Basic Analysis of TATRA Air Cooled Engine Block by Finite Element Method

VŠB – Technical University of Ostrava Faculty of Mechanical Engineering

Department of Applied Mechanics

Basic Analysis of TATRA Air Cooled Engine Block by Finite Element Method

Základní analýza vzduchem vzduchového bloku motoru TATRA pomocí metody

konečných prvků

Student: Abdulaziz Suliman H. Alawaji

Diploma thesis supervisor: Assoc. Prof. M.Sc. Karel Frydrýšek, Ph.D., ING-PAED IGIP

Ostrava 2020

ii

iii Student’s affidavit

I declare that I have prepared the whole diploma thesis including appendices independently under the leadership of the diploma thesis supervisor, and I stated all the documents and literature used.

In the thesis, I used internal information about the technical parameters of the vehicle obtained from the company TATRA Trucks a. s., the company agrees to their disclosure.

In Riyadh, Saudi Arabia on July 11, 2020.

...

Student’s signature

iv I declare that:



I am aware that Act No. 121/2000 Coll., Act on copyright, rights related to copyright and amending some laws (the Copyright Act), in particular Section 35 (Use of a work in the civil or religious ceremonies or in official events organized by public authorities, in the context of university performance and use of university work) and Section 60 (university work) shall apply to my final diploma thesis



I understand that VŠB – Technical University of Ostrava (hereinafter referred to as “VŠB-TUO”) has the right to use this final diploma thesis non- commercially for its internal use (Section 35 Subsection 3 of the Copyright Act)



if requested, a copy of this diploma thesis will be deposited with the thesis supervisor,



if VŠB-TUO is interested, I will make a licensing agreement with it permitting to use the thesis within the scope of Section 12 Subsection 4 of the Copyright Act,

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I can only use my thesis, or grant a license to use it with the consent of VŠB- TUO, which is authorized in such a case to demand an appropriate contribution to the costs that were incurred by VŠB-TUO to create the thesis (up to the actual amount),

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I understand that - according to Act No. 111/1998 Coll., on higher education institutions and on changes and amendments to other acts (Higher Education Act), as amended - that this diploma the thesis will be available for public before the defence at the thesis supervisor’s workplace, and electronically stored and published after the defence at the Central Library of VŠB-TUO, regardless of the outcome of its defence.

In Riyadh, Saudi Arabia on July 11, 2020.

...

Signature of the author

Name and surname of the thesis author: Abdulaziz Alawaji

Permanent address of the thesis author: Saudi Arabia, Riyadh, 102463/11675.

v

Abstrakt

Diplomová práce se zabývá pevnostní analýzou motorové skříně osmiválcového vzduchem chlazeného motoru TATRA. Hlavním cílem práce bylo posouzení skříně motoru seřízeného na parametry Euro 6, které způsobí nárůst spalovacích taků o přibližně 14% oproti stávajícímu sériovému stavu. Důraz byl kladen na hodnocení napjatosti meziválcové přepážky, která je nejvíce namáhanou součístí motorové skříně. V rešeržní části práce jsou zmíněny zejména experimentální postupy zjišťování deformací a následně napjatosti meziválcové přepážky jakož i ostatních částí skříně motoru. Analýza napjatosti byla provedena metodou konečných prvků s využitím software Siemens NX-12.

The thesis deals with the strength analysis of the engine block of the eight-cylinder air-

cooled TATRA engine. The main objective of the work was to assess the engine block

for Euro 6 parameters, which will cause an increase in combustion systems by

approximately 14% compared to the current serial state. Emphasis was placed on the

strength evaluation of the inter-cylinder counters, which are the most exposed parts of

the engine block. In the research part of the thesis, the experimental procedures for

detecting deformations and consequently the stress of the inter-cylinder counters as

well as the other parts of the engine block are mentioned. The stress analysis was

carried out by the Finite Element Method using Siemens NX-12 software.

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Acknowledgments

I would like to express my special appreciation and thanks to my advisor Assoc.

Prof. M.Sc. Karel Frydrýšek, Ph.D., ING-PAED IGIP. for the useful comments, remarks and engagement through the learning process of this master thesis. He consistently allowed this paper to be my work, but steered me in the right direction whenever he thought I needed it.

I would like to express my deepest appreciation to all those who provided me the possibility of TATRA TRUCKS experts to complete the thesis. A special gratitude I give to my boss and mentor M.Sc. Miroslav Křížek, Ph.D. whose contribution in stimulating suggestions and encouragement helped me to coordinate my thesis. I cannot say thank you enough for his tremendous support and help.

Finally, I must express my very profound gratitude to my parents and to my

brothers and sisters for providing me with unfailing support and continuous

encouragement throughout my years of study and through the process of

researching and writing this thesis. This accomplishment would not have been

possible without them. Thank you.

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Contents

Abstrakt ... v

Acknowledgments ... vi

List of Figures ... viii

List of Tables: ... x

List of used designations: ... xi

1 Introduction ... 1

2 State of the art and overview of the current state of the problem solution. .... 4

2.1 Computational model of the engine block inter-cylinder counter. ... 4

2.2 Strain gauge deformation measurement and determination of engine block strength. ... 5

2.3 Load assessment of the main T3B-928 engine parts and nodes ... 6

2.4 Strength finite element analysis of diesel engine block ... 6

2.5 Outline And Optimization of Engine Block by using Finite Element Analysis 7 3 Analytical approach ... 8

3.1 Experimental data analysis ... 8

3.2 Theoretical background ... 10

3.3

Substituting and results ... 15

4 FEM analysis and results ... 17

4.1 Geometry ... 17

4.2 Material properties ... 18

4.3 Creating FE mesh ... 19

4.4 Boundary conditions ... 21

4.4.1 Fixed geometry:... 21

4.4.2 Applying forces: ... 23

4.5 FEM Results ... 25

5 Redesign engine block geometry ... 34

5.1 FEM new revision results ... 36

6 Recommendation for future ... 39

7 Conclusion ... 40

8 References ... 42

Appendices ... 43

viii

List of Figures

Figure 1-1: TATRA Truck T 815–7T3RC1 8x8.1R. ... 1

Figure 1-2 TATRA air-cooled engine block. ... 2

Figure 1-3 TATRA air-cooled engine full assembly ... 3

Figure 3-1 crank angle [degree] versus pressure [bar] for two speeds 1200 rpm and 1800 rpm. Source: (TATRA Kopřivnice laboratory, Engine type T3D-928-RE, engine serial number 004, test number 240) ... 8

