Virtual and Physical Prototyping Virtual manufacturing of various types of gears and validation of the technique using rapid prototype

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Virtual manufacturing of various types of gears andvalidation of the technique using rapid prototypeG. Pohit a & K. Kumar ba Department of Mechanical Engineering, Jadavpur University, Kolkata, 700032, Indiab Department of Polymer Engineering, Birla Institute of Technology, Mesra, Ranchi, India

Version of record first published: 20 Jun 2012

To cite this article: G. Pohit & K. Kumar (2012): Virtual manufacturing of various types of gears and validation of thetechnique using rapid prototype, Virtual and Physical Prototyping, 7:2, 153-171

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Virtual manufacturing of various types of gears and validation of thetechnique using rapid prototype

A method to simulate gear manufacturing process with chip formation and amethod to validate the simulation by using rapid prototyping techniques are

presented in this paper

G. Pohita* and K. Kumarb

aDepartment of Mechanical Engineering, Jadavpur University, Kolkata 700032, IndiabDepartment of Polymer Engineering, Birla Institute of Technology, Mesra, Ranchi, India

(Received 10 June 2011; final version received 17 April 2012)

Virtual manufacturing of gears is carried out to illustrate the fairly complicated gear

generation process and the associated simultaneous motions being provided to the gear

blank and the gear cutter. An attempt has been made to capture the phenomenon of chip

formation as well. Generation of various types of gears are shown employing two types of

operation, one being use of a gear hobbing cutter having multiple cutting edges. As such

validation of the virtual manufacturing technique is always a difficult task. Using rapid

prototype technology, a novel approach is proposed to ascertain the efficacy of the virtual

manufacturing process being followed. The methodology is quite general and can be used

for validation of any other virtual manufacturing process as well.

Keywords: virtual manufacturing; gear cutting; chip formation

Introduction

Virtual reality is an artificial environment that is created by

means of software in such a fashion that the user accepts it

as a real environment. The majority of the current virtual

reality environments are primarily visual experiences dis-

played on a computer screen. Virtual reality can be the

development of an imagined environment, for example, a

game or interactive story or simulation of a real environ-

ment for training and education. The growing develop-

ments in virtual reality (VR) systems have created a growing

potential for applications of VR in product design, as an

ancillary tool for engineering in simulating complicated

manufacturing processes, for development of product pro-

totypes etc. Gears are extensively used in industry for

transmission of power. In order to meet the difficult service

condition, the gear should have robust construction, close

dimensional tolerance, reliable performance and long life.

By virtue of its configurations, gear manufacturing has

become not only a specialised field but also a fairly

complicated operation. People may find it difficult to

understand the complex geometries and the manufacturing

arrangement of different gear manufacturing processes

from two-dimensional sketches generally provided in text

books. However, the clarity of the complex gear generation

process and the associated simultaneous motions of the

gear blank and the gear cutter can be represented very

efficiently with the help of the virtual manufacturing

technique. In a recent paper (Willis 1993), the state of the

*Corresponding author. Email: [email protected]

Virtual and Physical Prototyping, Vol. 7, No. 2, June 2012, 153�171

Virtual and Physical PrototypingISSN 1745-2759 print/ISSN 1745-2767 online # 2012 Taylor & Francis

http://www.tandfonline.comhttp://dx.doi.org/10.1080/17452759.2012.686696

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http://dx.doi.org/10.1080/17452759.2012.686696

art VR applied in the field of design and manufacturing

process is dealt with in a comprehensive manner.

Like any other manufacturing processes, chip formation

and chip breaking mechanism play vital roles while

simulating any kind of gear manufacturing operation.

Starting from the Merchant chip formation model in

1945, many researchers have focused their attention on

understanding the phenomenon based on simple cutting

tools having the same tool geometry and cutting parameters

along the cutting edge. However, in the case of the gear

cutting process, it is a bit more complicated as geometry

and cutting parameters differ along the cutting edges. A

considerable amount of literature is available on virtual

manufacturing of different engineering components and

chip formation during cutting operation in an open

domain. They are presented in the following section.

Balyliss and Bowler (1994) presented a seminar at CSG 94

conference on theoretic solid modelling techniques using the

VM tools like VRML (Virtual Reality Manufacturing

Language). They have developed solid modeller SVLIS

written in C�� language and used it for a 3 axis numerical

control (NC) mill. The modelling technologies had been

developed by Kimera (1993) using product and process

modelling as a kernel for a virtual manufacturing environ-

ment. In his work Kimura has incorporated significant

modelling issues like representation, representation language,

abstraction, standardisation, reuse and configuration control.

