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Diameter of Wire of Engine Valve Spring Formula

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GoDiameter of Wire of Engine Valve Spring given Mean Coil Diameter Formula

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GoDiameter of Wire of Engine Valve Spring given Torsional Shear Stress in Wire Formula

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Wire Diameter of Valve Spring is the diameter of the wire of a valve spring, which constitutes the coils of the spring. Check FAQs

d w = \sqrt{\frac{8 \cdot K \cdot ((P i + k \cdot h max) \cdot C)}{π \cdot f s}}

d_w - Wire Diameter of Valve Spring?K - Wahl Factor of Valve Spring?P_i - Initial Spring Force on Valve?k - Stiffness of Valve Spring?h_max - Lift of Valve?C - Spring Index for Valve Spring?f_s - Shear Stress in Valve Spring?π - Archimedes' constant?

Diameter of Wire of Engine Valve Spring Example

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With units

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Here is how the Diameter of Wire of Engine Valve Spring equation looks like with Values.

Here is how the Diameter of Wire of Engine Valve Spring equation looks like with Units.

Here is how the Diameter of Wire of Engine Valve Spring equation looks like.

4.2244 = \sqrt{\frac{8 \cdot 1.2 \cdot ((120 + 9 \cdot 11) \cdot 8)}{3.1416 \cdot 300}}

4.2244mm = \sqrt{\frac{8 \cdot 1.2 \cdot ((120N + 9N/mm \cdot 11mm) \cdot 8)}{3.1416 \cdot 300N/mm²}}

4.2244 = \sqrt{\frac{8 \cdot 1.2 \cdot ((120 + 9 \cdot 11) \cdot 8)}{3.1416 \cdot 300}}

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Diameter of Wire of Engine Valve Spring Solution

Follow our step by step solution on how to calculate Diameter of Wire of Engine Valve Spring?

FIRST Step Consider the formula

d w = \sqrt{\frac{8 \cdot K \cdot ((P i + k \cdot h max) \cdot C)}{π \cdot f s}}

Next Step Substitute values of Variables

∴

d w = \sqrt{\frac{8 \cdot 1.2 \cdot ((120N + 9N/mm \cdot 11mm) \cdot 8)}{π \cdot 300N/mm²}}

Next Step Substitute values of Constants

∴

d w = \sqrt{\frac{8 \cdot 1.2 \cdot ((120N + 9N/mm \cdot 11mm) \cdot 8)}{3.1416 \cdot 300N/mm²}}

Next Step Convert Units

∴

d w = \sqrt{\frac{8 \cdot 1.2 \cdot ((120N + 9000N/m \cdot 0.011m) \cdot 8)}{3.1416 \cdot 3E+8Pa}}

Next Step Prepare to Evaluate

∴

d w = \sqrt{\frac{8 \cdot 1.2 \cdot ((120 + 9000 \cdot 0.011) \cdot 8)}{3.1416 \cdot 3E+8}}

Next Step Evaluate

∴

d w = 0.00422442013287126m

Next Step Convert to Output's Unit

∴

d w = 4.22442013287126mm

LAST Step Rounding Answer

∴

d w = 4.2244mm

Diameter of Wire of Engine Valve Spring Formula Elements

Variables

Constants

Functions

Wire Diameter of Valve Spring

Wire Diameter of Valve Spring is the diameter of the wire of a valve spring, which constitutes the coils of the spring.

Symbol: d_w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Wahl Factor of Valve Spring

Wahl Factor of Valve Spring is a stress factor used in order to take into account the effect of direct shear and change in coil curvature.

Symbol: K

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Initial Spring Force on Valve

Initial Spring Force on Valve is the preset amount of force exerted by the spring onto the body and contributed to the total force exerted by the spring.

Symbol: P_i

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Stiffness of Valve Spring

Stiffness of Valve Spring is a measure of the resistance offered by an elastic spring to deformation, every object in this universe has some stiffness.

Symbol: k

Measurement: Stiffness ConstantUnit: N/mm

Note: Value should be greater than 0.

Lift of Valve

Lift of Valve is the height to which the valve is lifted during operation for the flow of gases.

Symbol: h_max

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Spring Index for Valve Spring

Spring Index for Valve Spring is the ratio of the mean coil diameter of the spring to the diameter of the spring Wire.