Figure 3-2 crank angle versus the pressure for eight piston cylinders. ... 9

Figure 3-3 piston location numbering. ... 9

Figure 3-4 four stroke cycle (diesel). ... 10

Figure 3-5 sample of crank mechanism, connecting rod and piston inside the block-engine of TATRA air-cooled engine type (T3D-928-RE). ... 10

Figure 3-6 Parametric representation of the crankshaft, connecting rod, and piston assembly ... 11

Figure 4-1 final geometry of engine block before meshing. ... 17

Figure 4-2 name of material of each part of TATRA engine. ... 18

Figure 4-3 CTETRA element connection... 19

Figure 4-4 3D CTATRA FE mesh assembly... 20

Figure 4-5 3D CTATRA FE mesh assembly... 20

Figure 4-6 summary of number mesh and nodes. ... 21

Figure 4-7 four fixed supports using 1D connection ... 21

Figure 4-8 1D connection, element type used. ... 22

Figure 4-9 engine block including cylinder heads. ... 23

Figure 4-10 typical example of solution number 5 action and reaction boundary conditions. ... 24

Figure 4-11 results of eight calculations solution. ... 25

Figure 4-12 engine block solution number 8, Von-Mises stress in MPa. ... 26

Figure 4-13 engine block solution number 8, Von-Mises stress in MPa. ... 26

Figure 4-14 cross section engine block solution number 8, Von-Mises stress in MPa. ... 27

Figure 4-15 cross section engine block solution number 8, Von-Mises stress in MPa. ... 27

Figure 4-16 engine block solution number 8, maximum Von-Mises stress on the rip support. ... 28

Figure 4-17 engine block solution number 8, Von-Mises stress iso-lines view in MPa. ... 28

Figure 4-18 inter-cylinder counters reaction in Newton solution number 8 (contact force). ... 29

Figure 4-19 inter-cylinder counters reaction in MPa solution number 8 (contact pressure). ... 29

Figure 4-20 engine block solution number 8, displacement in mm. ... 30

Figure 4-21 engine block solution number 8, max shear stress in MPa. ... 30

ix

Figure 4-22 engine block solution number 7, maximum Von-Mises stress on the

rip support. ... 31

Figure 4-23 cross section engine block solution number 7, Von-Mises stress in MPa. ... 31

Figure 4-24 engine block solution number 3, maximum Von-Mises stress on the rip support. ... 32

Figure 4-25 cross section engine block solution number 3, Von-Mises stress in MPa. ... 32

Figure 4-26 engine block solution number 5, maximum Von-Mises stress on the inter-counter cylinder hole. ... 33

Figure 4-27 cross section engine block solution number 5, Von-Mises stress in MPa. ... 33

Figure 5-1 TATRA engine block piston numbers. ... 34

Figure 5-2 engine block rear support original model. ... 34

Figure 5-3 modified rear left support engine block. ... 35

Figure 5-4 modified rear left support engine block ... 35

Figure 5-5 modified rear right support engine block. ... 36

Figure 5-6 modified engine block, solution number 8 Von-Mises stress MPa. . 37

Figure 5-7 cross section modified engine block, solution number 8 Von-Mises stress MPa. ... 37

Figure 5-8 cross section modified engine block, solution number 7 Von-Mises stress MPa. ... 38

Figure 5-9 modified engine block, solution number 3 Von-Mises stress MPa. . 38

Figure 0-1 linear acceleration motion of the piston. ... 43

Figure 0-2 force acting on piston number one. ... 43

x

List of Tables:

Table 3-1 pressure on eight pistons at constant crankshaft angle (14 degree). 15 Table 3-2 different given data needed to the calculation. 15 Table 3-3 forces acting on pistons for a full rotation of crankshaft in Newton. 16 Table 4-1 physical and mechanical properties of each part. 18

Table 4-2 typical application for element. 22

Table 4-3 results of eight calculations solution. 25

Table 5-1 results of maximum Von-Mises stress for original and modified model.

36

xi

List of used designations:

𝑎_𝑝𝑥 ^𝑚

𝑠²

Linear acceleration of piston in X direction 𝑎_𝑟𝑥 , 𝑎_𝑟𝑦 ^𝑚

𝑠²

Linear acceleration of connection rod in X and Y direction

𝑅_𝑝 𝑚

Radius of the piston

𝐹_𝑎𝑥 , 𝐹_𝑎𝑦 𝑁

X, Y components of reaction forces on the crankpin

Force at the piston pin end of the connecting rod in X

direction

𝐼_𝑧𝑧 𝑘𝑔. 𝑚²

Moment of inertia about z axis located at the center of gravity of connecting rod

𝐿₁ 𝑚

Crank radius

𝐿₂ 𝑚

Connecting rod length

𝐿_𝑔 𝑚

Distance of the center of gravity of connecting rod from crankpin end center

𝑚_𝑝 , 𝑚_𝑟 𝑘𝑔

Mass of piston assembly, mass of connection rod

Pressure in the cylinder on the top of the piston

Location of center of gravity of the connection rod

𝑟_𝑔𝑥, 𝑟_𝑔𝑦 𝑚

Location of center of gravity of connection rod in X and Y direction

𝑟_𝑝𝑥, 𝑟_𝑝𝑦 𝑚

X and Y component of piston pin location

𝑠

Linear velocity of center of gravity of connecting rod for X and Y direction

𝑣_𝑝𝑥 ^𝑚

𝑠

Linear velocity of the piston

𝛼₁ , 𝛼₂ ^𝑟𝑎𝑑 𝑠²

Angular acceleration of crankshaft and connecting rod

β

degrees Connecting rod angle

θ

degrees Crank angle

𝜔₁ , 𝜔₂ ^𝑟𝑎𝑑 𝑠

Angular velocity of crankshaft and connection rod

1

1 Introduction

TATRA TRUCKS a.s. is producer of heavy-duty off-road trucks, particularly well- known for its original chassis concept with a central backbone tube and independently suspended half-axles. TATRA produces a vast number of different models of vehicles for various purposes - commercial, military, mining, firefighting and others. TATRA also developed and manufactures air-cooled engines that have been verified in the most difficult off-road and climatic conditions. The mentioned engine will also be the subject of the thesis. Namely, this work will deal with the strength analysis of the engine block.

