Spring/Mass/Damper system example

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Spring/Mass/Damper system example
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• Example of a shock absorption system
• http//cherokeesprayer.okstate.edu/bitmaps/side.jp
  g
• http//nue.okstate.edu/VRT_Applicator/2003/Field_S
  cale_VRT2003.htm
• http//www.deere.com/servlet/com.deere.u90785.prod
  uctcatalog.view.servlets.ProdCatProduct?tMFRpNbr
  4720XN
• http//www.caseih.com/products/series.aspx?navid
  105RLENNAseriesid32lineid16featuresid7058
• Purpose to allow high machine speeds under
  undulating field conditions
• 10 mph vs 20 mph field speeds double the machines
  capacity
• 20 to 40,000 acres per year coverage is necessary
  for the machine to be cost effective
• Design task
• Select effective shock absorbers that will allow
  necessary machine speeds while preventing frame
  failures and adequately smooth boom travel.

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Damper model
Flow through an orifice
Definition of pressure
This can be linearized using a Taylor series
expansion
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Spring equation
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Suspension schematic
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Force balance
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First order, linked, linear, ordinary D. E.s
Need these in terms of yin and yo
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Simulink form

• Re-arrange in integral form for Simulink

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Simulink

• Simulink Model (Matlab)

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System Diagram

• Consider the following suspension system.
• Solve for y given yin

Suspension system example MacPherson Strut
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Derivation of fundamental equations

• Forces in the y direction on M

At steady state
Subtracting the steady state equation from the
original
Replacing the y in the derivitive terms with Y
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Manipulation and transform
Transforming the equation
Selecting values for C, K, and M C0.1N-s/m,
M2kg, K1N/m
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Use of MATLAB for Step input
Selecting values for C, K, and M C0.1N-s/m,
M2kg, K1N/m

• MATLAB
• n0.1 1
• n
• 0.1000 1.0000
• d2 .1 1
• d
• 2.0000 0.1000 1.0000
• step(n,d)

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• Selecting values for C, K, and M C1N-s/m,
  M2kg, K1N/m

MATLAB n1,1 n 1 1 d2,1,1 d
2 1 1 step(n,d)
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• Selecting values for C, K, and M C100N-s/m,
  M2kg, K1N/m

MATLAB n10,1 n 100 1
d2,10,1 d 2 100 1 step(n,d)