Mechanical Design Home Assignment — Design of Threaded Joints
Introduction
A rod with a helical groove on the external cylindrical surface is called a screw or bolt. A hollow rod which has a helical groove on the internal cylindrical surface is called a nut. The joint which is formed by using screw or bolt and nut the joint is called a screwed or threaded joint. It is a temporary joint, which is easily dismantled as required. In general, ‘V’ threads are used to join.
Threaded joints are extensively used in mechanical assemblies. It has been observed that over 60% of the parts have threads. The popularity of threaded joints is due to certain advantages offered by them.
Types of Threaded Joints
Threaded joints are specified below for the way a joint is made, or for its purpose.
Direct joints -
The component parts to be joined have internal or external thread and are directly screwed together. No additional fastening elements are needed.
Indirect joints -
The component parts to be joined are held together by standardized components, i.e., bolts, screws and nuts. Locking devices and washers may be used additionally.
Where a component part has a female thread, the joint may be made without a nut. The walls of the work-piece must be sufficiently thick for this kind of joint.
Fastening joints -
The component parts are to be joined directly or indirectly only for the purpose of connecting them. The vee-thread, ISO metric vee-thread or Whitworth thread, are the preferred types of thread. Both threads are self-retaining.
Adjustable joints -
The component parts are joined for the purpose of connecting them and transmitting movements or forces. The preferred types of thread are round thread, acme standard screw thread or saw-tooth thread.
These are less self-retaining
Advantages of threaded joints:
· They are reliable
· Less force is required to tighten a joint because of the mechanical advantage offered by spanner
· They have small overall dimensions and are compact in construction
· Threads have self-locking property hence they can be used in any position either vertical or horizontal
· Their manufacturing is simple hence they are cost effective
· Parts joined by them are easily detachable
· Wide variety of threaded fasteners are available in market with standardized dimensions
Disadvantages of threaded joints:
· Parts joined by threaded joints are vulnerable to failure due to stress concentration near the holes.
· Due to time and labor taken in manual assembly the cost in tightening a screw can be up to six times the cost of screw itself.
Important Terminologies:
Before we begin getting into the details regarding the design of the joints, we need to familiarize ourselves with some of the terms we’ll be coming across.
1. Major Diameter
The major diameter is the diameter of an imaginary cylinder that bounds the crest of an external thread (d) or the root of an internal thread (D). The major diameter is the largest diameter of the screw thread. It is also called the nominal diameter of the thread.
2. Minor Diameter
The minor diameter is the diameter of an imaginary cylinder that bounds the roots of an external thread (dc) or the crest of an internal thread (Dc). The minor diameter is the smallest diameter of the screw thread. It is also called the core or root diameter of the thread.
3. Pitch Diameter
The pitch diameter is the diameter of an imaginary cylinder, the surface of which would pass through the threads at such points as to make the width of the threads equal to the width of spaces cut by the surface of the cylinder. It is also called the effective diameter of the thread. Pitch diameter is denoted by dp for external threads and Dp for internal threads.
4. Pitch
Pitch is the distance between two similar points on adjacent threads measured parallel to the axis of the thread. It is denoted by the letter p.
5. Lead
Lead is the distance that the nut moves parallel to the axis of the screw, when the nut is given one turn.
6. Thread Angle
Thread angle is the angle included between the sides of the thread measured in an axial plane. Thread angle is 60 degrees for ISO metric threads.
Factors affecting the design of threaded joints:
Maximum Tensile Stress
A bolted joint subjected to tensile force P is shown.
The cross-section at the core diameter dc is the weakest section. The maximum tensile stress in the bolt at this cross-section is given by,
The height of the nut h can be determined by equating the strength of the bolt in tension with the strength in shear.
The procedure is based on the following assumptions:
i. Each turn of the thread in contact with the nut supports an equal amount of load.
ii. There is no stress concentration in the threads.
iii. The yield strength in shear is equal to half of the yield strength in tension (Ssy = 0.5Syt).
iv. Failure occurs in the threads of the bolt and not in the threads of the nut.
Permissible shear stress is given by:
Substituting this in the previous equation, we get:
The strength of the bolt in shear is given by,
Equating the above equations,
h = 0.5dc
Assuming (dc = 0.8d),
h = 0.4d
Therefore, for standard coarse threads, the threads are equally strong in failure by shear and failure by tension, if the height of the nut is approximately 0.4 times of the nominal diameter of the bolt.