Figure 1-1: TATRA T 815–7 8x8.

Source: https://www.TATRA.cz/underwood/download/files/TATRA-military-vehicles_en.pdf

The engine block is a complex spatial body of tunnel-shaped shape with a certain number of reinforcing walls formed by inter-cylinder counters. The engine block is loaded with a set of spatial forces from which, according to the experimental results, the forces given by the engine adjustment are decisive for its dimensioning. This means that the combustion pressures in engines is the main parameter of increasing the load on all parts of the engine. It has been confirmed that the size of the

combustion pressures is decisive for deformation and strength of the engine block

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and its parts, in particular, for the inter-cylinder counters, which are the most exposed parts of the engine block.

Figure 1-2 TATRA air-cooled engine block.

In addition to that, due to engine block weight ratio to the total engine weight, the engine block is also a critical part of the weight optimization to ensure the low engine power weight while ensuring a high service life of the main engine parts.

The optimal engine block dimensioning has been paid considerable attention in the past in TATRA. Determining the deformations and strength of the engine block was an experimental approach due to the possibilities of the computer technology at that time.

Later, with the development of computer technology, the results of experimental research were used both as input data, especially for calculations using the Finite Element Method and also for supplementing the overall picture of the results and, last but not least, for their verification.

The subject of the thesis is V8 diesel engine with direct fuel injection,

displacement of 12.7 liters is supercharged using a turbocharger and with filling air

intercooler positioned directly above the engine. The engine, equipped with a

mechanically controlled in-line injection pump, has a unique technical solution with a

split crankshaft, bolted from the individual segments. The engine is available in various

variants within the range of 230 KW - 325 KW and 1,300 Nm – 2,100 Nm respectively.

3

Figure 1-3 TATRA air-cooled engine full assembly

Source: https://www.TATRA.cz/underwood/download/files/TATRA-military-vehicles_en.pdf

The task is to perform a strength analysis of the engine block in order to evaluate

the suitability of its existing structure for higher power and torque, or to propose

modification of its design to achieve the required parameters. Specifically, the usability

of the existing E5 engine block for increased combustion pressures corresponding to

the adjustment of the engine to Euro 6 emission limits and thus an increase in power

and torque of 355 KW and 2400 Nm will be subject of strength analysis. The method

of investigating the results is using the FEM by NX software, perform basic finite

element method by creating a mesh on interest area of the part, boundary conditions

and find the best approach to get the most accurate results.

4

2 State of the art and overview of the current state of the problem solution.

Many studies about the TATRA air- cooled engine has been done along the years trying to study the influence of heat, bearings, stress, deformation etc. These studies are to make sure the engine can be in the best condition and performance. The scientific researches were experimental, concluded and summarized into points as shown below, in addition to other researches related to different engine blocks has been investigate about it. TATRA air-cooled engine was tested experimentally for different purposes; the texts below shows the topic, author name, published year, place and the results.

2.1 Computational model of the engine block inter-cylinder counter.

Assoc. Prof. M.Sc. Přemysl Janíček, Ph.D. and M.Sc. Daniel Hajduk carried out extensive experimental and theoretical research with the aim of creating a computer- oriented calculation model of the engine block (TATRA air-cooled engine), allowing interactively optimize the shape of the inter-cylinder counters. The conclusion and results of their paper is:

 Significant proportional deformation and thus strain in the inter-cylinder

counter arises only under load in adjacent cylinders.

 The distribution of proportional deformations in the circumferential direction

around the circumference of the bearing ring of the inter-cylinder counter has a characteristic kidney-shaped course. From this, we can consider that the inter-cylinder counter behaves as a ring with variable rigidity in both radial and circumferential direction, which is loaded with forces at the attachment point of the anchor screws of the cylindrical units and at the bottom of the bearing ring continuously distributed by the pressure load.

 From the course of proportional deformations in the radial direction on both

sides of the bridge of the inter-cylinder counter indicates that the bridge is bent during operation.

 With increasing pre-injection angle and as well as increasing engine loads,

proportional deformations in almost all parts of the engine block are increased.

 The proportional deformation of the engine block does not depend

significantly on the engine speed, from which it can be assessed the small

5

effect of inertia from rotating and sliding materials on the engine block strength.

 Immediately after the engine stops, there is a sharp increase in

temperature on the cylinder heads associated with the formation of large tensile stresses in the anchor screws. This creates a similar situation to the tightening of screws when installing cylinder heads.

 The dynamic load of the engine block is determined by the course of

combustion pressures in the cylinders. The measurement confirmed that the partition are more significantly loaded when igniting those cylinders that separate from each other.

 Deformation and tension from pressing the outer bearing ring in the inter-

cylinder partition is not pronounced and has an obvious stochastic character.

 Proportional deformation and the resulting safety to the expected fatigue

is mainly related to the size of the maximum combustion pressures. The lug of the main bearing is an extremely loaded separate part of the engine block housing. Therefore, this part will have to pay appropriate attention.

2.2 Strain gauge deformation measurement and determination of engine block strength.

M.Sc. Zdeněk Hinner analyzed the results of strain gauge deformation measurements on the engine block of the T5-928 engine in Kopřivnice 1989. The purpose of the measurement was to check the designed engine block shape in relation to the engine load, the material used and its fatigue properties. In addition, the purpose was to use the results of strain gauge measurements to verify the calculation model of deformation and strength of inter-cylinder counters by the finite element method. The results of the measurements was:

 The deformations and strain observed by strain gauge indicate that the

relative deformation and the resulting safety to the expected fatigue are mainly related to the size of the combustion pressures.

 The reduction of the expected safety of the inter-cylinder counter when

adjusting the engine to higher internal combustion pressures is in

proportion to the maximum combustion pressures.

