FRICTIONAL FORCES ON SCREWS

In-Class Activities:• Check Homework, if any• Reading Quiz• Applications• Analysis of Impending

motion• Analysis of a self locking

screw• Concept Quiz• Group Problem Solving• Attention Quiz

Today’s Objectives:

Students will be able to:

a) Determine the forces on a square-threaded screw.

READING QUIZ

1. A screw allows a ______ moment M to lift a _________ weight W.

A) (large, large) B) (small, small)

C) (small, large) D) (large, small)

2. A screw is self locking if it remains in place under __________ loads.

A) any axial B) small axial

C) any rotational D) small rotational

W

APPLICATIONS

How can we determine the force required to turn a screw?

Some screws are self locking, meaning it remains in place under any axial load. How do we determine if this is the case?

Screws are sometimes used not as fasteners, but as mechanisms for transmitting power from one part of a machine to another.

How much friction is needed to create a self locking apparatus?

APPLICATIONS (continued)

The design of a turnbuckle requires knowledge of self locking properties and the minimum moment M required to turn the machine.

ANALYSIS OF A SCREW

A square threaded screw is a cylinder with a square ridge wrapped around it. The slope of the thread is the lead angle, determined from

An FBD of the entire unraveled thread can be represented as a block.

WA screw is a simple machine in which a small Moment M is used to lift a large weight W.

To determine the force required to turn the screw, it is necessary to draw an FBD of the screw thread.

ANALYSIS OF A SCREW (continued)

Four Cases can the be analyzed:

1. Upward impending motion

2. Self-Locking

3. Downward impending motion

4. Downward impending motion (not-self locking)

The reaction R has both frictional and normal components.

Note that this assumes impending motion

ANALYSIS OF A SCREW (continued)

A screw is self locking if with no applied moment

If a screw is self locking, a moment M’ must be applied to make and lead to downward motion

If a screw is not self locking, then a moment M’’ must be applied to keep the screw from falling

EXAMPLE

1. Draw a FBD of the screw thread.

2. Determine the lead angle

3. Assume impending motion

4. Apply the E-of-E to the screw thread.

Given: The turnbuckle has a square thread with a mean radius of 5 mm and a lead of 2 mm. = 0.25.

Find: The moment M to draw the screws closer together

Plan:

EXAMPLE (continued)

FX = -N sin(Θ) + M/r – .25 N cos(Θ) = 0

FY = N cos(Θ) – .25 N sin(Θ) - W = 0

Solving the above two equations, we get M = 6.37 N * m

M/r

W

F

N

GROUP PROBLEM SOLVING

Given: The square threaded screw has a mean diameter of 0.5 in and a lead of 0.2 in. .

Find: The torque M that should be applied to the screw to start lifting the 6000 lb load