Applied Thermal Engineering 114 (2017) 545–553
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Advanced heat transfer analysis of continuously variable transmissions (CVT) Johannes Wurm a, , Matthias Fitl b, Michael Gumpesberger b, Esa Väisänen c, Christoph Hochenauer a ⇑
a
Graz University of Technology, Graz, Austria BRP Powertrain GmbH & Co KG, Gunskirchen, Austria c BRP Finland Oy, Rovaniemi, Finland
b
h i g h l i g h t s
Detailed numerical modelling of a continuously variable transmission (CVT). Motion and heat transfer effects are taken into account. Verification of a developed extension to the MRF method is presented. Surface temperatures of fast rotating pulleys are measured online with SAW technology. Low computational times enable a fast evaluation of new designs.
a r t i c l e
i n f o
Article history: Received 18 August 2016 Revised 24 November 2016 Accepted 2 December 2016 Available online 7 December 2016 Keywords: CFD CVT Continuously variable transmission Heat transfer Automatic Automatic transmission
a b s t r a c t
The presented paper focuses on heat transfer analysis of rubber-belt continuously variable transmissions (CVT). The huge advantage of this system is the continuous change of the transmission ratio without interrupting the torque output. The moderate efficiency of CVTs due to belt deformation and frictional forces, however, however, leads to increased thermal thermal loads. Especially the belt life span suffers under high temperatures. The numerical prediction of the resulting heat distribution at critical load cases is of key interest. In current literature it has hardly been investigated due to the complexity of the system. The numerical model introduced in this work is able to conduct time efficient heat transfer analysis within an enclosed CVT by using computational fluid dynamics (CFD). The transient process is transferred to a quasi-steadystate case reducing the computational time drastically. A new method to compute rotational symmetric tempera temperature ture profiles profiles for non-rota non-rotating ting pulleys pulleys has been develop developed. ed. As a result, result, the surface surface tempera temperature turess of each component can be computed accurately. Measurements, conducted on an engine test rig, confirm the the nume numeric rical al resul results. ts. The The prese presente nted d mode modell canbe appli applied ed to evalu evaluatedesig atedesign n chang changes es and and to redu reduce ce peak peak tempera temperature turess and hence hence increase increase product product reliabil reliability. ity. Moreove Moreover, r, the presente presented d method method offers offers a huge huge advantage for further transient processes which can be represented by a steady-state case and focus on heat transfer analysis. 2016 Elsevier Ltd. All rights reserved.
1. Introduction In general, a continuously variable transmission consists of two pulleys flexible in their diameter diameter and a belt wrapped around around them. them. The pulley, which is connected to the engine crankshaft is called drive pulley. The other pulley is attached to the drive shaft and is denoted as driven pulley. The torque, provided by the engine, is transmitted transmitted by the belt. The major advantage advantage of this system is that the transmission transmission ratio can be changed changed without interrupting interrupting the
⇑
Corresponding Corresponding author. E-mail address:
[email protected] (J.
[email protected] (J. Wurm).
http://dx.doi.org/10.1016/j.applthermaleng.2016.12.007 1359-4311/ 2016 Elsevier Ltd. All rights reserved.