Symbol: C

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Shear Stress in Valve Spring

Shear Stress in Valve Spring is the stress induced into the spring due to its compression and expansion.

Symbol: f_s

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

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

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)

Credits

Creator Image

Created by Saurabh Patil

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

Saurabh Patil has created this Formula and 700+ more formulas!

Verifier Image

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Formula and 2500+ more formulas!

Other Formulas to find Wire Diameter of Valve Spring

Go Diameter of Wire of Engine Valve Spring given Mean Coil Diameter

d w = \frac{D}{8}

Go Diameter of Wire of Engine Valve Spring given Torsional Shear Stress in Wire

d w = \sqrt{\frac{8 \cdot K \cdot P \cdot C}{π \cdot f s}}

See More

Other formulas in Valve Spring category

Go Spring Index of Engine Valve Spring given Shear Stress, Maximum Force and Wire Diameter

C = \frac{π \cdot f s \cdot {d w}^{2}}{8 \cdot K \cdot P}

Go Wahl Factor for Engine Valve Spring given Spring Index

K = \frac{π \cdot f s \cdot {d w}^{2}}{8 \cdot C \cdot (P i + k \cdot h max)}

See More

How to Evaluate Diameter of Wire of Engine Valve Spring?

Diameter of Wire of Engine Valve Spring evaluator uses Wire Diameter of Valve Spring = sqrt((8*Wahl Factor of Valve Spring*((Initial Spring Force on Valve+Stiffness of Valve Spring*Lift of Valve)*Spring Index for Valve Spring))/(pi*Shear Stress in Valve Spring)) to evaluate the Wire Diameter of Valve Spring, The Diameter of wire of engine valve spring is the diameter of the wire of the helical spring used in engine valve actuation. Wire Diameter of Valve Spring is denoted by d_w symbol.

How to evaluate Diameter of Wire of Engine Valve Spring using this online evaluator? To use this online evaluator for Diameter of Wire of Engine Valve Spring, enter Wahl Factor of Valve Spring (K), Initial Spring Force on Valve (P_i), Stiffness of Valve Spring (k), Lift of Valve (h_max), Spring Index for Valve Spring (C) & Shear Stress in Valve Spring (f_s) and hit the calculate button.

FAQs on Diameter of Wire of Engine Valve Spring

What is the formula to find Diameter of Wire of Engine Valve Spring?

The formula of Diameter of Wire of Engine Valve Spring is expressed as Wire Diameter of Valve Spring = sqrt((8*Wahl Factor of Valve Spring*((Initial Spring Force on Valve+Stiffness of Valve Spring*Lift of Valve)*Spring Index for Valve Spring))/(pi*Shear Stress in Valve Spring)). Here is an example- 4224.42 = sqrt((8*1.2*((120+9000*0.011)*8))/(pi*300000000)).

How to calculate Diameter of Wire of Engine Valve Spring?

With Wahl Factor of Valve Spring (K), Initial Spring Force on Valve (P_i), Stiffness of Valve Spring (k), Lift of Valve (h_max), Spring Index for Valve Spring (C) & Shear Stress in Valve Spring (f_s) we can find Diameter of Wire of Engine Valve Spring using the formula - Wire Diameter of Valve Spring = sqrt((8*Wahl Factor of Valve Spring*((Initial Spring Force on Valve+Stiffness of Valve Spring*Lift of Valve)*Spring Index for Valve Spring))/(pi*Shear Stress in Valve Spring)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Wire Diameter of Valve Spring?

Here are the different ways to Calculate Wire Diameter of Valve Spring-

Wire Diameter of Valve Spring=Mean Coil Diameter of Valve Spring/8
Wire Diameter of Valve Spring=sqrt((8*Wahl Factor of Valve Spring*Axial Force on Valve Spring*Spring Index for Valve Spring)/(pi*Shear Stress in Valve Spring))
Wire Diameter of Valve Spring=((8*Mean Coil Diameter of Valve Spring^3*Stiffness of Valve Spring*Active Coils in Valve Spring)/(Modulus of Rigidity of Valve Spring))^(0.25)

Can the Diameter of Wire of Engine Valve Spring be negative?

No, the Diameter of Wire of Engine Valve Spring, measured in Length cannot be negative.

Which unit is used to measure Diameter of Wire of Engine Valve Spring?

Diameter of Wire of Engine Valve Spring is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Diameter of Wire of Engine Valve Spring can be measured.

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