Taylor (1994) has performed work on animation. He

imported the two-dimensional (2D) drawing from the AUTO-

CAD to the 3D-STUDIO-MAX and later by using the vital

animation tool of 3D-STUDIO-MAX, has done almost all

possible arrangements of objects and subsequently imparted

motion to them. A prototype of distributed simulation

manager is developed by Iwata et al. (1995) in real-time

processing for Transmission control protocol with adaptive

spacing (TCPAP) information networks. Gooch (1998) has

developed different types of ‘spindle-bearing’ arrangements

using the modelling techniques of virtual design and manu-

facturing on a platform of 3D- STUDIO-MAX. Pradhan and

Huang (1998) developed a virtual manufacturing information

system using Java, Java Database Connectivity and a properly

selected middleware. Tesic and Banerjee (1999) have worked in

the area of rapid prototyping, which is a new technology for

design, visualisation and verification. Graphical user inter-

faces, virtual reality technologies, distillation, segregation and

auto interpretation are some of the important features of their

work. Arangarasan (2000) contributed towards virtual proto-

typing using simulation of the planned production process on

a platform of MAYA, 3D- STUDIO-MAX and VRML etc.

Bao et al. (2002) proposed a scheme for modelling a

revolving milling cutter using the virtual manufacturing

technique. Jezernik and Hren (2003) worked for a solution

to integrate computer-aided design (CAD) and virtual reality

(VR) databases in design and manufacturing processes. They

described a system for VRML model visualisation that

enables changes in the configuration file that automatically

reviews the model including the functional behaviour.

Due to the complicated tooth geometry of worm gears,

the design process is often a tedious task. The researcher

(Baykasoglu 2003) developed an integrated approach con-

sisting of numerical analysis, virtual simulation and finite

element analysis to obtain a favourable result. Choi and

Chan (2004) proposed a virtual prototyping (VP) system

that integrates virtual reality with rapid prototyping (RP)

to create virtual or digital prototypes to facilitate product

development. In addition to numerical quantification of the

simulation results, the system also provided stereoscopic

visualisation of the product design and its prototype for

detailed analyses. Yao et al. (2006) obtained satisfactory

results by representing the machining error due to the

turning operation on a virtual work piece. Luo et al. (2010)

researched behaviour simulation of a multi-axis computer

numerical control (CNC) machine tool in a virtual environ-

ment. A virtual reality machine shop environment (Bilalis

et al. 2009) was developed and integrated with a graphical

model for the calculation of quantitative data affecting the

roughness of a machined surface. A comprehensive litera-

ture review (Cecil and Kanchanapiboon 2007) has been

given on virtual prototyping research efforts in various

engineering domains, including design and manufacturing.

At Jadavpur University, research work (Roy et al. 2003,

Pattanayak et al. 2003, Pohit 2006, Kumar et al. 2007a, 2007b)

have been being carried out to simulate the gear manufacturing

processes using AUTOCAD and 3D-STUDIO-MAX as the

platform. Computer simulation was very effectively used to

view and subsequently analyse the different complicated

manufacturing processes using the concept of design centred

virtual manufacturing. Gear teeth (Pohit 2006) had been

generated by a rack cutter following the principle of gear

shaping. The work does not include the simulation of chip

formation during the cutting operation. However, in subse-

quent papers (Kumar et al. 2008), a disc type form cutter is

employed for the gear cutting operation and the formation of

chip during the gear cutting operation is also captured in an

animated view. The software was developed using MAXScript,

an object contained programming language that can be run in

the 3D-STUDIO-MAX environment.

Since the aim of the present work is also to capture the

phenomenon of chip formation using virtual reality, a few

selected publications relevant to the present work are cited

here. Arshinov and Alekseev (1976) mentioned the type of

chip being generated with respect to various materials along

with the other aspects of chip formation. Later, Khanna

(1981) illustrated the basic mechanism by which chips are

formed during the gear cutting and the various equations

governing the path, chip formation and the type of chips.

