Maximum Acceleration of Follower for Tangent Cam with Roller Follower Calculator

✖Angular velocity of cam refers to how fast an object rotates or revolves relative to another point.ⓘ Angular Velocity of Cam [ω]			+10% -10%
✖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.ⓘ Radius of the Base Circle [r₁]			+10% -10%
✖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.ⓘ Radius of Roller [r_rol]			+10% -10%
✖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.ⓘ Angle Turned by the Cam for Contact of Roller [φ]			+10% -10%

✖Maximum Acceleration is the rate of change of the velocity of an object with respect to time.ⓘ Maximum Acceleration of Follower for Tangent Cam with Roller Follower [a_max]

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Maximum Acceleration of Follower for Tangent Cam with Roller Follower Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
a_max = ω^2*(r₁+r_rol)*((2-(cos(φ))^2)/((cos(φ))^3))
This formula uses 1 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Maximum Acceleration - (Measured in Meter per Square Second) - Maximum Acceleration is the rate of change of the velocity of an object with respect to time.
Angular Velocity of Cam - (Measured in Radian per Second) - Angular velocity of cam refers to how fast an object rotates or revolves relative to another point.
Radius of the Base Circle - (Measured in Meter) - 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.
Radius of Roller - (Measured in Meter) - 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.
Angle Turned by the Cam for Contact of Roller - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Angular Velocity of Cam: 27 Radian per Second --> 27 Radian per Second No Conversion Required
Radius of the Base Circle: 4.98 Meter --> 4.98 Meter No Conversion Required
Radius of Roller: 31 Meter --> 31 Meter No Conversion Required
Angle Turned by the Cam for Contact of Roller: 0.5 Radian --> 0.5 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a_max = ω^2*(r₁+r_rol)*((2-(cos(φ))^2)/((cos(φ))^3)) --> 27^2*(4.98+31)*((2-(cos(0.5))^2)/((cos(0.5))^3))

Evaluating ... ...

a_max = 47728.3554974283

STEP 3: Convert Result to Output's Unit

47728.3554974283 Meter per Square Second --> No Conversion Required

FINAL ANSWER

47728.3554974283 ≈ 47728.36 Meter per Square Second <-- Maximum Acceleration

(Calculation completed in 00.007 seconds)

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Home » Physics » Theory of Machine » Cams » Mechanical » Acceleration of the Follower » Maximum Acceleration of Follower for Tangent Cam with Roller Follower

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National Institute Of Technology (NIT), Hamirpur

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< Acceleration of the Follower Calculators

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

LaTeX Go Acceleration of Follower = Angular Velocity of Cam^2*Distance b/w Cam Center and Nose Center*(cos(Angle Turned by Cam When Roller is at Nose Top)+(Distance b/w Roller Centre and Nose Centre^2*Distance b/w Cam Center and Nose Center*cos(2*Angle Turned by Cam When Roller is at Nose Top)+Distance b/w Cam Center and Nose Center^3*(sin(Angle Turned by Cam When Roller is at Nose Top))^4)/sqrt(Distance b/w Roller Centre and Nose Centre^2-Distance b/w Cam Center and Nose Center^2*(sin(Angle Turned by Cam When Roller is at Nose Top))^2))

Acceleration of Follower after Time t for Cycloidal Motion

LaTeX Go Acceleration of Follower = (2*pi*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Out Stroke^2)*sin((2*pi*Angle Through Which Cam Rotates)/(Angular Displacement of Cam During Out Stroke))

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

LaTeX Go Acceleration of Follower = Angular Velocity of Cam^2*(Radius of the Base Circle+Radius of Roller)*(2-cos(Angle Turned by Cam from Beginning of Roller))^2/((cos(Angle Turned by Cam from Beginning of Roller))^3)

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

LaTeX Go Acceleration of Follower = Angular Velocity of Cam^2*(Radius of Circular Flank-Radius of the Base Circle)*cos(Angle Turned by Cam)

Maximum Acceleration of Follower for Tangent Cam with Roller Follower Formula

LaTeX Go

What is tangent cam with reciprocating roller follower?

Tangent cam with reciprocating followers is an example of cams with specified contours. Tangent cams are symmetric about the centerline of the camshaft and hence they fall into a category of cams with specified contours. Tangent cams are symmetrical about the centerline of the camshaft.

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

Maximum Acceleration of Follower for Tangent Cam with Roller Follower calculator 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 calculate 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 calculate Maximum Acceleration of Follower for Tangent Cam with Roller Follower using this online calculator? To use this online calculator 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. Here is how the Maximum Acceleration of Follower for Tangent Cam with Roller Follower calculation can be explained with given input values -> 45101.84 = 27^2*(4.98+31)*((2-(cos(0.5))^2)/((cos(0.5))^3)).

FAQ

What is Maximum Acceleration of Follower for Tangent Cam with Roller Follower?

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 and is represented as a_max = ω^2*(r₁+r_rol)*((2-(cos(φ))^2)/((cos(φ))^3)) or 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)). Angular velocity of cam refers to how fast an object rotates or revolves relative to another point, 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, 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 & 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.

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

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 is calculated using 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 calculate Maximum Acceleration of Follower for Tangent Cam with Roller Follower, you need 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). With our tool, you need to enter the respective value for Angular Velocity of Cam, Radius of the Base Circle, Radius of Roller & Angle Turned by the Cam for Contact of Roller 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 Maximum Acceleration?

In this formula, Maximum Acceleration uses Angular Velocity of Cam, Radius of the Base Circle, Radius of Roller & Angle Turned by the Cam for Contact of Roller. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)

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