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machine design, Vol.9(2017) No.1, ISSN 1821-1259 pp. 29-34

*Correspondence Author’s Address: University Politehnica Timisoara, Faculty of Engineering Hunedoara, Revolutiei 5, 331128 Hunedoara, Romania, [email protected]

Research paper

DYNAMIC ANALYSIS AND PARAMETRIC OPTIMISATION OF THE CONNECTING ROD USING AUTODESK INVENTOR Vasile George CIOATĂ1, * - Imre KISS1

1 University Politehnica Timisoara, Faculty of Engineering Hunedoara, Hunedoara, Romania

Received (13.05.2016); Revised (14.09.2016); Accepted (19.09.2016) Abstract: This paper presents a case study on optimising a connecting rod, component of a spark-ignition engine, in order to minimise its weight and lower the inertia forces. For this purpose, we use the Autodesk Inventor Professional 2016 (AIP2016) software containing tools that enable either the dynamic analysis to determine the reactions of the connecting rod joints or the finite element analysis for optimising the connecting rod. The result of the optimisation is a lighter and slimmer connecting rod, which implies smaller inertial forces and reduced engine weight, resistant to the stresses subjecting it and ensuring safe operation. Key words: connecting rod, design, dynamic simulation, optimization, CAD, CAE 1. INTRODUCTION The connecting rod is the engine mobile part that kinematically connects the crankshaft with the piston. Due to the working regime and stresses subjecting the connecting rod, the continuous concern for optimising its form, design and operating mode is obvious. This is highlighted in the papers [1], [2], [3], [4] and [5]. By studying them, we found that the optimisation was performed in order to reduce the connecting rod weight and the inertial forces. In addition, the authors used CAD and CAE software to realise the 3D models and the finite element analysis, these ones enabling the simulation and study of the connecting rod behaviour, in order to be improved. The purpose of this paper is to conduct a study on optimising a connecting rod, component of a spark-ignition engine with 4 cylinders, for reducing its weight and inertial forces. As initial data, we considered that the cylinder diameter is 160 mm, the outer diameter of the bolt is 66 mm, and the maximum exhaust gas pressure is 78daN/cm2. The connecting rod is made of steel, with the following mechanical properties: density - 7850 kg/m3, Young’s modulus – 210000 MPa, Poisson’s ratio - 0.3, elasticity limit - 320 MPa and tensile strength - 610 MPa. The steps to be taken in achieving the proposed objective are shown in Figure 1. Based on the initial data and recommendations from literature [6, 7, 8], we established the main dimensions of the component parts of the connecting rod (foot, rod, head and cap), after which we built the 3D model. For three-dimensionally modelling of the connecting rod, we used the Autodesk Inventor Professional 2016 CAD system, developed by the company Autodesk. Further, after in the second stage we determined the reactions in the connecting rod joints by using the Dynamic Simulation module from AIP 2016, we conducted a preliminary finite element analysis of the connecting rod

using the Stress Analysis module, in order to determine the stresses, total displacement and safety factor.

Fig.1. Steps to take In the fourth stage, we optimised the connecting rod, establishing the design variables and objective functions; for this purpose, we used again the finite element analysis with the Stress Analysis module, selecting the Parametric Dimensions option. Finally, the conclusions have been drawn. 2. 3D MODELLING OF THE CONNECTING

ROD The 3D model of the connecting rod, as well as its main dimensions, realised by means of AIP 2016, are shown in Figure 2. It can be seen that we opted for large connection radii between the rod and the head of the connecting rod, for a more uniform and rational distribution of the pressures between the bushings and crankpin, and the stresses in the material. Regarding the connection radius between the foot and rod, we opted for a smaller radius, because the weight increases when the radius is large.

Vasile George Cioată, Imre Kiss: Dynamic Analysis and Parametric Optimisation of the Connecting Rod Using Autodesk Inventor; Machine Design, Vol.9(2017) No.1, ISSN 1821-1259; pp. 29-34

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3. DYNAMIC ANALYSIS OF THE CONNECTING ROD

The purpose of this analysis is to determine the reactions acting on the joints of the connecting rod (in its head and foot), considering that the force acting on it is the maximum force corresponding to the maximum gas pressure. For this, we used the Dynamic Simulation module from AIP2016.