torque output. CVTs are widely spread in the recreational vehicle industry industry like all-terrain-veh all-terrain-vehicles icles or snowmobiles. snowmobiles. Also scooters and even some cars work with a continuously variable transmission. Basically it must be differed between belt and chain driven CVTs. CVTs. A revi review ew,, wher where e both both syste systems ms have have been been exami examine ned, d, has has been been publish published ed by Srivasta Srivastava va and Haque Haque [1] [1].. The transmi transmissio ssion n efficien efficiency cy is a key key para parame mete terr and and has has been been unde underr inve investi stiga gatio tion n for for a lon long g time time [2,3].. Reasons for the power loss have already been identified in [2,3] earlier researches. E.g. Gerbert [4] [4] distinguish distinguish between losses due to external friction like sliding between belt and pulley and the losses due to internal friction like the sliding between moleculeshystere hysteresis. sis. Moreo Moreover ver,, the impact of small small pulley pulley radii radii and belt
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wedge angle on the power losses have been studied in [5,6]. Further experimental studies which focus on improving the transmission efficiencies of rubber V-belt CVTs have been conducted by Chen and Sung [7]. With increasing computational power, numerical modelling of the dynamic behaviour becomes more and more important. Basic investigations, which focus on steady state rubber V-belt CVTs analytically, have been conducted by Gerbert [8,9], Dolan and Worley [10] and Sorge [11]. Further researches focused on the transient case [12] and analytical approximations have been found e.g. [13,14]. A recently developed model, capable of predicting the power losses of a rubber V-belt CVT, has been published by Bertini et al. [15]. In their research, different effects which reduce the efficiency are discussed. Julió and Plante [16] present a model which is able to predict the transmission ratio time response when the conditions on the drive pulley are changing. Their model is sufficiently validated by experiments. This is especially interesting for CVT’s using electro-mechanical control devices for modulating the axial forces applied on the drive pulley [17]. This allows a separation of the transmission ratio from the engine speed and torque. Current researches focus on the impact on the fuel economy of these systems and the results look quite promising to increase the efficiency of CVTs. Especially in vehicles with high engine power the amount of kinetic energy which is transformed into heat is substantial. Zhu et al. [18] have carried out an experimental investigation on power losses of a rubber belt CVT which is used in snowmobiles. It points out that the efficiency of the transmission depends on the applied load as well as on the engine rpm and amounts approximately 0.7. Moreover, the efficiency is strongly influenced by the clamping forces as examined by Bonsen et al. [19]. Increasing the clamping pressure leads to a strong decrease of the efficiency, however, a certain pressure is necessary to ensure safety and to avoid high losses due to slip. In this study a metal push-belt is used and the measured efficiency factor is between 0.85 and 0.94 as it strongly depends on the working conditions. van der Sluis et al. [20] presented a study to optimize the efficiency of a metal push-belt CVT. The generated amount of heat in the CVT is huge and leads to high thermal loads. Particularly rubber belts, suffer from high temperature peaks and their life span reduces significantly. Therefore, efficient cooling must be guaranteed. This is already a delicate task for open systems but if the CVT is enclosed by a casing the conditions get even worse. In ATVs the CVT needs to be protected from dust, mud and water to avoid belt slipping, hence a casing is built around which makes sufficient cooling airflow and intelligent component design indispensable. Whereas the dynamics of a continuously variable transmission are well understood and the reasons for the occurring power losses are known, hardly any studies are focusing on the thermal aspect. Small scale thermal analysis where simulation results are compared and validated with experiments are presented by Junhui et al. [21,22]. Moreover, experiments have been carried out in [23,24] where the temperatures inside a CVT housing were measured. Main scope was to increase the convective heat transfer to reduce the temperature level by redesigning the casing. Additionally, numerical tools are used to compute the flow field inside the domain. Karthikeyan et al. [25] use computational fluid dynamics (CFD) to reduce dust ingress into a CVT housing. For scooters, a design study to improve the airflow through the housing has been published, see [26]. Both works use state-of-the-art numerical settings. However, important physical aspects like belt motion and temperature equalization are neglected. In the presented research study, a numerical model is developed to compute the thermal effects within an enclosed CVT. The design is taken from a commercial available system and measurements have been conducted on an engine test stand. Computational fluid dynamics
(CFD) is used to compute the heat transfer and the flow conditions resulting from the pulley rotation and the belt movement. All simulations were executed by STARCCM+, a state-of-the-art commercial CFD code. To reduce the computational effort, the transient case has been reduced to a quasi-steady-state case. However, some issues come along with this simplification. First, the static belt and pulley leads to static contact regions which is inappropriate for a running CVT. To model motion in a steady-state case the moving reference frame (MRF) method has been used. Nevertheless, the computed flow around the pulley is strongly asymmetric because of the casing and thus the local cooling of the pulley greatly differs, which is inappropriate for a fast rotating part. Therefore, a novel method has been developed in a previous work [27] and its applicability is verified in this paper. The main target is to implement the rotation of the temperature profile to the state-of-the-art MRF method. Finally, the developed model is verified by conducted measurements.
