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Multi-objective optimization on the timing system of a small 2-wheeler engine (SOHC): methodology and case study


Fig. 1 - Snapshot of the workflow of the entire optimization process

In recent years 2-wheeler engine companies have been focused on increasing overall engine efficiency, which can be achieved by resolving factors such as, engine down-speeding, engine down-sizing and by reducing the frictions. However, to maintain or improve vehicle performance, it is necessary to provide a corresponding increase in specific power. In accordance with these trends, the studied approaches and methodologies have been exploited, during the development of the new Piaggio small scooter engine.
In this project, a multi-objective analysis was applied to the valve train system design, in order to optimize the engine performance in terms of friction reduction, power curve and timing system response. These calculation methodologies have been followed using the modeFRONTIER platform for the multi-objective optimization analysis and the commercial simulation software GT–SUITE®.
The several configurations investigated obtained the desired trade-off between the appropriate and efficient valve train behavior and the engine performance. The global engine friction reduction was therefore obtained thanks to low resisting cam torque profiles and a specific valve springs set up.

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Fig. 2 - Half-cam profile acceleration curve

The growing demands for fuel economy in recent years calls for development and application of new efficient technologies, resulting in resolving rising fuel prices, adhering to the more stringent government fuel economy standards and awareness of increasing environmental impact. In view of this scenario, the control of engine frictions (in other terms fuel efficiency) and performance in internal combustion engines becomes decisive to provide a competitive vehicle for 2-wheels mobility and the use of numerical models and calculation methodologies provide an important support in pursuing these goals.
The methodology followed is based on the development of an optimization model. It investigates and finds out the appropriate valve lift event shape, with the objective of maintaining or increasing engine performance and also fulfilling the objective to minimize the resisting cam torque in conjunction with design constraints satisfaction.
The cam design started from a multi-polynomial valve lift curve and is fundamental in designing the timing system to take into account valve train stability, durability and noise, as well as engine breathing.
The valve train system is one of the major parts of internal combustion engine: the valves draw the air and fuel into the cylinders and allow the exhaust gas out. Therefore the method to design valve lift profiles and the valve train components are essential in defining the engine performance, valve train durability and NVH. The valve train system should be optimized to avoid abnormal valve movement (jump or bounce phenomena) throughout the engine’s speed range.


Fig. 3 - Snapshot of the GT-Power® engine 1D model

Another advantage of in optimizing valve events is that, cam follower separation speed is increased, valve spring margin is improved and cam torque resistance is reduced. This allows the design of a new valve spring setup, with lower loads and mass, in order to reduce frictions.
This work aims to demonstrate the effectiveness of the optimization methodology and its robust practical application to the scooter’s engine valve timing: the described approaches have been exploited for the development of the new Piaggio scooter engine (125cc, 4-stroke, 1-cylinder, 4-valves), whose valve train arrangement includes a SOHC (Single OverHead Camshaft) with a roller follower.
The project start with existing valve lift profiles (intake and exhaust), referring to the 125cc 3-valves engine. These profiles have been adopted initially for 4-valves new engine. The exploitation of the methodology described provided a new optimized valve lift event configuration.

Valve lift profile design optimization
The valve lift event is one of the most important factors when improving an engine’s performance by maximizing the area under the valve lift curve. But it is also true that each engine working condition needs a certain amount of charge to be trapped into the cylinder, depending on engine speed is required to optimize.


Fig. 4 - Engine torque and power curves: comparison between measured and computed

It would be desirable if the valves were opened and closed as quickly as possible, however the lift area integral is limited by certain kinematic constraints. Therefore when a new valve lift profile is conceived the designer needs to evaluate whether the guidelines are satisfied or not, such as maximum positive and minimum negative acceleration, valve-piston distance, Hertzian stress at the cam lobes-roller interface, minimum cam radius of curvature, spring margin to avoid cam-follower separation, etc.
Manually modifying the lift event can be time consuming when trying to satisfy the valve train recommendations and have a direct feedback of the engine response across the operating speed range. It is therefore becomes important to automate the process of controlling the engine and valve train system behavior.

