MEMS

Technique of combining
Electrical and Mechanical
Disciplines
• MEMS or Micro-Electro Mechanical System is
a technique of combining Electrical and
Mechanical components together on a chip, to
produce a system of miniature dimensions.
sensors
• Sensor is a device that measures information
from a surrounding environment and provides
an electrical output signal in response.
• Actuator is a device that converts an electrical
signal into action.
386 l Theory of Machines
Sometimes, the gear of a shaft meshes externally and internally with the gears in a *straight
line, as shown in Fig. 12.4. Such type of gear is called rack and pinion. The straight line gear is called
rack and the circular wheel is called pinion. A little consideration will show that with the help of a
rack and pinion, we can convert linear motion into rotary motion and vice-versa as shown in Fig.
12.4.
4. According to position of teeth on the gear surface. The teeth on the gear surface may be
(a) straight, (b) inclined, and (c) curved.
We have discussed earlier that the spur gears have straight teeth where as helical gears have
their teeth inclined to the wheel rim. In case of spiral gears, the teeth are curved over the rim surface.

Internal gears Rack and pinion

12.5. Terms Used in Gears

The following terms, which will be mostly used in this chapter, should be clearly understood
at this stage. These terms are illustrated in Fig. 12.5.

Fig. 12.5. Terms used in gears.

1. Pitch circle. It is an imaginary circle which by pure rolling action, would give the same
motion as the actual gear.
* A straight line may also be defined as a wheel of infinite radius.
 Chapter 12 : Toothed Gearing l 387
2. Pitch circle diameter. It is the diameter of the pitch circle. The size of the gear is usually
specified by the pitch circle diameter. It is also known as pitch diameter.
3. Pitch point. It is a common point of contact between two pitch circles.
4. Pitch surface. It is the surface of the rolling discs which the meshing gears have replaced
at the pitch circle.
5. Pressure angle or angle of obliquity. It is the angle between the common normal to two
gear teeth at the point of contact and the common tangent at the pitch point. It is usually denoted by φ.
The standard pressure angles are 14 12 ° and 20°.
6. Addendum. It is the radial distance of a tooth from the pitch circle to the top of the tooth.
7. Dedendum. It is the radial distance of a tooth from the pitch circle to the bottom of the tooth.
8. Addendum circle. It is the circle drawn through the top of the teeth and is concentric with
the pitch circle.
9. Dedendum circle. It is the circle drawn through the bottom of the teeth. It is also called
root circle.
Note : Root circle diameter = Pitch circle diameter × cos φ, where φ is the pressure angle.
10. Circular pitch. It is the distance measured on the circumference of the pitch circle from
a point of one tooth to the corresponding point on the next tooth. It is usually denoted by pc.
Mathematically,
Circular pitch, pc = π D/T
where D = Diameter of the pitch circle, and
T = Number of teeth on the wheel.
A little consideration will show that the two gears will mesh together correctly, if the two
wheels have the same circular pitch.
Note : If D1 and D2 are the diameters of the two meshing gears having the teeth T 1 and T 2 respectively, then for
them to mesh correctly,
π D1 π D2 D1 T
pc = = or = 1
T1 T2 D2 T2
11. Diametral pitch. It is the ratio of number of teeth to the pitch circle diameter in millimetres.
It is denoted by pd . Mathematically,
T π  πD 
Diametral pitch, pd = = ... 3 pc = 
D pc  T 
where T = Number of teeth, and
D = Pitch circle diameter.
12. Module. It is the ratio of the pitch circle diameter in millimeters to the number of teeth.
It is usually denoted by m. Mathematically,
Module, m = D /T
Note : The recommended series of modules in Indian Standard are 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16,
and 20. The modules 1.125, 1.375, 1.75, 2.25, 2.75, 3.5, 4.5, 5.5, 7, 9, 11, 14 and 18 are of second choice.
13. Clearance. It is the radial distance from the top of the tooth to the bottom of the tooth, in
a meshing gear. A circle passing through the top of the meshing gear is known as clearance circle.
14. Total depth. It is the radial distance between the addendum and the dedendum circles of
a gear. It is equal to the sum of the addendum and dedendum.
388 l Theory of Machines
15. Working depth. It is the radial distance from the addendum circle to the clearance circle.
It is equal to the sum of the addendum of the two meshing gears.
16. Tooth thickness. It is the width of the tooth measured along the pitch circle.
17. Tooth space . It is the width of space between the two adjacent teeth measured along the pitch
circle.
18. Backlash. It is the difference between the tooth space and the tooth thickness, as mea-
sured along the pitch circle. Theoretically, the backlash should be zero, but in actual practice some
backlash must be allowed to prevent jamming of the teeth due to tooth errors and thermal expansion.
19. Face of tooth. It is the surface of the gear tooth above the pitch surface.
20. Flank of tooth. It is the surface of the gear tooth below the pitch surface.
21. Top land. It is the surface of the top of the tooth.
22. Face width. It is the width of the gear tooth measured parallel to its axis.
23. Profile. It is the curve formed by the face and flank of the tooth.
24. Fillet radius. It is the radius that connects the root circle to the profile of the tooth.
25. Path of contact. It is the path traced by the point of contact of two teeth from the
beginning to the end of engagement.
26. *Length of the path of contact. It is the length of the common normal cut-off by the
addendum circles of the wheel and pinion.
27. ** Arc of contact. It is the path traced by a point on the pitch circle from the beginning
to the end of engagement of a given pair of teeth. The arc of contact consists of two parts, i.e.
(a) Arc of approach. It is the portion of the path of contact from the beginning of the
engagement to the pitch point.
(b) Arc of recess. It is the portion of the path of contact from the pitch point to the end of the
engagement of a pair of teeth.
Note : The ratio of the length of arc of contact to the circular pitch is known as contact ratio i.e. number of pairs
of teeth in contact.

