01A1004
AN ENGINE FRICTION MODEL TO SUPPORT EXPERIMENTAL ACTIVITY AND COMPONENT DESIGN - PART II: COMPUTER MODEL V. D'Agostino, D. Guida, A. Ruggiero, A. Senatore Department of Mechanical Engineering University of Salerno Fisciano (SA), Italy Phone +39 89 964325 Fax +39 89 964037 E-mail:
[email protected]
1. ABSTRACT The aim of this paper is to introduce the theoretical results obtained using computer codes realized to investigate on the dynamic behaviours and the friction losses in a reciprocating internal combustion engine. This paper shows the structure of an additional module of CRAFT (Code for Rapid Assessment on Frictional Torque), a computer program developed by the Applied Mechanics Group of the Department of Mechanical Engineering - University of Salerno [1]. This computer code takes into account the effects lubrication regime about piston assembly (piston skirt and piston ring pack), crankshaft and connecting rod journal bearings and valve train to evaluate the friction losses in a sparked ignited internal combustion engine. The CRAFT algorithms are based on more sub-models developed to investigate on the specific friction loss. The following pages show the engine dynamics and friction physical models with the description of engine design data module and the operating conditions user defined. The realized additional modules allow to analyse the piston secondary motions with extremely contained computational time in comparison to the numerical FEM procedures previously used. 2. PISTON ASSEMBLY FRICTION MODEL Compression rings and oil ring have been modelled in the CRAFT sub-models considering pressure cycle values and radial tension of each ring [2-4]. The algorithm assumptions involve mixed and hydrodynamic lubrication, piston ring fully flooded hypothesis, profile and design parameters. The friction of the piston skirt-cylinder liner contact behaves similar to a piston ring, but secondary motions influence notably the lubrication regime as well as the possibility that a contact solid-solid is present. The determination of the friction factor about the piston skirt is strongly influenced from the correct definition of the piston secondary motion. Therefore, a numerical subroutine or an analytical formulations has to be involved in the piston assembly block program to perform simulations on the effects of normal force due to hydrodynamic film pressure and its moment about wrist-pin; normal force due to contacts between surfaces and its moment about wrist-pin; friction force due to hydrodynamic film pressure and its moment about wrist-pin; friction force due to contacts between surfaces and its moment about wrist-pin. The next paragraph describes briefly the introduction of a solid-to-solid contact model, while the following figure shows the improved subroutines of the used computer program in order to get assessments on the piston secondary motions and friction losses considering a dynamical model closer to the analysed phenomena.
TOP RING
CRAFT
SECOND RING
PISTON ASSEMBLY
FRICTION SUBSUB-MODELS
OIL RING PISTON SKIRT
CONTACT FORCES
HYDRODYNAMIC PRESSURE
SECONDARY MOTIONS FRICTION LOSSES
Figure 1: Piston assembly CRAFT additional modules Contact model and symmetry The implementation of an algorithm that allows to simulate the secondary dynamics of the piston has to contemplate the presence of a skirt-cylinder liner contact mathematical model for the modeling of the piston kinematical constrain in radial direction. Such contact condition modeling is realized through a system of elastic elements of opportune stiffness positioned on the top and bottom of the piston, as shown by the following figure:
Figure 2 - Elastic springs system (contact modeling) By running a simulation of the piston dynamics in presence of the force field introduced by the elastic springs system - when a contact condition happens - a graph with the typology in the figure 3 is obtained (with assigned set of initial condition on displacement and speed). The plot periodicity is characteristic of the conservative force systems introduced:
Spostamenti 20000
