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

GoDiameter of Fulcrum Pin of Rocker Arm given Bearing Pressure Formula

GoDiameter of Fulcrum Pin of Rocker Arm given Length of Fulcrum Pin Formula

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Diameter of Fulcrum Pin is the diameter of the pin used at the fulcrum joint. Check FAQs

d 1 = \sqrt{\frac{2 \cdot \sqrt{{P e}^{2} + {P c}^{2} - 2 \cdot P c \cdot P e \cdot \cos (θ)}}{π \cdot τ f}}

d₁ - Diameter of Fulcrum Pin?P_e - Total Force on Rocker Arm of Exhaust Valve?P_c - Force on Roller Pin?θ - Angle Between Rocker Arms?τ_f - Shear Stress in Fulcrum Pin?π - Archimedes' constant?

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

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Here is how the Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin equation looks like with Values.

Here is how the Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin equation looks like with Units.

Here is how the Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin equation looks like.

24.8768 = \sqrt{\frac{2 \cdot \sqrt{1926^{2} + 1925^{2} - 2 \cdot 1925 \cdot 1926 \cdot \cos (135)}}{3.1416 \cdot 3.66}}

24.8768mm = \sqrt{\frac{2 \cdot \sqrt{{1926N}^{2} + {1925N}^{2} - 2 \cdot 1925N \cdot 1926N \cdot \cos (135°)}}{3.1416 \cdot 3.66N/mm²}}

24.8768 = \sqrt{\frac{2 \cdot \sqrt{1926^{2} + 1925^{2} - 2 \cdot 1925 \cdot 1926 \cdot \cos (135)}}{3.1416 \cdot 3.66}}

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

Follow our step by step solution on how to calculate Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin?

FIRST Step Consider the formula

d 1 = \sqrt{\frac{2 \cdot \sqrt{{P e}^{2} + {P c}^{2} - 2 \cdot P c \cdot P e \cdot \cos (θ)}}{π \cdot τ f}}

Next Step Substitute values of Variables

∴

d 1 = \sqrt{\frac{2 \cdot \sqrt{{1926N}^{2} + {1925N}^{2} - 2 \cdot 1925N \cdot 1926N \cdot \cos (135°)}}{π \cdot 3.66N/mm²}}

Next Step Substitute values of Constants

∴

d 1 = \sqrt{\frac{2 \cdot \sqrt{{1926N}^{2} + {1925N}^{2} - 2 \cdot 1925N \cdot 1926N \cdot \cos (135°)}}{3.1416 \cdot 3.66N/mm²}}

Next Step Convert Units

∴

d 1 = \sqrt{\frac{2 \cdot \sqrt{{1926N}^{2} + {1925N}^{2} - 2 \cdot 1925N \cdot 1926N \cdot \cos (2.3562rad)}}{3.1416 \cdot 3.7E+6Pa}}

Next Step Prepare to Evaluate

∴

d 1 = \sqrt{\frac{2 \cdot \sqrt{1926^{2} + 1925^{2} - 2 \cdot 1925 \cdot 1926 \cdot \cos (2.3562)}}{3.1416 \cdot 3.7E+6}}

Next Step Evaluate

∴

d 1 = 0.0248767677909713m

Next Step Convert to Output's Unit

∴

d 1 = 24.8767677909713mm

LAST Step Rounding Answer

∴

d 1 = 24.8768mm

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

Variables

Constants

Functions

Diameter of Fulcrum Pin

Diameter of Fulcrum Pin is the diameter of the pin used at the fulcrum joint.

Symbol: d₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Fulcrum Pin

Total Force on Rocker Arm of Exhaust Valve

Total Force on Rocker Arm of Exhaust Valve is the total force acting onto the rocker arm of the exhaust valve.

Symbol: P_e

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Total Force on Rocker Arm of Exhaust Valve

Force on Roller Pin

Force on Roller Pin is the force acting onto the roller pin ( the pivot about which a lever rolls freely) used as a joint.

Symbol: P_c

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Force on Roller Pin

Angle Between Rocker Arms

Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle Between Rocker Arms

Shear Stress in Fulcrum Pin

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.

Symbol: τ_f

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Shear Stress in Fulcrum Pin

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Diameter of Fulcrum Pin

Go Diameter of Fulcrum Pin of Rocker Arm given Bearing Pressure

d 1 = \frac{R f}{l 1 \cdot P bf}

Go Diameter of Fulcrum Pin of Rocker Arm given Length of Fulcrum Pin

d 1 = \frac{l 1}{1.25}

Go Diameter of Fulcrum Pin of Rocker Arm given Reaction at Pin

d 1 = \sqrt{\frac{2 \cdot R f}{π \cdot τ f}}

Other formulas in Design of Fulcrum Pin category

Go Reaction at Fulcrum Pin of Rocker Arm

R f = \sqrt{{P e}^{2} + {P c}^{2} - 2 \cdot P c \cdot P e \cdot \cos (θ)}

Go Reaction at Fulcrum Pin of Rocker Arm for Equal Arm Lengths

R f = P e \cdot \sqrt{2 \cdot (1 - \cos (θ))}

Go Angle between Two Arms of Rocker Arm

θ = π - \arccos (- \frac{{P e}^{2} + {P c}^{2} - {R f}^{2}}{2 \cdot P e \cdot P c})

Go Bearing Pressure at Fulcrum Pin of Rocker Arm

P bf = \frac{R f}{d 1 \cdot l 1}

How to Evaluate 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 evaluator 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 evaluate 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 evaluate Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin using this online evaluator? To use this online evaluator for Diameter 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.

FAQs on Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin

What is the formula to find Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin?

The formula of Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin is expressed as 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)). Here is an example- 24876.77 = sqrt((2*sqrt(1926^2+1925^2-2*1925*1926*cos(2.3561944901919)))/(pi*3660000)).

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

With 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) we can find Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin using the 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)). This formula also uses Archimedes' constant and , Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Diameter of Fulcrum Pin?

Here are the different ways to Calculate Diameter of Fulcrum Pin-

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))

Can the Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin be negative?

No, the Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin, measured in Length cannot be negative.

Which unit is used to measure 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 is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin can be measured.

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

​GoDiameter of Fulcrum Pin of Rocker Arm given Bearing Pressure Formula

​GoDiameter of Fulcrum Pin of Rocker Arm given Length of Fulcrum Pin Formula

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

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

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

Other Formulas to find Diameter of Fulcrum Pin

Other formulas in Design of Fulcrum Pin category

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

FAQs on Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin

Variable Name

GoDiameter of Fulcrum Pin of Rocker Arm given Bearing Pressure Formula

GoDiameter of Fulcrum Pin of Rocker Arm given Length of Fulcrum Pin Formula