Lab 2

LAKEHEAD UNIVERSITY

DEPT OF MECHANICAL ENGINEERING

MANUFACTURING PROCESSES &

PRODUCTION SYSTEMS

ENGI – 0537

EXPERIMENT #4

KAILASH BHATIA

LAB INSTRUCTOR

MANUEL DE LA FUENTE MORALES

STUDENT NUMBER 0480955

OCTOBER 22, 2010

i | P a g e

ABSTRACT

This lab report describes the theory, procedure, calculations and

measurements required in order to cut a spur gear out of a blank.

A number of calculations were made once the outside diameter and the

material of the blank and cutter were known in order to set up the vertical

milling machine used to cut the teeth of the spur gear.

The diametral pitch and pressure angle required were given as 10 and 14½

respectively, the outside diameter of the blank was measured at 1.703 in,

then calculated spindle speed was 138.9 rpm, and the feed rate was 1.75

in/min.

The cutter used was only good for up to 13 teeth but was used anyway

since the 15 tooth cutter was missing. The cutter material was High Speed

Steel (HSS), medium carbon steel. It was lubricated with an air and oil mix

of 1 ml per minute. A vertical milling machine was used along with a

dividing head and a dead head point. Since the job was not considered as

heavy duty conventional type cutting method was used.

After the gear was cut, it was then inspected. The calculated cordal

measurement was 0.4643 in, and the actual was 0.468, the difference was

attributed to the wrong cutter being used. The tooth thickness was

according to the calculated 0.157 in.

An engineering drawing for the gear was produced.

ii | P a g e

TABLE OF CONTENTS

ABSTRACT .................................................................................................................................... i

TABLE OF CONTENTS .............................................................................................................. ii

LIST OF FIGURES ........................................................................................................................ ii

INTRODUCTION ........................................................................................................................ 1

THEORETICAL BACKROUND ................................................................................................ 2

GEARS ........................................................................................................................................................ 2

FORM MILLING .......................................................................................................................................... 5

DIVIDING HEAD ......................................................................................................................................... 7

CALCULATIONS ........................................................................................................................ 9

EXPERIMENTAL FACILITIES AND PROCEDURES .......................................................... 11

APPARATUS ............................................................................................................................................. 11

PROCEDURE ............................................................................................................................................ 12

SET UP ................................................................................................................................................. 12

GEAR MILLING ..................................................................................................................................... 14

INSPECTION ......................................................................................................................................... 15

EXPERIMENTAL RESULTS AND DISCUSSION ................................................................. 16

CONCLUSION ........................................................................................................................... 16

LIST OF FIGURES

Figure 1 – Terms used in gears .................................................................................................. 2

Figure 2 Convex and involute cutter and work piece ............................................................ 5

Figure 3 - Climb and conventional milling .............................................................................. 6

1 | P a g e

INTRODUCTION

The objective of the experiment is expose students to cut a spur gear on a

vertical milling machine using a standard dividing head, while calculating

cutting speeds and feeds. An inspection of the gear was performed and

AutoCAD drawing made.

Gears are an important part of our society since they are used to transmit

and control power and motion in a reliable way. Gears are used in our

everyday lives from automobile transmissions, bike sprockets, blind

mechanisms, computer mouse’s, watch mechanisms, etc.

In this experiment a vertical milling machine was used, which is a

machine used for the shaping of metal and other solid materials1. Milling

machines are very important in the engineering world because they allow

us to create custom parts with great flexibility.

A dividing head was also used which is a work holding device bolted on

the machine table. The work may be mounted on a chuck fitted on the

dividing head spindle and supported between a live or dead center. It is

principally used for dividing the periphery of a work piece in equal

number of divisions for machining equally spaced slots, or groves2.

1 http://www.mechanicalebook.com/definitions/defM1.htm 2 http://hubpages.com/hub/Milling-Machine-Attachments-and-Accessories

2 | P a g e

THEORETICAL BACKROUND

GEARS

Gears are toothed wheels that engage another toothed mechanism in

order to change the speed or direction of transmitted motion and torque.3

Gears have a lot of specific dimensions due to their complicated shape.