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 The smallest values reach safety in the direction of maximum dynamic

forces, which is simultaneously in the direction of the cylinders axis.

 The extremely loaded separate part of the inter-cylinder counter is the

stirrup of the main bearing.

2.3 Load assessment of the main T3B-928 engine parts and nodes

M.Sc. Zdeněk Hinner assessed the dimensioning of the main engine parts for the Euro 3 emission standard in Kopřivnice, 1998 of TATRA air- cooled engine. Results and conclusion of the scientific research:

 The main engine parts were checked - crankshaft, crankshaft bearings,

timing mechanism, engine block, head-cylinder joint, connecting rod and piston pin.

 Due to the increase in combustion pressures, it was recommended to

optimize all parts, including the engine block.

2.4 Strength finite element analysis of diesel engine block

An Indian journal named by Biotechnology has published in 2014 a full paper of

“Strength finite element analysis of diesel engine block” made by School of Automobile and Traffic Engineering, Jiangsu University, Zhenjiang, Jiangsu, 212013, (P.R.China), and School of Energy and Power Engineering, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, 212003, (P.R.China). The paper is simulate the strength of diesel in-line engine block of four cylinders by finite element method using ANSYS software, starting by doing the calculation of body load, lateral force of piston, main bearing load and bolt axial load and the results and conclusion of the paper is:

 In the case of a cylinder maximum explosion pressure, the cylinder pistons

lateral force is the largest.

 Maximum stress of the block cylinder wall appeared in the same time of

piston location of reaction.

 The piston lateral force of the cylinder barrier which is next to the doing

work cylinder is significantly influence by the doing action cylinder.

 The force on the main holding bearing which just under the doing work

cylinder is the largest, the load of the rest of the cylinders main holding

bearing is smaller.

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 The cylinder bolts around the action work cylinder were forced evenly; the

force on the external of the piston top was equally split among them.

2.5 Outline And Optimization of Engine Block by using Finite

Element Analysis

M. ARUN KUMAR and K.B.G TILAK, Dept. of Mechanical, Nalla Narasimha Reddy Education Society’s, Telangana, India. Are published a paper under the name of “Outline and Optimization of four cylinders in-line Engine Block by using Finite Element Analysis” in 2017. The design was considered under integrated structure comprising the cylinders using ANSYS software and thermal analysis, starting by sketch module and design parameters of engine block and finishing by material selection and the design conclusion was:

 Comparing between three material selections (cast iron, aluminum alloy

and magnesium alloy), the results of all Von-Mises stresses was under the yielding limits of all material used.

 The engine block of cast iron material has the lowest Von-Mises stress.

 The factor of safety of cast iron used for engine block is higher than the

other materials (aluminum alloy and magnesium alloy).

 The result of dynamic analysis of stresses and deflection is obtained in the

harmonic analysis and was under the design limits.

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3 Analytical approach

3.1 Experimental data analysis

Pressure of one-piston cylinder was tested experimentally in TATRA Kopřivnice laboratory on 22 of August 2019, TATRA facilities within Euro 6 project, Engine type T3D-928-RE,see table A1 in the appendices. The test was with two rotational speeds of crankshaft, the first speed was at 1800 rpm (which consist the maximum power of the engine 355 KW), the second speed was with 1200 rpm and in this speed we have the maximum torque which equal to 2400 Nm, the test is measure the pressure in different angle of crank shaft from -360 degree to 360 degree as it shows in figure 3-1 below.

The figure 3-1 describes the rotational motion of the crankshaft and the four- stroke pressure on one cylinder and it can be noted that the maximum pressure will be at 1200-rpm speed exactly when the crankshaft at 14 degree and the pressure at the highest peak will be 161.23 bar.

Figure 3-1 crank angle [degree] versus pressure [bar] for two speeds 1200 rpm and 1800 rpm. Source: (TATRA Kopřivnice laboratory, Engine type T3D-928-RE, engine serial number 004, test number 240)

In addition, because the engine has a cylinder spacing angle 90 degrees that

mean the compression is happen every 90 degree in different piston cylinder (8

pistons), the length of cycle period is 720 deg. Figure 3-2 below shows the pressure

level for the eight pistons cylinders at 1200 rpm.

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Figure 3-2 crank angle versus the pressure for eight piston cylinders.

Figure 3-2 shows the four-stroke cycle (diesel) for different pistons, which is induction-compression-power-exhaust figure 3-4 below illustrated the diesel cycle.

The firing order number, which is 1, 6, 3, 5, 4, 7, 2, 8 respectively. On figure 3-3 describe the location numbering of piston according to TATRA Trucks standards.

Figure 3-3 piston location numbering.

10

Figure 3-4 four stroke cycle (diesel).

Source: http://automobiles-hariadhikari.blogspot.com/2010/12/4-stroke-engine-principle.html

3.2 Theoretical background

The TATRA air-cooled engine type (T3D-928-RE) is designed as V- engine type with eight cylinders. In the first step of doing analysis, all the forces acting on the piston from the compression on each cylinder had to be calculated. The forces that acting on the piston is also effecting on the internal bearing that holding the crankshaft and it must be considered in the calculation. Figure 3-5 is one of the mechanisms of eight pitons of the engine including the piston, connecting rod and the crank.

Figure 3-5 sample of crank mechanism, connecting rod and piston inside the block- engine of TATRA air-cooled engine type (T3D-928-RE).

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According to the theory of mechanisms, the crank mechanism can be simplified into schematic form and assign the symbols as shown in figure 3-6.

Figure 3-6 Parametric representation of the crankshaft, connecting rod, and piston assembly

Where:

L

: Length of the crank.

L

: Length of connecting rod.

L_𝑔

: Distance of the center of gravity of connecting rod from crankpin end center.

m

: Mass of the crank.

m

: Mass of connection rod.

m

: Mass of piton assembly including pin, rings, etc.

θ : Crank angle.

β : Connecting rod angle.

r

: Distance of the piston with respect to the A (origin).

𝑃_𝑐: Pressure acting on the piston.

𝑟

: Distance of the center of gravity of the connected rod from the origin of A.