The automated process has been created within modeFRONTIER to perform a multi-objective optimization of the calculation software (GT-SUITE®), used to evaluate engine performance and valve train system behaviour.
In Figure 1 a snapshot of the workflow of the entire optimization model is shown (to improve the readability, the data workflow is represented by subsystems).


Fig. 5 - Snapshot of the GT® valve train model

The model workflow in Figure 1 shows two data flows: logical and data flow. The first is the sequence of operations performed automatically by modeFRONTIER during the optimization. This logical flow consists of initial DOE and Scheduler “node”. These are the twin “node” that drives the whole optimization process. In particular the scheduler is the “engine” that learns from results of each simulation and plans the next step to improve the input variables and fulfill the objectives. Central to this process are two nodes built using GT-SUITE® to perform the operations to reach the goal.
The data flow begins from the input variables and ends with the output variables, which can become objectives or design constraints (the details of this phase will be described hereafter).

Input parameters for the multi-polynomial design approach
The optimization model starts with the definition of a certain valve lift event. A valve profile design process generally begins with defining the shape of the valve acceleration curve. In this work a representation with a multi-polynomial approach is described and applied to the valve acceleration and consequently to the valve lift definition.


Fig. 6 - Valve displacement: kinematic and dynamic profiles:
comparison between measured and computed

The design technique to identify the valve acceleration is based on a multiple-polynomial scheme. The profile is divided into a total of 14 zones and the shape of the profile in each zone is modeled with a 5th order polynomial. In this process of lift curve synthesis the constraints on derivatives of lift are expressed in terms of non-dimensional design parameters.


Table 1 - Design parameters defined in the model

The half-cam profile acceleration curve schematic (excluding ramps) and zone lengths and non-dimensional design parameters are shown in Figure 2 (in the model described a symmetrical type of the lift profile has been defined).
Therefore 10 design parameters have been selected in the optimization analysis to modify the shape of the acceleration curve and they have been constrained in modeFRONTIER to vary in a certain range conveniently defined. They are shown in Table 1. The total lift event duration, computed indirectly using lengths of zones 1-6, has been constrained to maintain an appropriate value. The duration of the cam ramp is calculated by the solver based on the input for ramp type, ramp height and ramp velocity. Afterwards, specifying the maximum lift, the solver is able to find a solution for flank and nose acceleration (Figure 2). The valve timing anchor has been maintained constant.


Fig. 7 - Optimization flow-chart

The choice adopted during this application with regard to the input variables definition until now described, as well as the output variables, in particular objectives and constraints settled for the optimization process, is meant to represent one of the potential applications in relation to using this methodology. Any other considered problem configuration could be applied and evaluated, in order to satisfy any other design constraint and fulfill whichever objective based on user needs and targets. The model build-up in modeFRONTIER follows a modular approach to the problem.

Engine CFD and valve train model node description
During the optimization loop the first step has consisted in having the solver node run the engine simulation. The commercial code used to build the numerical model has been GT-POWER® (the blocks diagram of engine model is shown in Figure 3). The above mentioned 125cc displacement, 4-stroke engine has been modeled (1D simulation).
The good predictivity of the model about the behavior of the engine related phenomena, can be seen in Figure 4.
The next step has been to carry out the valve train simulation in the relevant solver node. The specific lumped mass model has been built using GT-VALVETRAIN® (the schematic diagram of the valve train analysis model is shown in Figure 5, where a roller rocker arm layout has been evaluated).
The graph in Figure 6 shows the good numerical-experimental matching in relation to the dynamic valve displacement at engine over-speed, confirming the good level of prediction of the model.


