Effect of preload in mechanical systems

Slides:



Advertisements
Similar presentations
Finite Element Methodology Planar Line Element Planar Line Element v1  1  2 v2 21 v(x) x.
Advertisements

FEA as an aid in Design 1.Applying FEA to a fairly complex design can initially overburden us with information. We therefore need a method of analysing.
8.6 Frictional Forces on Collar Bearings, Pivot Bearings and Disks
Statically Determinate and Indeterminate System of Bars.
Indeterminate Structure Session Subject: S1014 / MECHANICS of MATERIALS Year: 2008.
1 Bolts in Tension pt1 Andrei Lozzi. The flanges at the end of the two turbine shafts seen above, are bolted together to form a very rigid friction coupling.
Some Ideas Behind Finite Element Analysis
Strength of Materials I EGCE201 กำลังวัสดุ 1
1 TRC 2008 The Effect of (Nonlinear) Pivot Stiffness on Tilting Pad Bearing Dynamic Force Coefficients – Analysis Jared Goldsmith Research Assistant Dr.
Fasteners, Powers Screws, Connections
Screws, Fasteners, and the Design of Nonpermanent Joints
Matrix Methods (Notes Only)
MECh300H Introduction to Finite Element Methods Finite Element Analysis (F.E.A.) of 1-D Problems – Applications.
Leaning objectives Axial Stress
2005 February, 2 Page 1 Finite Element Analysis Basics – Part 2/2 Johannes Steinschaden.
ANALYSIS OF STRESS DISTRIBUTION IN ROOTS OF BOLT THREADS Gennady Aryassov, Andres Petritshenko Tallinn University of Technology Department of Mechatronics.
Axially loaded member Axial load and normal stress under equilibrium load, Elastic Deformation.
MANE 4240 & CIVL 4240 Introduction to Finite Elements
1 THERMAL STRESSES Temperature change causes thermal strain Constraints cause thermal stresses Thermo-elastic stress-strain relationship (a) at T = T.
Bending Shear and Moment Diagram, Graphical method to construct shear
Finite Element: Theory, Applications & Implementation Presented By: Arthur Anconetani Barbara Gault Ryan Whitney.
MECHANICS OF MATERIALS 7th Edition
Shear stress versus shear strain For homogeneous & isotropic materials pure shear causes angular distortion of a material as shown above. Pure shear is.
2004 March, 4 Page 1 Finite Element Analysis Basics – Part 2/2 Johannes Steinschaden.
Analyses of Bolted Joint for Shear Load with Stainless Steel Bushing and Frictionless Shim-Flange Interface Two cases of shim plates were investigated.
 2005 Pearson Education South Asia Pte Ltd TUTORIAL-1 : UNIAXIAL LOAD 1 PROBLEM-1 1 m P A composite A-36 steel bar shown in the figure has 2 segments,
Strengths Chapter 10 Strains. 1-1 Intro Structural materials deform under the action of forces Three kinds of deformation Increase in length called an.
Chapter 1: Stress Review important principles of statics
Mechanical Testing of Flag Joint Assembly. TF Flag Assembly to be Tested.
1 20-Oct-15 Last course Lecture plan and policies What is FEM? Brief history of the FEM Example of applications Discretization Example of FEM softwares.
STRENGTHS Chapter Intro Dealing with relationship between the external loads applied to an elastic body and the intensity of the internal forces.
MECH593 Finite Element Methods
 2005 Pearson Education South Asia Pte Ltd TUTORIAL-1 : UNIAXIAL LOAD 1 PROBLEM-1 1 m P A composite A-36 steel bar shown in the figure has 2 segments,
Chapter 4 Axial Load. Saint -Venant's Principle Saint-Venant's Principle claims that localized effects caused by any load acting on a body will dissipate.
1 FEA an aid in - the short story - Find out how the load is transmitted, from application to reaction. Are there stiff paths and soft paths ? Are the.
CTC / MTC 322 Strength of Materials
11/11/20151 Trusses. 11/11/20152 Element Formulation by Virtual Work u Use virtual work to derive element stiffness matrix based on assumed displacements.
CTC / MTC 222 Strength of Materials Chapter 1 Basic Concepts.
1 Bolts in Tension pt1 Andrei Lozzi. The flanges at the end of the two turbine shafts seen above, are bolted together to form a very rigid friction coupling.
Machine Design I (MCE-C 203)
Analyses of Bolted Joint for Bolt Preload and Shear Load
Introduction to Stiffness Matrix Method of Structural Analysis By Prof
Strength of Material-1 Introduction. Dr. Attaullah Shah.
Problem c 240 mm b x B A z y Collars A and B are connected by the wire AB and can slide freely on the rods shown. Knowing that the length of the.
§3.2 Cables, bars and springs Topics for this section: Why do we assume cables and ropes are inextensible, and bars are rigid? Springs: what are they,
UNIT-01. SIMPLE STRESSES & STRAINS Lecture Number - 06 Prof. S.C.SADDU MECHANICAL DEPARTMENT SIT LONAVALA Strength of Materials.
Finite Element: Theory, Applications & Implementation Presented By: Arthur Anconetani Barbara Gault Ryan Whitney.
Structural Drafting Shear stress in Bolts. Fastener Loads and Stresses Load:External force applied to a member. Stress: Internal force acting on a member.
AAE 3521 AAE 352 Lecture 08 Matrix methods - Part 1 Matrix methods for structural analysis Reading Chapter 4.1 through 4.5.
Mechanics of Materials – MAE 243 (Section 002) Spring 2008 Dr. Konstantinos A. Sierros.
Structures Matrix Analysis
PS Internal Dump - actuation system
Design Procedure of Helical Compression Spring
Muhannad Al_Waily_Machines Systems Design
1D OF FINITE ELEMENT METHOD Session 4 – 6
Chapter 1 Stress and Strain.
Fasteners, Powers Screws, Connections
FEA convergence requirements.
Ch. 2: Fundamental of Structure
Introduction to Finite Element Analysis for Skeletal Structures
Preliminary Test.
4.7 STRESS CONCENTRATIONS
Part II Design of Fasteners and Joints
Screw and screw selection
Course Title: Analytic Mechanics
Simple Harmonic Motion
Structure I Course Code: ARCH 208 Dr. Aeid A. Abdulrazeg.
Structure I Course Code: ARCH 208 Dr. Aeid A. Abdulrazeg
Fasteners, Powers Screws, Connections
Presentation transcript:

Effect of preload in mechanical systems

Definition and examples Basic example with springs Conclusions FE analysis

Such a system is hyperstatic Principle A mechanical system is under preload when an internal load exists inside the system, having no external loads. Such a system is hyperstatic Studying the internal stress requires to set the balance of loads the balance of displacements the relationship between loads and displacements for each preloaded component 3

Angular bearings Bolt assemblies Main industrial uses 01 02 4 Bâti Arbre Bâti Bolt assemblies 4

Definition and examples Basic example with springs Conclusions FE analysis

Fulfill your graphic when this image is shown

Without preload: L = L01+L02 Example with springs Without preload: L = L01+L02 Fe Initial equilibrium Position L01 L02 7

Load-length relation: Example with springs Without preload: L = L01+L02 Fe Load-length relation: Fe = K2 da = F2 F2 da Fe abruption 8

Load-length relation: Example with springs Without preload: L = L01+L02 Fe Load-length relation: Fe = K1 da = -F1 -F1 da Fe abruption 9

Equilibrium of the washer Example with springs With preload: L = L01+L02 - e Fe Preload length F2 e Equilibrium of the washer F1 + F2 = 0 Thus : Abs(F1) = Abs(F2) Preload length F1 ? e 10

With preload: L = L01+L02 - e Abs(F2) Abs(F1) e F0 da02 da01 Example with springs With preload: L = L01+L02 - e Abs(F1) Preload length Abs(F2) e Preload force F0 da02 da01 Equations: F1 - F2 = 0 da01 + da02 = e F1 = K1 da01 F2 = K2 da02 e 11

Equilibrium of displacement Example with springs Equations: F1 - F2 = 0 da01 + da02 = e F1 = K1 da01 F2 = K2 da02 Load balance Equilibrium of displacement Load-displacement relation for each component

With preload and positiveFe Example with springs With preload and positiveFe FALSE! Abs(F1) Abs(F2) F0 F2 F1 F2 = F0+ Fe F1 = F0 - Fe No load balance Fe + F1 - F2 ≠ 0 No displacement equilibrium Fe e 13

With preload and positiveFe Example with springs With preload and positiveFe Abs(F1) Abs(F2) Fe + F1 - F2 = 0 Thus Fe = F2 - F1 e F2 F1 da2 da1 Equations: Fe + F1 - F2 = 0 da1 + da2 = e F1 = K1 da1 F2 = K2 da2 da = da2 - da02 da > 0 Fe e 14

With preload and negativeFe Example with springs With preload and negativeFe Abs(F1) Abs(F2) Fe + F1 - F2 = 0 D’où Fe = F2 - F1 e F2 F1 da2 da1 Equations: Fe + F1 - F2 = 0 da1 + da2 = e F1 = K1 da1 F2 = K2 da2 da = da2 - da02 da < 0 Fe e 15

Rigidity increased in the preloaded zone Example with springs Study of the global sttifness Abs(F1) Abs(F2) Rigidity increased in the preloaded zone Fe da 16

Definition and examples Basic example with springs Conclusions FE analysis

Preload => hyperstaticsystem Conclusions Preload => hyperstaticsystem No clearance Stiffness increased (A.2 page 1) Load balance Equilibrium of displacements Load-displacements relations (A.3 page 1) 18

Definition and examples Basic example with springs Conclusions FE analysis Back to the preliminary exercise

Example of FEA No preload preloaded e e/2 F0 e 20

Example of FEA No stress Compression tension 21

Example of FEA da1 F0 e e da2 22

Example of FEA Fe da1 Fe F0 e e da2 23

Example of FEA Fe da1 = 0 Fe F0 e e da2 24

Example of FEA Fe da1 Fe F0 e e da2 25

Example of FEA da1 F0 e e da2 26

Example of FEA Fe da1 F0 e e Fe da2 27

Example of FEA Fe F0 e e da1 Fe da2 = 0 28

Definition and examples Basic example with springs Conclusions FE analysis Back to the preliminary exercise

Initial equilibrium (middle) 2 compression springs : free length 39 mm ; Rate 0,5 KgF/mm A Washer is in contact between the 2 springs Available axial space : 66 mm (including the washer) Determine the required axial force to obtain an axial displacement of the washer of 5 mm 10 mm Initial equilibrium (middle) 30

With preload: L = L01+L02 - e Abs(F2) Abs(F1) 12 mm F0 e Example with springs With preload: L = L01+L02 - e In Preloaded area F = (K1 + K2)*d F = (0.5 + 0.5)*5 F = 5 kgF Abs(F1) Abs(F2) 12 mm F0 Out of Preloaded area F = K2* (d0 + d) F = (0.5)*(6 + 10) F = 8 kgF 5 10 e 31