12.6. Gear Materials

The material used for the manufacture of gears depends upon the strength and service condi-
tions like wear, noise etc. The gears may be manufactured from metallic or non-metallic materials.
The metallic gears with cut teeth are commercially obtainable in cast iron, steel and bronze. The non-
metallic materials like wood, raw hide, compressed paper and synthetic resins like nylon are used for
gears, especially for reducing noise.
The cast iron is widely used for the manufacture of gears due to its good wearing properties,
excellent machinability and ease of producing complicated shapes by casting method. The cast iron
gears with cut teeth may be employed, where smooth action is not important.
The steel is used for high strength gears and steel may be plain carbon steel or alloy steel. The
steel gears are usually heat treated in order to combine properly the toughness and tooth hardness.
The phosphor bronze is widely used for worm gears in order to reduce wear of the worms
which will be excessive with cast iron or steel.
12.7. Condition for Constant Velocity Ratio of Toothed Wheels–Law of
Gearing
Consider the portions of the two teeth, one on the wheel 1 (or pinion) and the other on the

* For details, see Art. 12.16.

** For details, see Art. 12.17.
 Chapter 12 : Toothed Gearing l 395
changeability. The tooth profile of this system has cycloidal curves at the top and bottom and involute
curve at the middle portion. The teeth are produced by formed milling cutters or hobs. The tooth
profile of the 14 1 ° full depth involute system was developed for use with gear hobs for spur and
2
helical gears.
The tooth profile of the 20° full depth involute system may be cut by hobs. The increase of
the pressure angle from 14 1 ° to 20° results in a stronger tooth, because the tooth acting as a beam is
2
wider at the base. The 20° stub involute system has a strong tooth to take heavy loads.
12.15. Standard Proportions of Gear Systems
The following table shows the standard proportions in module (m) for the four gear systems
as discussed in the previous article.
Table 12.1. Standard proportions of gear systems.
S. No. Particulars 14 12 ° composite or full 20° full depth 20° stub involute
depth involute system involute system system
1. Addenddm 1m 1m 0.8 m
2. Dedendum 1.25 m 1.25 m 1m
3. Working depth 2m 2m 1.60 m
4. Minimum total depth 2.25 m 2.25 m 1.80 m
5. Tooth thickness 1.5708 m 1.5708 m 1.5708 m
6. Minimum clearance 0.25 m 0.25 m 0.2 m
7. Fillet radius at root 0.4 m 0.4 m 0.4 m

12.16. Length of Path of Contact

Consider a pinion driving the wheel as shown in Fig. 12.11. When the pinion rotates in
clockwise direction, the contact between a pair of involute teeth begins at K (on the flank near the
base circle of pinion or the outer end of the tooth face on the wheel) and* ends at L (outer end of the
tooth face on the pinion or on the flank near the base circle of wheel). M N is the common normal at
the point of contacts and the common tangent to the base circles. The point K is the intersection of the
addendum circle of wheel and the common tangent. The point L is the intersection of the addendum
circle of pinion and common tangent.

Fig. 12.11. Length of path of contact.

* If the wheel is made to act as a driver and the directions of motion are reversed, then the contact between
a pair of teeth begins at L and ends at K.
PRESSURE VESSELS
 Introduction
A pressure vessel is considered as any closed vessel that is capable of
storing a pressurized fluid, either internal or external pressure, regardless
of their shape and dimensions. The cylindrical vessels, to which we refer in
this volume, are calculated on the principles of thin-walled cylinders.

 The first step in designing a container is choosing the best type for the
service for which it is intended.