Fig. 8 - Correlation matrix chart: relationships between input and output variables

GT-SUITE® and modeFRONTIER have been interfaced by means of the valve lift profile definition. Thus, the parameters of the multiple-polynomial scheme have been the input variables in the modeFRONTIER environment. The output variables controlled during the optimization have been the engine torque and power curves on the one hand, the valve-train kinematic and dynamic characteristic parameters on the other hand.

Logical flow and followed approach during the optimization analysis
The optimization process has been conducted at more levels, involving first a statistical analysis and then a proper optimization analysis.
A pre-statistical analysis has been carried out to check workflow redundancies, to perform a sensitivity analysis and to be able to simplify the following optimization analysis.


Fig. 9 - Parallel coordinates chart (maximum valve lift vs minimization cam driving torque)

The second step consists of a robust optimization for a global search, based on guidelines coming from the previous analysis. Subsequently, it has been possible to select a rank of the top lift profiles based on the valve train and engine performance results. The last step of the project, to address user needs and targets for the specific application and consistency with the computational time, could be a final refined optimization to precisely hit an optimum using an accurate optimizer, for a refinement, starting from the previous global search result. In this work this last step has not been reported, being beyond the scope of this work.
The analysis has focused on minimizing the cam driving torque resistance, maximizing the engine torque at maximum torque speed rotation and maximizing the engine power at maximum power speed rotation. The constraints to be satisfied have been related to the most significant valve train recommendations and guidelines; additionally a target power curve as a lower boundary condition has been considered (this numerical curve has represented the engine performance before to perform the optimization process). Objectives and constraints investigated are shown in the Table 2.
In Figure 7 the optimization process flow-chart implemented on modeFRONTIER is shown.
According to the flow-chart, the data flow has started from the 10 input variables, whose values define the valve lift event. After the analysis of each design is completed the output values have generated. Once each numerical analysis has performed (running engine performance and valve train models), they have been evaluated by means of suitable instruments for post-processing: the best configurations will be those that meet targets and guidelines chosen.


Fig. 10 - t-Student distribution charts

Statistical analysis
A starting DOE has been selected for the statistical analysis taking care that the set of configurations had to be representative of the whole design space and that the input values had to be not correlated to avoid redundancies.
Cases studied have shown that 3000÷5000 DOE input profiles provide enough resolution to explore the investigated design space. The “DOE Sequence” has been used to determine the general behavior of the examined objective functions.
Table 3 summarizes the number of blocks used in modeFRONTIER model during the statistical analysis.
After the DOE table has been evaluated, it has been possible to post-process the results extracting important information about the problem.


Fig. 11 - Scatter matrix chart


Table 2 - Objectives and constraints defined in the model


Data post-processing has shown there have been some inputs that have interfered insignificantly with outputs variables, while others have affected the output results in a more or less substantial way. This can be seen in the matrix correlation (Figure 8), that illustrates a first order dependency. The correlation value is a normalized index spanning from -1 to +1: a value equal to +1 (-1) denotes a full direct (inverse) correlation, while a low absolute value means low correlation. The same correlation is identified by shades of red (direct) and blue (inverse) color. It has been found that some variables are the least significant input variables and others have been found to affect significantly the results of the analysis (in relation to the ranges defined during the entire process). This is summarized in the Table 4. Finally it has been found that some pairs of objectives or outputs are negatively correlated, that means that such objectives (outputs) are conflicting and thus an optimization strategy should be used to find a good compromise.


Fig. 12 - Bubble chart and Pareto Frontier

During the next step of optimization some design variables will be considered a constant and a more suitable range for other input parameters will be adopted, according to the indications coming from the statistical analysis. As an example, the Parallel coordinates chart (Figure 9) clearly indicates (applying filters to reduce the ranges defined for the single variables evaluated) how it is possible to make investigations on variables sensitivity. In this type of graph, firstly a set of parallel axes is drawn with the aim to represent each variable, either input or output. Each design is then represented by a single line intersecting each variable axes at the value held by that variable for that design. Since the parallel coordinates chart permits the modification in real time of the range of every single variable, it can be used to filter the most interesting solutions in the database. The Figure 9 shows the convenience to adopt low values for the maximum valve lift profile, in particular to follow the target of reduce the resisting cam torque
Similar considerations have been made using the method based on t-Student distribution, which has once again allowed to see specific relations amongst all the inputs and a single output. This tool adopts both pie chart and histogram representations (Figure 10).