2. Test rig All tests have been carried out on an engine test stand to provide reproducible boundary conditions. The CVT under investigation, is fully enclosed and has two inlets and outlets, respectively. Therefore, the heat release can be balanced when the mass flows and temperature differences are known. This is essential for validating the developed numerical model. This is of specific interest because it enables an insight into the temperature distribution of the pulleys and provides further data which can be used for the validation of the numerical simulation. The test rig is shown in Fig. 1. Mass flow sensors require sufficient damping sections. Hence, pipes are mounted on the inlet and outlet ports to calm down the airflow and minimize the measurement error. The drive pulley is connected to an internal combustion engine and the driven pulley is attached to a dynamometer. Thus it is possible to monitor the provided engine torque and the torque acting on the drive shaft. The rotational speed of both pulleys is also measured and therefore the engine power and the power output of the CVT can be computed. The difference is the power loss of the CVT unit which is converted into heat, warming up the whole system. Beside of monitoring the engine operating point, additional sensors are used to supervise the working conditions of the CVT. The temperature, mass flow and the differential pressure of the inflow and outflow are measured. Moreover, a novel system has been developed for the wireless measurement of the pulley surface temperatures during operation. It is based on the surface acoustic wave (SAW) technology and consists of a reader, a SAW transponder and a transponder antenna. The principle idea is that temperature influences the velocity of the SAW signal which is evaluated by the radar unit. Hence, the environmental temperature of the passive SAW transponder can be determined. A detailed description of a comparable test rig can be found in [28]. The radial distribu-
Drive Inlet
Driven Inlet Drive Outlet
Driven Outlet
Enclosed CVT
Fig. 1. CVT-test setup.
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tion of the SAW temperature sensors on the surface of the pulleys can be seen in Fig. 2. The corresponding dimensions are given in Table 1 for the drive pulley and the driven pulley, respectively. Two readers are placed close to the CVT casing to capture the signal of the sensors.
547
Table 1
Temperature sensor position.
R1 R2 R3
Drive pulley (mm)
Driven pulley (mm)
92.5 62.5 49.5
130 95 –
2.1. Load case With regard to the numerical modelling, one specific load case has been defined. The enginespeed was set to 7500rpmand it runs onfull load which is approximately 100 kW. This is one of the most crucial load cases concerning heat generation inside the casing. During the test runs the outflow temperature and the surface temperature of the pulleys were monitored. A measurement point was taken as soon as constant temperatures were reached and thus steady conditions can be assumed. The transmission ratio and the position of the pulleys are well known for this load case and a virtual model representing the corresponding conditions can be generated.
3. Numerical modelling The main challenge of the presented task is the generation of a quasi-steady state case. A transient CFD simulation of a CVT is currently not feasible because the computational time would exceed reasonable limits. The reason is that on the one hand very small time steps would be necessary to model the pulley rotation adequately. E.g. for a pulley which is rotating with 7500 rpm the time step should be set to 0.000022 s to rotate the pulley one degree per time step. On the other hand, the measurements have shown that the minimum time to reach thermodynamic equilibrium amounts approximately 5 min. Main reason is the thermal inertia of the solid components. In other words, 13.5 million time steps would be necessary. State-of-the-art methods to transfer motion into a steady state case are widespread. However, only rotational and translational movements can be modelled and they can only be applied if the motion is symmetric. The existing case has three major issues which need to be taken into account for the modelling. First, the complex movement of the belt needs to be separated into rotational and translations regions. Second, special attention needs to be paid to the contact faces between belt and pulley. These zones are static in a steady state simulation. However, they obviously vary as soon as the pulleys are rotating. Moreover, the heat transfer coefficient h at the pulley surface depends on the current position of the disk. Without the developed method this would lead to inhomogeneous cooling of the pulley surface. Considering the thermal analysis, this must be considered to gain a tangential homogeneous and radial symmetric temperature profile. Finally, the heat generation inside the domain needs to be defined and validated.
3.1. CAD model and meshing The CAD model shown in Fig. 3 represents the computational domain. The assembly contains the cover, drive and driven pulley and the rubber belt. In total there are four ports, two inlet ports and two outlet ports. Beside of the fluid domain also the solid parts are taken into account to model heat conduction inside the pulleys accordingly. In a first step a grid independency study has been carried out using 2.5 million, 5 million and 10 million cells and it canbe shown that the surface temperatures, outlet temperatures and flow velocities hardly vary between the last two versions. Therefore, an approximate cell number of 5 million is sufficient to resolve the computational domain. The meshing process starts with the generation of a triangular surface mesh. As polyhedrons are the preferred mesh type in StarCCM+ the whole domain is discretized with this kind of cells. Their advantage is that they are numerically less diffusive and the solution is more accurate than a comparable tetrahedral mesh. Moreover, the number of cells is approximately five times lower which is helpful to reduce computational time. For the accurate modelling of convective heat transfer near the wall regions, three prism layers have been extruded from the contact interfaces separating the fluid and the solid region. In Fig. 4 the polyhedral structure of the cells is shown in two cutting planes, one through the fluid domain on the left and one through the solid domain on the right. In the enlargement the wall near prism layers are visible which grow with a rate of 1.25. The final mesh consists of 3.4 million cells in the fluid region and 2 million cells discretising the solid region which leads to a total amount of 5.4 million cells.