Young et al. (1987) modified the approach of Okushima

and Minato (1959) assuming the magnitude of the friction

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force for the chip produced by each element along the

cutting edge to be proportional to the corresponding uncut

chip area. Bouzakis et al. (2008) created Finite element

modeling (FEM)-supported simulation of chip formation

and flow in gear hobbing of spur and helical gears. They

created an integrated procedure for simulating the compli-

cated chip formation and flow in gear hobbing. Hortig and

Svendsen (2007) simulated chip formation during high-

speed cutting.

It has been found from the literature review that spur and

helical gears had been created using a disc type form cutter

in a virtual environment. In a particular case (Kumar et al.

2008), simulation of chip formation phenomenon during

gear cutting had also been displayed with illustrations.

However, no attempt has so far been made to simulate

relatively complicated gear manufacturing processes, for

example, creation of bevel gear or generation of gears

through hobbing. In addition, another major aspect

pertaining to the entire process has not been addressed at

all. From a visual aspect, the software seems to be quite

efficient in depicting different gear manufacturing pro-

cesses. However, users may not be able to ascertain the

degree of accuracy of the virtual gear thus produced. In

other words, whether the profile of the gear matches well

with the involute curve as has been assumed during the

virtual manufacturing operation or whether or not dimen-

sional accuracy of the product is properly maintained.

In the present paper, an attempt has been made to project

the entire procedure of spur, helical, and bevel gear

manufacturing using a form cutter in a virtual environment.

The software also includes the generation process of a spur

gear using a hob cutter. Special emphasis is provided on the

chip formation during the cutting operation except for the

bevel gear process.

Next, in order to validate the simulation process, an

arrangement is made to transform the virtual object into

reality using the rapid prototype technique. The dimensions

of these actual solid models are then compared with the

virtual gears to ascertain the accuracy of the gears produced

through the virtual manufacturing technique. The valida-

tion of the methodology and checking of the dimensional

accuracy of the object thus created by VR is achieved by

means of RP technology.

Methodology

The present work aims to develop user-friendly software to

animate different gear manufacturing processes highlight-

ing the intricacies of each technique. The number of

different gear-cutting processes is so many that it will be a

herculean task to cover the entire range of the spectrum.

Therefore, the present work is limited to the virtual gear

manufacturing of the following techniques:

(1) Creation of spur and helical gear with form milling

cutter

(2) Creation of bevel gear

(3) Generation of gear by hobbing

In general gears may have different types of tooth

profiles. The involute profile, being most common in

industry, is preferred for the present study. Before proceed-

ing to the details of virtual manufacturing techniques, it is

worthwhile to understand the principles underlying the

methods by which the gear teeth are generally produced.

Spur and helical gear using disc type form milling cutter

The detailed methodology being followed for the creation of

spur and helical gears using a disc type form milling cutter

has been described by Kumar et al. (2008). Various

simultaneous movements imparted to a gear blank and

cutter during cutting operations are also shown there. The

basic mechanism by which chips are formed during the gear

cutting operation has been illustrated with sufficient details.

These will not be repeated here. However, in the case of the

helical gear, selection of the cutter is not based on the virtual

number of teeth as has been outlined by Kumar (2010).

Bevel gear using disc type form milling cutter

The relative position and the associated motion during the

cutting operation of a bevel gear are shown in Figure 1. A

Figure 1. Schematic diagram of the cutting process of the

bevel gear showing various movements of the gear blank

and the cutter.

155Virtual and Physical Prototyping

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disc type form cutter mounted on a special milling machine

is employed for the purpose. In the present simulation, the

entire cutting cycle is made automatic, including fast return

of the tool and indexing of the blank until all the teeth are

generated. Thus, a form cutter passes through the gear

blank to remove the material forming the tooth gap.

The requisite depth of cut is introduced by adjusting the

axis of the gear blank and the axis of the cutter appro-

priately. It is achieved in a number of cuts as specified by

the user in the input data. After the completion of one

tooth of the gear, the blank rotates and the cycle repeats.

The process continues until all the teeth are cut. An attempt

has been made to incorporate all the features mentioned

above so as to make the software realistic and user-friendly.

Selection of bevel gear cutter

Bevel gears are created on a milling machine using a special

form relieved cutter. This cutter is almost identical in shape

and size to that used to cut a spur gear, but with thinner

teeth. The cutter generates a face width not greater than one-

third of the distance from the back of the gear to the apex of

the cone. The cutter tooth profile is made to suit the large

end of the gear. It should be pointed out that the selection of

the cutter is based not on the number of teeth in the bevel

gear but on the virtual number of teeth (Kumar 2010) which

a spur gear of the radius equal to the back cone radius would

have with a pitch equal to that of the bevel gear.

