspension and better high frequency insulation due to low spring rate and low
friction.
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
General information
Suspensions with air springs (pneumatic suspension)
Disadvantages of air suspension:
Mendia-Garcia et al. A survey on the modelling of air springs–secondary suspension in railway vehicles. Vehicle System Dynamics. 2020.
•High maintenance costs.
•Increased risk of injury from hot or sharp objects.
•Low spring rates usually require an increase in roll stiffness by special means.
•Damage to an air spring or pneumatic system can leave the crew without suspension; for this
reason, an emergency rubber spring is placed under the bellows.
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
General information
Suspensions with air springs (pneumatic suspension)
Typical air suspension for a passenger railway car
Auxiliary chamber
Reservoir
Comp-
ressor
Leveling valve
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
General information
Pneumatic elements in UM9:
•Air springs
•Rigid chambers
•Pneumatic lines
•Orifices
•Height control valves, HCV (leveling valves)
•Compressors
•Line connection (simple node)
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
General information
Basic governing equations
Ideal gas law
Sutherland's law for dynamic viscosity
Polytropic thermodynamics process
Pilytropic index for air: (isothermal process)
(adiabatic process)
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
General information / Общая информация
Pneumatic elements and models / Пневматические элементы и их модели
Finite element model of air spring bellows / МКЭ модель баллона
пневморессоры
Verification and example / Тестирование и пример
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
Chamber with constant volume
Polytropic process
Mass exchange
Temperature (for oscillations only)
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
Air spring
•Tabular model
•Nishimura model
•Berg model
•Thermodynamic model
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
Tabular model of air spring
Static model
1T15-M0 Numatics ASNS10-2-1
Manufacturers often supply information about air spring properties:
load/height and volume/height diagrams for different pressure (static data)
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
Tabular model of air spring
Mathematical model
Polytropic process
Mass exchange
Interpolation of static data
Nonlinear equation for
computation of pressure in
dependence of height and mass
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
Tabular model of air spring
Mathematical model of an isolated air spring
Force versus height for static and dynamic load are compared in the figure. Plots for dynamics
load are drawn by the thick line.
Results are computed for n = 1.38, static load and height F=12kN, h = 0.5m.
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
Pneumatic lines
A stationary line model includes a dependence of the mass flow rate on the
pressure drop
•“Atlas “
•Fluid mechanics
•Darcy-Weisbach
“Atlas” model
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
Pneumatic lines
P. Beater, Pneumatic Drives, Berlin Heidelberg: Springer-Verlag, 2007
The dynamic line model is based on the continuity equations, the equation for the dynamics
of a small section of the flow, and the equation for a polytropic process.
The line is divided into N equal segments, partial derivatives are replaced by finite differences.
As a result, we have a system of ordinary differential equations.
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
Height control valve
HCV –height control valve LV –leveling valve
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
Height control valve
HCV casing Control arm
link
Neutral position
Supply position (increase pressure) Exhaust position (decrease pressure)
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
Height control valve
The main HCV characteristic is the dependence of the volume flow rate on the control
arm angle
Examples of flow rate curves
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Pneumatic elements and models
Equations of an arbitrary pneumatic system
1. Chamber and air spring
+ for an air spring
2. Pneumatic line
a) Stationary model
b) Dynamic model
3. Connection of lines .
In the case of stationary models of lines we have a system of nonlinear algebraic
equations, which is solved by the Newton-Raphson method.
In the case of dynamic models of tubes, we have a system of differential and algebraic
equations, which is solver by a special solver.
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Finite element model of air spring bellows
General information / Общая информация
Pneumatic elements and models / Пневматические элементы и их модели
Finite element model of air spring bellows / МКЭ модель баллона
пневморессоры
Verification and example / Тестирование и пример
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Finite element model of air spring bellows
A special finite element has been developed that allows modeling the dynamics of an
air spring bellows.
Pogorelov, D.Y. The trapezoidal finite element in absolute coordinates for dynamic modeling of automotive tire
and air spring bellows. Part 1: Equations of motion / D.Y Pogorelov, A.N. Rodikov // Transport Problems. 2021. –
V.16. –No. 2. –P. 141-152
Model verification will be carried out jointly with Chinese colleagues from Shijiazhuang
Tiedao University using experimental test data.
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Finite element model of air spring bellows
Computation of lateral force in
dependence on displacement
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Finite element model of air spring bellows
Computation of vertical force in
dependence on displacement
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Finite element model of air spring bellows
Torsional buckling
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Verification and example
General information / Общая информация
Pneumatic elements and models / Пневматические элементы и их модели
Finite element model of air spring bellows / МКЭ модель баллона
пневморессоры
Verification and example / Тестирование и пример
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Verification and example
Verification
Air spring connected with auxiliary chamber by a pipeline
Katsuya Toyofuku, Chuuji Yamada, Toshiharu Kagawa, Toshinori Fujita, "Study on dynamic characteristic analysis
of air spring with auxiliary chamber," JSAE Review, vol. 20, no. 3, pp. 349-355, 1999.
Experiment scheme
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Verification and example
Verification
Comparison of simulation with experiment. Amplitude 1 mm
Polytropic index for auxiliary chamber
n = 1.2 n=1.38
Dynamic stiffness graph
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Verification and example
Verification
Comparison of simulation with experiment. Amplitude 5 mm
Polytropic index for auxiliary chamber
n = 1.2 n=1.38
Dynamic stiffness graph
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Verification and example
Railway model with air suspensions
KTX motor car
Comparison of suspensions with isolated and interconnected air springs
Interconnected air springs
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Verification and example
Railway model with air suspensions
Comparison of vertical accelerations for various suspension configurations of air suspensions
Isolated air springs. Vertical dampers in operation
Interconnected air springs. Vertical dampers disabled.
Computer simulation in railway transport: dynamics, strength, wear. Bryansk, Russia, 2022
Modeling of pneumatic suspensions in
"Universal Mechanism" software
Моделирование пневмоподвесок в программном комплексе «Универсальный механизм»
Dmitry Pogorelov & Alexander Rodikov
Laboratory of Computational Mechanics
Bryansk State Technical University
General information / Общая информация
Pneumatic elements and models / Пневматические элементы и их модели
Finite element model of air spring bellows / МКЭ модель баллона
пневморессоры
Verification and example / Тестирование и пример