12

The аnаlysis is required to find the forces аnd loаd history аpplied on the crаnkshаft beаrings аnd to cаlculаte the forces on the piston heаd, the cаlculаtion mechаnism is bаsed on single DOF mechаnism.

The аngulаr velocity of ω

crаnkshаft is given by:

ω

=

𝑑𝑡

(1)

Where θ is the crаnkshаft аngle in degrees аs it’s shown in figure 3-6 аbove. The аngulаr аccelerаtion is the differentiаl of the аngulаr velocity with respect of time аs in the following equаtion:

𝛼

=

𝑑𝑡

(2)

And by sin law we can obtаin the аngle β since it’s relаted to θ by:

sin(β) =

𝐿₂

(3)

By the sаme procedure of equаtion (1) аnd (2), differentiаting the аngle β аnd 𝜔

with respect to time, respectively:

𝜔

=

𝑑𝑡

(4) 𝛼

=

𝑑𝑡

(5)

Solving 𝜔

by differentiаting equаtion (3) with respect to time аs the following:

𝜔

cos(β) =

𝐿₂

(6)

Finding the vаlue of cos(β) by the equаtion:

cos(β) = √1 −

𝐿₂²

(7)

By substitute the equаtion of (7) in (6), we got 𝜔

аs а function of θ:

𝜔

=

𝐿₂√1− ^{𝐿12 𝑠𝑖𝑛2(θ)} 𝐿22

(8)

𝛼₂

of the connecting rod is find by differentiаting equаtion (8) with respect to time

аnd replаcing from equаtion (1) аnd (2) we got:

13

𝛼

=

𝐿₂√1− ^{𝐿12 𝑠𝑖𝑛2(θ)} 𝐿22

+

𝐿22 )

(9)

The coordinаte of the center of grаvity of the connected rod 𝑟

, from the origin of А in X-аxis аnd Y-аxis аs figure 3-6 is by the equаtions:

𝑟

= 𝐿

cos(θ) + 𝐿

cos (β) (10) 𝑟

= 𝐿

sin(θ) − 𝐿

sin(β) (11)

Substituting the equаtions (3) аnd (7) into (10) аnd (11), we got:

𝑟

= 𝐿

cos(θ) + 𝐿

√1 −

𝐿₂²

(12) 𝑟

= 𝐿

sin(θ) − 𝐿

𝐿₂

(13)

Lineаr velocity of the center of grаvity of the connecting rod 𝑣

in the X аnd Y- аxis is solved by differentiаting equаtion (12) аnd (13) with respect the time:

𝑣

= −𝐿

𝜔

sin(θ) −

2 𝜔₁ sin (2θ) 2 𝐿₂² √1− ^{𝐿12 𝑠𝑖𝑛2(θ)}

𝐿22

(14)

𝑣

= 𝐿

𝜔

cos(θ) −

𝐿₂

(15)

By differentiаting the lineаr velocity of the equаtions (14) аnd (15) with respect of time, we will hаve the lineаr аccelerаtion of on both X аnd Y- аxis of the center of mаss of the connecting rod:

𝑎_𝑟𝑥 = −𝐿₁ 𝛼₁sin(θ) − 𝐿₁ 𝜔₁²cos(θ) − ^{𝛼1 𝐿𝑔 𝐿1}

2sin(2θ) 2𝐿₂²√1− ^{𝐿12 𝑠𝑖𝑛2(θ)}

𝐿22

−

1

𝐿22(2−^{2 𝐿12 𝑠𝑖𝑛2(θ)} 𝐿22 )

(

𝜔₁² 𝐿_𝑔 𝐿₁² (

2 cos(2θ) √1 −^{𝐿12 𝑠𝑖𝑛2(θ)}

𝐿22 + ^{𝐿12 𝑠𝑖𝑛2(2θ)}

2𝐿22√1− ^{𝐿12 sin(θ)} 𝐿22

))

(16)

𝑎

= 𝐿

𝛼

cos(θ) − 𝐿

𝜔

sin(θ) −

𝐿₂

+

𝐿₂

(17)

14

While the locаtion of the piston 𝑟

with respect to the А (origin) is giving by:

𝑟

= 𝐿

cos(θ) + 𝐿

cos(

) (18)

In other hаnd 𝑟

substituting from equаtion (7) into equаtion (18) we got аn equаtion аs а function of θ:

𝑟

= 𝐿

cos(θ) + 𝐿

√1 −

𝐿₂²

(19)

Differentiаte the displаcement of equаtion (19) to hаve the lineаr velocity of the piton with respect to the time:

𝑣

= −𝐿

𝜔

sin(θ) −

2 𝐿₂√1− ^{𝐿12 𝑠𝑖𝑛2(θ)} 𝐿22

(20)

Differentiаte the lineаr velocity of the piton with respect to time to get the lineаr аccelerаtion of the piton:

𝑎_𝑃𝑥 = −𝐿₁ 𝛼₁sin(θ) − 𝐿₁ 𝜔₁²cos(θ) − ^{𝛼1 𝐿12sin(2θ)}

2𝐿22√1−^{𝐿12 𝑠𝑖𝑛2(θ)} 𝐿22

−

1

𝐿22(2−^{2 𝐿1}2 𝑠𝑖𝑛2(θ) 𝐿22 )

(

𝜔₁² 𝐿₁² (

2 cos(2θ) √1 −^{𝐿12 𝑠𝑖𝑛2(θ)}

𝐿₂² + ^{𝐿12 𝑠𝑖𝑛2(2θ)}

2 𝐿22√1−^{𝐿12 sin(θ)} 𝐿22

))

(21)

Аnаlysing the forces on the piston аcting in the X-аxis direction will be:

𝐹

= 𝑚

𝑎

+ 𝜋 𝑅

𝑃

(22)

Where 𝑅

is the rаdius of the piston, 𝑃

is the pressure аcting on the piston which is given on tаble А0 experimentаlly.