Milling of bevel gear teeth

The position of the gear blank on the dividing head with

respect to the cutter is shown in Figure 1. The gear blank is set

to the cutting angle by swivelling the dividing head in the

vertical plane. In order to determine the cutting angle, the

dedendum angle is subtracted from the pitch cone angle. It is

to be noted that the cutting angle is not the same angle as the

one to which the gear blank was machined in the lathe.

Three distinct operations are involved while milling the

bevel gear teeth. In the first operation, the selected cutter is

mounted on the milling machine arbor and the blank is

centred on the cutter. Then the milling machine table

is brought up to cut the whole depth as determined for the

larger end of the gear. In the second and third operations,

milling of the sides of the teeth, that were formed in the

gashing operation, is done. After cutting the first tooth,

the gear blank is indexed in the same manner as it would be

for cutting a spur gear. The remaining teeth are then gashed.

Since a bevel gear is cut with the help of milling machine

only, precaution should be taken in providing the correct

amount of offsetting of the cutter (moving the milling

machine table by a calculated amount) and subsequent

rolling of the gear blank to produce the correct profile on

the gear tooth (Figure 2). The detailed procedure of the

bevel gear cutting process has been described by Kumar

(2010) with due consideration of appropriate setting angle

and offsetting distance of the cutter.

Gear generation by hobbing

Hobbing is a process of generating a gear by means of a

cutter, called a hob, that revolves and cuts like a milling

cutter. It is basically a straight cylindrical tool around

which a thread with the same cross section as that of the

rack tooth has been helically wound. Simultaneous motions

involved during hobbing are shown in Figure 3. The

requisite depth of cut, achieved in a number of cuts as

specified by the user, is introduced by adjusting the axis of

the gear blank and the axis of the cutter appropriately.

After the completion of one full tooth and two half

consecutive teeth (one before and one after) of the gear,

the blank rotates and the cycle repeats. The process

continues until all the teeth are cut. In the software an

attempt has been made to capture all the features men-

tioned above so as to make it realistic and user-friendly.

Chip formation

There exist two types of cutting operation based on the angle

(l) between the cutting edge and the velocity vector. When

angle l�0, it is called orthogonal cutting (Figure 4) and

when 900�l�0, it is termed as oblique cutting (Figure 5).

Interestingly in the case of hobbing both types are present

since multiple cutting edges are in action. The centred hob

Figure 2. Setting up of the gear blank to the cutting angle.


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tooth removes a chip with l�0 where as the hob teeth

before and after the centre remove the chip with l"0.

The curling of the chip can be depicted in Figure 6. It is

quite clear from the figure that the chip rotation has only two

components of angular velocity, vx and vz, since vz is zero.

The expressions for angular velocities (Khanna 1981) can

be given by

xx ¼ V0 cos g0

qx0

(1)

xz ¼V0

qz0

(2)

where rzo and rxo being the components of radius of the

curling. Hence

x ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2

x þ x2y

q¼ V0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficos g0

qx0

!2

þ 1

qz0

!2vuut (3)

The resultant radius of the curling (r0), found geometrically

and can be represented as

q0 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 � sin2 g0 cos2 h

cos g0=qx0ð Þ2þ 1qz0

� 2

vuuut (4)

where

u is the angle between the v axis and x axis,

V0 is the linear velocity of the cutter at the point from

where the chip formation starts,

h0 is the angle the velocity vector makes with the y axis.

Since there are several factors that affect the chip

formation process, simulation of the hobbing operation

becomes a commendable task. In the present case, two of

the major factors have been considered. They are, namely,

the type of cutting and the mechanics of chip curl. The

cutting process of hobbing resembles a milling operation

and hence removal of material from the blank can be

depicted as shown in Figure 7.Figure 4. Orthogonal cutting (l�0).

Figure 5. Oblique cutting (908�l�0).

Figure 3. Simultaneous motion involved during hobbing.


