Deflection of Center of Leaf Spring in Pickering Governor Calculator

✖Mass attached at the center of the leaf spring is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.ⓘ Mass Attached at the Center of the Leaf Spring [m]			+10% -10%
✖Angular speed of the governor spindle is the speed of the governor spindle in rotational motion.ⓘ Angular Speed of the Governor Spindle [ω_s]			+10% -10%
✖Distance from spindle axis to centre of gravity when governor is rotating is a numerical measurement of how far apart objects or points are.ⓘ Distance from Spindle Axis to Centre of Gravity [D_a+δ]			+10% -10%
✖Distance between fixed ends of spring is a numerical measurement of how far apart objects or points are.ⓘ Distance between Fixed Ends of Spring [l]			+10% -10%
✖Young’s modulus of the material of the spring is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression.ⓘ Young’s Modulus of the Material of the Spring [E]			+10% -10%
✖Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia [I]			+10% -10%

✖Deflection of center of leaf spring is a numerical measurement of how far apart objects or points are.ⓘ Deflection of Center of Leaf Spring in Pickering Governor [δ]

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Deflection of Center of Leaf Spring in Pickering Governor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection of Center of Leaf Spring = (Mass Attached at the Center of the Leaf Spring*Angular Speed of the Governor Spindle^2*Distance from Spindle Axis to Centre of Gravity*Distance between Fixed Ends of Spring^3)/(192*Young’s Modulus of the Material of the Spring*Moment of Inertia)
δ = (m*ω_s^2*D_a+δ*l^3)/(192*E*I)
This formula uses 7 Variables

Variables Used

Deflection of Center of Leaf Spring - (Measured in Meter) - Deflection of center of leaf spring is a numerical measurement of how far apart objects or points are.
Mass Attached at the Center of the Leaf Spring - (Measured in Kilogram) - Mass attached at the center of the leaf spring is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.
Angular Speed of the Governor Spindle - (Measured in Radian per Second) - Angular speed of the governor spindle is the speed of the governor spindle in rotational motion.
Distance from Spindle Axis to Centre of Gravity - (Measured in Meter) - Distance from spindle axis to centre of gravity when governor is rotating is a numerical measurement of how far apart objects or points are.
Distance between Fixed Ends of Spring - (Measured in Meter) - Distance between fixed ends of spring is a numerical measurement of how far apart objects or points are.
Young’s Modulus of the Material of the Spring - (Measured in Pascal) - Young’s modulus of the material of the spring is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.

STEP 1: Convert Input(s) to Base Unit

Mass Attached at the Center of the Leaf Spring: 8.5 Kilogram --> 8.5 Kilogram No Conversion Required
Angular Speed of the Governor Spindle: 8 Radian per Second --> 8 Radian per Second No Conversion Required
Distance from Spindle Axis to Centre of Gravity: 0.085 Meter --> 0.085 Meter No Conversion Required
Distance between Fixed Ends of Spring: 13 Meter --> 13 Meter No Conversion Required
Young’s Modulus of the Material of the Spring: 10 Newton per Square Meter --> 10 Pascal (Check conversion here)
Moment of Inertia: 2.66 Kilogram Square Meter --> 2.66 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = (m*ω_s^2*D_a+δ*l^3)/(192*E*I) --> (8.5*8^2*0.085*13^3)/(192*10*2.66)

Evaluating ... ...

δ = 19.8913847117794

STEP 3: Convert Result to Output's Unit

19.8913847117794 Meter --> No Conversion Required

FINAL ANSWER

19.8913847117794 ≈ 19.89138 Meter <-- Deflection of Center of Leaf Spring

(Calculation completed in 00.004 seconds)

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< Pickering Governor Calculators

Deflection of Center of Leaf Spring in Pickering Governor

LaTeX Go Deflection of Center of Leaf Spring = (Mass Attached at the Center of the Leaf Spring*Angular Speed of the Governor Spindle^2*Distance from Spindle Axis to Centre of Gravity*Distance between Fixed Ends of Spring^3)/(192*Young’s Modulus of the Material of the Spring*Moment of Inertia)

Deflection of Center of Leaf Spring in Pickering Governor given Value of Load

LaTeX Go Deflection of Center of Leaf Spring = (Load*Distance between Fixed Ends of Spring^3)/(192*Young’s Modulus of the Material of the Spring*Moment of Inertia)

Moment of Inertia of Pickering Governor Cross-Section about Neutral Axis

LaTeX Go Moment of Inertia = (Width of Spring*Thickness of Spring^3)/12

Deflection of Center of Leaf Spring in Pickering Governor Formula

LaTeX Go

What is Pickering governor?