Substituting equаtion (21) in (22):

𝐹_𝑝𝑥= −m_p 𝐿₁ 𝛼₁sin(θ) − m_p 𝐿₁ 𝜔₁²cos(θ) −^{mp 𝛼1 𝐿12sin(2θ)}

2𝐿₂²√1−^{𝐿12 𝑠𝑖𝑛2(θ)}

𝐿22

−

m_p 𝐿₂²(2−^{2 𝐿1}2 𝑠𝑖𝑛2(θ)

𝐿22 )

(

𝜔₁² 𝐿₁² (

2 cos(2θ) √1 −^{𝐿12 𝑠𝑖𝑛2(θ)}

𝐿₂² + ^{𝐿12𝑠𝑖𝑛2(2θ)}

2 𝐿₂²√1−^{𝐿12 sin(θ)}

𝐿22

))

+ 𝜋 𝑅_𝑝² 𝑃_𝑐

(23)

15

3.3 Substituting and results

From the given data we have from the experiment, we got the pressure on each piston at 14 degrees of crankshaft rotational movement; table 3-1 shows the pressure in MPa on each piston at 14 degrees crankshaft angle:

Table 3-1 pressure on eight pistons at constant crankshaft angle (14 degree).

Given data necessary of the calculation to calculate the forces acting on the pistons from the crankshaft mechanism shown on the table below:

Table 3-2 different given data needed to the calculation.

By the given data on table 3-2 and by using the formula on the previous pages we will be able to calculate the forces on each piston based on the pressure given.

From equation (22), by calculating the force acting on the piston 𝐹

of each piston for a full rotation of crankshaft at highest pressure on each piston according to

piston number at 14 degree Cylinder pressure [MPa]

1 16.123

6 0.754

3 0.271

5 0.240

4 0.243

7 0.200

2 0.379

8 1.539

Engine type T3D-928-RE

Max. power 355 kW / 1800 rpm Max. torque 2400 Nm / 1200 rpm Engine displacement 12667 ccm

Number of cylinders 8

Piston stroke 140 mm

Piston diameter 120 mm

Piston mass (mp) 3.064 kg moment of inertia (Izz) 0.050995 Kg m^2

length of crank (L1) 0.07 m length of connecting rod (L2) 0.26 m

crankshaft speed (ω1) 125.664 rad/sec piston raduies (Rp) 0.06 m mass of connecting rod (mr) 3.4339 kg length of center of mass of connecting

rod (Lg) 0.19125 m

16 figure 3-2 we got:

Table 3-3 forces acting on pistons for a full rotation of crankshaft in Newton.

From the table 3-3 it is obvious that it should test the engine block eight times for a different crankshaft angle, to simulate the real life scenario of engine based on ignition on each piston. For example, the test will start by changing the crankshaft angle to 14 degree and applying the forces on each piston (according to figure 3-3) and study the results. Thin changing the crankshaft to -166 degree (solution number 2) and applying the forces on each piston thin study the results, and so on.., that’s mean we have eight solution of engine block, each solution represent for different piston ignition.

The red diagonal forces on the table 3-3 values is represent to the ignition on those piston, which is the highest pressure. Moreover, as it mention earlier the firing order on the engine will be on pistons 1 (14 degree crankshaft angle), 6 (104 degree crankshaft angle), 3 (194 degree crankshaft angle), 5 (284 degree crankshaft angle), 4 (-346 degree crankshaft angle), 7 (-256 degree crankshaft angle), 2 (-166 degree crankshaft angle), 8 (-76 degree crankshaft angle) respectively.

1 2 3 4 5 6 7 8

1 14 178252.8054 186.3842 -1030.26 -1346.09 -1377.16 4425.674 -1832.84 13307.96 2 -166 5542.419577 184825.5 5226.592 6759.067 4739.843 5195.527 19880.64 10998.36 3 194 6759.066987 5226.592 184825.5 5542.42 10998.36 19880.64 5195.527 4739.843 4 -346 -1346.09094 -1030.26 186.3842 178252.8 13307.96 -1832.84 4425.674 -1377.16 5 284 2274.685561 2730.37 17415.49 8533.199 182360.3 4293.909 3077.262 2761.434 6 104 19054.23932 3913.439 10171.95 4369.123 4716.016 183999.1 4400.188 5932.663 7 -256 4369.123413 -1247.8 3913.439 19054.24 5932.663 4400.188 183999.1 4716.016 8 -76 8533.199184 17415.49 2730.37 2274.686 2761.434 3077.262 4293.909 182360.3

Force on pitons [N]

crankshaft angle [DEGREE]

solution #

17

4 FEM analysis and results

Using Siemens NX-12 software www.sw.siemens.com , to do the FEM analysis and study the influence of all boundary conditions from the calculation of the previous chapter, then study all the necessary stress and deformation on the engine block.

4.1 Geometry

TATRA TRUCKS engine design department designs the entire assembly engine using I-DEAS (Integrated Design and Engineering Analysis Software).

In the meantime, the same CAD of engine block has been used again using NX- 12 software to develop and test it, by collecting all the parts as a one assembly that it’s important to the engine block and doing the necessary constrains, the final geometry that will be doing simulation on it will be:

Figure 4-1 final geometry of engine block before meshing.

Where:

1. Engine block (main part)

2. Connecting rod (8 connecting rods).

3. Supports of engine block (4 supports).

4. Outer Flywheel case.

5. Inner flywheel case.

6. Crankshaft.

18

4.2 Material properties

After the engine has been assembled with all necessary parts, the next step is to assign the material of each part; each part has different mechanical and physical properties that shows in the figure:

Figure 4-2 name of material of each part of TATRA engine.

The most important material for the calculation is the engine block. The table below clarify the standard name of each part and its properties:

Table 4-1 physical and mechanical properties of each part.

young modulus (GPa) yield stress (MPa) ultimate strength (MPa) Poisson's Ratio density (Kg/m^3)

1 iron_cast_G25 90 215 270 0.26 7150

2 cast steel CSN 42 2660 (EN EG-300) 209.4 300 590 0.29 7830

3 steel CSN 14 230.9 (16MnCr5) 200 590 780 0.29 7850

4 spherulitic cast iron CSN 42 2305

(EN-GJS-500-7) 169 320 500 0.3 7050

5 aluminium CSN 42 4331

(AlSi10MgMn, EN AC-43000) 70 180 240 0.32 2650

6 grey cast iron CSN 42 2420 (EN GJL-

200) 110 200 260 0.26 7180

7 steel CSN 11 373 (S235J0) 200 235 340 0.29 7850

material properties material name

#

19

4.3 Creating FE mesh

Creating FE mesh by Siemens NX-12 for all assembly including crankshaft, connecting rod, inner flywheel case, outer flywheel case and engine block. The mesh is choose to be 3D mesh with element size 15 mm; element type is CTETRA (10).