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The intermittent limited period of engagement of each

tooth of the hob cutter with the blank makes the

characteristic form of the chip different from other

processes. The chips produced are short and discontinuous

segments. In order to simulate the chip properly, the

dimensions of the following parameters should be known:

a) The maximum undeformed chip thickness (am)

b) The undeformed chip length (l)

c) The inherent roughness height (h)

The expression (Kumar et al. 2008) of maximum

undeformed chip thickness (am) and undeformed chip

length (l) are given by

am ¼ s0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD

h� 1

�=

D

2h

�2

1 þ v

V

�2

þ v � D

V � h

s24

35 cos k (5)

and

l ¼ D

2k � d

v

V

� ffiffiffiffiD

h

r� 1 (6)

where

D is diameter of cutter, mm

h is depth of cut, mm

v is feed rate, mm/minute

V is cutter velocity, mm/minute and

l is helix angle, 8

Figure 6. Curling of the chip.


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R ¼ s0

Ds0

h i� 8Z

p

(7)

Z�number of teeth in cutter

N�cutter RPM

R�Roughness height

s0 ¼ vNZ

feed, mm/tooth

In the present work it is assumed that V �� v and (h/D)

BBB1. Hence the above equations become:

am � 2s0

ffiffiffiffih

D

s24

35 cos k (8)

l �ffiffiffiffiffiffiffiDh

p� v

2ZN(9)

R � s20

4D(10)

where

w ¼ cos�1 1 � 2h

D

�; radians

Since the cutter has multiple teeth (Figure 8) the above

equations are supplemented with the following equations to

complete all the required factors for the chip generation.

Amax ¼ Bs0 sin w1 þ sin w2 þ sin w3½ � ¼ Bs0

XZi

1

sin wi (11)

where B is the width of the blank and A �Amax when hi�h

and l�0, where A�uncut area of cross section of the chip.

The software has been created using the combined radial-

tangential feed method for the gear generation and using

the equations mentioned above.

Description of the software

The main motivation of the work is to present a virtual

environment to view different gear generation processes. In

order to capture the impact of parametric variations, it is

developed using MAXScript, an object contained program-

ming language that can be run in the 3D-STUDIO-MAX

environment with the help of user-friendly screens. It

illustrates stepwise from the creation of three dimensional

(3D) models of the gear blank along with the cutter, various

cutting motions, generation of chip during cutting opera-

tion etc. As the final output is stored in the form of frames

Figure 7. Cutting and formation of chip.

Figure 8. Cutter with multiple teeth.


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or a movie clip, the user not only visualises the gradual

forming of the gear tooth but also gets a realistic view of the

actual machining including chip formation.

From the flow chart shown in Figure 9, it is evident that

the software has been made in modular form so that further

enhancement can be carried out at a later stage if required.

A brief description of each of these modules is mentioned

below.

Start module

The start module contains all the files of the program

written in Max-script. The first operation that occurs is

resetting of the 3D-MAX-STUDIO, so that if there is any

program running, the start module would reset the software

and make it ready for the user to start working. Then on

instruction of the user it would proceed to input module.

Input module

Selection of a particular cutting process is made among the

available processes. Various cutting parameters and gear

specifications are entered through the input dialogue box.

For the benefit of the user, the software indicates the

possible upper and lower bound of each parameter so that

erroneous data are disallowed at the initial stage with a

warning message. This feature helps a beginner to run the

program independently. Unlike the actual cutting process,

modification of input data is possible at this stage by

recalling the program once more.

Figure 9. Flow chart of the software.


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Cutter generation module

Even before proceeding to simulate the cutting process,

there is a need to create the cutter first by means of which

the subsequent cutting operation of the gear blank can be

depicted by the software. Depending on the type of cutting

process, the corresponding cutter is developed as outlined in

the previous section.

Generation of disc type form milling cutter

In the case of the disc type form cutter, the cutter profile

follows a path as per the equations given below:

x ¼ �r� sin hð Þ; y ¼ r� cos hð Þ � Rd (12)

The value of u is obtained from the user defined

values of number of teeth, module and the pressure

angle of the gear to be produced; r and Rd being the

radii of curvature of the tooth profile and dedendum

circle respectively.

Once the requisite inputs are fed into the dialogue box

(also known as rollout) of the cutter, the software first

creates a core cutter body. Then the solid model of a single

tooth is created on the core body consisting of a few

planar surface patches and a NURBS sweep surface. Next,

the rest of the teeth are created with the aid of a polar

array. The final form of the cutter, thus produced, is shown

in Figure 10.

