Assignment 2: «DESIGN OF SPRINGS»staff.fit.ac.cy/eng.la/AMEM317/Assig_2 springs(Example).pdf ·...

PROGRAMME: «BSc in MECHANICAL ENGINEERING»

COURSE: Machine Elements I I - AMEM 317

ACADEMIC YEAR: 2010-11

INSTRUCTOR: Dr. Antonios Lontos

DATE: 06/05/2011

Assignment 2:

«DESIGN OF SPRINGS»

Prepared by:

Georgiou Georgios

Reg. Num.: 1010

NICOSIA - CYPRUS

2

TABLE OF CONTENTS

Contents Assignment 2: ........................................................................................................... 1

1. INTRODUCTION AND INPUT DATA .............................................................. 3

1.1 TABLES................................................................................................... 6

2. GENERAL CALCULATIONS .......................................................................... 8

2.1 USEFUL DATA ........................................................................................ 8

2.2 NUMBER OF ACTIVE COILS (Na) .......................................................... 8

2.3 ESTIMATION OF SPRING WIRE DIAMETER ......................................... 8

2.4 ACTUAL SPRING RATE (K) .................................................................... 9

2.5 ACTUAL SPRING DEFLECTION (Yi) ..................................................... 9

2.6 ACTUAL SPRING FREE LENGTH (Lf) .................................................... 9

2.7 SPRING INDEX ....................................................................................... 9

2.8 SHEAR STRESS FACTOR (KB) .............................................................. 9

2.9 SPRING PITCH DIAMETER (P) .............................................................. 9

3. LOAD AT OPERATING AND AT SOLID LENGTH POSSITION ................... 10

3.1 SPRING LOADING AT OPERATING POSSITION ................................ 10

3.2 SPRING LOADING AT SOLID POSSITION .......................................... 10

4. TENSILE AND TORTIONAL YIELD STRENGTH OF WIRE ......................... 10

4.1 ULTIMATE TENSILE STRENGTH ......................................................... 10

4.2 TENSILE YIELD STRENGTH ................................................................ 10

4.3 TORTIONAL YIELD STRENGTH .......................................................... 10

5. GENERAL CALCULATION FOR DYNAMIC LOADING ................................ 11

5.1 FORCE Fa ............................................................................................. 11

5.2 MEAN FORCE Fm .................................................................................. 11

5.3 SHEAR STRESS AMPLITUDE (τa) ........................................................ 11

5.4 MIDRANGE SHEAR STRESS (τm) ........................................................ 11

5.5 LOAD LINE SLOPE ............................................................................... 11

6. SAFETY AGAINST FATIGUE USING GERBER CRITERION ...................... 12

6.1 ENDURANCE STRENGTH (Sse) ........................................................... 12

6.2 AMPLITUDE COMPONENT OF STRENGTH ........................................ 12

6.3 SAFETY FACTOR AGAINST FATIGUE ................................................ 12

7. THE SPRING CRITICAL FREQUENCY ....................................................... 13

7.1 CRITICAL FREQUENCY ....................................................................... 13

8. REFERANCES ............................................................................................. 14

9. DRAWINGS .................................................................................................. 14

3

1. INTRODUCTION AND INPUT DATA Subject: AMEM 317 (AUTO 309) - Machine Elements and Analysis II Academic Year: 2014 (Spring Semester) Lecturer: Dr. Antonios Lontos ([email protected])

Assignment No. 2: Design of springs

Figure shows an old type of internal combustion engine and a new modification. The

position of the camshaft will change as well as all the other components related to

that part. A helical compression spring made of chrome-vanadium wire A232 will be

use in the new engine valve as shown in the figure. When the valve is closed the

compression load of the spring is (a) 70 N. The ends of the spring are square with (b)

5,5 total turns. At that position the installed length is (c) Li=63 mm. The operation

length is (d) Lo=49. mm.

A. Calculations

1. Calculate the proper spring for this valve. (Diameter of the wire, pitch diameter,

spring rate k). Calculate the load when is compressed at Lo and at solid length.

Calculate the stresses of the valve (cross section of stem) when spring is

operating at Li and Lo. Specify the valve material.

2. Estimate the tensile and torsional yield strength of the wire.

3. Estimate the factor of safety guarding against fatigue using Gerber criterion.

Determine the critical frequency of the spring.