The sides of the teeth are described mostly by involute or cycloidal curves

that mesh in a tangent with the opposing tooth to provide the desired

effect. The following figure shows the common terms used to describe

gear terms.4

3 http://wordnetweb.princeton.edu/perl/webwn?s=gear 4 A textbook of Machine Design, R.S. Khurmi and J.K. Gupta, 14th Ed.

Figure 1 – Terms used in gears

3 | P a g e

The material used for the manufacture of gears depends upon the

application, strength and service conditions like wear, noise etc. The gears

may be manufactured from metallic or non-metallic materials. The

metallic gears with cut teeth are commercially obtained in cast iron, steel

and bronze. The non-metallic materials like wood, rawhide, compressed

paper and synthetic resins like nylon are used in gears specifically for

reducing noise.5

The number of teeth of a gear per inch of its pitch diameter is called

diametral pitch (DP). It is related to the number of teeth and the outside

diameter of the gear as follows.

�� =� + 2

��

If we are given the DP and the outside diameter of the gear blank we can

calculate the number of teeth by rearranging the equation above.

� = ��� × ��� − 2

Pressure angle is the angle between a tooth profile and a radial line at its

pitch point. In involute teeth, the pressure angle is often described as the

angle between the line of action and the line tangent to the pitch circle.

5 A textbook of Machine Design, R.S. Khurmi and J.K. Gupta, 14th Ed.

4 | P a g e

Standard pressure angles are established in connection with standard

tooth proportions6. In the imperial or English system, the two standard

pressure angles are 14½° or 20°.

There are various ways gears are manufactured, the most popular one

being hobbing, since it is relatively quick and inexpensive, other types of

gear manufacturing include gear milling, shaping, broaching, casting and

injection moulding.

6 Machinery’s Handbook, Industrial press, 28th edition, page 2033

5 | P a g e

FORM MILLING

The manufacturing method used on this lab was form milling which is the

process of machining special contours composed of curves and straight

lines, or entirely of curves, at a single cut. This is done with formed

milling cutters, shaped to the contour to be cut, or with a fly cutter ground

for the job7. The following image shows how the convex shape cutter

attached to the spindle cuts the work piece, in our case an involute shaped

cutter was used8.

The parameters required to successfully cut the material are based on the

material properties of the cutter and the work piece. These parameters are

spindle speed in rpm, and feed rate in inches per minute. Note that the

first of the two speeds is an angular speed and the other is linear speed.

7 http://www.tpub.com/content/armyordnance/od16448/od164480048.htm 8 Image modified to match our setup. Convex cutter shown.

Figure 2 Convex and involute cutter and work piece

6 | P a g e

The spindle speed was calculated using the relationship below.

����������� ��� ������ � 12 ������� � � 12 � � �

���������� �

11.375

����������� � � !

The feed rate is based on the surface finish required, most machinists will

perform a rough quick pass to remove most of the material and then do a

finishing pass to create the surface finish and tolerances required.

The rough pass feed rate is between 0.005 – 0.020 inches per revolution

and the finishing feed rate is between 0.001 – 0.005 inches per revolution.

The table feed rate was calculated the relationship below.

�������� � ������� �� �������������� � ����������������� � �� ����������

There are two ways in which the material is fed into the cutter; it is either

in the direction of the cutter or against the cutter, these are called climb or

conventional milling respectively as shown in the figure below9.

9 http://engineering.dartmouth.edu/mshop/facilities/mill_vertical.shtml

Figure 3 - Climb and conventional milling

7 | P a g e

In conventional milling the work is fed against the cutter which

compensates for backlash in the table. Each tooth of the cutting tool starts

its cut in clean metal, prying the material off the work.

Climb milling will give a better quality of work and is better suited for

thin pieces of material since the cutting action forces the work into the

table. This method should not be used on hard materials and the machine

has to be rigid so backlash cannot occur. The cutting tool will also last

longer using climb milling as long as good tool pressure is maintained.10

DIVIDING HEAD

An indexing head, also known as a dividing head or spiral head, is a

specialized tool that allows a work piece to be circularly indexed; that is,

easily and precisely rotated to pre-set angles or circular divisions.

