Analysis and Implementation of Input Load Effects on an Air Compressor Piston in MSC.ADAMS

Analysis and Implementation of Input Load Effects on an Air Compressor Piston in MSC.ADAMS

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 177 (2017) 554 – 561 XXI International Polish-Slovak Conference “Machin...

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Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 177 (2017) 554 – 561

XXI International Polish-Slovak Conference “Machine Modeling and Simulations 2016”

Analysis and implementation of input load effects on an air compressor piston in MSC.ADAMS Alzbeta Sapietova*, Juraj Bukovan, Milan Sapieta, Lenka Jakubovicova Faculty of Engineering, Department of Applied Mechanics, University of Žilina, Slovak Republic

Abstract The solver often knows the theoretical background very well, but its application into a virtual prototype in a specific software environment requires thorough knowledge of the environment as well as a lot of experience. This paper presents modelling of load effects on a piston in a V-type twin-piston air compressor in the MSC. ADAMS software environment. 2017The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license © 2017 © Published by Elsevier Ltd. This (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of MMS 2016. Peer-review under responsibility of the organizing committee of MMS 2016 Keywords: MSC. ADAMS; piston compressor; modelling; simulation; analysis;

1. Introduction A necessity when using any calculation method is the knowledge of theoretical background of the issue. It is a prerequisite for creating a proper mathematical model, analysis of the results and their subsequent application in technical practice [1, 2]. Each solving professional aims at creating a virtual prototype (VP) in the manner that the results of solving are consistent with reality, thus bringing the desired benefits [3]. The solver often knows the theoretical background very well, but its application into a virtual prototype in a specific software environment requires thorough knowledge of the environment as well as a lot of experience. This paper presents modelling of load effects on a piston in a V-type twin-piston air compressor (Fig. 3). It must be said that compressor, in a broader sense, is a working machine designed to compress gasses and vapours. In other words, compressor is an electromechanical device used to convert mechanical energy into pressure energy (compressed gas energy). The compressor operating cycle consists of four strokes (Fig.1). The entire

* Corresponding author. Tel.: +421 41 5132950; fax: +421 41 56 52 940 E-mail address: [email protected]

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of MMS 2016

doi:10.1016/j.proeng.2017.02.260

Alzbeta Sapietova et al. / Procedia Engineering 177 (2017) 554 – 561

compressor cycle takes only one crank turn, and consists of the strokes shown in Fig. 1 [4]. It follows that the forces acting on the piston must be modelled so as to be in conformity with the theoretical background [5].

Fig. 1. Diagram of the cycle of an idealized single-stage reciprocating compressor with clearance space Vs.

2. Action force effects acting on hydraulic motor piston Figure 2 shows the course of the loading force acting on the piston from compressed air, depending on the instantaneous piston position within the entire operating cycle. The force carrier in the virtual prototype (VP) acts perpendicular to the piston front surface. A constant force from atmospheric pressure acts from the opposite side, from the crankcase, during the entire operating cycle.

Fig. 2. Courses of force effects acting on the piston.

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2.1. Forces acting on the piston during compression and discharge During compression, the increasing pressure causes the increase in the force acting on the piston until the overpressure in the cylinder reaches the value Δp (Fig. 1). Then the discharge valve opens, pressure and force (Fmax) do not rise further and remain constant until reaching the top dead centre. The polytropic process is described by the following equation:

‫ ݊ ݒ݌‬ൌ ‫ ݊ͳݒ ͳ݌‬,

(1)

where ݊ is the polytropic exponent taking the values ‫ۃ‬1;1,4‫ ۄ‬for diatomic gases that include air as well. Its actual size basically depends on the heat exchange between the gas and the environment. For our calculation we choose the coefficient 1.2, which is often used in practice for conventional air compressors, in which one part of the generated heat passes through the cylinder walls, and the other part increases the gas internal energy [4]. Substituting in equation (1) the values known from the bottom dead centre, i.e. atmospheric pressure ‫ ܣ݌‬and volume at the cycle beginning ‫ Ͳݒ‬, we obtain the equation for pressure in any piston position during compression: ݊

ܸ

‫ ݌‬ൌ ‫ ܣ݌‬ቀ ܸͲ ቁ .

(2)

After the substitution, where we apply ‫ ݌‬ൌ ‫ܨ‬Ȁܵ; ܸ ൌ ܵ‫ݔ‬, and after modifications we obtain the equation for the force acting on the piston during compression, depending on its distance from the cylinder upper wall: ‫ݔ‬

݊

‫ ܨ‬ൌ ‫ ܵ ܣ݌‬ቀ ‫ Ͳݔ‬ቁ .

