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))
amax = ω^2*(r1+rroller)*((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: 3 Meter --> 3 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
amax = ω^2*(r1+rroller)*((2-(cos(φ))^2)/((cos(φ))^3)) --> 27^2*(3+31)*((2-(cos(0.5))^2)/((cos(0.5))^3))
Evaluating ... ...
amax = 45101.8367679978
STEP 3: Convert Result to Output's Unit
45101.8367679978 Meter per Square Second --> No Conversion Required
FINAL ANSWER
45101.8367679978 45101.84 Meter per Square Second <-- Maximum Acceleration
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Birsa Institute of Technology (BIT), Sindri
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12 Maximum Accelaration Calculators

Maximum Acceleration of Follower for Tangent Cam with Roller Follower
Go 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))
Max Acceleration of Follower during Return Stroke if Follower Stroke is Known Uniform Acceleration
Go Maximum Acceleration = (4*Angular velocity of cam*Stroke of Follower)/(Angular displacement of cam during return stroke*Time required for the return stroke)
Max Acceleration of Follower during Outstroke if Stroke of Follower is known Uniform Acceleration
Go Maximum Acceleration = (4*Angular velocity of cam*Stroke of Follower)/(Angular Displacement of Cam during Out Stroke*Time required for the outstroke)
Maximum Acceleration of Follower during Return Stroke for Cycloidal Motion
Go Maximum Acceleration = (2*pi*Angular velocity of cam^2*Stroke of Follower)/(Angular displacement of cam during return stroke^2)
Maximum Acceleration of Follower during Outstroke for Cycloidal Motion
Go Maximum Acceleration = (2*pi *Angular velocity of cam^2*Stroke of Follower)/(Angular Displacement of Cam during Out Stroke^2)
Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM
Go Maximum Acceleration = (pi^2*Angular velocity of cam^2*Stroke of Follower)/(2*Angular displacement of cam during return stroke^2)
Maximum Acceleration of Follower on Outstroke when Follower Moves with SHM
Go Maximum Acceleration = (pi^2*Angular velocity of cam^2*Stroke of Follower)/(2*Angular Displacement of Cam during Out Stroke^2)
Maximum Uniform Acceleration of Follower during Return Stroke
Go Maximum Acceleration = (4*Angular velocity of cam^2*Stroke of Follower)/(Angular displacement of cam during return stroke^2)
Maximum Uniform Acceleration of Follower during Outstroke
Go Maximum Acceleration = (4*Angular velocity of cam^2*Stroke of Follower)/(Angular Displacement of Cam during Out Stroke^2)
Maximum Acceleration of Follower for Circular Arc Cam Contacting with Circular Flank
Go Maximum Acceleration = Angular velocity of cam^2*(Radius of circular flank-Radius of the base circle)
Max Acceleration of Follower during Return Stroke if Follower Speed is known Uniform Acceleration
Go Maximum Acceleration = (2*Maximum velocity of follower)/Time required for the return stroke
Max Acceleration of Follower during Outstroke if Outstroke Velocity is known Uniform Acceleration
Go Maximum Acceleration = (2*Maximum velocity of follower)/Time required for the outstroke

Maximum Acceleration of Follower for Tangent Cam with Roller Follower 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))
amax = ω^2*(r1+rroller)*((2-(cos(φ))^2)/((cos(φ))^3))

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 is defined as the rate of change of the velocity of an object with respect to time. Maximum Acceleration is denoted by amax 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 (rroller) & 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*(3+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 is defined as the rate of change of the velocity of an object with respect to time and is represented as amax = ω^2*(r1+rroller)*((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 is defined as the rate of change of the velocity of an object with respect to time 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 (rroller) & 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 11 other way(s) to calculate the same, which is/are as follows -
  • Maximum Acceleration = (4*Angular velocity of cam^2*Stroke of Follower)/(Angular displacement of cam during return stroke^2)
  • Maximum Acceleration = (4*Angular velocity of cam^2*Stroke of Follower)/(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 = (pi^2*Angular velocity of cam^2*Stroke of Follower)/(2*Angular Displacement of Cam during Out Stroke^2)
  • Maximum Acceleration = Angular velocity of cam^2*(Radius of circular flank-Radius of the base circle)
  • Maximum Acceleration = (2*pi*Angular velocity of cam^2*Stroke of Follower)/(Angular displacement of cam during return stroke^2)
  • Maximum Acceleration = (2*pi *Angular velocity of cam^2*Stroke of Follower)/(Angular Displacement of Cam during Out Stroke^2)
  • Maximum Acceleration = (4*Angular velocity of cam*Stroke of Follower)/(Angular displacement of cam during return stroke*Time required for the return stroke)
  • Maximum Acceleration = (2*Maximum velocity of follower)/Time required for the return stroke
  • Maximum Acceleration = (4*Angular velocity of cam*Stroke of Follower)/(Angular Displacement of Cam during Out Stroke*Time required for the outstroke)
  • Maximum Acceleration = (2*Maximum velocity of follower)/Time required for the outstroke
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