Angle of Rotation of Arbor with Respect to Drum Calculator

✖Bending moment in spiral spring is the reaction induced in a spiral spring when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending moment in spiral spring [M]			+10% -10%
✖The Length of Spiral Spring Strip is defined as the length of the thin strip of which spiral spring coils are manufactured.ⓘ Length of Spiral Spring Strip [l]			+10% -10%
✖Modulus of elasticity of spiral spring is a quantity that measures the spring's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of elasticity of spiral spring [E]			+10% -10%
✖The Width of Strip of Spiral Spring is defined as the thickness of the wired strip measured in the lateral direction and by which the spiral spring is manufactured.ⓘ Width of Strip of Spiral Spring [b]			+10% -10%
✖The Thickness of Strip of Spring is defined as the thickness of the wired strip by which the spiral spring is manufactured.ⓘ Thickness of Strip of Spring [t]			+10% -10%

✖Angle of rotation of arbor is defined as how many degrees the arbor is rotated with respect to the drum line.ⓘ Angle of Rotation of Arbor with Respect to Drum [θ]

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Formula

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Angle of Rotation of Arbor with Respect to Drum

Formula

`"θ" = 12*"M"*"l"/("E"*"b"*("t"^3))`

Example

`"18.48889rad"=12*"1200N*mm"*"5980mm"/("207000N/mm²"*"11.52mm"*(("1.25mm")^3))`

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Angle of Rotation of Arbor with Respect to Drum Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of rotation of arbor = 12*Bending moment in spiral spring*Length of Spiral Spring Strip/(Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*(Thickness of Strip of Spring^3))
θ = 12*M*l/(E*b*(t^3))
This formula uses 6 Variables

Variables Used

Angle of rotation of arbor - (Measured in Radian) - Angle of rotation of arbor is defined as how many degrees the arbor is rotated with respect to the drum line.
Bending moment in spiral spring - (Measured in Newton Meter) - Bending moment in spiral spring is the reaction induced in a spiral spring when an external force or moment is applied to the element, causing the element to bend.
Length of Spiral Spring Strip - (Measured in Meter) - The Length of Spiral Spring Strip is defined as the length of the thin strip of which spiral spring coils are manufactured.
Modulus of elasticity of spiral spring - (Measured in Pascal) - Modulus of elasticity of spiral spring is a quantity that measures the spring's resistance to being deformed elastically when stress is applied to it.
Width of Strip of Spiral Spring - (Measured in Meter) - The Width of Strip of Spiral Spring is defined as the thickness of the wired strip measured in the lateral direction and by which the spiral spring is manufactured.
Thickness of Strip of Spring - (Measured in Meter) - The Thickness of Strip of Spring is defined as the thickness of the wired strip by which the spiral spring is manufactured.

STEP 1: Convert Input(s) to Base Unit

Bending moment in spiral spring: 1200 Newton Millimeter --> 1.2 Newton Meter (Check conversion here)
Length of Spiral Spring Strip: 5980 Millimeter --> 5.98 Meter (Check conversion here)
Modulus of elasticity of spiral spring: 207000 Newton per Square Millimeter --> 207000000000 Pascal (Check conversion here)
Width of Strip of Spiral Spring: 11.52 Millimeter --> 0.01152 Meter (Check conversion here)
Thickness of Strip of Spring: 1.25 Millimeter --> 0.00125 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = 12*M*l/(E*b*(t^3)) --> 12*1.2*5.98/(207000000000*0.01152*(0.00125^3))

Evaluating ... ...

θ = 18.4888888888889

STEP 3: Convert Result to Output's Unit

18.4888888888889 Radian --> No Conversion Required

FINAL ANSWER

18.4888888888889 ≈ 18.48889 Radian <-- Angle of rotation of arbor

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 10+ Spring Material Mechanics Calculators

Modulus of Elasticity given Deflection of one End of Spring with Respect to Other End

Go Modulus of elasticity of spiral spring = 12*Bending moment in spiral spring*Length of Spiral Spring Strip*Distance of CG of Spiral Spring/(Deflection of Spiral Spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3)

Length of Strip from Outer end to inner End given Deflection of one End of Spring

Go Length of Spiral Spring Strip = Deflection of Spiral Spring*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3/(12*Bending moment in spiral spring*Distance of CG of Spiral Spring)

Modulus of Elasticity of Spring Wire given Strain Energy Stored in Spring

Go Modulus of elasticity of spiral spring = (6*(Bending moment in spiral spring^2)*Length of Spiral Spring Strip)/(Strain energy in spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3)