Eccentrically Loaded Bolted Joints in Shear
In structural connections, a group of bolts is frequently employed.
In order to find the shear stress, we must first find the center of gravity of all the bolts used. Quite often, the center of gravity is located by symmetry. An eccentrically loaded bolted connection is shown below:
The eccentricity of the external force P is e from the center of gravity. Eccentric force can be considered as equivalent to an imaginary force P at the center of gravity and a moment (P x e) about the same point.
P x e = P1r1 + P2r2+P3r3+P4r4
It is assumed that the secondary shear force at any bolt is proportional to its distance from the center of gravity.
P=Cr
The primary and secondary shear forces are added by vector addition method to get the resultant shear forces P1, P2, P3, and P4. In this analysis, it is assumed that the components connected by the bolts are rigid and the bolts have the same cross- sectional area.
Eccentric Load Perpendicular to the axis of the bolt
As shown in the figure below, a bracket is fixed to the steel structure by means of four bolts. It is subjected to eccentric force P and this force P is perpendicular to the axis of each bolt.
Following assumptions are made in the analysis –
(i) The bracket and the steel structure are rigid.
(ii) The bolts are fitted in reamed and ground holes.
(iii) The bolts are not preloaded and there are no tensile stresses due to initial tightening.
(iv) The stress concentration in threads is neglected.
(v) All bolts are identical.
Each bolt is stretched by an amount (d) which is proportional to its vertical distance from the point C.
Therefore, the resisting force induced in any bolt, due to the tendency of the bracket to tilt under the moment (P X e), is proportional to its distance from the tilting edge.
C — Proportionality constant
Substituting and Equating the moment due to resisting forces with the moment due to external force P about the edge C,
Hence, a bolt, which is located at the farthest distance from the tilting edge C, is subjected to maximum force.
The bolts can be designed on the basis of principal stress theory or principal shear stress theory-
The principal stress σ1 is given by,
The principal shear stress is given by,
Therefore, using the following relationships
the cross-sectional area of the bolts and their size can be determined.
The bolt material is usually ductile. Therefore, it is appropriate to use the maximum shear stress theory of failure.
Eccentric Load on circular base
Figure shows, a round flange bearing fastened by means of four bolts. It is subjected to an external force P at a distance l from the support.
The following assumptions are made:
(i) All bolts are identical.
(ii) The bearing and the structure are rigid.
(iii) The bolts are not preloaded and there is no tensile stress due to initial tightening.
(iv) The stress concentration in the threads is neglected.
(v) The bolts are relieved of shear stresses by using dowel pins.
When the load tends to tilt the bearing about the point C, each bolt is stretched by an amount (d), which is proportional to its vertical distance from the point C.
Therefore, the resisting force acting on any bolt due to the tendency of the bearing to tilt, is proportional to its distance from the tilting edge.
The force acting on the bolt 1 is given by,
Suppose,
a = radius of the flange
b = radius of the pitch circle of the bolts
From figure,
Therefore,
Hence general equation for n equally spaced bolts is -
Therefore,
Substituting α=180°
The above equation gives absolute maximum value of the force acting on any of the bolts. It should be used for finding out the size of the bolts, when the direction of the external force P can change with respect to the bolts, as in case of the base of a vertical pillar crane.
When the direction of the external force P is fixed and known, the maximum load on the bolts can be reduced, so that the two of them can be equally stressed. Therefore, for a general case with n as number of bolts,
The above equation is applicable only when two bolts are equally stressed. This condition can be satisfied under the following circumstances:
(i) the direction of the external force P is fixed with respect to the bolts;
(ii) the number of bolts is even
(iii) two bolts at the top are symmetrically spaced with angle b on either side of the vertical line.
Conclusion:
Here, we’ve looked at the various advantages and disadvantages of threaded joints, as well as the calculations that go into designing a threaded joint that can endure the required load and work efficiently in a particular application.
To reiterate, the parameters that come into play when we are designing a threaded joint are:
· Tensile Failure
· Shear Failure
· Effect of eccentric load
· Effect of eccentric load acting perpendicular
· Effect of eccentric load acting on the base
References:
1. Design of Machine Elements by V B Bhandari
2. A Textbook of Machine Design by RS Khurmi
