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Maximum Acceleration of Follower for Tangent Cam with Roller Follower Formula

GoMaximum Acceleration of Follower on Outstroke when Follower Moves with SHM Formula

GoMaximum Acceleration of Follower on Return Stroke when Follower Moves with SHM Formula

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Maximum Acceleration is the rate of change of the velocity of an object with respect to time. Check FAQs

a max = ω^{2} \cdot (r 1 + r rol) \cdot (\frac{2 - {(\cos (φ))}^{2}}{{(\cos (φ))}^{3}})

a_max - Maximum Acceleration?ω - Angular Velocity of Cam?r₁ - Radius of the Base Circle?r_rol - Radius of Roller?φ - Angle Turned by the Cam for Contact of Roller?

Maximum Acceleration of Follower for Tangent Cam with Roller Follower Example

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Here is how the Maximum Acceleration of Follower for Tangent Cam with Roller Follower equation looks like with Units.

Here is how the Maximum Acceleration of Follower for Tangent Cam with Roller Follower equation looks like.

47728.3555 = 27^{2} \cdot (4.98 + 31) \cdot (\frac{2 - {(\cos (0.5))}^{2}}{{(\cos (0.5))}^{3}})

47728.3555m/s² = {27rad/s}^{2} \cdot (4.98m + 31m) \cdot (\frac{2 - {(\cos (0.5rad))}^{2}}{{(\cos (0.5rad))}^{3}})

47728.3555 = 27^{2} \cdot (4.98 + 31) \cdot (\frac{2 - {(\cos (0.5))}^{2}}{{(\cos (0.5))}^{3}})

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Theory of Machine » fx Maximum Acceleration of Follower for Tangent Cam with Roller Follower

Maximum Acceleration of Follower for Tangent Cam with Roller Follower Solution

Follow our step by step solution on how to calculate Maximum Acceleration of Follower for Tangent Cam with Roller Follower?

FIRST Step Consider the formula

a max = ω^{2} \cdot (r 1 + r rol) \cdot (\frac{2 - {(\cos (φ))}^{2}}{{(\cos (φ))}^{3}})

Next Step Substitute values of Variables

∴

a max = {27rad/s}^{2} \cdot (4.98m + 31m) \cdot (\frac{2 - {(\cos (0.5rad))}^{2}}{{(\cos (0.5rad))}^{3}})

Next Step Prepare to Evaluate

∴

a max = 27^{2} \cdot (4.98 + 31) \cdot (\frac{2 - {(\cos (0.5))}^{2}}{{(\cos (0.5))}^{3}})

Next Step Evaluate

∴

a max = 47728.3554974283m/s²

LAST Step Rounding Answer

∴

a max = 47728.3555m/s²

Maximum Acceleration of Follower for Tangent Cam with Roller Follower Formula Elements

Variables

Functions

Maximum Acceleration

Maximum Acceleration is the rate of change of the velocity of an object with respect to time.

Symbol: a_max

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Maximum Acceleration

Angular Velocity of Cam

Angular velocity of cam refers to how fast an object rotates or revolves relative to another point.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity of Cam

Radius of the Base Circle

Radius of the base circle is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

Symbol: r₁

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of the Base Circle

Radius of Roller

Radius of Roller is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

Symbol: r_rol

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Roller

Angle Turned by the Cam for Contact of Roller

Angle turned by the cam for contact of roller is the angle through which the cam turns while the follower remains stationary at the highest or the lowest position.

Symbol: φ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle Turned by the Cam for Contact of Roller

cos

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

Syntax: cos(Angle)

Other Formulas to find Maximum Acceleration

Go Maximum Acceleration of Follower on Outstroke when Follower Moves with SHM

a max = \frac{π^{2} \cdot ω^{2} \cdot S}{2 \cdot {θ o}^{2}}

Go Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM

a max = \frac{π^{2} \cdot ω^{2} \cdot S}{2 \cdot {θ R}^{2}}

Go Maximum Uniform Acceleration of Follower during Return Stroke

a max = \frac{4 \cdot ω^{2} \cdot S}{{θ R}^{2}}

Go Max Acceleration of Follower during Outstroke if Stroke of Follower is known Uniform Acceleration

a max = \frac{4 \cdot ω \cdot S}{θ o \cdot t o}

Other formulas in Acceleration of the Follower category

Go Acceleration of Follower after Time t for Cycloidal Motion

a = \frac{2 \cdot π \cdot ω^{2} \cdot S}{{θ o}^{2}} \cdot \sin (\frac{2 \cdot π \cdot θ r}{θ o})

Go Acceleration of Follower for Circular Arc Cam if there's Contact on Circular Flank

a = ω^{2} \cdot (R - r 1) \cdot \cos (θ t)

Go Acceleration of Follower for Roller Follower Tangent Cam, there's Contact with Straight Flanks

a = ω^{2} \cdot (r 1 + r rol) \cdot \frac{{(2 - \cos (θ))}^{2}}{{(\cos (θ))}^{3}}

Go Acceleration of Follower of Roller Follower Tangent Cam, there's Contact with Nose

a = ω^{2} \cdot r \cdot (\cos (θ 1) + \frac{L^{2} \cdot r \cdot \cos (2 \cdot θ 1) + r^{3} \cdot {(\sin (θ 1))}^{4}}{\sqrt{L^{2} - r^{2} \cdot {(\sin (θ 1))}^{2}}})

How to Evaluate Maximum Acceleration of Follower for Tangent Cam with Roller Follower?