Strain Energy Stored in Spiral Spring

Go Strain energy in spiral spring = 6*(Bending moment in spiral spring^2)*Length of Spiral Spring Strip/(Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3)

Length of Strip from Outer end to Inner End given Strain Energy Stored in Spring

Go Length of Spiral Spring Strip = Strain energy in spiral spring*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*Thickness of Strip of Spring^3/(6*Bending moment in spiral spring^2)

Length of Strip from Outer end to inner End given Angle of Rotation of Arbor

Go Length of Spiral Spring Strip = Angle of rotation of arbor*Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*(Thickness of Strip of Spring^3)/(12*Bending moment in spiral spring)

Modulus of Elasticity given Angle of Rotation of Arbor

Go Modulus of elasticity of spiral spring = 12*Bending moment in spiral spring*Length of Spiral Spring Strip/(Angle of rotation of arbor*Width of Strip of Spiral Spring*(Thickness of Strip of Spring^3))

Angle of Rotation of Arbor with Respect to Drum

Go Angle of rotation of arbor = 12*Bending moment in spiral spring*Length of Spiral Spring Strip/(Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*(Thickness of Strip of Spring^3))

Maximum Bending Stress induced at outer end of Spring

Go Bending Stress in Spiral Spring = 12*Bending moment in spiral spring/(Width of Strip of Spiral Spring*Thickness of Strip of Spring^2)

Force given Bending Moment Due to that Force

Go Force on spiral spring = Bending moment in spiral spring/Distance of CG of Spiral Spring

Angle of Rotation of Arbor with Respect to Drum Formula

Define Angle of Rotation?

The angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle. A clockwise rotation is considered a negative rotation,

How to Calculate Angle of Rotation of Arbor with Respect to Drum?

Angle of Rotation of Arbor with Respect to Drum calculator uses Angle of rotation of arbor = 12*Bending moment in spiral spring*Length of Spiral Spring Strip/(Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*(Thickness of Strip of Spring^3)) to calculate the Angle of rotation of arbor, The Angle of Rotation of Arbor with Respect to Drum formula is defined as a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle. Angle of rotation of arbor is denoted by θ symbol.

How to calculate Angle of Rotation of Arbor with Respect to Drum using this online calculator? To use this online calculator for Angle of Rotation of Arbor with Respect to Drum, enter Bending moment in spiral spring (M), Length of Spiral Spring Strip (l), Modulus of elasticity of spiral spring (E), Width of Strip of Spiral Spring (b) & Thickness of Strip of Spring (t) and hit the calculate button. Here is how the Angle of Rotation of Arbor with Respect to Drum calculation can be explained with given input values -> 18.48889 = 12*1.2*5.98/(207000000000*0.01152*(0.00125^3)).

FAQ

What is Angle of Rotation of Arbor with Respect to Drum?

The Angle of Rotation of Arbor with Respect to Drum formula is defined as a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle and is represented as θ = 12*M*l/(E*b*(t^3)) or Angle of rotation of arbor = 12*Bending moment in spiral spring*Length of Spiral Spring Strip/(Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*(Thickness of Strip of Spring^3)). Bending moment in spiral spring is the reaction induced in a spiral spring when an external force or moment is applied to the element, causing the element to bend, The Length of Spiral Spring Strip is defined as the length of the thin strip of which spiral spring coils are manufactured, Modulus of elasticity of spiral spring is a quantity that measures the spring's resistance to being deformed elastically when stress is applied to it, The Width of Strip of Spiral Spring is defined as the thickness of the wired strip measured in the lateral direction and by which the spiral spring is manufactured & The Thickness of Strip of Spring is defined as the thickness of the wired strip by which the spiral spring is manufactured.

How to calculate Angle of Rotation of Arbor with Respect to Drum?

The Angle of Rotation of Arbor with Respect to Drum formula is defined as a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle is calculated using Angle of rotation of arbor = 12*Bending moment in spiral spring*Length of Spiral Spring Strip/(Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*(Thickness of Strip of Spring^3)). To calculate Angle of Rotation of Arbor with Respect to Drum, you need Bending moment in spiral spring (M), Length of Spiral Spring Strip (l), Modulus of elasticity of spiral spring (E), Width of Strip of Spiral Spring (b) & Thickness of Strip of Spring (t). With our tool, you need to enter the respective value for Bending moment in spiral spring, Length of Spiral Spring Strip, Modulus of elasticity of spiral spring, Width of Strip of Spiral Spring & Thickness of Strip of Spring and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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