Driven Outlet
Drive Inlet
Driven Inlet
Measurement Point
Drive Outlet
Drive Pulley Belt Fig. 2. Radial distribution of the temperature sensors on the pulley surface.
Driven Pulley
Fig. 3. CAD model of the CVT inclusive casing.
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Fig. 4. Generated mesh: (a) cutting plane through the fluid domain; (b) cutting plane through the solid domain.
3.2. Modelling motion
Table 2
Defined regions.
As aforementioned, the belt motion is split into two rotational and two translational regions. Therefore, the belt is enwrapped to separate the belt near region from the common fluid domain and thus the according rotational and translational velocities can be specified for each section. The same procedure is applied on each side of both pulleys to define the rotational regions close to the pulley surface. The separated regions are highlighted in Fig. 5. In total, the fluid domain consists of nine regions which are connected via interfaces. Additionally, three solid regions are defined representing the drive pulley, driven pulley and belt. A list of the various regions is given in Table 2. The separated zones allow the definition of multiple reference frames (MRFs). This method is used to imply motion in a steady state case. Its effectiveness has been investigated by Gullberg et al. [29] who also compared numerical results to experimental data [30].
3.3. Modelling of generated heat As mentioned before, the efficiency factor of common CVTs is moderate for the defined load case. The power loss leads to an increase of the component temperatures because the kinetic energy is converted into heat. Generally, three different mechanisms are responsible for the power losses in rubber belt CVTs. First, there are sliding losses between belt and pulley resulting from contact forces and relative slip. Second, there are hysteresis losses resulting from cyclic deformation of the belt in longitudinal and the transverse directions and third, work is required to engage and disengage the belt in and from the pulley, compare [15].
a)
Region
Physical state
Motion
Fluid domain MRF drive pulley left side
Fluid Fluid
MRFdrive pulleyrightside
Fluid
MRF belt on drive pulley
Fluid
MRF driven pulley left side
Fluid
MRF driven pulley right side MRF belt on driven pulley
Fluid Fluid
MRF belt 1 MRF belt 2 Solid drive pulley Solid driven pulley Solid belt
Fluid Fluid Solid Solid Solid
Static Rotational motion of drive pulley Rotational motion of drive pulley Rotational motion of drive pulley Rotational motion of driven pulley Rotational motion of driven pulley Rotational motion of driven pulley Translation in positive direction Translation i n negative d irection Static Static Static
However, these effects cannot be modelled in CFD and thus, alternative methods need to be found to enable a heat transfer analysis. A useful approach is the definition of a constant temperature on the flanks of the belt, as well as in the contact surface. In Fig. 6 theses zones are highlighted.
3.4. Modelling of heat transfer between solid and fluid region Convective heat transfer between fluid and solid regions depends on the flow profile within the fluid region and on the temperature gradient between wall and fluid zones. In the present
b) Translation 1 Rotation 2
Rotation 1 Translation 2
Fig. 5. (a) Separation of pulley motion into four independent regions; (b) separated regions encasing the moving components to induce motion.
J. Wurm et al. / Applied Thermal Engineering 114 (2017) 545–553
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Pulley surface
Solid regions
temperature Radial averaged pulley heat flux Belt surface temperature Average surface heat flux Fluid region
Fig. 6. Constant wall temperature for contact faces.
case, the flow profile inside the casing is strongly asymmetric. As a result, the local boundary heat release varies significantly on the pulley surface, whereas it should be rotational symmetric because of the high rotational speed. This effect is pointed out in the left contour plot of Fig. 7. It shows the relative surface heat flux with regard to the surface averaged heat flux. However, the rotational symmetric profile, shown on the right side of Fig. 7, is far more realistic. This result has been computed by using the heat flux averaging method developed in the previous study [27]. The homogenization of the heat flux profile is necessary to compute accurate temperature values. The applied approach to define the thermal boundary conditions for the interfaces between solid and fluid region is based on coordination transformation and interpolation. A schematic sketch is presented in Fig. 8. In contrast to the fluid-fluid interfaces, where the flow quantities are directly transferred from one region to another, the fluid-solid interfaces are operated before they interact with each other. Starting with an initialized surface wall temperature a corresponding heat flux profile is computed in the fluid domain. The profile is highly asymmetric as shown before on the left side of Fig. 7. Before the subsequent iteration, the cell value of each surface cell is extracted and stored in a matrix. Furthermore, the matrix contains the coordinates of each cell referring to a cylindrical body fixed coordinate system CSYS. Thus, it consists of 4 columns and n rows, where n corresponds to the number of surface cells.