Generation of hob cutter

The hob cutter, shown in Figure 11, is classified as a rack

type cutting tool. The geometry of the cutter (Figure 12) is

such that the normal section of the cutter’s tooth edges has

the same profile as that of a basic rack cutter generally used

for generation of a gear from a gear blank. Therefore, tooth

edges are formed by three straight lines with different

pressure angles and an arc. In the simulation of the cutter,

the straight cutting edge with the largest pressure angle has

been used to generate the clearance angle. The straight edge

with the second largest pressure angle is then used to

generate the relief angle, while the edge with the smallest

pressure angle generates the radial rake angle and part of

the undercut tooth profile. The flute is then generated by

the curved cutting edge. Thus, one tooth profile of the hob

cutter is generated.

For subsequent generation of the entire cutter, two

objects are created � a cylinder and a single tooth of the

cutter rack. Utilising the parametric and associative nature

of the software, the tooth of the hob is generated from a

single cutting tooth through translation and rotation of

appropriate coordinate systems. It should be noted that the

hob cutter tooth profile depends on the cutter parameters

as specified in Figure 13. The software assembles together

the solid models of the hob tooth and the cylinder and

creates the visuals of the hob. The advantage of the

software is that the user can change the parameter values

Figure 10. Final form of the cutter.


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at any stage and re-run the virtual manufacturing module

to create a hob cutter with modified values.

Gear generation module

According to the choice of gear and cutting process

mentioned at the start of the program, the gear blank and

corresponding cutter are generated. The detailed cutting

operation of spur and helical gears using a disc type form

milling cutter has already been described by Kumar et al.

(2008). During simulation, the underlying principle being

followed for the removal of material through chip forma-

tion is also presented with an appropriate flow chart. In the

case of a bevel gear and generation of a spur gear using a

hob cutter, a similar method has been followed with the

exception that chip formation is included during the bevel

gear cutting process.

Virtual manufacturing module

In this module, a large number of still pictures of the entire

cutting operation pertaining to a particular method are

created sequentially with a slight change of position of the

objects from the previous one. Using the MAXScript

programming environment of 3D-STUDIO-MAX, a movie

file is developed from these pictures also known as frames.

For proper animation, selection of the time interval

between successive frames is vital (Kumar et al. 2008).

Sometimes it may be necessary to add special effects for

creating a proper illusion of animation.

Results and discussion

In this section, an attempt is made to present the output of

the software in a fashion that may illustrate the animation

capability of the software in the context of the virtual

manufacturing of different types of gears using various

methods.

Spur and helical gear cutting

The results obtained for spur and helical gear cutting using

a disc type form milling cutter have already been presented

by Kumar et al. (2008). In both types of gears, the same

methodology has been adopted. Figure 14(a) and (b) show

top and side views of the spur and helical gears along with

Figure 11. Hob cutter.

Figure 12. Hob cutter geometry.


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the cutter, while Figure 15 exhibits a close up view of the

chip formation during the cutting operation.

Bevel gear cutting

The cutting operation of a bevel gear is shown in Figure 16.

Frames 1 to 6 illustrate the intermittent snap shot of the

entire operation as the number of teeth formed is gradually

increased from one to the final one. Frames 7 to 9 display the

same operation with changed camera angle. In Figure 17,

gradual formation of a particular tooth is being depicted by

three consecutive frames. Here the frames are shown in close

up for better understanding of the process. The gear blank

and cutter at the beginning of the cutting operation and the

final product at the end are presented in Figure 18.

Offsetting of cutter

In the case of bevel gear operation using a disc type form

cutter, two cuts are incorporated through each tooth space

with the gear blank slightly off centre, first on one side and

then on the other, to obtain a tooth of approximately the

correct form. The gear blank is also rotated proportionately

to obtain the proper tooth thickness at the large and small

ends. Figure 19(a) and (b) illustrate the two offset positions

of the cutter, the first one captures a snap shot of the first

cut whereas the second one displays a frame during the

second cut. Once both the cuts are completed, one tooth

space of the bevel gear is finished.

Figure 13. Input dialogue windows for hob.

Figure 14. (a). Top views spur and helical gears.

(b). Side views spur and helical gears.

Figure 15. Close up view of chip formation.


