# Homework Help: Linear Actuator Motion Profile

1. Oct 27, 2013

### alzabroo

1. The problem statement, all variables and given/known data
The problem deals with a linear rail system not unlike the one displayed in the image below

The relevant variables include:
Load speed required = 2.3 m/s
Cycle time = 9 sec
Capacity of actuator = 33,000 N

With the given information:
A. determine the values for the graph below

B. ...and the life of the actuator in meters
C. ...and the life of the actuator in hours
2. Relevant equations
Eq. 1

Where:
L10= actuator lifetime (in millions of revolutions)
Eq. 2

Where:
n = rotation speed (min-1)
this second equation results in unit of hours
Eq. 3
Vm = (V1q1+V2q2+....+Vnqn)/100%
Where:
V1,V2,...Vn = speed at phases of motion profile (in m/min)
q1,q2,...qn = % of time for each phase

Eq. 4
L10 (hrs) var=(L10*105)/(60*Vm)
Where:
L10 (hrs) var = actuator life in hours modified for variable speed
Vm = equivalent speed

3. The attempt at a solution
There are a few assumptions I've made in my solution attempt to this problem, but I don't know where else to start.

First I assume that the dynamic load rating (Cr) is synonymous with the load capacity of the actuator
Second I assume that the Equivalent Load factor (Pr) is synonymous with the load provided (because no details of load distribution were provided)

To determine the life of the actuator in (millions of revolutions) I input the given values into Eq. 1:

L10=(33,000N/311.5N)3=1.2*106

Eq. 2:

L10 (hrs)=(106/(60*n))*(L10)=(2.0*1010)/n

I'm very unsure of how to determine n, but since the cycle time is 10 sec:
n = 6(min-1) ???

Assuming this, then:
L10 (hrs)=3.3*(109)

In order to use Eq. 3 account for the variable speed of the actuator, I believe I need to determine the values (time increments) of the graph given, but I'm unclear on how to do this with the given info.

I realize this a very long post, but I wanted to be as clear as possible.
Any pointers on how to where I have gone wrong in my process and/or how to proceed would greatly appreciated.
Thank you