Fig.2. The 3D model of the connecting rod and its dimensions

The dynamic simulation (using the Dynamic Simulation module) and the finite element analysis (using the Stress Analysis module) are complementary and work well together in AIP2016. The dynamic loads applied to a part are determined using the Dynamic Simulation module, and then they can be automatically transferred to the Stress Analysis module to determine the stresses and displacements. The analysed part is in dynamic equilibrium throughout the dynamic simulation. The finite element analysis is performed at a certain time without taking into account the time variation of the loads [9, 10]. The steps necessary to perform a finite element analysis with loads taken from the Dynamic Simulation module are: 1. Calculation of the reactions in joints and inertial forces

acting on the part studied with the Dynamic Simulation module.

2. Transfer of the loads, determined at the considered time, to the analysed part. The loads consist of reaction and inertia forces, and the part is in dynamic equilibrium.

3. Calculation of displacements and stresses, considering the selected part as being in static equilibrium, by using the Stress Analysis module.

3.1. Assembly modelling

To determine the reactions in the joints of the connecting rod, it is necessary to build the assembly whose part it is. For this purpose, the component parts of the cylinder - piston - bolt - connecting rod - crankshaft assembly is three-dimensionally modelled (Fig. 3), and then it is assembled, imposing certain assembly constraints.

Fig.3. Components of the assembly subjected to dynamic simulation

3.2. Definition of the kinematic couplings

The software is automatically converting the assembly constraints in kinematic couplings, is connecting the degrees of freedom of the immovable parts (Grounded) and is grouping the component parts between which there is no relative motion (Welded). According to Figure 4, we made five kinematic couplings, whose properties are listed in Table 1.

Fig.4. Joints


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Table 1. Joints properties

Joint dof Damping

value Friction

coefficient Radius (mm)

Spherical 1 dof

3(R) 0,05

Nmm s/deg 0,2 127,56

Point-Line 2 dof

3(R) 0,05

Nmm s/deg 0,2 127,56

Revolution 3 dof

1(R) 0,05

Nmm s/deg 0,2 112

Point-Line 4 dof

3(R) 0,05

Nmm s/deg 0,2 70

Prismatic 5 dof 1(T)

0,05 Ns/mm

0,2 –

3.3. Definition of the environment

At this stage, we add information about the gravitational force and external forces. It is considered that the maximum force developed by the gas pressure is acting on the piston:

(daN) 15682784

16

4

2

max

2

gpD

F (1)

where D=16 cm represents the cylinder diameter, and pgmax=78daN/cm2 –maximum gas pressure. The force is applied to the piston head, in the direction of the cylinder axis and oriented towards the piston. As the force developed by the gas pressure must acting only at the expansion stroke (downward), we imposed an application restriction to this force depending on the piston speed and crankshaft rotational speed. Thus, the force will act only when the piston speed is less than or equal to 0 mm/s and the crankshaft rotational speed is below 3000 rpm, in this way limiting also the crankshaft rotational speed [10].

3.4. Results

In this stage, it is generated the information about simulation, including positions, speeds, accelerations, reactions, forces and momentums. After running the simulation, we determine the reactions in the kinematic couplings corresponding to the connecting rod (Revolution: 3 - head and Point-Line: 4 - foot), and we identify the times at which they are maximal. In this situation, the two times are 0.07s and 0.075s (Fig. 5), and they are exported for analysis using Stress Analysis.

Fig.5. The reactions in the connecting rod joints

4. PRELIMINARY FINITE ELEMENT ANALYSIS OF THE CONNECTING ROD

For the finite element analysis of the connecting rod, we used the Stress Analysis module implemented in AIP2016. It enables the assessment of the part or assembly in operation, analysis of stresses and displacements based on several resistance theories, determination of the safety factor, integration with the dynamic simulation module, transfer of loads and constraints determined in the dynamic simulation module, animation of the obtained results, etc. Since the values of the reactions afferent to the two points in time are very close, we are going to perform the analysis only for the time 0.07s, i.e. the reaction in the joint of the connecting rod head is maximal (115274 N) and the reaction in the joint of the connecting rod head is 49036 N). The loads, taken from the dynamic analysis, are: the part weight (Gravity), force and moment of inertia (Body Loads), reactions in joints (Remote Force) and moments in joints (Moment) – Fig. 6.

