Engine Mount Analysis Methodology S. S. Sane Sr.Vice President Engineering and R&D Piaggio Vehicles Private Limited Baramati, Pune, India [email protected]

Vyankatesh Madane

Gaurav Upadhyay

Manager - Design Piaggio Vehicles Private Limited Baramati, Pune, India [email protected]

Traniee - Design Piaggio Vehicles Private Limited Baramati, Pune, India [email protected]

Keywords: Engine mounts, Vibration isolation, Transmissibility Abstract Good NVH is becoming must feature in recent commercial vehicles. One of the major discomforts caused to driver by Engine vibration during idling. The power train is suspended on the vehicle frame on several flexible mounts, whose purpose is to isolate the vibration between engine and frame. Total 6 different modes of Engine like roll, yaw, pitch and Vertical, lateral and longitudinal need to isolate. Engine mount stiffness and position is critical and need to have methodology to verify in early stage of designing. In this methodology, existing linear finite element software (Raddios-linear) is used. Advantage of using linear FE software is, same model immediately can be used for durability analysis. In this methodology, engine rubber mounts are model separately. By applying unit force and calculating displacement, stiffness is calculated for specific “Modulus of Elasticity (E)” value. From this model, mathematical rubber E value is estimated to achieve desirable mount stiffness. Once separate rubber mount model is ready, it is imported in FE model of frame and power pack. In FE model, this Engine mounts are connected to frame and power pack. Once this complete assembly model is ready, modal analysis is done to get different Engine modes. Results of this modal analysis are compared to Experimental modes to have correlation of analysis with testing. Different Engine modes frequencies are checked with Target. To achieve Engine modes frequency target, different iterations are done by varying mount position and stiffness (E value).

1. Introduction: The task of delivering low cost, quality products well ahead of competitors is forcing OEMs to cut down development cost and time. This is leading to increased emphasis on simulation tools for product design and validation. Considering the major contribution of the powertrain vibrations to overall vehicle NVH, the use of simulation tools during powertrain design stages is a critical stage of the vehicle NVH development. Reduced levels of engine idle shake are required to produce satisfactory levels of overall NVH perceived by the customer. Major factors governing the same are either a part of the power train or its ancillaries. Power train mounting system and its transmissibility characteristics are also the key governing factors. Engine mounts protect the engine from excessive movement and forces due to low frequency road and high frequency engine excitations. On the other hand, body mounts protect the cabin from vibration forces exerted by the body. Normally, a complete set of mounts is conceived at early stages of design, subsequently the set is tuned in the refinement stage to improve the vehicle’s noise, vibration, and harshness (NVH) response.

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1.1 Theory of Vibration Idle vibrations of any automotive system originate from the power train. The major causes being: Unbalanced Mechanical and Combustion Forces of the Engine Fig. 1 shows the typical vibration generating mechanism of an engine. An important parameter influencing engine vibration especially at low speed is combustion. The excitation of the system originates from cylinder pressure, which causes a thrust force against cylinder liner wall and acts on crank train components which results in various modes of the power train. At higher running speeds of the engine mechanical noise is dominant. The factors contributing to it are the inertial forces and the variable torque generation of the engine. This leads to problems like piston slap and bearing impact forces, which gets radiated as noise or as vibration through different engine parts like crank pulley, crank case, oil pan etc. The usual way of reducing the unbalanced forces of the engine is by addition of counter balancing masses. These are features which need to be incorporated at the earlier stages of engine design.

Fig 1: Unbalanced Mechanical and Combustion Forces of the Engine

. Idle and low speed comfort can also be influenced due to changes of the engine excitation and the transfer mechanisms. The main transfer paths for the vibrations are the engine mounts, wheel suspensions and components mounted on to the body. The excitation becomes more critical when the main firing orders coincide with the Eigen frequencies of different components. The rigid body modes of the power train normally occur at very low frequencies. Care need to be taken while designing the mounting system so that the highest mode of the power train is at least √2 times lower than the first firing frequency of the engine. The presence of power train modes in the operating frequencies leads to higher transmissibility during low speed operation. When an engine is fastened directly to its support frame, it has a direct path for the transmission of vibration and noise. When the engine is attached to its support by means of properly selected resilient isolators, the path of vibration and noise disturbances is broken.

