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PROGRAMME: «BSc in Automotive Engineering»

COURSE: Machine Elements 2 - AUTO 309

ACADEMIC YEAR: 2015-16

INSTRUCTOR: Dr. Antonios Lontos

DATE: 13-5-16

Assignment 2:

«Design of Springs»

Prepared by:

Aaa

Reg. Num.: 8000

NICOSIA - CYPRUS

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TABLE OF CONTENTS

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 ....................................................... 12 7.1 CRITICAL FREQUENCY ....................................................................... 12 8. REFERENCES ............................................................................................. 13 9. DRAWINGS .................................................................................................. 13

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1. INTRODUCTION AND INPUT DATA 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) 75 N. The ends of the spring are square with (b) 6 total turns. At that position the

installed length is (c) Li=61 mm. The operation length is (d) Lo=50 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

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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= 6 Compression load: F= 75 N Installed length: Lf= 61 mm Operating length: Lo= 50 mm 2.2 NUMBER OF ACTIVE COILS (Na) Na = Nt-2 = 6-2 = 4 2.3 ESTIMATION OF SPRING WIRE DIAMETER We assume that the deflection during the installation is Yi= 5mm

I Choose 4mm Wire Diameter from the tables

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2.4 ACTUAL SPRING RATE (K)

2.6 ACTUAL SPRING FREE LENGTH (Lf)

2.7 SPRING INDEX

2.8 SHEAR STRESS FACTOR (KB)

2.9 SPRING PITCH DIAMETER (P)

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3. LOAD AT OPERATING AND AT SOLID LENGTH POSSITION 3.1 SPRING LOADING AT OPERATING POSSITION

3.2 SPRING LOADING AT SOLID POSSITION

4. TENSILE AND TORTIONAL YIELD STRENGTH OF WIRE 4.1 ULTIMATE TENSILE STRENGTH

4.2 TENSILE YIELD STRENGTH

4.3 TORTIONAL YIELD STRENGTH

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5. GENERAL CALCULATION FOR DYNAMIC LOADING 5.1 FORCE Fa

5.2 MEAN FORCE Fm

5.3 SHEAR STRESS AMPLITUDE (τa)

5.4 MIDRANGE SHEAR STRESS (τm)

5.5 LOAD LINE SLOPE

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6. SAFETY AGAINST FATIGUE USING GERBER CRITERION 6.1 ENDURANCE STRENGTH (Sse)

6.2 AMPLITUDE COMPONENT OF STRENGTH

6.3 SAFETY FACTOR AGAINST FATIGUE

7. THE SPRING CRITICAL FREQUENCY 7.1 CRITICAL FREQUENCY

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8. REFERENCES [1] Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering) 10th Edition

[2] Design of Machinery with Student Resource DVD (McGraw-Hill Series in Mechanical Engineering) 5th Edition

[3] Machine Design (5th Edition) 5th Edition

[4] Machine Elements in Mechanical Design (5th Edition)

[5] Analysis of Machine Elements Using SOLIDWORKS Simulation 2015

9. DRAWINGS

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