Indexing heads are usually used on the tables of milling machines. They

are commonly used to machine the flutes of a milling cutter or reamer or

the teeth of a gear. The tool is similar to a rotary table except that it is

designed to be adjustable through at least 90°. Most adjustable designs

allow the head to be tilted from 10° below horizontal to 90° vertical, at

which point the head is parallel with the machine table. 11

10 http://engineering.dartmouth.edu/mshop/facilities/mill_vertical.shtml 11 http://en.wikipedia.org/wiki/Dividing_head#CITEREFBurghardt1922

8 | P a g e

The work piece can be held with a collet or a chuck in the indexing head,

or between centers with the help of an accompanying tailstock with a live

or dead center point.

In this lab a chuck in the indexing head and a dead center point on the

tailstock were used. A dead center was preferred because it is fixed and as

the machine is cutting it will not have any slack or adjustment and will

allow a true straight cut. Lubricant grease is used on the dead center point

in order for the point not to seize in place and allow for rotation and

removal.

A standard dividing head will usually have a worm gear that turns the

head with a ratio of 40:1, which means that 40 crank turns will produce

one full revolution of the chuck.

An indexing plate is used along with the dividing head. An indexing plate

has a definite number of equally spaced holes along a diameter, it is used

to measure or divide the crank rotation into specific and accurate steps.

It is important to note that while turning the crank one must be careful not

to over crank it past the required point because while trying to turn the

head backwards the backlash of the gear will create some play and it will

not be as accurate. If this happens it must be turned backwards enough

that when turned forwards again the backlash will be absorbed and pure

rotation will occur.

9 | P a g e

CALCULATIONS

Some specifications for the gear were given, such as the outside diameter

of the gear and the diametral pitch the gear needed to have.

The outside diameter was 1.700 in and the diametral pitch was 10

Using the equation from the theory section the number of teeth on the

gear was calculated.

� = �10 × 1.700� − 2 = �����

The surface speed of the cutter was known and with it the spindle speed

was calculated.

����������� = 100 �� ��� × 12 ���ℎ��� � × 1

2 × � �������� ×1

1.375 ������ℎ�� = ���.����

The feed rate or movement of the table was calculated knowing that only

one rough pass was going to be used to cut the gear.

������� = 0.0126 � ���ℎ������������� × 138.9����� = �.�� � !"#$%

& !'($�

Every time a cut is performed the gear must be turned one 15th of a turn.

To do this the dividing head is used, which has a turn ratio of 40:1,

therefore to find out how many turns of the crank the following relation

was used.

)�����*�ℎ�����+ =40

� =40

15= ,�

�-./0

10 | P a g e

To make sure only two thirds of a turn is made the indexing plate is used,

the circle with 27 holes was used because it is divisible by three, and

therefore the following relation was used.

2

3����+ × 27

ℎ��������+ = �1#23$%

This means that once the groove is cut, the crank must be turned two full

turns and then 18 holes must be counted on the indexing plate.

The full depth of the cut was calculated using the equation from the

Machinery’s handbook as follows.

��4�ℎ�*����ℎ =1

�� +1.157

�� =2.157

10= 5.,��� !"#$%

11 | P a g e

EXPERIMENTAL FACILITIES AND PROCEDURES

APPARATUS

The equipment used in this experiment consisted of a gear blank, Vernier

callipers, dial gages, vertical milling machine, dividing head, indexing

plate and gear tooth cutter.

The gear blank was already made by first year students in their respective

lab. It was made to have an outside diameter of 1.700 in and a face width

of 0.875 in.

The vernier calliper used was digital, it was used to obtain the true outer

diameter and face width of the gear after the gear was cut it was used to

inspect the gear by taking the cordal measurement. The precision of the

digital display is of one thousands of an inch or a hundredth of a

millimetre.

The dial gage was used to set up the work piece on the machine so that

there is a true and accurate movement of the cutter as it moves through

the gear blank.

The dividing head was used along with an indexing plate to hold the

blank and turn it specifically the right amount for the cutter to cut in

between the teeth.

12 | P a g e

The HSS involute cutter was used in order to cut the grooves or the sides

of the teeth, it was chosen so the gear would have 14½° pressure angle.

PROCEDURE

SET UP

1. Setup the dividing head and the tailstock with a dead head point

on the vertical milling table and secure it.

2. Attach the cutter to the spindle.

3. Lubricate the gear blank with grease on the end where the dead

head point will be.