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The engine produces two types of disturbances. We have to identify these in order to position the mounts correctly and also to choose the right dynamic characteristics (stiffness etc.) of the isolators. The first type consists of disturbances originating in torsional dynamic pulses caused by variations in Cylinder gas pressure. This is the firing frequency. The firing frequency can be calculated as follows: With a 2 stroke engine. Fd = (RPM * Number of cylinder)/ 60 (1) With a 4 stroke engine. Fd = (RPM * Number of cylinder)/ (2*60)

(2)

In practice, however uneven piston firing occurs because of uneven fuel mixture distribution. Therefore, we should consider isolating the ½ order (in 4 cycle engines) and 1st order (in 2 cycle engines) disturbances as well as harmonics: 1-1/2, 2, 2-1/2, etc. (First order=1* RPM; second order=2*RPM etc.). The firing frequency is the most disturbing mode, the isolation of which is our primary concern. The second type of disturbance consists of unbalanced forces caused by reciprocating pistons or rotating crankshaft and rod masses within the engine. Disturbances in 6 or 8 cylinder engine, as a rule, are easily balanced. But the inertia forces are unbalanced in 1, 2, 3, 4, or even five-cylinder engine, and must be dealt with in the design of an isolation system. Depending on the number of cylinders and the crank arrangement, the inertial forces combine or cancel in varying degrees. As the number of cylinders increases, these forces are usually more balanced and simpler to isolate. 1.2 Fundamentals of vibration isolation: In general, the transmission of vibration can be thought of in terms of a source, which generates an excitation force or displacement, the path, through which the vibratory disturbance is transmitted, and a receiver. The objective of isolation is to minimize the transmission of vibratory disturbances from the source to the receiver. The single degree of freedom model, which defines the uniaxial behavior of a linear system consisting of a lumped mass and spring and dampening elements, is fundamental to the understanding of vibration isolation. The model for the undamped condition is shown in Figure 2.

Fig 2: Undamped Single Degree of Freedom Model.

If a steady state sinusoidal excitation force, F, is applied to the mass, M, the displacement of the mass is:

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Y

Fo K sin( wt ) ( K M )  w2

(3)

The natural frequency of the system (Radians / second), is defined as:

n 

K M

(4)

Dividing the numerator and denominator of equation (3) by K / M and substituting for Ώn, results in the following expression for the displacement of the lumped mass:

Y

Fo K sin( wt ) 2 1  w2 /  n





(5)

Examination of the numerator and denominator in equation (5) indicates the dynamic displacement is a function of the static deflection divided by the ratio between the frequencies of the sinusoidal excitation force (ω) to the natural frequency (Ώn) of the system. The goal of an isolation system is to reduce the magnitude of the force transmitted to the support to a level below that of the excitation force acting on the mass. The force acting on the support can be expressed as:

Fs  ( K ) * (Y )

(6)

The transmissibility through the spring is the ratio between the force applied on the mass and the force acting on the support.

T

Fs ( K ) * (Y )  F Fo sin( wt ) T

T

(7)

K ( Fo K ) sin( wt ) 2 [1  ( w 2  n )] Fo sin( wt )

1 2 1  ( w2  n )

(8)

The magnitude of equation (8) is represented graphically in Figure 3. Examination of equation (8) indicates some important characteristics of the behavior of the undamped system. When ω / Ώn =1, the transmissibility is infinite. When ω / Ώn transmitted force becomes less than the excitation force.

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Also from equation (8), a positive value of transmissibility occurs when ω < Ώn, which indicates the force acting on the support is in-phase with the excitation force. A negative value of transmissibility, which occurs when ω > Ώn, indicates the reaction force is out of phase with the excitation.

Fig 3: Transmissibility of an Undamped System.

The derived expression for transmissibility, formulated as the ratio between the force originating in the supported mass and the force transmitted to the supporting structure, is comparable to the case of an engine mount which supports a portion of the engine mass and which isolates the engine vibration from the body structure.

If the isolator exhibits a linear force vs. deflection curve, the natural frequency of the system is a function of the static deflection of the isolator due to the weight of the mounted body. Because transmissibility is a function of the natural frequency of the system, transmissibility can therefore be expressed as a function of static deflection of the isolator.

2.

Methodology

In this paper methodology is divided in to two steps:I. II. III.

Physical Mount stiffness Evaluation. Mathematical Modeling of Rubber Mounts. Modal analysis of Engine-frame assembly with derived rubber mounts

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2.1. Physical Mount Evaluation: In this method, to find out the stiffness of rubber mounts for vertical direction, they are tested on UTM (as shown in below fig).

