class12 2005SImpact Print · PDF file Linear & Bending Impact Assumptions: •No mass...

Click here to load reader

  • date post

    07-Jul-2020
  • Category

    Documents

  • view

    1
  • download

    0

Embed Size (px)

Transcript of class12 2005SImpact Print · PDF file Linear & Bending Impact Assumptions: •No mass...

  • also called shock, sudden or impulsive loading Impact

    Compare Time of Load Application t with Natural Period of Vibration τ

    a) Rapidly moving

    dashpot

    ■driving a nail with a hammer, automobile collisions ….

    b) Suddenly applied c) Direct Impact ■Combustion in

    engine cylinder ■ vehicles crossing

    a bridge ■ pile drive, ■ drop forge, ■ car crash

    To distinguish:

    k m

    π= 2

    Carrying loads

    Absorbing energy

    t > 3 τ Static load “Gray area” Impact load

    3 τ > t > 1/2 τ t < 1/2 τ

    Design for

  • Impact Factor

    material properties vary with loading speed Impact

    Su

    Sy

    Sy/Su

    elongation

    ksi % •Works favorably

    •Promotes brittle fracture

    •Loading rate only approximated

    In praxis: •Static properties known

    ■ x4 for automobile suspension parts

  • Linear & Bending Impact

    Assumptions:

    •No mass of structure

    •No deflection within impacting mass

    •No damping

    dynamic = static deflection curve only multiplied by impact factor

    all energy goes into structure

    most severe impact

    W

    W k k

    h δ

    Fe

    W

    Guide rod

    δst δ h

    Elastic-strain energy stored in structure = 0.5Feδ

    Work of falling weight = W(h+δ)

    W (h + δ) = 0.5 Fe δ Fe = k δ

    k = W / δst Fe = W δ/δst

    ⎟ ⎟ ⎠

    ⎞ ⎜ ⎜ ⎝

    ⎛ ++=

    st st

    h211 δ

    δδ

    ⎟ ⎟ ⎠

    ⎞ ⎜ ⎜ ⎝

    ⎛ ++=

    st e

    h211WF δ

    Impact Factor

    Impact Deflection …

    Impact Load …

    ⎟ ⎟ ⎠

    ⎞ ⎜ ⎜ ⎝

    ⎛ ++=

    st ste

    h211 δ

    σσImpact Stress …

  • Linear & Bending Impact W

    W k k

    h δ

    Fe

    W

    Guide rod

    δst δ h

    Elastic-strain energy stored in structure = 0.5Feδ

    Work of falling weight = W(h+δ)

    W (h + δ) = 0.5 Fe δ Fe = k δ

    k = W / δst Fe = W δ/δst

    v2 = 2gh → h= v2/2g

    h = 0 or v=0 suddenly applied load

    Impact Factor = 2 (Double Safety Factor)

    Impact Factor

    For h >> δst

  • Linear & Bending Impact W

    W k k

    h δ

    Fe

    W

    Guide rod

    δst δ h

    Elastic-strain energy stored in structure = 0.5Feδ

    Work of falling weight = W(h+δ)

    W (h + δ) = 0.5 Fe δ Fe = k δ

    k = W / δst Fe = W δ/δst

    Impact Factor

    For h >> δst

    Vertical movement

    Horizontal movement

    W = k δst = g m

    Impact kin. Energy … U = 0.5 m v2

    As greater Stiffness and kin. Energy as greater Equivalent static force

  • Linear Impact of Straight Bar

    σ = Fe / A k = A E / L

    Impact Energy Capacity of a straight rod

    • Basic relationship → Gives optimistic results

    • Calculates stress lower than actual stress because of - Non-uniform loading & stress distribution - Mass of the impacted rod

    σ

  • Linear Impact of Straight Bar

    How compare Energy-Absorbing Capacaties ?

    Set δ = Sy

    But Vb = 2½ Va

    …mass specific energy capacity

    Shows Importance of Section Uniformity

  • Impact Absorption Capacity

    A

    bumper

    U = 0.5 Fe δ Fe = Se A

    δ = Fe L / AE

    …mass specific energy capacity

    Se…elastic limit

  • Bending Impact

    Scan p285 u equations Scan p286 o equations

  • Effect of Stress Raisers on Impact

    Ratio 2.25 : 1 : 1/64

    225% : 100% : 1.56%

  • Effect of Stress Raisers on Impact

    Due to combination of Impact and Stress Raiser Brittle fracture is promoted

    with stress concentration factor almost equal Kt

  • Effect of Stress Raisers on Impact

    Improved Design

    pilot

    Reduce Stress Concentration and design for Uniform Stress Distribution

    < Head/Pilot

    Shank

  • E f f e c t o f S t r e s s R a i s e r s o n I m p a c t

    Improved Design

    pilot

    Reduce Stress Concentration and design for Uniform Stress Distribution Raiser

    Axial holepilot

  • Torsional Impact

    Te…eq. static Torque [Nm]Fe…eq. static force [N]

    U…kin. energy [Nm]U…kin. energy [Nm] ω…velocity [rad/s]v…velocity [m/s] K…spring rate [Nm/rad]k…spring rate [N/m] I…moment of inertia [kgm2]m…mass [kg]

    θ…deflection [rad]δ…deflection [m] TorsionalLinear

  • Torsional Impact

    sheave

    2400rpm

    G=79GPa

    ρ=2000kg/m3

    suddenly stopped U=0.5 I ω2 …kin. energy

    I=0.5 m r2 …moment of inertia of wheel m= π r2 b ρ …mass of wheel

    U=0.25 π r4 b ρ ω2

    U=0.25 π (0.060)4 (0.002) (2000) (2400x2π/60)2 Nm U=25.72 Nm

    T=τJ/r

  • Exam

    Monday April 18

    Chapter 5: Elastic Strain Deflection Stability

    Chapter 6: Failure Theories Safety Factors

    Chapter 7: Impact

    Chapter 8: Fatigue

    5.1-2, 5.5-7, 5.10-12

    6.1-2, 6.5-8, 6.10-12

    7.1-2, 7.4

    8.1-11