Fig. 13 - Parallel coordinates chart showing the three most
promising solutions (the arrows point out the objectives to
minimize or maximize)

Analyzing these charts it is easy to guess that one of the benefits of this procedure is the possibility to understand how each cam design parameter affects the valve train system (in terms of kinematic, quasi-dynamic and dynamic characteristics) and engine performance (torque and power curve). Using this post process data as a sensitivity tool, the cam designer is able to parametrically define the valve lift profile in order to change any output response, conscious that the time is over when the simulation brought good results only after long working experience.
Once the statistical analysis had been carried out, the following stage of the procedure has been aimed at performing an optimization analysis, having the main purpose to define one or more appropriate valve lift events.

Optimization analysis
During the optimization analysis a traditional MOGA II algorithm has been used. This is a multi-objective genetic algorithm. The number of starting population and the number of Generations have been a trade-off focused to increase robustness, accuracy and calculation time. Although the choice to use a genetic (and robust) algorithm, particular care has been taken to provide a DOE able to cover sufficiently the dominium of the functions, so that it can provide multiple starting point for the optimization.


Fig. 14 - Valve lift and acceleration
profiles: comparison between the
original and the optimized solution

Run times have been reduced launching multiple designs simultaneously. The percentage of feasible designs depends on how strict the constraints are. The conflict between some outputs or objectives negatively correlated has to be considered too. The calculation time also depends on how the problem has been formulated. In this work the choice adopted has been to evaluate unfeasible designs too (from point of view of performance) and to run valve train analysis (the solver node that follows the engine performance node) regardless of the result coming from the performance node. In fact the design constraints have been defined rigidly and therefore it has been preferred to evaluate even the designs not fulfilling all the constraints. Alternatively it would have been possible to include in the optimization model a logic “if” node and redirect the workflow path to the exit node if the performance constraints hadn’t been respected.
During this phase the input number has been reduced (from 10 to 7 variables). Additionally a more suitable range for all the input parameters has been adopted.


Fig. 15 - Engine indicated torque and power curve: comparison between
original and optimized solution (highlighted the engine speeds most
significant for the analysis).

The optimization analysis has generated a small number of feasible design, demonstrating that the formulation problem has been rather rigid (in terms of design constraints) and highlighting the inverse correlation characterizing the output variables (as shown in the scatter matrix in Figure 11, that confirms the statistical analysis’s trends). The scatter matrix chart contains three kinds of information: the Probability Density Function chart for each variable (along the diagonal) , all the pairwise scatter plot (above the diagonal) and the correlation values between the variables (below the diagonal, as described in relation to Figure 8). Despite that, the few feasible designs generated, reached the goal planned during the analysis, respecting settled constraints.


Table 3 - Number of blocks used in modeFRONTIER model during the statistical analysis

Having more than two objectives, the so-called “Pareto Frontier” (the set of all non-dominated solutions in the search space) is no longer a curve and becomes an hyper-surface. Otherwise the modeFRONTIER’s user can use a Bubble chart representation (Figure 12), where the two Cartesian axes represent two objectives and the third is pictured by bubble size. The feasible designs lying on the Pareto Frontier are circled in green in Figure 12.
The three most promising solutions are highlighted in blue in the Parallel coordinates chart (Figure 13).
According to the priorities for each objective, an unique final design ID has been selected. The valve lift and acceleration profiles are shown in Figure 14: the comparison between the original and the optimized solution is shown.
The new valve lift has provided the valve train results displayed in Table 5.