Fig. 4 Experimental Setup

Two rubber mounts having different shore hardness are tested and stiffness of these two mounts are calculated as mention in below table Rubber Shore Hardness (HRC) Stiffness (kgf/mm) 55 20 65 30 Table 1 Experimental Result of stiffness 2.2. Mathematical Modeling of Rubber Mounts: In this method, engine rubber mounts are model separately. By applying unit force and calculating displacement, stiffness is calculated for specific “Modulus of Elasticity (E)” value. From this model, mathematical rubber E value is estimated to achieve desirable mount stiffness. In this analysis we have consider Rubber material as isometric material and elastic modulus, E = 50N/mm2.

Fig. 5 Rubber Material Properties

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Fig. 6 Rubber model with E=50

Fig. 7 Deformation result Rubber model with E=50

Load of 1000N is applied at one face and opposite face of rubber is constraint this setup is same as actual testing. Deformation plot is shown above. F=1000N=100kg (approx.) Deformation = 0.26mm (this value is from deformation result) Stiffness of rubber from analysis = Force / Deformation = 100/0.26 = 384.6 kg/mm

From analysis it is clear that stiffness of actual rubber is much lower than stiffness of modeled rubber. To change stiffness we decided to change elastic modulus, E to achieve desire stiffness of rubber. As we have consider isometric material for rubber, we can assume that there is linear relationship between Elastic modulus and Stiffness of rubber. Hence, to achieve stiffness of 55HRC rubber, E value is calculated as: = = E = 2.6N/mm2 should be enter to achieve stiffness value of rubber equal to stiffness value of actual rubber. In similar way, to model 65HRC rubber, E value should be 3.9N/mm2 (approx. 4 N/mm2 )

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Fig 9 Deformation plot for 65HRC rubber

Fig 8 Deformation plot for 55HRC rubber

2.3. Modal analysis of Engine-frame assembly with derived rubber mounts: For this analysis, vehicle is divided into three parts: engine, engine mounts and frame. The engine is modeled as a rigid mass with six degrees of freedom and rubber mounts of isotropic material. In Radioss, modal analysis done to get different Engine modes.

Fig. 10 FEA Model of Vehicle with Rubber mounts

3. Results & Discussion: Modal analysis results with different rubber HRC is listed in below table. With 55HRC Rubber mounts Frequency(Hz) Mode 4.6 Lateral 5.8 Longitudinal 7.7 Vertical

With 65HRC Rubber mounts Frequency(Hz) Mode 5.7 Lateral 7 Longitudinal 9.4 Vertical

Table 2. Result of Modal analysis

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Fig 11 Longitudinal Mode

The engine use for this vehicle is 2cylinder engine having idling rpm of 900rpm. Therefore, Firing frequency of engine = (900*2)/ (2*60) = 15 Hz With 55HRC Transmissibility for longitudinal mode = (1/(1-(5.8/15)2)) = 1.17 Transmissibility for vertical mode = (1/(1-(7.7/15)2)) = 1.35

With 65HRC Transmissibility for longitudinal mode = (1/(1-(7/15)2)) = 1.27 Transmissibility for vertical mode = (1/(1-(9.4/15)2)) = 1.64 Transmissibility with 55HRC for longitudinal (8%) and vertical mode (18%) is less than with 65 HRC, hence 55HRC rubber mount is better option for this engine.

4. Experimental Verification: To validate analysis results, acceleration measurement is carried out on test vehicle with 55 HRC and 65 HRC mounts. The locations for accelerometer mountings are as shown below. For test vehicle, measurement done with 2 type of rubber mounts, 55HRC rubber mount and 65HRC rubber mount.

Fig 12 Accelerometers mounting locations

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Competitor Vehicle Existing vehicle Test Vehicle with 65HRC mount

Test Vehicle with 55HRC mount

Fig 13 RMS acceleration at mounting locations

Channel 1 2 3 4 5 6

Channel Title Steering- Z axis Steering- X axis Floor- Z axis Floor- X axis Wind screen- X axis Wind screen- Z axis Table 3: Accelerometers channel location

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Test Vehicle with 55HRC mount Test Vehicle with 65HRC mount

Fig 14 Acceleration at steering X (longitudinal) direction

Both fig. 13 and 14, clearly indicate that, Vibration levels are lower with 55HRC rubber mount than 65HRC rubber mount.

5. Conclusion: Based on analysis 55HRC rubber mounts are suitable for this type of vehicle, same results can be seen in experimental verification. Hence there is a correlation between analysis and experimental.

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