It cаn usе thrее-dimеnsionаl еlеmеnts, commonly rеfеrrеd to аs solid еlеmеnts, to modеl structurеs thаt cаnnot bе modеlеd using bеаm or plаtе еlеmеnts. For instаncе, а solid еlеmеnt is usеd to modеl аn еnginе block bеcаusе of thе block’s thrее-dimеnsionаl nаturе. If howеvеr, crеаting а modеl of thе аutomobilе hood, thе bеst choicе is onе of thе plаtе еlеmеnts. CTЕTRА Four-sidеd solid (tеtrаhеdrаl) еlеmеnt with 4 to 10 nodеs sее figurе 4-3. Thе CTЕTRА еlеmеnt is аn isopеrimеtric tеtrаhеdron еlеmеnt with four vеrtеx nodеs аnd up to six аdditionаl midsizе nodеs. If midsizе nodеs hаd bееn usеd, it should includе аll six nodеs. Thе аccurаcy of thе еlеmеnt dеgrаdеs if somе but not аll thе еdgе nodеs аrе usеd. Thе CTЕTRА solid еlеmеnt is usеd widеly to modеl complicаtеd systеms (i.е. еxtrusions with mаny shаrp turns аnd fillеts, turbinе blаdеs). It should аlwаys usе CTЕTRАs with tеn nodеs points for аll structurаl simulаtions (е.g. solving for displаcеmеnt аnd strеss). Thе CTЕTRА with four nodеs is ovеrly stiff for thеsе аpplicаtions. NX Nаstrаn cаlculаtеs еlеmеnt strеssеs (σ

, σ

, σ

,

,

, аnd

), аt thе еlеmеnt’s cеntеr аnd Gаuss points.

Thеsе strеssеs аrе еxtrаpolаtеd to obtаin thе strеssеs аt thе cornеr nodе points.

Figure 4-3 CTETRA element connection

Source:https://docs.plm.automation.siemens.com/data_services/resources/nxnastran/10/help/en_US/td ocExt/pdf/element.pdf

After choosing the appropriate mesh type and size, we got the meshed model

with no errors or failed mesh has been obtained as shown in the figures below:

20

Figure 4-4 3D CTATRA FE mesh assembly.

Figure 4-5 3D CTATRA FE mesh assembly.

Summarizing the number of nodes and element of the engine block assembly by

the figure below:

21

Figure 4-6 summary of number mesh and nodes.

4.4 Boundary conditions 4.4.1 Fixed geometry:

The four-engine support is fixed by 1D connection with RBE2 element properties:

Figure 4-7 four fixed supports using 1D connection

22

RBЕ is dеfinеs as Rigid Body Еlеmеnt, this typе of еlеmеnt with indеpеndеnt DOF that arе spеcifiеd at a onе nodе and with dеpеndеnt DOF that spеcifiеd at an arbitrary numbеr of nodеs.

Thе RBЕ2 еlеmеnt usеs constraint еquations to link thе motion of thе dеpеndеnt DOF to thе motion of thе indеpеndеnt DOF. Thе RBЕ2 shows a vеry suitablе tool for rigid connеcting thе samе componеnts of sеvеral nodеs togеthеr.

Figure 4-8 1D connection, element type used.

Based from NX software there is recommended and typical application for elements type shows on the table below:

Table 4-2 typical application for element.

Source:https://docs.plm.automation.siemens.com/data_services/resources/nxnastran/10/help/en_US/td ocExt/pdf/element.pdf

23

Table 4-2 recommended using RBE2 element type for rigid engine block. As it been used in all the engine four supports

4.4.2 Applying forces:

Since the engine block contained eight piston cylinders, and from table 3-3 from the previous chapter, the best scenario is to solve the model eight times, by changing the crankshaft angle eight times in other words, full cycle (720 degrees). Each crankshaft angle degree on the table 3-3 is represent to the combustion ignition in different piston of the eight pistons. The forces that applied on the engine block is divided into action forces and reaction forces. The action forces is represent the force that comes from the combustion inside the piston. the piston it should be connected in the top of the connecting rod, however because we know the mass of the piston and by using equation (22), we calculated the total force without installing the piston in the model, and applied the force on the top of connecting rod, using 1D collectors (RBE2 collector). Moreover, as a result of an action there is a reaction on the four bolts that holding the cylinder head. Each bolt will take a value equal to (F/4) in opposite direction of the action force (every piston has a four blots), where F is the action force on the top of the connecting rod; figure 4-9 shows the cylinder heads and the bolts that holding the cylinder head assembly:

Figure 4-9 engine block including cylinder heads.

24

Figure 4-10 typical example of solution number 5 action and reaction boundary conditions.

All those action forces in other pistons on figure 4-10 is based on table 3-6 values,

figure 4-10 is a typical example of solution number 5 (ignition on piston 5), crankshaft

angle has been shifted to 284 degrees, and action and reaction has been applied to

the pistons. The yellow arrows is the action forces and the red arrows represent the

reaction forces.

25

4.5 FEM Results

All the results from post-processing data are summarized as Von-Misses stress in MPa, displacement in mm and maximum shear stress in MPa. The engine block has been tested eight times for different boundary conditions and different crankshaft angle to simulate two rotation of crankshaft (full cycle 720 degree). These solutions are made by using NX Nastran solver, structural analysis type (SOL 101 Linear statics). The maximum stress was on solution 8 (ignition on piston 8) and it was 150.18 MPa, therefore the figures below will focus on the results of solutions which has high Von-Mises stress, the rest of the results will represented in one table:

Table 4-3 results of eight calculations solution.

Figure 4-11 results of eight calculations solution.

From table 4-3 and figure 4-11 describes the results of the eight pistons, all of these results is under the yielding limit stress of the cast iron material, which is 215 MPa. It also notes that most of the high stresses is concentrate in the front supports engine block such as solution 3, 4, 7and 8 and exceed the fatigue limit stress of cast iron (120 MPa).