Fig. 16 - Cam torque: comparison between original and optimized solution.

The impact on the engine performance in full load condition is depicted in Figure 15: despite the slight worsening at low engine speeds (within the tolerance constraints), the optimized curves display the numerical improvement at the two engine operating conditions considered, in particular at high regimes. The slight improvement is clearly due to the problem formulation, where many objectives and design constraints overlap reciprocally. The multi-objective approach permits the analyst to assign a priority to each objective or constraint; making the thermodynamic objective the top-priority one could have been another way to go (to the detriment of the valve-train aspects).
The entire optimization procedure has been exploited both for the intake and the exhaust valve lift (this last analysis has not been reported, being beyond the scope of this paper). The graph in Figure 15 takes account of both optimized diagrams.


Table 4 - Input variables influence

As shown above the effects on gas exchange have not involved any significant variation in engine performance.

The graph in Figure 16 shows the improvement in resisting cam torque and therefore in friction reduction, between the original and the optimized curve at over-speed. The original data refers to the cam design initially adopted for the 4-valves engine, before the exploitation of the current methodology.
As a result of the new optimized valve lift event it has been possible to modify the valve spring characteristics (Figure 17), using a new spring setup with lower loads and mass, in order to reduce the frictions. The original data refers again to valve spring configuration used prior to the optimization analysis.

In this project the optimization procedure for the intake valve lift event has been described. The same approach has then been used and applied for the exhaust valve lift (as mentioned earlier this last analysis has not been reported, being beyond the scope of the present work). The whole valve train system has benefitted from this optimization procedure, involving a new valve spring setup and a new cam design. These changes have allowed the improvement of the engine friction as well as stability and durability issues due to the decreased stress; the engine performance has slightly improved without any significant variation.


Table 5 - Optimized valve train characteristics


With market pressure to decrease the environmental impact of new engines and with increasing software reliability, it’s imperative to find new efficient methods to improve exiting solutions by numerical optimization approaches. The idea at the basis of the paper has been to build a numerical tool for the valve lift profile definition, focusing on valve train system working and on engine performance. Thus, it becomes possible to have a new robust methodology to test effectively and efficiently valve lift solutions. In this work modeFRONTIER has been used to perform a multi-objective optimization. The multi-polynomial valve lift has been the starting point to drive the integrated procedure in optimizing the cam definition with a view to the valve train behavior and to the engine performance. The optimized profile has been found with the use of genetic algorithm tools. Therefore an integrated approach between the modeFRONTIER platform and the GT-SUITE® numerical code has been performed in order to build a methodology to define the valve lift event and to give support to the analyst during the design of a cam profile.


Fig. 17 - Valve spring characteristics: comparison between original and modified solution.

This work has focused on the valve train system, because it is an integral part of any engine and is closely related to the flow efficiency, the performance of the engine and impacts on high durability and low frictions of the timing system.
Firstly, a statistical analysis has been performed that has sped up the optimization phase by reducing the complexity of the problem, limiting the number of variables and the variables definition range. The subsequent optimization problem has therefore been used to improve the timing system lift event, in terms of the valve train system’s dynamic characteristics and thermodynamic performance requirements. Particular care has been taken to verify some important characteristics, like the engine power and torque, the resisting camshaft torque, the cam-follower separation speed, the Hertz stress, etc.
This approach has allowed the simultaneous modification of both the valve springs set-up and the cam profile shapes, in order to obtain the required response as for the engine friction reduction; furthermore the whole timing system has benefitted from this procedure, improving stability and durability issues.
To conclude, this project demonstrates the use of state of the art simulation tools and their correct implementation into the development process. It also highlights the great benefit of such a process in the development of Piaggio‘s new small 4 valve scooter engines.



Articolo pubblicato sulla Newsletter EnginSoft Anno 12 n°1

Marco Serafini

Francesco Maiani
Piaggio & C.

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