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Gear cutting by hob cutter

In the present study, simulation of worm gear generation by

a hob cutter is considered. Accordingly, the software first

creates a gear blank and the hob cutter as shown in Figure

20 following the principle described in cutter generation

module. In this process, more than one tooth is produced at

a time as multiple cutting edges of the hob cutter come in

contact with the gear blank. Simulation of chip formation is

much more complicated compared to spur and helical

gears. A close up view of chip formation by the cutter is

demonstrated in Figure 21. It may be noted that multiple

chips are formed simultaneously during the cutting opera-Figure 16. Frames showing the various manufacturing

operations of the gear.

Figure 17. Cutting operation of a particular tooth.


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tion. A few frames of the cutting operation are captured in

Figure 22. Frame 8 shows a view when the cutting operation

of the worm gear is finished and the hob is in the

disengaged position.

Special effects

The software has the ability to provide special effects during

the gear cutting processes. Adding lights to a scene can help

to give it a more realistic appearance. The proper lighting

would also generate a shadow which makes the output look

real. This phenomenon can be perceived in Figure 23 where

shadows of the chips being formed are cast on the gear

blank. The cameras used in the software to get custom

views of a scene behave in many respects just like real-world

cameras. The user can select from a variety of preset stock

lenses, including 35 mm, 80 mm, and even 200 mm. The

cameras also offer complete control over the camera’s focal

length, field of view, and perspective for wide-angle or

telephoto shots.

Validation

In the previous part of the paper, different types of gears

have been created using virtual manufacturing techniques.

Capabilities of the software are displayed with illustrations.

From a visual aspect, the software seems to be quite

efficient in depicting different gear manufacturing pro-

cesses. However, users may not be absolutely sure whether

the virtual gear thus produced conforms to the actual one in

Figure 18. Gear blank, cutter and final product.

Figure 19. Offsetting of cutter for bevel gear generation.


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all respects, i.e. whether the profile of the gear matches

well with the involute curve as has been assumed during

virtual manufacturing operation or whether or not dimen-

sional accuracy of the product is properly maintained.

In order to validate the simulation process, an arrange-

ment is made to transform the virtual object into reality

using the rapid prototype technique. The database of the

output product of the software serves as the input file for

Figure 20. Models created by software.

Figure 21. Close up view of chip formation.

Figure 22. Different frames of gear hobbing.


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the RP machine and plastic gears are manufactured. The

dimensions of these actual solid models are then compared

with the virtual gears. Various rapid prototyping (RP)

processes have been developed and used in the past decade.

Primary criteria for the selection of the RP technique is

based on the fact that built gears will have the optimum

combination of strength, dimensional accuracy and surface

finish. It has been ascertained that Fused Deposition

Modelling (FDM) is most suited for the present case

(Kumar 2010).

The detail of the validation procedure is mentioned in the

next section.

Exporting virtually manufactured product to the FDM

machine

Figure 24 represents the steps being followed for conversion

of the virtual products into real objects using the FDM

machine. Proper transfer of data from the CAD domain to

the RP system is a crucial part.

In the present case, the models are created in the 3D-

STUDIO-MAX environment which is also a standard CAD

software. The output of the software creates models devel-

oped in a 3D environment with ‘max’ extension. This is then

converted as a ‘stl’ extension. It should be emphasised that

in order to retain the shape and other design properties, the

model must be saved with proper mesh density; the higher

the density, the lower the mesh size will be, however

preparation time would be more. The model contour

becomes deformed in the case of a lower mesh density.

Processing in FDM

Once the input parameters, say layer thickness, orientation,

model fill and support type are fixed, the model is packed

and the layers with support are first visualised even before

Figure 23. Effects of light and shadow to the output.

Figure 24. Data transfer between the CAD and the RP

system.

Table 1. A comparative study between the virtual manufac-tured gears and the RP gears.

Sl. No. Parameters

Ideal

values

Average values of gears

manufactured using FDM

SPUR GEAR No. of teeth 24 24

Outside diameter

(mm)

97.6 97.65

Root diameter (mm) 81.32 81.39

Inside diameter

(mm)

22.27 22.25

Tooth thickness

(mm)

8 8.34

HELICAL

GEAR

No. of teeth 24 24

Outside diameter

(mm)

97.91 97.94

Root diameter (mm) 81.66 81.69

Inside diameter

(mm)

22.2 22.23

Tooth thickness

(mm)

8 8.2

BEVEL

GEAR

No. of teeth 24 24

Taper angle 520 510 45?Major diameter

(mm)

73 72.95

Root diameter at

bigger end (mm)

60 60.20

Root diameter at

smaller end (mm)

42 42.30

Tooth thickness

(mm)

18.75 18.76

Figure 25. Spur gear developed using FDM.


