Machine Design 3(2+1)

LESSON 25 INTRODUCTION TO POWER SCREWS

Power screw comprises of two main components: screw and nut, and can operate in following three ways:

1. Screw rotates in bearings and nut moves axially
2. Screw rotates and also moves axially while nut is kept fixed
3. Nut rotates and screw moves in axial direction

Power screws have large load carrying capacity, are compact, provide large mechanical advantage, provide very accurate and precise linear motion, have smooth and noiseless operation, are reliable and have lesser cost. Disadvantages are that power screws have poor efficiency and high rate of wear.

25.2         Materials

Screw is subjected to torque, axial compressive load and bending moment also, sometimes. Screws are generally made of C30 or C40 steel. As the failure of power screws may lead to serious accident, higher factor of safety of 3 to 5 is taken. Threads may fail due to shear, which can be avoided by using nut of sufficient height. Wear is another possible mode of thread failure as the threads of nut and bolt rub against each other. Nuts are made of softer material than screws so that if at all the failure takes place, nut fails and not the screw, which is the costlier member and is also difficult to replace. Plastic, bronze or copper alloys are used for manufacturing nuts. Plastic is used for low load applications and has good friction and wear properties. Bronze and copper alloys are used for high load applications.

25.3          Thread Forms for Power Screws

Thread forms used in threaded fasteners are not suitable for power screws. The purpose of threads used in fasteners is to provide high friction to minimize the chances of loosening. But in power screws, low friction between nut and bolt is desired as those are to be used for power transmission. Types of threads commonly used for power screws are:

i) Square Threads ii) Acme or Trapezoidal Threads iii) Buttress Thread

These thread forms are shown in figure 25.1.

Figure 25.1 Thread Forms for Power Screws

 

25.3.1    Square Threads

Square thread can be used to transmit power in either direction. Square threads have maximum efficiency and there is no radial or bursting pressure on the nut, increasing the life of the nut and making its motion uniform. But it is difficult to manufacture square threads. These are difficult to cut with taps and dies and are usually cut on a lathe with a single point cutting tool, making it expensive. Also, it is not possible to compensate for wear in square threads as split nut cannot be used with it. Therefore, nut or screw has to be replaced, when worn out. The square threads are used in screw jacks, presses and clamping devices.

25.3.2    Acme or Trapezoidal Threads

Acme thread is used for power transmission. It has higher load carrying capacity in comparison to square threads, because of larger root thickness. Acme threads are manufactured on a milling machine using a multi-point cutting tool and are therefore economical to cut. Due to the slope provided on its sides, efficiency of acme threads is less than the square threads and the nut is subjected to radial or bursting pressure. Wear can be compensated in this case by using split nut, which is a nut cut into two halves along its diameter. These two halves are tightened together after certain intervals to take care of the wear taken place.

25.3.3    Buttress Thread

Buttress thread is designed to take large loads in one direction. This is the strongest of the thread forms due to greater root thickness. Its efficiency is comparable with the square threads, is easier to cut and is compatible with the split nut also. Buttress thread finds its application in light jack screws and vices.

25.4          Torque Required to Raise & Lower the Load

Figure 25.2 Development of Thread

Power screws are used to convert the applied torque into useful axial force, e.g. screw jack converts torque into axial force which is used to lift load. It is important to know the torque required to raise or lower a given load.

Let       p          = Pitch of the screw

d_m        = Mean diameter of the screw

α          = Helix angle

l           = Lead of the screw

P          = Effort applied at the circumference of the screw to lift the load

W         = Load to be lifted

μ          = Coefficient of friction,

   between the screw and nut

A screw thread can be considered as an inclined plane wrapped around a cylinder to form helix and the relative motion between the nut and the screw against the external load is analogous to the movement of a weight on an inclined plane. For simplicity of the analysis, this is assumed to be a point load, though the actual load is distributed on the thread surface. Figure 25.2 shows the right angled triangle formed by un-wrapping a single thread. Thread forms the hypotenuse of the triangle and can be considered as an inclined plane. Length of the base of the triangle is p d_m and its height is equal to lead, l. This gives the following relation between helix angle, mean diameter and lead of the screw:

 

Figure 25.4 Force Diagram for Lowering Load

 

Figure 25.3 Force Diagram for Raising Load

Figure 25.3 and figure 25.4 show the forces acting at a point on the inclined plane, while raising and lowering the load respectively. Forces acting at the point are: P – Applied Effort, W – Load to be raised and lowered, N – Normal Reaction and mN – Frictional Force.

Both the cases are discussed below:

Figure 25.5 shows load acting on the surface of a trapezoidal thread. In this case the load acting normal to the surface of the thread is W.secq. As frictional force is a function of the normal load, it increases by a factor ‘secq’. Effort and torque required to lift or lower the load in case of trapezoidal threads can be obtained by replacing ‘m’ with ‘m secq’. For example:

 

Figure 25.5 Force Diagram for Trapezoidal Thread

25.5          Condition for Self-locking

The torque required to lower the load is given by,

From the equation, it is clear that if , the torque required to lower the load is negative i.e. in such condition load will descend without requiring any external torque. Such condition is known as overhauling of the screw. But this an undesired condition for applications like screw jacks as it may lead to accident. On the other hand, if φ > a, a positive torque is required to lower the load and the load cannot descend on its own without application of external torque. Such screws are called self-locking screws. So the condition for the screw to be self-locking is:

25.6          Efficiency of a Square Screw Thread

Referring to figure 25.3, suppose the load W moves from the lowest point to the highest point along the inclined plane. Then the output and input work is given by,

The efficiency of the screw is given by,

 

 

 

References

1. Design of Machine Elements by VB Bhandari
2. Analysis and Design of Machine Elements by V.K. Jadon
3. Machine Design by R.S. Khurmi
4. Design of Machine Elements by C.S. Sharma & K. Purohit
5. Mechanical Design by Peter Childs