Pickering governor is a governor in which the revolving balls act against curved flat springs. The Pickering governor consists of three straight leaf springs each placed at an equal angular interval around the spindle.

How to Calculate Deflection of Center of Leaf Spring in Pickering Governor?

Deflection of Center of Leaf Spring in Pickering Governor calculator uses Deflection of Center of Leaf Spring = (Mass Attached at the Center of the Leaf Spring*Angular Speed of the Governor Spindle^2*Distance from Spindle Axis to Centre of Gravity*Distance between Fixed Ends of Spring^3)/(192*Young’s Modulus of the Material of the Spring*Moment of Inertia) to calculate the Deflection of Center of Leaf Spring, The Deflection of center of leaf spring in Pickering governor happens when the speed of the spindle increases the weight on the leaf spring tends to move outside. Deflection of Center of Leaf Spring is denoted by δ symbol.

How to calculate Deflection of Center of Leaf Spring in Pickering Governor using this online calculator? To use this online calculator for Deflection of Center of Leaf Spring in Pickering Governor, enter Mass Attached at the Center of the Leaf Spring (m), Angular Speed of the Governor Spindle (ω_s), Distance from Spindle Axis to Centre of Gravity (D_a+δ), Distance between Fixed Ends of Spring (l), Young’s Modulus of the Material of the Spring (E) & Moment of Inertia (I) and hit the calculate button. Here is how the Deflection of Center of Leaf Spring in Pickering Governor calculation can be explained with given input values -> 14.04098 = (8.5*8^2*0.085*13^3)/(192*10*2.66).

FAQ

What is Deflection of Center of Leaf Spring in Pickering Governor?

The Deflection of center of leaf spring in Pickering governor happens when the speed of the spindle increases the weight on the leaf spring tends to move outside and is represented as δ = (m*ω_s^2*D_a+δ*l^3)/(192*E*I) or Deflection of Center of Leaf Spring = (Mass Attached at the Center of the Leaf Spring*Angular Speed of the Governor Spindle^2*Distance from Spindle Axis to Centre of Gravity*Distance between Fixed Ends of Spring^3)/(192*Young’s Modulus of the Material of the Spring*Moment of Inertia). Mass attached at the center of the leaf spring is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied, Angular speed of the governor spindle is the speed of the governor spindle in rotational motion, Distance from spindle axis to centre of gravity when governor is rotating is a numerical measurement of how far apart objects or points are, Distance between fixed ends of spring is a numerical measurement of how far apart objects or points are, Young’s modulus of the material of the spring is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression & Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.

How to calculate Deflection of Center of Leaf Spring in Pickering Governor?

The Deflection of center of leaf spring in Pickering governor happens when the speed of the spindle increases the weight on the leaf spring tends to move outside is calculated using Deflection of Center of Leaf Spring = (Mass Attached at the Center of the Leaf Spring*Angular Speed of the Governor Spindle^2*Distance from Spindle Axis to Centre of Gravity*Distance between Fixed Ends of Spring^3)/(192*Young’s Modulus of the Material of the Spring*Moment of Inertia). To calculate Deflection of Center of Leaf Spring in Pickering Governor, you need Mass Attached at the Center of the Leaf Spring (m), Angular Speed of the Governor Spindle (ω_s), Distance from Spindle Axis to Centre of Gravity (D_a+δ), Distance between Fixed Ends of Spring (l), Young’s Modulus of the Material of the Spring (E) & Moment of Inertia (I). With our tool, you need to enter the respective value for Mass Attached at the Center of the Leaf Spring, Angular Speed of the Governor Spindle, Distance from Spindle Axis to Centre of Gravity, Distance between Fixed Ends of Spring, Young’s Modulus of the Material of the Spring & Moment of Inertia 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 Deflection of Center of Leaf Spring?

In this formula, Deflection of Center of Leaf Spring uses Mass Attached at the Center of the Leaf Spring, Angular Speed of the Governor Spindle, Distance from Spindle Axis to Centre of Gravity, Distance between Fixed Ends of Spring, Young’s Modulus of the Material of the Spring & Moment of Inertia. We can use 1 other way(s) to calculate the same, which is/are as follows -

Deflection of Center of Leaf Spring = (Load*Distance between Fixed Ends of Spring^3)/(192*Young’s Modulus of the Material of the Spring*Moment of Inertia)

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