(3)

The value x0 at the beginning of the cycle is obtained using the equation for proportional clearance space:

ߝൌ

ܸ‫ݏ‬ ܸ‫ݖ‬

ܵ‫ݏ ݔ‬

ͳͲͲ ൌ

ܵ‫ݖ ݔ‬

ͳͲͲ ൌሶ ͷΨǤ

(4)

Equation (4) shows that if xz=100mm, then xs=5mm. Following from Fig. 2 the following applies:

‫ Ͳݔ‬ൌ ‫ ݖݔ‬൅ ‫ ݏݔ‬Ǥ

(5)

Knowing the general formulas for force and pressure during compression, we can use them to find a distance at which the discharge valve opens. We know the absolute pressure ‫ ͳ݌‬ൌ ͸Ǥ ͳͲͷ ܲܽ which opens the valve (Fig. 2). Based on equation (1), and after modification we obtain: ‫݌‬

‫ ͳݔ‬ൌ ‫ Ͳݔ‬ට ‫ ܣ݌‬Ǥ

(6)

ͳ

Formulas for the maximum force Fmax and the force from atmospheric pressure Fa: ݊

‫ݔ‬

‫ ݔܽ݉ܨ‬ൌ ‫ ܵ ܣ݌‬ቀ‫ Ͳ ݔ‬ቁ ǡ ͳ

‫ݔ‬

݊

‫ ܣܨ‬ൌ ‫ ܵ ܣ݌‬ቀ Ͳ ቁ Ǥ ‫Ͳݔ‬

(7)

(8)

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2.2. Forces acting on the piston during expansion and intake At the beginning of expansion, in the top dead centre, and at clearance space volume Vs, the cylinder has the pressure p1, but with increasing volume the pressure very quickly drops to the value pA. Similarly, the value of force decreases from Fmax to FA (Fig. 2). Then the intake valve opens and the force and pressure are constant until reaching the bottom dead centre. Based on equation (1) we obtain:

‫ ݊ʹܸ ʹ݌‬ൌ ‫ ݊ݏܸ ͳ݌‬՜ ‫ ʹ݌‬ሺܵ‫ ʹݔ‬ሻ݊ ൌ ‫ ͳ݌‬ሺܵ‫ ݏݔ‬ሻ݊ Ǥ

(9)

We express the pressure p2, which is directly proportional to the force F2: ݊

‫ݔ‬

‫ ʹ݌‬ൌ ‫ ͳ݌‬ቀ ‫ ݏ‬ቁ ǡ

(10)

‫ʹݔ‬

݊

‫ݔ‬

‫ ʹܨ‬ൌ ‫ ܵ ͳ݌‬ቀ‫ ݏ ݔ‬ቁ Ǥ

(11)

ʹ

We seek x2 and obtain it from equation (9): ݊

ܲ

‫ ʹݔ‬ൌ ‫ ݏݔ‬ටܲͳ .

(12)

ʹ

The distance at which the intake valve opens: ݊

ܲ

‫ ʹݔ‬ൌ ‫ ݏݔ‬ටܲͳ Ǥ

(13)

‫ܣ‬

3. Virtual prototype in the ADAMS/View software environment Figure 3 shows a virtual prototype of a twin-piston air compressor with one degree of freedom, modelled parametrically in the MSC. ADAMS software environment.

Fig. 3. Virtual prototype 2 of a piston compressor in ADAMS/View.

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Dynamic analysis is performed in the full scope of the mechanism movement. We consider that the compressor intakes air of atmospheric pressure pA = 105 Pa. The gas overpressure at discharge is Δp = 5.105 Pa. Proportional clearance space ε = 5% is chosen from the interval for real piston compressors: εR = 2÷8%. The piston diameter is d = 60mm. For the purposes of calculating we find the weights of the bodies together with mass moments of inertia directly in the MSC.ADAMS software. 4. Applying forces Before the very force constructing we must prepare the environment in which it would be possible to read the values of forces depending on the piston position. We crate two markers: one for the frame (cylinder) and one for the piston. These are: MARKER_36 [245.0, 45.0, 0.0] and MARKER_37 [245.0, 135.0, 0.0]. The created Point-to-Point meters (MEA_ZDVIH1 and MEA_ZDVIH_2) will measure the distance of these markers (Translational displacement): MEA_ZDVIH_1 >> MARKER_36 vs. PIEST1.cm. >> Component: R (Cylindrical) MEA_ZDVIH_2 >> MARKER_37 vs. PIEST2.cm. >> Component: R (Cylindrical) Further we will propose sensors to stop the simulation upon achieving the prescribed distance of the piston from the upper cylinder wall x1 or x2. The times obtained in this way are required to compile commands to control the simulation. Expressions monitored by sensors (Expression) are the created meters MEA_ZDVIH_1 and MEA_ZDVIH_2, for which we set the appropriate values (Value) x1 and x2 calculated from equations (6) and (13). Modifying the sensor we specify error tolerance by one order, since the values x1 and x2 are accurate to 2 decimal places. We also set a higher temporal accuracy of the sensor, because this time will be needed to create a script for controlling the simulation. It is also necessary to identify the following functions: x Generate additional Output Step at event; x Terminate current simulation step and Stop – the sensor stops the simulation run and a warning window is displayed, informing which sensor stopped the simulation and in which moment. The sensor creation environment is shown in Fig. 4.