The factors influencing the choice of type are

a) The function of the container
b) The location
c) The nature of the fluid that has to be stored
d) The temperature and operating pressure
Classification of Pressure Vessels
Pressure vessels can be classified according to their intended service,
temperature and pressure, materials and geometry.

Different types of pressure vessels can be classified as follows:

According to the intended use of the pressure vessel, they can be divided
into storage containers and process vessels.
The first classes are only used for storing fluids under pressure, and in
accordance with the service are known as storage tanks.
Process pressure vessels have multiple and varied uses, among them we can
mention heat exchangers, reactors, fractionating towers, distillation towers,
etc.
According to the shape, pressure vessel may be cylindrical or spherical.
The former may be horizontal or vertical, and in some cases may have coils
to increase or lower the temperature of the fluid.

Spherical pressure vessels are usually used as storage tanks, and are
recommended for storing large volumes.
Since the spherical shape is the "natural" form bodies adopt when
subjected to internal pressure, this would be the most economical way to
store pressurized fluids. However, the manufacture of such containers is
much more expensive compared with cylindrical containers.
Pressure vessel parts
The following two sample vessels are presented: vertical and horizontal. In
both cases the main parts are shown:
Geometry definition
To define the geometry of a pressure vessel, the inner diameter of the
equipment and the distance between tangent lines is used.
The inner diameter should be used, since this is a process requirement.

 Welding line: point at which the head and shell are welded
 Tangent line: point at which the curvature of the head begins

Depending on the head fabrication method, heads come with a straight skirt.
To set the length of the pressure vessel (regardless the type of heads), the
distance between tangent lines is used since this distance is not
dependent on the head manufacturing method. It is very rare that the weld
and tangent lines coincide.

Manufacturing sequence
1. Design codes
The purpose of using design codes is to avoid disasters that can affect
humans. Therefore, they comprise a range of experiences and good practices.

While there are several rules that apply, developed by countries with
recognized technical expertise in the subject, the code that is the most
internationally recognized and the most used is Section VIII "Pressure
Vessels" part of the Boiler and Pressure Vessel Code (BPVC) of the
American Society of Mechanical Engineers (ASME).

Other than the code above, the most commonly codes used for pressure
vessels are:
 Europe: EN-13445
 Germany: A. D. Merkblatt Code
 United Kingdom: British Standards BS 5500
 France: CODAP
 China: GB-150

The rules found in the design codes represent many years of experience. If
used wisely, the code requirements can:
 Communicate design requirements
 Utilize know-how and technology
 Keep equipment costs low
 Reduce insurance costs
 Provide rules for the design of equipment adequate for design
conditions determined by others.
 Do not provide rules or guidance for the determination of design
conditions.
 Do not provide rules or guidance for the determination of the required
material(s) of construction or corrosion allowance.
 Design scope of most design codes includes new construction only, not
revamps, repairs or rerates.
2. ASME BPVC – Boiler and pressure vessel code

BPVC Sections

The ASME BVPC code is a set of standards, specifications, and design rules
based on many years of experience, all applied to the design, fabrication,
installation, inspection, and certification of pressure vessels.
It was created in the United States of America; several insurance companies
demanded a design code in order to reduce losses and casualties. The ASME
Boiler and Pressure Vessel is divided into the following sections:

Those shown in the figure above are the twelve sections of the code. To
properly design a pressure vessel, it is necessary to understand Section VIII of
course, and additionally, the designer will need to be familiar with Sections II, V
and IX.
According to the scope of each section, the 12 parts can be grouped as
follows:
 Construction codes: Sections I, III, IV, VIII, X & XII
 Reference codes: Sections II, V, IX
  Rules for operating, inspection and in service maintenance: Section VI &
VII.

3. ASME BPVC Section VIII, Div.1

Scope
The extent of coverage of VIII-1 is defined in section U-1. The word “Scope”
actually refers to two terms: the type of equipment considered as well as
the geometry of the pressure vessel.
Before any design, it is recommended that the designer carefully reviews the
paragraph U-1, to determine whether the equipment can be designed according
to the code and its implications.

Code organization
Section VIII, division 1 is organized and divided according to the following:
Sub-section A: general requirements

Part UG
General Requirements for all construction methods and all materials

Paragraphs go from UG-1 to UG-137.

Since they are general requirements, they are the most important part of all.

If the goal is to create safe and technically and economically feasible designs,
the designer should be familiar with all paragraphs and figures

A simplified summary of the division of this part is as follows:

UG-4 to UG-15: Materials
UG-16 to UG-55: Design
UG-36 to UG-45: Openings and reinforcements
UG-75 to UG-85: Fabrication
UG-90 to UG-103: Inspection and tests