B. Drawings and Assembly

1. Design the spring with all the dimensions. Design the spring in the unloading and

loading condition (when the spring length is Li and Lo).

2. Design the cross section of the engine in 2D

3. Design the spring with the valve in 3D and explain how they will assemble.

VERY IMPORTANT NOTES

* Estimate all dimensions that are not given.

* Useful documents: Cover for Assignment, Drawing template example

* You must submit one hard copy and one pdf file with all calculations and

drawings

* Example for the pdf file “Georgiou Georgios 6820 (Assignment 2)”

mailto:[email protected]

http://staff.fit.ac.cy/eng.la/AMEM316/AMEM316%20Sample%20Contents%20for%20Assignment1.doc

4

Fig. 1: New configuration of the machine (Cross-section)

5

Fig. 2: Old engine with components (Cross-section)

Fig. 3: valves and springs

6

Fig. 4: Engine cross section

1.1 TABLES

8

2. GENERAL CALCULATIONS

2.1 USEFUL DATA Material: Chrome –Vanadium A232

Modulus of rigidity: G=77200 MPa

Constant A from table 10-4: A=2005 MPa.mmm

Exponent m from table 10-4: m=0.168 m

Ssa’= 241 MPa

Ssm= 379 MPa

Ssu= 0.67 sut

Spring End Type: Square

Total turns: Nt= 5.5

Compression load: F= 70 N

Installed length: Lf= 63 mm

Operating length: Lo= 49 mm

2.2 NUMBER OF ACTIVE COILS (Na)

Na = Nt – 2 = 5.5-2 = 3.5 turns

2.3 ESTIMATION OF SPRING WIRE DIAMETER We assume that the deflection during the installation is Yi=5mm. K = Fi / Yi = 70 / 5 = 14 N/mm The required diameter is given by :

√

√

d= 3.59mm from tables the nearest available wire diameter is 3.5mm

9

2.4 ACTUAL SPRING RATE (K)

K = 12.6264 N/mm

2.5 ACTUAL SPRING DEFLECTION (Yi) K=Fi / Yi => Yi = Fi / K = 70 / 12.6264 Yi = 5.5 mm

2.6 ACTUAL SPRING FREE LENGTH (Lf) Lf = Li + Yi = 63+5.55 Lf = 68.55 mm

2.7 SPRING INDEX C = D / d = 32 / 3.5 = 9.14

2.8 SHEAR STRESS FACTOR (KB)

2.9 SPRING PITCH DIAMETER (P)

Due to the approximations and decimal places during the calculations we have error in P value. The real value due to design program SolidWork 2013 P = 11.82 mm

10

3. LOAD AT OPERATING AND AT SOLID LENGTH POSSITION

3.1 SPRING LOADING AT OPERATING POSSITION YO = Lf – LO = 68.5 - 49 = 19.5 mm FMAX = K * YO = 12.6*19.5 = 245.7 N

3.2 SPRING LOADING AT SOLID POSSITION LS = d * (NT+1) = 3.5*(5.5+1) = 22.75 mm YS = LF – LC = 68.5 – 22.75 = 45.75 mm FSOLID = K*YS = 12.6 * 45.75 = 576.45 N

4. TENSILE AND TORTIONAL YIELD STRENGTH OF WIRE

4.1 ULTIMATE TENSILE STRENGTH SUT = A / dm = 2005 / 3.50.168 = 1624.5 MPa

4.2 TENSILE YIELD STRENGTH SSU = 0.67 * SUT = 0.67 * 1624.5 = 1088.4 MPa

4.3 TORTIONAL YIELD STRENGTH SSY = 0.45 * SUT = 0.45* 1624.5 = 731 MPa

11

5. GENERAL CALCULATION FOR DYNAMIC LOADING

5.1 FORCE Fa Fa = FMAX – FMIN / 2 = 245.7-70 / 2 = 87.85 N

5.2 MEAN FORCE Fm Fm = FMAX + FMIN / 2 = 245.7 + 70 / 2 = 157.85 N

5.3 SHEAR STRESS AMPLITUDE (τa)

5.4 MIDRANGE SHEAR STRESS (τm)

5.5 LOAD LINE SLOPE

12

6. SAFETY AGAINST FATIGUE USING GERBER CRITERION

6.1 ENDURANCE STRENGTH (Sse)

( )

( )

6.2 AMPLITUDE COMPONENT OF STRENGTH

[ √ (

)

]

[ √ (

)

]

Ssa = 233.47 MPa

6.3 SAFETY FACTOR AGAINST FATIGUE nf = Ssa / τa = 233.47 / 192 = 1.216

13

7. THE SPRING CRITICAL FREQUENCY

7.1 CRITICAL FREQUENCY

CHANGES PER SECOND

14

8. REFERANCES

[1] Mechanical Engineering Design, Ch. R. Mischke, J. Edward Shigley, McGraw-Hill, 7th edition, 2004.

