Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin Calculator

✖Total Force on Rocker Arm of Exhaust Valve is the total force acting onto the rocker arm of the exhaust valve.ⓘ Total Force on Rocker Arm of Exhaust Valve [P_e]			+10% -10%
✖Force on Roller Pin is the force acting onto the roller pin ( the pivot about which a lever rolls freely) used as a joint.ⓘ Force on Roller Pin [P_c]			+10% -10%
✖Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms.ⓘ Angle Between Rocker Arms [θ]			+10% -10%
✖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.ⓘ Shear Stress in Fulcrum Pin [τ_f]			+10% -10%

✖Length of Fulcrum Pin is the total length of the pin used at the fulcrum joint.ⓘ Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin [l₁]

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Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
l₁ = 1.25*sqrt((2*sqrt(P_e^2+P_c^2-2*P_c*P_e*cos(θ)))/(pi*τ_f))
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

Length of Fulcrum Pin - (Measured in Meter) - Length of Fulcrum Pin is the total length 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

l₁ = 1.25*sqrt((2*sqrt(P_e^2+P_c^2-2*P_c*P_e*cos(θ)))/(pi*τ_f)) --> 1.25*sqrt((2*sqrt(1926^2+1925^2-2*1925*1926*cos(2.3561944901919)))/(pi*3660000))

Evaluating ... ...

l₁ = 0.0310959597387141

STEP 3: Convert Result to Output's Unit

0.0310959597387141 Meter -->31.0959597387141 Millimeter (Check conversion here)

FINAL ANSWER

31.0959597387141 ≈ 31.09596 Millimeter <-- Length of Fulcrum Pin

(Calculation completed in 00.008 seconds)

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Home » Physics » IC Engine » Design of IC Engine Components » Rocker Arm » Mechanical » Design of Fulcrum Pin » Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin

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Created by Saurabh Patil

Shri Govindram Seksaria Institute of Technology and Science (SGSITS ), Indore

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< Design of Fulcrum Pin Calculators

Angle between Two Arms of Rocker Arm

LaTeX 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

LaTeX 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

LaTeX Go Force at Fulcrum Pin = Total Force on Rocker Arm of Exhaust Valve*sqrt(2*(1-cos(Angle Between Rocker Arms)))

Bearing Pressure at Fulcrum Pin of Rocker Arm

LaTeX Go Bearing Pressure for Fulcrum Pin = (Force at Fulcrum Pin)/(Diameter of Fulcrum Pin*Length of Fulcrum Pin)

Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin Formula

LaTeX Go

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 Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin?

Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin calculator uses 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)) to calculate the Length of Fulcrum Pin, The Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin is the total length of the fulcrum pin used at the fulcrum joint of the two rocker arms. Length of Fulcrum Pin is denoted by l₁ symbol.

How to calculate Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin using this online calculator? To use this online calculator for Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin, enter Total Force on Rocker Arm of Exhaust Valve (P_e), Force on Roller Pin (P_c), Angle Between Rocker Arms (θ) & Shear Stress in Fulcrum Pin (τ_f) and hit the calculate button. Here is how the Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin calculation can be explained with given input values -> 31095.96 = 1.25*sqrt((2*sqrt(1926^2+1925^2-2*1925*1926*cos(2.3561944901919)))/(pi*3660000)).

FAQ

What is Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin?

The Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin is the total length of the fulcrum pin used at the fulcrum joint of the two rocker arms and is represented as l₁ = 1.25*sqrt((2*sqrt(P_e^2+P_c^2-2*P_c*P_e*cos(θ)))/(pi*τ_f)) or 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)). 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 Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin?

The Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin is the total length of the fulcrum pin used at the fulcrum joint of the two rocker arms is calculated using 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)). To calculate Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin, you need Total Force on Rocker Arm of Exhaust Valve (P_e), Force on Roller Pin (P_c), Angle Between Rocker Arms (θ) & Shear Stress in Fulcrum Pin (τ_f). 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 Length of Fulcrum Pin?

In this formula, Length 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 -

Length of Fulcrum Pin = Force at Fulcrum Pin/(Diameter of Fulcrum Pin*Bearing Pressure for Fulcrum Pin)
Length of Fulcrum Pin = Diameter of Fulcrum Pin*1.25
Length of Fulcrum Pin = 1.25*sqrt((2*Force at Fulcrum Pin)/(pi*Shear Stress in Fulcrum Pin))

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