M Heat Flux : ¼
0 B@
q_
r
u
z
.. .
.. .
.. .
.. .
q_ n
r n
un
z n
1 CA
Fig. 8. Schematic sketch of the thermal boundary condition defined on the interface between solid and fluid regions.
Fig. 9. Principle of the heat flux averaging method.
Fig. 9 points out the theory of the spatial averaging approach. Two points (P A and P B ) are based on the same circle but shifted by the angle h. Beside of the body fixed CSYS 1 a new cylindrical coordinate system is defined, indicated by the index 2. CSYS 2 has the same z-axis but is rotated by the same angle h .
Fig. 7. Relative boundary heat flux related to the resulting maximum value in percent; (a) computed without homogenization; (b) using homogenization.
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A function is defined which extracts the flow quantity at a defined position referring to a specified coordinate system. In view of CSYS 2 , the point P B has the same coordinates as P A seen from CSYS 1 . Going back into the previously defined matrix the corresponding flow quantity can be extracted due to the fact that the displacement vector from CSYS 1 to CSYS 2 is known. Finally, the arithmetic average of the extracted heat flux values is computed and a tangential homogenous and radial symmetric temperature profile can be achieved which grants that the energy balance is fulfilled. It must be mentioned that the developed method works only, if the pulley geometry is symmetric. Afterwards, the averaged profile of the surface heat flux is used as boundary condition (BC) for the solid region. In accordance to these BCs a surface wall temperature is computed. Again, the resulting temperature profile is stored in a matrix M Temperature which is used as BC for the solid region in the following iteration.
M Temperature : ¼
0 B@
T
r
u
z
.. .
.. .
.. .
.. .
T n
r n
un
z n
1 CA
The developed method is capable to compute the heat distribution on rotating disks in steady-state cases and can therefore be seen as expansion to the state-of-the art MRF method which has not been published before. In [27] a more detailed description of the numerical scheme can be found.
3.5. Numerical settings An implicit pressure based coupled solver has been used to solve the governing equations for fluid dynamics. The statistic modelling of the turbulent flow, known as Reynolds Averaged Navier Stokes (RANS)-method, demand the definition of a turbulence model. The 2-equation SST k-x- model has been chosen because of its good stability and acceptable computational time. The fluid medium is air and its density is computed by the incompressible ideal gas equation. This assumption is appropriate due to the reason that the maximum temperature is 130 C and only low Mach number occur within the fluid domain. Thus the change of the fluid density is negligible. The relevant governing equations in integral form which are solved via the Finite Volume Method are listed below: @
Z
j
@ t V
W dV þ
I
Z
j
½ F G da ¼
H dV
V
with
2 3 2 64 75 64 2 3 2 3 64 75 64 75
qðv
q
W ¼
qv ;
F ¼
qE
qðv
T
3 75
Þ v þ p I ; qðv v g ÞH þ pv g v g
S u
0
G ¼
Þ
v g
;
H ¼
_ Tv þ q00
f ; S u
where q and v represents the density and the velocity of the fluid, respectively. E denotes the total energy per unit mass and p is the pressure. The occurring heat flux is given by q_ and v g is the grid velocity vector. W denotes the vector of conserved quantities, F represents the inviscid terms, G is the vector of viscous terms and the body forces are given by the vector H. Two additional transport equations are necessary for the SST k- x- model: 00
@ @ y ðqkÞ þ ðqkv Þ ¼ @ t @ x @ x @
e Ck
@ k
@ x
þ G k Y k
@
@
@ y
ðqxÞ þ ðqxv Þ ¼ @ t @ x @ x
Cx
@ x @ x
þ Gx Y x þ Dx
here, e G k and Gx represent the generation of the kinetic energy k and x. C k and Cx denote the effective diffusivity of k and x. Y k and Y x represent the dissipation of k and x resulting from turbulence. Finally, Dx is needed as a cross diffusion term to blend the k- xmodel with the k-e-model. This leads to the huge advantage of the SST k-x-model, which combines the robustness of the k- xmodel in the wall near region with the free stream independence of the k-e-model in the far field. Detailed information on modelling strategies of the various terms can be found in [31]. The model constants have been remained as the default parameters. For a coupled solver it is necessary to define a Courant number, also denoted as CFL number. The reason is that StarCCM+ uses a time marching scheme to derive a steady state form of the governing equations. In the presented case the CFL number has been set to 5 as recommended in [32]. The second-order-upwind scheme is used for the spatial discretization of the governing equations. For the solid region two different parameters have been defined. The pulleys consist of an aluminium alloy with constant density and conductivity. For the belt, a specific material is defined with an extraordinary high thermal conductivity of 350 W=mK. This is necessary to ensure that the heat is spread in the belt region homogeneously, like in a fast rotating belt. Moreover, a surface-to-surface (S2S) radiation model has been applied to investigate the impact of radiation. However, it can be stated that its influence is marginal. The advantages of these numerical settings were scrutinized in previous simulations, see [33].