15000 εt
10000
εb
µm 5000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
sec
-5000
-10000
-15000
Figure 3 - Piston dynamics in presence of elastic forces The calculation of the hydrodynamic force requires a precise statement. In the part I of this paper devoted to the description of this pressure field, a geometric method has been used to evaluate the pressure acting on the anti-thrust side, since the pressure on the thrust side is known. The evaluation of the hydrodynamic forces can also use this simplification introduced by the particular symmetry of the system. In fact, when the pressure distribution is known, to get the hydrodynamic force on the thrust side an integration (voiding the contributions of the cavitated zones) is enough. Supposing to reverse the piston move (sign changing on et and eb): the oil wedge is formed by the thrust side is to perfectly speculate in comparison to the axle of the cylinder liner to ones formed by the antithrust side before reversing the moves. Then the hydrodynamic forces - and moments about the wrist-pin - acting on the anti-thrust side can be calculated when the analytical expression of ones on the thrust side are known. The following relationships reassumes this particular symmetry property:
FhAT (e t , e b , eD t , eD b , U ) = − FhTR (− e t ,− e b ,− eD t ,− eD b , U )
M hAT (et , eb , eDt , eDb , U ) = − M hTR (− et ,−eb ,−eD t ,−eDb , U )
F fhAT (et , eb , eDt , eDb , U ) = − F fhTR (− et ,−eb ,−eDt ,−eDb , U )
(− et ,−eb ,−eDt ,−eDb ,U ) M fhAT (et , eb , eDt , eDb , U ) = − M TR fh
Figure 4: piston position and oil wedge configuration on the thrust side
Engine operational data The table 1 describes the CRAFT engine data-input file corresponding to the geometry of the engine component, the inertia data and lubricant viscosity: Cylinder bore (2 R) Stroke (2 r) Connecting-rod length (l) Engine speed Piston skirt length (L) Piston skirt angle (α) Nominal radial clearance (C) Wrist-pin/axis of piston distance (Cp) Horizontal distance piston center of mass/wrist-pin (Cg) Vertical distance from top of piston skirt to the wrist-pin (a) Vertical dist. from top of piston skirt to the piston centre of mass (b) Wrist-pin mass (mwrist-pin) Piston mass (mpis) Piston rotary inertia about its center of mass (Ipis) Lubricant dynamic viscosity (µ) Solid-to-solid contacts friction factor (fc)
83.00 mm 83.60 mm 133.00 mm 4000 rpm 33.8 mm 37.50° 13.5 µm 1.00 mm 2.00 mm 12.50 mm 1.50 mm 0.090 Kg 0.295 Kg 8.0 10-4Kg m2 0.016 Pa s 0.150
Table 1: Engine operational data 3. SOME SIMULATION RESULTS DISCUSSION The piston secondary motions simulations have been obtained by using an analytical approximated model describing the hydrodynamic fluid film force in the piston skirt-cylinder liner interaction. Such approach to the behaviour of a dynamical system makes it possible to study not only the individual case but also the whole class to which the system in question belongs. Besides, the analytical approach proposed requires less computational time than a numerical investigation; in fact, because the latter requires a FEM (or FDM) Reynolds equation solving scheme for each calculus step, the integrations to get the forces and moments and, finally, the evaluation of the position at the following step. In figure five, six and seven are shown some results of the piston secondary dynamics for Engine operational data in table 1. The combustion gas force is obtained by an experimental data sheet in the full load conditions. Particularly, in figures 5a, 6a and 7a is plotted the piston motion at 1500, 4000 and 6000 rpm, respectively. Similarly, in figures 5c, 6c and 7c the hydrodynamic and contact normal forces are shown. Finally, in figures 5d, 6d and 7d the hydrodynamic and contact friction forces are presented. Likewise, other simulations can be performed in order to evaluate the influence of the engine parameters on the secondary motions and on the friction losses. A complete validation of the proposed computer program requires extensive experimental investigation and the development of new experimental techniques.
