- #1

alzabroo

- 6

- 0

## Homework Statement

The problem deals with a linear rail system not unlike the one displayed in the image below

The relevant variables include:

Load = 70 Lbs

Load travel = 2.2 m

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

## Homework Equations

**Eq. 1**

Where:

L

_{10}= actuator lifetime (in millions of revolutions)

Cr = Dynamic Load Rating

Pr = Equivalent Load Factor

**Eq. 2**

Where:

n = rotation speed (min

^{-1})

this second equation results in unit of hours

**Eq. 3**

V

_{m}= (V

_{1}q

_{1}+V

_{2}q

_{2}+...+V

_{n}q

_{n})/100%

Where:

V

_{1},V

_{2},...V

_{n}= speed at phases of motion profile (in m/min)

q

_{1},q

_{2},...q

_{n}= % of time for each phase

**Eq. 4**

L

_{10 (hrs) var}=(L

_{10}*10

^{5})/(60*V

_{m})

Where:

L

_{10 (hrs) var}= actuator life in hours modified for variable speed

V

_{m}= equivalent speed

## 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**:

L

_{10}=(33,000N/311.5N)

^{3}=1.2*10

^{6}

**Eq. 2**:

L

_{10 (hrs)}=(10

^{6}/(60*n))*(L

_{10})=(2.0*10

^{10})/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:

L

_{10 (hrs)}=3.3*(10

^{9})

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