3.6. Boundary conditions On both inlets a constant ambient pressure has been defined, thus the mass flow rate of air, entering the domain, is determined by the rotation of the pulleys. Again, ambient pressure is defined at both outlets. The wall of the casing is defined as adiabatic walls. As measured, the belt flank temperature is held constant at 130 C in the simulation.
4. Results and discussion In a first step the results gained from the simulation will be compared to the measurements. CFD enables an insight on the temperature distribution which is hard to achieve on a test rig. However, it needs to be mentioned, that experiments are indispensable to validate the computed results to ensure an appropriate conclusion. Once a validated modelling strategy exists, important information concerning flow conditions and heat transfer can be gained from the numerical results. In Fig. 10 the computed surface temperature can be seen. Obviously, the highest temperatures occur in the contact regions between belt and pulleys. The pulleys are made out of an aluminium alloy with a thermal conductivity of 350 W=mK. Hence, the heat transport to colder regions is rather efficient and the temperature gradients within the solid are low. Nevertheless, the temperature difference in radial direction between the contact zone and the outer border is 50 K on the driven pulley. On the drive pulley similar ranges can be observed in axial direction. The measurement values presented in Fig. 11, have been taken after running the engine on full load for 5 min at 7500 rpm. As described in Section 2, in total five temperature sensors have been mounted on the pulleys to observe the surface temperatures online. The temperature spread between to outer sensor (P3) and the inner sensor (P1) amounts 28 K. Almost the same range, namely 29 K, is computed by the numerical model. Taking into
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140 ) 130 C ° ( e 120 r u t a 110 r e p 100 m e T 90 80 -0.2
-0.1
0
0.1
0.2
Distance in radial direction (mm) Fig. 12. Radial surface temperature distribution on one side of the driven pulley.
Fig. 10. Temperature contour plot of pulley and belt surface.
=3 K
140
=4 K
=2 K
) 120 C ° ( 100 e r 80 u t a r 60 e p m 40 e T 20
0 Drive pulley P1
Drive pulley P2
Drive pulley P3
Measurement Simulation
) C ° ( e r u t a r e p m e T
100
=3 K
80
=1 K
60 40 20 0 Driven pulley P4
Driven Pulley P5
Fig. 11. Comparison of the computed and measured surface temperatures on drive and driven pulley.