4. Insert the gear blank into the chuck and center the dead head point

on the other end and secure it in place.

Note: the next three steps are made in order to ensure the gear blank is

properly aligned with the spindle head in all dimensions.

5. Attach the dial indicator to the spindle head and place the sensor

tip on the blank’s face, then turn the crank on the dividing head.

The dial should not move or the movement should be very small

(ie, less than one thousand of an inch). This ensures the chuck,

blank and tailstock is centered.

6. Place the sensor tip of the dial indicator on the side of the gear

blank and move the table in the direction of the cut. Once again the

13 | P a g e

dial should not move very much, this ensures that the depth of the

cut will remain consistent throughout the entire cut.

7. Place the sensor tip on top of the gear blank and move the table in

the direction of the cut. This check will ensure that the cut is

aligned with the centerline of the blank.

Note: If any of the three previous tests are not passed move your

set up to align the work piece.

8. Using a vernier height gage measure the distance from the table

surface to the top of the gear blank (8.720 in) then subtract the

radius of the gear to find the center (8.720 – 0.8515 = 7.8685 in)

9. Measure the distance from the table surface to the top of the cutter

(8.05 in), and subtract half the thickness of the cutter to find the

center of the cutter (8.05 – (0.360/2) = 7.87 in). In our case no

adjustment was necessary.

10. Set the stops on the table so that the cutter will not run into the

chuck or the tailstock. This will also allow us to save time because

we can use the fast return and not be worried about damaging the

equipment.

11. Apply a quick spray of blue tool dye on the gear blank. This allows

us to find the surface of the blank.

14 | P a g e

12. Set machine spindle speed at 140 rpm since it is the closest to the

calculated required speed, in reality we would like to set it up

lower than required if it is not an exact match.

13. Set feed rate on the machine, closest to the calculated speed.

14. Start the spindle and bring the cutter slowly in towards the gear

blank until it starts shaving the paint off.

GEAR MILLING

Note: Safe standard practices dictate that chips should always fly away

from the operator (Conventional milling). Safety glasses must be worn,

chips should be brushed from the table and not blown with compressed

air, and cutters should be handled with a rag.

15. Turn on the air with lubricant that is already set up at one drop per

minute. Lubricant helps keep the cutter sharp and keeps the

temperature of the work piece low enough to prevent change of the

properties (hardness) due to the heat.

16. Look at the digital coordinate on the display and move the cutter

0.2157 inches since we will only cut it in one pass.

17. Now start cutting the gear by setting the clutch into gear at the

designated feed rate.

18. Verify that the chips are not discoloured and overly hot.

15 | P a g e

19. Once the table has stopped disengage the clutch and return the

cutter to starting position using a fast moving speed.

20. Rotate the gear blank, by turning the crack handle on the dividing

head 2 full turns and 18 pin holes on the indexing plate. A template

is in place to prevent counting 18 holes every time.

21. Repeat steps 17-20 until the 15 teeth are cut.

22. Remove the gear from the machine and safely turn it off.

INSPECTION

23. Inspect the gear’s cordal measurement using the vernier calliper by

measuring across two teeth at the pitch diameter and compare it to

theoretical values from the Machinery’s Handbook.

24. Measure the tooth thickness using the gear tooth vernier calliper

and compare it to theoretical values.

25. Make an AutoCAD engineering drawing of the produced gear.

16 | P a g e

EXPERIMENTAL RESULTS AND DISCUSSION

The tooth thickness according to the machinery’s handbook was 1.570 in

and the measured one match, meaning the dividing head was used

properly.

The cordal measurement according to the Machinery’s handbook was

0.4643 and the measured result was 0.468, this is due to the fact that we

used the cutter that was good for up to 13 teeth and our gear had 15.

Some burring occurred due to the fact that conventional milling was used

and that the cutter was used to the full depth of the tooth, by the final cuts

it was pushing some of the material instead of cutting. More lubrication

and a two-step process would have helped to get a better surface finish.

CONCLUSION

The experiment was successful in exposing the students to the actual

manufacturing of a spur gear using a vertical milling machine and a

dividing head. It also exposed us to the different calculations required for

proper machining and set up of the work piece before even starting to cut.

Safe practices were always followed and a gear was produced along with

AutoCAD engineering drawings.