[2] Fundamentals of Machine Elements, B. J. Hamrock, B. Jacobson, S. R. Scmid, Mcgraw-Hill, 1999

[3] Design of Machine Elements and Machines by Jack A. Collins, George H. Staab, Henry R. Busby, John Wiley & Sons, 2002

[4] Machine Design: An Integrated Approach by Robert L. Norton, Robert L Norton, Prentice Hall, 2nd edition, 2000

[5] Machine Elements in Mechanical Design by Robert L. Mott, Prentice Hall, 3rd edition, 1998

9. DRAWINGS

68,

50

35,50

28,50

3,50

FREE LENGTH

SPRING'S FREE LENGTHLf

3/5/14

WEIGHT:

A3

SHEET 1 OF 1SCALE:1: 2

DWG NO. 1

TITLE:

REVISIONDO NOT SCALE DRAWING

MATERIAL:

DATESIGNATURENAME

DEBUR AND BREAK SHARP EDGES

FINISH:UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES: LINEAR: ANGULAR:

58A/A

R.No. 8650Manolas George

63

35,50

28,50

3,50

INSTALLED LENGTH

SPRING'S INSTALLED LENGTH Li

3/5/14

WEIGHT:

A3


DWG NO. 2

TITLE:


MATERIAL:

DATESIGNATURENAME



58A/A


49

28,50

35,50

3,50

OPERATING LENGTH

SPRING'S OPERATING LENGTH Lo

3/5/14

WEIGHT:

A3


DWG NO. 3

TITLE:


MATERIAL:

DATESIGNATURENAME



58A/A


40

15

2

2

CAP 45

5

R2

38

,50

16

20 20

10

GUIDE

R3

R9

6

18

12

5,83

6

5

SAFE 1,2

36

28

,50

11

5

4,50

10,82

15,86

RETAINER

36

28,50

11 130

5

10

104

,61

5

6

2,2

7

R1

R11,16

15,

39

6,67

VALVE

34

20

,79

10

8

COMPONENTS3/5/14

WEIGHT:

A3


DWG NO. 4

TITLE:


MATERIAL:

DATESIGNATURENAME



58A/A


40

15

2

2

CAP 45

5

R2

38

,50

16

20 20

10

GUIDE

R3

R9

6

18

12

5,83

6

5

SAFE 1,2

36

28

,50

11

5

4,50

10,82

15,86

RETAINER

36

28,50

11 130

5

10

104

,61

5

6

2,2

7

R1

R11,16

15,

39

6,67

VALVE

34

20

,79

10

8

COMPONENTS 3D3/5/14

WEIGHT:

A3


DWG NO. 4.1

TITLE:


MATERIAL:

DATESIGNATURENAME



58A/A


ASSEMBLY 1 3/5/14

WEIGHT:

A3


DWG NO. 5

TITLE:


MATERIAL:

DATESIGNATURENAME



58A/A


2

1435

6

8 7

ITEM NO. PART NUMBER DESCRIPTION QTY.1 body half hole2 1

2 valve 13 spring Li 1

4 guide 1

5 keeper 1 1

6 keeper 2 1

7 retainer cap 1

8 cap 1

ASSEMBLY 1 EXPOADED VIEW

3/5/14

WEIGHT:

A3


DWG NO. 6

TITLE:


MATERIAL:

DATESIGNATURENAME



58A/A


ASSEMBLY1 CROSS SECTION

3/5/14

WEIGHT:

A3


DWG NO. 7

TITLE:


MATERIAL:

DATESIGNATURENAME



58A/A


engine cross section2D

3/5/14

WEIGHT:

A3


DWG NO. 8

TITLE:


MATERIAL:

DATESIGNATURENAME



58A/A


Assignment 2: «DESIGN OF SPRINGS»staff.fit.ac.cy/eng.la/AMEM317/Assig_2 springs(Example).pdf ·...

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