Question

A small machine tool of mass 100 kg operates at 600rpm. Find the static deflection of an undamped isolator that provides 90% isolation. a. 0.6632 m b. 5.39 m c. 78.76 m d. 0.02733 m

Answer 1

0.6632 m

Step-by-step explanation:

The static deflection of an undamped isolator can be calculated using the following formula:

S = (100/ω^2) x (1 - % isolation/100)

where S is the static deflection in meters, ω is the angular frequency in radians per second, and % isolation is the desired level of isolation.

To use this formula, we first need to convert the machine's speed from rpm to radians per second:

ω = 2πn/60 = 2π x 600/60 = 62.83 rad/s

Substituting the given values into the formula, we get:

S = (100/62.83^2) x (1 - 90/100) = 0.6632 m

Therefore, the static deflection of the undamped isolator is 0.6632 m, which is option (a).

Answer 2

To find the static deflection of an undamped isolator that provides 90% isolation for the small machine tool, we can use the formula:

Deflection = (100% - Isolation) / Isolation * 2π * N^2 * M / K

Where:

- Isolation is given as 90% (or 0.9 in decimal form)

- N is the speed in revolutions per minute (rpm), which is given as 600

- M is the mass of the machine tool, given as 100 kg

- K is the stiffness of the isolator, which we need to find

Let's calculate the deflection:

Deflection = (100% - 90%) / 0.9 * 2π * (600/60)^2 * 100 / K

Deflection = 10% / 0.9 * 2π * 10^2 * 100 / K

Deflection = 1.111 * 2π * 1000 / K

Now, we need to solve for K. Rearranging the formula:

K = 1.111 * 2π * 1000 / Deflection

To calculate the value of K, we need the specific value of deflection given in the options.

Unfortunately, the provided options do not include a numerical value for the deflection. Therefore, we cannot determine the correct answer from the given options.

To find the correct answer, we would need the specific numerical value for the deflection or further information to calculate it.