Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin Solution

STEP 0: Pre-Calculation Summary
Formula Used
Diameter of Fulcrum Pin = sqrt((2*sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Shear Stress in Fulcrum Pin))
d1 = sqrt((2*sqrt(Pe^2+Pc^2-2*Pc*Pe*cos(θ)))/(pi*τfulcrum))
This formula uses 1 Constants, 2 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Diameter of Fulcrum Pin - (Measured in Meter) - Diameter of Fulcrum Pin is the diameter of the pin used at the fulcrum joint.
Total Force on Rocker Arm of Exhaust Valve - (Measured in Newton) - Total Force on Rocker Arm of Exhaust Valve is the total force acting onto the rocker arm of the exhaust valve.
Force on Roller Pin - (Measured in Newton) - Force on Roller Pin is the force acting onto the roller pin ( the pivot about which a lever rolls freely) used as a joint.
Angle Between Rocker Arms - (Measured in Radian) - Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms.
Shear Stress in Fulcrum Pin - (Measured in Pascal) - Shear Stress in Fulcrum Pin is the shear stress induced into the pin, the force per unit area tending to cause deformation of the pin by slippage along a plane parallel to the imposed stress.
STEP 1: Convert Input(s) to Base Unit
Total Force on Rocker Arm of Exhaust Valve: 1926 Newton --> 1926 Newton No Conversion Required
Force on Roller Pin: 1925 Newton --> 1925 Newton No Conversion Required
Angle Between Rocker Arms: 135 Degree --> 2.3561944901919 Radian (Check conversion here)
Shear Stress in Fulcrum Pin: 3.66 Newton per Square Millimeter --> 3660000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d1 = sqrt((2*sqrt(Pe^2+Pc^2-2*Pc*Pe*cos(θ)))/(pi*τfulcrum)) --> sqrt((2*sqrt(1926^2+1925^2-2*1925*1926*cos(2.3561944901919)))/(pi*3660000))
Evaluating ... ...
d1 = 0.0248767677909713
STEP 3: Convert Result to Output's Unit
0.0248767677909713 Meter -->24.8767677909713 Millimeter (Check conversion here)
FINAL ANSWER
24.8767677909713 24.87677 Millimeter <-- Diameter of Fulcrum Pin
(Calculation completed in 00.020 seconds)

Credits

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS ), Indore
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17 Design of Fulcrum Pin Calculators

Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin
Go Length of Fulcrum Pin = 1.25*sqrt((2*sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Shear Stress in Fulcrum Pin))
Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin
Go Diameter of Fulcrum Pin = sqrt((2*sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Shear Stress in Fulcrum Pin))
Shear Stress in Fulcrum Pin of Rocker Arm
Go Shear Stress in Fulcrum Pin = (2*(sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Diameter of Fulcrum Pin^2))
Angle between Two Arms of Rocker Arm
Go Angle Between Rocker Arms = pi-arccos(-(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-Force at Fulcrum Pin^2)/(2*Total Force on Rocker Arm of Exhaust Valve*Force on Roller Pin))
Reaction at Fulcrum Pin of Rocker Arm
Go Force at Fulcrum Pin = sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms))
Reaction at Fulcrum Pin of Rocker Arm for Equal Arm Lengths
Go Force at Fulcrum Pin = Total Force on Rocker Arm of Exhaust Valve*sqrt(2*(1-cos(Angle Between Rocker Arms)))
Length of Fulcrum Pin of Rocker Arm given Reaction at Pin
Go Length of Fulcrum Pin = 1.25*sqrt((2*Force at Fulcrum Pin)/(pi*Shear Stress in Fulcrum Pin))
Diameter of Fulcrum Pin of Rocker Arm given Reaction at Pin
Go Diameter of Fulcrum Pin = sqrt((2*Force at Fulcrum Pin)/(pi*Shear Stress in Fulcrum Pin))
Bearing Pressure at Fulcrum Pin of Rocker Arm
Go Bearing Pressure for Fulcrum Pin = (Force at Fulcrum Pin)/(Diameter of Fulcrum Pin*Length of Fulcrum Pin)
Diameter of Fulcrum Pin of Rocker Arm given Bearing Pressure
Go Diameter of Fulcrum Pin = Force at Fulcrum Pin/(Length of Fulcrum Pin*Bearing Pressure for Fulcrum Pin)
Length of Fulcrum Pin of Rocker Arm given Bearing Pressure
Go Length of Fulcrum Pin = Force at Fulcrum Pin/(Diameter of Fulcrum Pin*Bearing Pressure for Fulcrum Pin)
Reaction at Fulcrum Pin of Rocker Arm Considering bearing Pressure
Go Force at Fulcrum Pin = Diameter of Fulcrum Pin*Length of Fulcrum Pin*Bearing Pressure for Fulcrum Pin
Shear Stress in Fulcrum Pin of Rocker Arm given Reaction at Pin
Go Shear Stress in Fulcrum Pin = (2*Force at Fulcrum Pin)/(pi*Diameter of Fulcrum Pin^2)
Reaction at Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin
Go Force at Fulcrum Pin = (Shear Stress in Fulcrum Pin*pi*Diameter of Fulcrum Pin^2)/2
Outside Diameter of Boss of Rocker Arm at Fulcrum Pin
Go Outside Diameter of Boss of Rocker Arm = 2*Diameter of Fulcrum Pin
Length of Fulcrum Pin of Rocker Arm given Diameter of Fulcrum Pin
Go Length of Fulcrum Pin = Diameter of Fulcrum Pin*1.25
Diameter of Fulcrum Pin of Rocker Arm given Length of Fulcrum Pin
Go Diameter of Fulcrum Pin = Length of Fulcrum Pin/1.25

Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin Formula

Diameter of Fulcrum Pin = sqrt((2*sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Shear Stress in Fulcrum Pin))
d1 = sqrt((2*sqrt(Pe^2+Pc^2-2*Pc*Pe*cos(θ)))/(pi*τfulcrum))

Design of Rocker Arm

It is a two-arm lever with the fulcrum in the middle. One end of the rocker arm that is actuated by the cam is forked and carries a roller. The other arm of the rocker arm consists of a plain boss where a tappet is screwed. In order to reduce the weight and inertia force, the cross-section of the rocker arm is I-section. The arms of the rocker arm are made of uniform strength by tapering the width and depth dimensions. However, the thickness of the web and flanges is kept uniform. Rocker arms are made of grey cast iron, malleable cast iron, or cast steel.

How to Calculate Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin?

Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin calculator uses Diameter of Fulcrum Pin = sqrt((2*sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Shear Stress in Fulcrum Pin)) to calculate the Diameter of Fulcrum Pin, The Diameter of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin is the diameter of the fulcrum pin used at the fulcrum joint of the two rocker arms. Diameter of Fulcrum Pin is denoted by d1 symbol.

How to calculate Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin using this online calculator? To use this online calculator for Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin, enter Total Force on Rocker Arm of Exhaust Valve (Pe), Force on Roller Pin (Pc), Angle Between Rocker Arms (θ) & Shear Stress in Fulcrum Pin fulcrum) and hit the calculate button. Here is how the Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin calculation can be explained with given input values -> 24876.77 = sqrt((2*sqrt(1926^2+1925^2-2*1925*1926*cos(2.3561944901919)))/(pi*3660000)).

FAQ

What is Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin?
The Diameter of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin is the diameter of the fulcrum pin used at the fulcrum joint of the two rocker arms and is represented as d1 = sqrt((2*sqrt(Pe^2+Pc^2-2*Pc*Pe*cos(θ)))/(pi*τfulcrum)) or Diameter of Fulcrum Pin = sqrt((2*sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Shear Stress in Fulcrum Pin)). Total Force on Rocker Arm of Exhaust Valve is the total force acting onto the rocker arm of the exhaust valve, Force on Roller Pin is the force acting onto the roller pin ( the pivot about which a lever rolls freely) used as a joint, Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms & Shear Stress in Fulcrum Pin is the shear stress induced into the pin, the force per unit area tending to cause deformation of the pin by slippage along a plane parallel to the imposed stress.
How to calculate Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin?
The Diameter of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin is the diameter of the fulcrum pin used at the fulcrum joint of the two rocker arms is calculated using Diameter of Fulcrum Pin = sqrt((2*sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Shear Stress in Fulcrum Pin)). To calculate Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin, you need Total Force on Rocker Arm of Exhaust Valve (Pe), Force on Roller Pin (Pc), Angle Between Rocker Arms (θ) & Shear Stress in Fulcrum Pin fulcrum). With our tool, you need to enter the respective value for Total Force on Rocker Arm of Exhaust Valve, Force on Roller Pin, Angle Between Rocker Arms & Shear Stress in Fulcrum Pin and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Diameter of Fulcrum Pin?
In this formula, Diameter of Fulcrum Pin uses Total Force on Rocker Arm of Exhaust Valve, Force on Roller Pin, Angle Between Rocker Arms & Shear Stress in Fulcrum Pin. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Diameter of Fulcrum Pin = Force at Fulcrum Pin/(Length of Fulcrum Pin*Bearing Pressure for Fulcrum Pin)
  • Diameter of Fulcrum Pin = Length of Fulcrum Pin/1.25
  • Diameter of Fulcrum Pin = sqrt((2*Force at Fulcrum Pin)/(pi*Shear Stress in Fulcrum Pin))
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