1
0.5
-0.5
-1
0.32
0.1
1500 rpm
−
0.2
cinque
ed elastica
0.36
CICLI
− Quinto
0.3
ciclo
0.38
εt
Forza di attrito
0.18
sude
1500 rpm
side
−
Quinto
0.36
idrodinamico N e di contatto
-100
-200
-300
-400
CICLO
− Terzo
0.22
0.38
ciclo
1
0.5
-0.5
-1
t Tempo
t
Tempo
Ff h + Ff c
Ff c
Figure 5d: Hydrodynamic and contact friction forces (1500 rpm)
0.24
Figure 5b: Piston secondary motion (1500 rpm)
0.34
thrust
anti thrust
εt
0.32
εb
0.16
εb
anti thrust sude
t
Tempo
Tempo t
thrust side
N
0.4
-5000
-4000
-3000
-2000
-1000
Figure 5a: Piston secondary motion (1500 rpm) Forza idrodinamica
0.34
Fh + Fe l Fh -6000
Figure 5c: Hydrodynamic and contact normal forces (1500 rpm)
1
0.5
-0.5
N
-1
-2000
-4000
-6000
0.025
0.075
4000 rpm
0.05
−
0.125
sei CICLI
0.1
ed elastica
0.075
− Terzo
0.08
0.15
ciclo
εt εb
t
0.09
side
Tempo t
Tempo
side
anti thrust
0.175
thrust
0.085
Figure 6a: Piston secondary motion (4000 rpm)
0.07
Forza idrodinamica
0.065
Fh + Fe l Fh
Figure 6c: Hydrodynamic and contact normal forces (4000 rpm)
1
0.5
-0.5
-1
100
-100
-200
-300
-400
-500
N
0.065
4000 rpm
0.07
−
0.08
terzo CICLO
0.075
0.085
0.05
e di contatto
0.045
idrodinamico
0.04
0.09
− Terzo
Tempo t
ciclo
0.055
0.06
t
εt
εb
anti thrust sude thrust side
Tempo
Figure 6b: Piston secondary motion (4000 rpm) Forza di attrito
0.035
Ff h + Ff c
Ff c
Figure 6d: Hydrodynamic and contact friction forces (4000 rpm)
-0.2
-0.4
-0.6
-0.8
-1
N
0.02
1000
-1000
-2000
-3000
-4000
-5000
6000 rpm
0.04
−
0.06
sei CICLI
0.08
0.03
0.1
ed elastica
0.12
t
Tempo
ciclo
0.035
− Secondo
εt εb
side
anti thrust
0.04
thrust
Figure 7a: Piston secondary motion (6000 rpm) Forza idrodinamica
0.025
Fh + Fe l Fh
sude
t
Tempo
Figure 7c: Hydrodynamic and contact normal forces (6000 rpm)
-0.4
-0.6
-0.8
200
-200
-400
N
6000 rpm
0.105
−
0.11
0.115
sesto CICLO
idrodinamico
e di contatto
0.03
0.12
− Terzo
0.035
Tempo t
ciclo
0.04
εt
εb
anti thrust sude thrust side
t
Tempo
Figure 7b: Piston secondary motion (6000 rpm) Forza di attrito
0.025
Ff h + Ff c
Ff c
Figure 7d: Hydrodynamic and contact friction forces (6000 rpm)
4. NOTATION εt , εb = t= C= α= µ= Fh , Mh = Fc , Mc = Ffh , Mfh = Ffc , Mfc = a= b= FG , FIP , FIC = Cp , Cg = u =
dimensionless eccentricities of piston at the top and the bottom point time nominal radial clearance between piston and cylinder bore piston skirt angle (θ - hydrodynamic lubrication boundary) Dynamic viscosity normal force due to hydrodynamic film pressure and its moment about wrist-pin normal force due to contacts between surfaces and its moment about wrist-pin friction force due to hydrodynamic film pressure and its moment about wrist-pin friction force due to contacts between surfaces and its moment about wrist-pin vertical distance from top of piston skirt to the wrist-pin vertical distance from top of piston skirt to the piston center of mass combustion gas force, wrist-pin inertia force, piston inertia force distance wrist-pin/axis of piston, horizontal dist. piston center of mass/wrist-pin time derivative of u(t)
5. REFERENCES [1] V. D’Agostino, D. Guida, A. Ruggiero, A. Senatore: “CRAFT: Code for Rapid Assessment on Frictional Torque ”, Software documentation, Dept. of Mech. Eng. - University of Salerno, September 2000 [2] V. D'Agostino, D. Guida, A. Ruggiero, A. Senatore: “A four stroke engine friction model”, 2000 AITC International Tribology Conference, Sept 2000, L’Aquila [3] D. Guida, A. Senatore: "A computer program for friction losses appraisals in a medium powered sparked ignited engine", Internal Report, Dept. of Mech. Eng. - University of Salerno, November 2000 [4] D. Guida, A. Senatore: "Modello dinamico di un motore a combustione interna per la simulazione della fase di avviamento", Internal Report, Dept. of Mech. Eng. - University of Salerno, November 2000