Fig.6. Loads imported from Dynamic Simulation After running the analysis, the results are shown as von Mises stresses (Fig. 7), total displacement (Fig. 8) and safety factor with respect to the yield strength (Fig. 9).

Fig.7. Von Mises Stress


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Fig.8. Total deformation

Fig.9. Safety Factor 5. PARAMETRIC OPTIMIZATION OF THE

CONNECTING ROD The optimisation can be performed quickly and efficiently using the Stress Analysis module, found in AIP2016, and selecting the Parametric Dimension option. The method involves the selection of a number of parameters (design variables), imposition of a variation range and determination of their values for which the design constraints are met (objective functions). These ones can be: Stresses, displacements, deformations lower than the

allowable ones or included in a certain range of values;

Minimum weight; Minimum volume; Safety factor higher than a setpoint; etc.

5.1. The design variables

The design variables are established in the three-dimensional modelling phase, and are used to generate the geometric shapes that make up the connecting rod. To optimise the rod, we chose as design variables the values given in Figure 10.

Fig.10. Design variables

The ranges are selected in accordance with the conditions imposed to the connecting rod (mounting, maximum size), etc. In this case, the ranges of the design variables are listed in Table 2. Table 2. The design variables for connecting rod

Design variables

ParameterInitial value

Range No.

valuesRadius of the

connecting rod foot

rad_foot 20 mm 16-24 5

Radius of the connecting rod

head rad_head 35 mm 30-40 5

Outer diameter of the connecting rod

foot dia_ext 94 mm 92-96 3

Free length of the piston rod rack

E 14,5 mm

14-15 3

5.2. The objective functions

The objective functions are established in such way to meet the design requirements. In our case, we opted for: Minimisation of the connecting rod weight; The safety factor in relation to the minimum yield

strength to be less than or equal to 1.2; The total displacement to be minimal.

5.3. Results

After conducting the simulation, we obtained the values of the design variables which satisfy the objective functions. In Figure 11, which presents the results obtained for the optimised connecting rod, we see that all the objective functions are fulfilled.

Fig.11. Results after simulation


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The parameter values, for which the objective functions are fulfilled, are given in Table 3.

Table 3. The optimal values of the design variables

Design variables

Parameter Initial value

Optimal value

Radius of the connecting rod foot

rad_foot 20 mm 16 mm

Radius of the connecting rod head

rad_head 35 mm 30 mm

Outer diameter of the connecting rod

foot dia_ext 94 mm 92 mm

Free length of the piston rod rack

E 14,5 mm 15 mm

In Figures 12, 13 and 14, we plotted the values afferent to von Mises stress fields, the total displacement and the safety factor for the optimal values of the design variables.

Fig.12. Von Mises Stress of the optimized connection rod

Fig.13. Total displacement of the optimized connecting rod

Fig.14. Safety Factor of the optimized connecting rod 6. CONCLUSIONS

By comparing the two versions (preliminary and optimised), we found the following: The weight of the optimised connecting rod decreased by 0.241 kg compared to the preliminary version, which means that the optimisation goal, from this point of view, has been reached.

Table 4. Comparison between the preliminary and the optimized connecting rod

Objective function

Versions Difference

Preliminary Optimized Mass 8,735 kg 8,494 kg 0,241 kg Safety Factor

0,994 1,467 -0,473

Maximum total displacement

0,252 mm 0,264 mm -0,012 mm

The minimum safety factor relative to the yield strength for the optimal variant is higher than the imposed one (1.2), so this imposed objective function has been fulfilled. Compared to the preliminary version, the maximum total displacement afferent to the optimised version is higher, but its value is within the imposed limits found in the literature. By using the dynamic simulation with the module Dynamic Simulation, we waive many simplifying assumptions taken into account in the classical method of calculation. Practically, by dynamic simulation we obtain the reactions in the kinematic couplings at a certain time, without taking into account the variation in time of the loads, which are then transferred to the Stress Analysis module to calculate the stresses and displacements. In this paper, we determined the moments in time when the reactions in the kinematic couplings are maximal, and then we performed the finite element analysis. In conclusion, the activity of connecting rod optimisation has reached its goal, resulting in a lighter and slimmer part, which implies smaller inertial forces and reduced engine weight, it is resistant to the stresses to which it is subjected and ensures safe operation.


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