Von-Mises stress (MPa) Max Shear stress (MPa) Total Displacement (mm)

86.31 48.64 0.26 829657 piston rip

91.34 56.37 0.211 828032 right front support rip

141.57 77.03 0.139 654265 right front support rip

127.73 67.71 0.141 828035 right front support rip

89.15 50.14 0.418 830268 inter-cylinder counters hole

92.18 51.76 0.322 813397 left front support rip

135.45 71.93 0.262 828035 left front support rip

150.18 80.22 0.243 672743 left front support rip

node number of

maximum stress location of maximum stresses Solution number

Solution 6 Solution 7 Solution 8 Solution 1 Solution 2 Solution 3 Solution 4 Solution 5

maximum value

26

Figure 4-12 engine block solution number 8, Von-Mises stress in MPa.

Figure 4-13 engine block solution number 8, Von-Mises stress in MPa.

27

Figure 4-14 cross section engine block solution number 8, Von-Mises stress in MPa.

Figure 4-15 cross section engine block solution number 8, Von-Mises stress in MPa.

28

Figure 4-16 engine block solution number 8, maximum Von-Mises stress on the rip support.

Figure 4-17 engine block solution number 8, Von-Mises stress iso-lines view in MPa.

29

Figure 4-18 inter-cylinder counters reaction in Newton solution number 8 (contact force).

Figure 4-19 inter-cylinder counters reaction in MPa solution number 8 (contact pressure).

30

Figure 4-20 engine block solution number 8, displacement in mm.

Figure 4-21 engine block solution number 8, max shear stress in MPa.

31

Figure 4-22 engine block solution number 7, maximum Von-Mises stress on the rip support.

Figure 4-23 cross section engine block solution number 7, Von-Mises stress in MPa.

32

Figure 4-24 engine block solution number 3, maximum Von-Mises stress on the rip support.

Figure 4-25 cross section engine block solution number 3, Von-Mises stress in MPa.

33

Figure 4-26 engine block solution number 5, maximum Von-Mises stress on the inter- counter cylinder hole.

Figure 4-27 cross section engine block solution number 5, Von-Mises stress in MPa.

34

5 Redesign engine block geometry

The main factor that were considered during redesign is stress range under load, table 4-3 shows the maximum Von-Mises stresses on more than a solution such as solution 3, 4, 7 and 8 that exceed the fatigue stress limit of engine block cast iron which equal to 120 MPa, figure 5-1 shows the location of the pistons. The common locations of those high stresses is located on the front supports rips of the engine block, in both lift and right front supports. Therefore, some modification and redesign were done on front supports of the engine block to reduce the high stresses concentration. The propose design is done in the supports rip and increase the volume inside the support also increase the thickness of the rips as shown in the figures below:

Figure 5-1 TATRA engine block piston numbers.

Figure 5-2 engine block front support original model.

35

Figure 5-3 modified front left support engine block.

Figure 5-3 shows the new modification on the front support of engine block, the cavity in figure 5-2 in the middle of the support has been filled, the two rips under the

support thickness has been exposed 10 mm for each rip (two rips). Those modifications for both left and right front supports.

Figure 5-4 modified front left support engine block

36

Figure 5-5 modified front right support engine block.

5.1 FEM new revision results

After calculating the model with the new modification on the engine block we succeed by reducing the von-mesis stress on solution 8 (ignition on piston number 8) from 150.18 MPa to 86.41 MPa. In addition to the other solutions like 3, 4 and 7 as it shown in the table:

Table 5-1 results of maximum Von-Mises stress for original and modified model.

86.11 89.15 87.37 Original model Modified model

Von-Mises stress (MPa) Maximum Value

86.31

135.45 150.18

86.31

Solution 5 Solution 6 Solution 7 Solution 8

91.34 141.57 127.73 89.15 92.18

82.93 86.41 89.09 76.61 Solution number

Solution 1 Solution 2 Solution 3 Solution 4

37

Figure 5-6 modified engine block, solution number 8 Von-Mises stress MPa.

Figure 5-7 cross section modified engine block, solution number 8 Von-Mises stress MPa.

38

Figure 5-8 cross section modified engine block, solution number 7 Von-Mises stress MPa.

Figure 5-9 modified engine block, solution number 3 Von-Mises stress MPa.

39

6 Recommendation for future

Thе main objеctivе of thе thеsis is to study thе influеncе of strеssеs that comеs from thе pistons of thе structurе of cast iron еnginе block by FЕM. Thеrеforе, thеrе is diffеrеnt ways of doing analysis using different approach. Usually the research and development at any company or institute try to increase the efficiency and enhance their product as much as it could be developed, to be reliable and in the best condition and at the lowest costs. After the TATRA air-cooled engine block has been tested statically using advanced software, it is the time to develop the engine block using several methods and techniques of the mechanical and structural point of view. It could be summarized into:

 Applying topology optimization of the structure of TATRA engine block.

Topology optimization is an еffеctivе tеchniquе to rеducе thе structurе dеsign and to minimizе wastе. In othеr words, еliminatе of wеight morе than it nееds to. Topology optimization is conductеd using thе rеsults of FЕM, rеmoving dеsign constraints and opеning up nеw possibilitiеs of dеsign suggеstions. Morеovеr, topology optimization is considеring multiplе static loads combinеd with optimization of natural frеquеnciеs, in addition it considеr thе rеquirеmеnts of minimum thicknеss matеrial. Siеmеns NX software and ANSYS or any advance design software able to do the topology optimization. It could bе onе of thе options to apply thе topology optimization on TATRA еnginе block basеd on thе еxtеrnal conditions of the engine and compare the results with original one.

 Reduce the engine block weight.

By reduce the thickness of engine block cast iron model, then study the results of stress, deformation, thermal analysis, dynamic analysis, etc. of the new revision of thickness to reduce the costs of mass production that could be lighter and cheaper of what was before.

 Changing the material of engine block and compare the results.

Trying to find other material instead of cast iron that could be suitable for TATRA air-

cooled engine block like aluminum alloy or magnesium alloy or others, thin comparing

the results with the results we got.