account that the measurement tolerance lies within 1.5 K, good accordance is given. Moreover, Fig. 11 shows that the simulation model slightly overestimates the surface temperature. The maximum deviation between measurement and simulation amounts 4 K in the middle section of the drive pulley. The radial surface temperature profile along the cross section through one side of the driven pulley is presented in Fig. 12. It points out that the peak temperatures are reached in the contact zones. It also shows that the temperature drop is stronger in the outer regions than towards the centre. One issue which has been discussed in Section 3, is the homogeneity of the radial temperature distribution. In Fig. 12 it can be shown that the resulting temperature profile is perfectly rotational symmetric like it can be expected for a fast rotating pulley. Another indicator, which is taken for the validation of the numerical model is the air temperature of the outflow. If the total mass flow is known, it can be used as indicator to compute the
total energy that is transformed into heat by the CVT. The comparison between the simulated and measured temperature is shown in Fig. 13. The inlet temperature used for the simulation is determined by the ambient conditions at the test rig. Inside the casing the air is heated up from 25 C to approximately 60 C. The measurements showed that the outflow temperature at the drive outlet is slightly higher than at the driven outlet. The same behaviour can be observed in the simulation model. Again, the CFD results are in good agreement with the data gained by testing and the maximum deviation amounts 2 K. Furthermore, the measured pressure value gives a good understanding of the airflow that is sucked in from the environment. The low-pressure value given in Fig. 14 is related to the ambient air pressure. On the drive inlet the pressure difference is rather small compared to the measured value at the driven inlet. One cause for this effect is the layout of the blades on the pulley surface and a second reason is the casing design. As previously mentioned, ambient pressure is defined at both inlet regions in the simulation, hence the airflow entering the fluid domain is determined by the low-pressure produced by the pulley rotation. Again, the simulation results show the same tendency as observed in the measurements. To summarise, the simulation model with constant belt temperature reproduces the measurement data accurately. This is substantiated by corresponding inflow and outflow condition and conforming component temperatures. A huge advantage of the simulation model is that spaceresolved results are available. The air velocity distribution inside the casing can be examined as shown in Fig. 15. Hence it is possible to visualize flow structures and identify dead water regions. Also peak temperatures can be spotted, as well as regions of high and low convective heat transfer. This is of special interest when it comes to the point of optimizing an existing system.
=2
70 ) 60 C ° ( 50 e r 40 u t a r 30 e p m 20 e T 10
0 Inlet
Outlet Drive
Measurements
Outlet Driven
Simulation
Fig. 13. Comparison of the in- and outflow temperature.
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552
0 -500
) a -1000 P ( e -1500 r u -2000 s s e r -2500 P -3000
-3500 Inlet drive
Measurment
Inlet driven
Simulation
Fig. 17. Heat transfer coefficient on pulley surface.
Fig. 14. Comparison of the computed and measured low-pressure in the inlet sections.
which can be gained from the previously described plots can be used. By comparing the results differences can be immediately identified. Hence the major advantage of the presented model is that new designs can be investigated and evaluated with little effort and costs.
Driven Outlet
Driven Inlet
Drive Inlet Drive Outlet
Fig. 15. Velocity vectors plotted in the middle cutting plane.
Fig. 16. Temperature contour plot in middle cutting plane.
Fig. 16 shows the resulting air temperature in the middle cutting plane through the cover. It clearly points out that between the pulleys the air temperature is rising. This correlates with Fig. 15 where it can be seen that the air velocity is comparatively low, thus the heat exchange is limited. Another indicator to evaluate the characteristics of the heat transfer is shown in Fig. 17. The heat transfer coefficient depends on the temperature gradient between wall and fluid as well as on the air flow conditions. Hence it is high on the driven pulley surface (right disk). Cold air is entering the domain and the fast rotating disk directly influences the forced convection. In contrast the heat transfer coefficient of the drive pulley (left) is approximately three times lower. The next step of an optimization process is to decide what kind of changes could have a positive effect. Therefore, the information
5. Conclusion With increasing engine performance, loads on the CVT components rise as well. The power loss of the transmission leads to high thermal loads and the resulting peak temperatures drastically reduce the life span of the belt. To overcome this issue new designs which focus on improving the heat transfer and reducing high temperature zones need to be found. The scope of the presented work is to build a numerical model which is capable of computing heat transfer effects within an enclosed CVT. Main target is the development of an efficient method to evaluate design changes rapidly and focus costintense experimental work to promising concepts only. The MRF approach has been used to imply motion of the belt and pulleys, however, the resulting surface temperature greatly depends on the flow conditions inside the casing and with ordinary approaches the computed results were insufficient. Therefore, a novel method has been developed which can be seen as add on to the state-ofthe-art MRF modelling. As a result, tangential homogenous and radial symmetric temperature distribution on the pulley surface can be computed. Moreover, the computational time needed for the presented steady-state case is drastically lower than the time needed for a transient simulation. Measurements have been conducted on an engine test stand to evaluate the generated virtual model and the comparison shows excellent accordance. The developed model includes full motion of all moving parts and predicts realistic temperature distributions and mass flow rates. Thus, it can be used to optimize the design of CVT components to increase the heat transfer rate and lower peak temperatures. Parameter studies as well as design changes can be evaluated within a short time.
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