Fig. 4. Parameter setting for SENSOR_1.

Alzbeta Sapietova et al. / Procedia Engineering 177 (2017) 554 – 561

For each stroke we create one sensor, i.e. four sensors altogether. We run interactive simulation with the time 0.04s and the number of steps 1000. Each sensor stops the simulation 2 times during the entire cycle – one time during compression and one time during expansion for the given cylinder. After finding the times necessary for controlling the simulation we must modify all sensors so that they would not later interfere with the course of dynamic simulation. We don not deactivate them, because they produce an additional step to the simulation at the moments of engagement and disengagement of forces. This means we switch off the function: Terminate current simulation step and... . On each piston we apply 4 different single-component forces (Single-Component) with parameters Run-time Direction: Body Moving || Construction: Pick Feature. For all forces we choose the following geometric elements: x PIEST1 ground.POINT_3 MARKER_20.Z x PIEST2 ground.POINT_4 MARKER_27.Z The correct orientation of forces is then provided by selecting positive or negative sign in front of the given force function. The functions of individual forces take the following form: 1. Constant force from atmospheric pressure inside the crankcase. SFORCE_ATM1: -10**5*pi*0.03**2 SFORCE_ATM2: 10**5*pi*0.03**2 2. Increasing force during compression (Equation 3). SFORCE_KOM1: 10**5*pi*0.03**2*(105/MEA_ZDVIH1)**1.2 SFORCE_KOM2: -10**5*pi*0.03**2*(105/MEA_ZDVIH2)**1.2 3. Force varying depending on x during expansion (Equation 11). SFORCE_EX1: 6E5*pi*0.03**2*(5/MEA_ZDVIH1)**1.2 SFORCE_EX2: -6E5*pi*0.03**2*(5/MEA_ZDVIH2)**1.2 4. Constant force during discharge Fmax. SFORCE_KONS1: 10**5*pi*0.03**2*(105/23.59)**1.2 SFORCE_KONS2: -10**5*pi*0.03**2*(105/23.59)**1.2 5. Simulation script The role of the created simulation script during simulation is change the load on the pneumatic compressor piston according to the previously presented theoretical background. We compile a new simulation prescription (Script) for the solver (Fig. 5). It is basically a code containing commands activating and deactivating, in this case, the prescribed forces at the right moment. The total duration of simulation is 0.04s and the time step (DTOUT) is chosen according to the number of decimal places of the final time of the specified section of simulation. Moreover, each sensor adds yet another necessary simulation step reducing the variation from the End time.

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Fig. 5 Simulation script controlling the forces in dynamic analysis.

6. Conclusion By running the simulation, and using the prepared simulation script, we can carry out a dynamic calculation of a VP of the pneumatic machine mechanism. Simulation type – DYNAMIC – allows us to carry out dynamic simulations on models that have any number of degrees of freedom (DOF). We can obtain time courses of task solving for position, velocity or acceleration [6]. We can also obtain time courses of response effects in the VP geometric constraints, driven by the system of external loading effects. Using the ADAMS/View environment we can perform analysis and synthesis of constrained mechanical systems in terms of their mechanical properties, with consideration of rigid and deformable bodies [7-9]. It must be said that during dynamic simulation Adams/Solver solves a complete set of nonlinear differential and algebraic equations (DAE) [10-13]. It is a complex and computationally intensive type of simulation, and it is designed for solving virtual prototypes having one or more degrees of freedom. Acknowledgements This work has been supported by grant project VEGA No. 1/0795/16. References [1] M. Kubiak, W. Piekarska, Z. Saternus, T. Domański, S. Stano, Simulations and Experimental Research on Laser Butt-welded T-joints, METAL 2014: 23rd International Conference on Metallurgy and Materials, Czech Republic, 2014, pp. 726-731. [2] M. Kubiak, W. Piekarska, Z. Saternus, T. Domański, Numerical prediction of fusion zone and heat affected zone in hybrid Yb:YAG laser + GMAW welding process with experimental verification, Procedia Engineering, 136 (2016) 88 – 94. [3] T. Domanski, W. Piekarska, M. Kubiak, Z. Saternus, Determination of the final microstructure during processing carbon steel hardening, Procedia Engineering, 136 (2016) 77-81. [4] M. Pavelek, etal. Thermo mechanics, Brno : Academic publishing CERM, 2003, pp. 284. [5] A. Sapietova, M. Sapieta, V. Dekys, P. Pechac, Application of computational and design approaches to improve carrier stability, Procedia Engineering, 96 (2014) 410-418. [6] J. Vavro, J. Vavro, jr., P. Kovacikova, P. Bezdedova, Kinematic and dynamic analysis of the manipulator for removal of rough tyres, Procedia Engineering, 136 (2016) 120-124.

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