Maximum Acceleration of Follower for Tangent Cam with Roller Follower evaluator uses Maximum Acceleration = Angular Velocity of Cam^2*(Radius of the Base Circle+Radius of Roller)*((2-(cos(Angle Turned by the Cam for Contact of Roller))^2)/((cos(Angle Turned by the Cam for Contact of Roller))^3)) to evaluate the Maximum Acceleration, Maximum Acceleration of Follower for Tangent Cam with Roller Follower formula is defined as the maximum acceleration experienced by the follower in a tangent cam with a roller follower, which is a critical parameter in designing and optimizing cam-follower systems to ensure smooth motion and minimize vibrations. Maximum Acceleration is denoted by a_max symbol.

How to evaluate Maximum Acceleration of Follower for Tangent Cam with Roller Follower using this online evaluator? To use this online evaluator for Maximum Acceleration of Follower for Tangent Cam with Roller Follower, enter Angular Velocity of Cam (ω), Radius of the Base Circle (r₁), Radius of Roller (r_rol) & Angle Turned by the Cam for Contact of Roller (φ) and hit the calculate button.

FAQs on Maximum Acceleration of Follower for Tangent Cam with Roller Follower

What is the formula to find Maximum Acceleration of Follower for Tangent Cam with Roller Follower?

The formula of Maximum Acceleration of Follower for Tangent Cam with Roller Follower is expressed as Maximum Acceleration = Angular Velocity of Cam^2*(Radius of the Base Circle+Radius of Roller)*((2-(cos(Angle Turned by the Cam for Contact of Roller))^2)/((cos(Angle Turned by the Cam for Contact of Roller))^3)). Here is an example- 45101.84 = 27^2*(4.98+31)*((2-(cos(0.5))^2)/((cos(0.5))^3)).

How to calculate Maximum Acceleration of Follower for Tangent Cam with Roller Follower?

With Angular Velocity of Cam (ω), Radius of the Base Circle (r₁), Radius of Roller (r_rol) & Angle Turned by the Cam for Contact of Roller (φ) we can find Maximum Acceleration of Follower for Tangent Cam with Roller Follower using the formula - Maximum Acceleration = Angular Velocity of Cam^2*(Radius of the Base Circle+Radius of Roller)*((2-(cos(Angle Turned by the Cam for Contact of Roller))^2)/((cos(Angle Turned by the Cam for Contact of Roller))^3)). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Maximum Acceleration?

Here are the different ways to Calculate Maximum Acceleration-

Maximum Acceleration=(pi^2*Angular Velocity of Cam^2*Stroke of Follower)/(2*Angular Displacement of Cam During Out Stroke^2)
Maximum Acceleration=(pi^2*Angular Velocity of Cam^2*Stroke of Follower)/(2*Angular Displacement of Cam During Return Stroke^2)
Maximum Acceleration=(4*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Return Stroke^2)

Can the Maximum Acceleration of Follower for Tangent Cam with Roller Follower be negative?

No, the Maximum Acceleration of Follower for Tangent Cam with Roller Follower, measured in Acceleration cannot be negative.

Which unit is used to measure Maximum Acceleration of Follower for Tangent Cam with Roller Follower?

Maximum Acceleration of Follower for Tangent Cam with Roller Follower is usually measured using the Meter per Square Second[m/s²] for Acceleration. Kilometer per Square Second[m/s²], Micrometer per Square Second[m/s²], Mile per Square Second[m/s²] are the few other units in which Maximum Acceleration of Follower for Tangent Cam with Roller Follower can be measured.

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Maximum Acceleration of Follower for Tangent Cam with Roller Follower Formula

​GoMaximum Acceleration of Follower on Outstroke when Follower Moves with SHM Formula

​GoMaximum Acceleration of Follower on Return Stroke when Follower Moves with SHM Formula

Maximum Acceleration of Follower for Tangent Cam with Roller Follower Example

Maximum Acceleration of Follower for Tangent Cam with Roller Follower Solution

Maximum Acceleration of Follower for Tangent Cam with Roller Follower Formula Elements

Other Formulas to find Maximum Acceleration

Other formulas in Acceleration of the Follower category

How to Evaluate Maximum Acceleration of Follower for Tangent Cam with Roller Follower?

FAQs on Maximum Acceleration of Follower for Tangent Cam with Roller Follower

Variable Name

GoMaximum Acceleration of Follower on Outstroke when Follower Moves with SHM Formula

GoMaximum Acceleration of Follower on Return Stroke when Follower Moves with SHM Formula