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actual ‘printing’. After being satisfied with the structure and

the individual layers, instruction may be given for final

‘printing’. The product with the support is then placed in an

ultrasonic tank (accessory of the machine) fitted with a

heater and the soluble support system dissolves leaving

behind the model in its final form.

Validation of the virtual manufacturing process

In order to validate the output of the software, and hence

the virtual manufacturing technique being proposed in the

paper, all types of gears described earlier were produced

using FDM. For each type of gear, three pieces were made.

Figures 25 to 27 show gears made of a plastic type of

material.

Nominal dimensions of these gears were measured and

the average values were obtained. Since the module and

number of teeth of these gears are known, dimensions of

the corresponding ideal gears can be obtained easily.

A comparative study is presented in Table 1. It has been

observed that deviation in the dimensions of the manufac-

tured gears is very close to their ideal values. It is evident

that the output of the FDM software is fairly accurate so

far as dimensional accuracy of the gears produced is

concerned.

However, in the case of gears, it is equally important to

ascertain correctness of the involute tooth profile actually

being formed during the virtual manufacturing process.

Here also assistance rapid prototype is sort for and top view

of the spur gear produced by the software is projected on

the top view of spur gear model developed in FDM.

A portion of the projection view is also enlarged for better

assessment. They are shown in Figure 28(a) and (b)

Figure 26. Helical gear developed using FDM.

Figure 27. Bevel gear developed using FDM.

Figure 28. Superimposition of the top view of the virtually

manufactured spur gear over the RP product.


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respectively. The RP gear is visible as a dotted object

whereas the outline of the gear produced by the software is

represented by a black line. From these figures, it is

observed that the output profiles of both systems closely

match with one another.

In the case of helical gears, it is essential to ascertain the

accuracy of the involute profile all along the face width also.

However, due to the presence of a helix angle, the top view

only gives comparison at one face of the gears. Therefore,

two of such projection views are taken along the face width

of the helical gear � one at the top face and another at the

bottom face. They are shown in Figures 29 and 30,

respectively. From these figures, it may be concluded that

the tooth profile obtained by the software closely matches

that of the model developed in RP.

The above test ensures that the gear tooth profile

produced by the software closely follows the profile

produced by the RP technique. However, it does not

mean that the tooth profile is actually following the involute

curve. Using the input parameters of the spur gear, a 2D

view of the spur gear is developed in AUTOCAD. Tooth

profile of this gear is assumed to be of involute profile with

a high degree of precision. Now this AUTOCAD view is

superimposed on the virtually manufactured gear obtained

from the software. They are shown in Figure 31 where the

red coloured gear is drawn using AUTOCAD and the blue

one is obtained from the output of the virtually manufac-

tured gear. It is evident from the figure that the tooth

profile of the virtually manufactured gear matches fairly

well with the involute profile.

The modelling process is the result of a sequence of

abstractions and approximations (idealisation, surface

approximation, and digitisation). As a consequence,

drafting and modelling software like AUTOCAD, PRO

Engineer, CATIA etc., models the real objects to different

degrees of precision. In the case of 3D�STUDIO-MAX,

which is basically animation software, although circles and

curves are approximated as polygons, since the dimensions

of the sides are very small the error may be neglected for

all practical purposes. This is evident from the super-

imposed view of the gear drawn using AUTOCAD on the

virtually manufactured gear obtained from the software

(Figure 31).

Figure 29. Superimposition of the top face of the virtually

manufactured helical gear over the RP product.

Figure 30. Superimposition of the bottom face of the

virtually manufactured helical gear over the RP product.


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Conclusion

The virtual manufacturing technique is successfully em-

ployed to simulate generation of different types of gears

starting from the creation of a gear blank and the gear

cutter. An attempt is made to capture the complex

phenomenon of chip formation during the cutting

operation along with the associated simultaneous motion

being provided for different types of gear generation

processes. Software is developed in a modular form to

accommodate additional features if required at a later

stage without disturbing the original software. Manufac-

turing processes of three different types of gears, namely

spur, helical and bevel gears have been simulated in a

virtual environment using a form milling cutter and gear

hobbing.

The software has the capacity to create movie files for a

better understanding of a complex manufacturing process

and hence can be an efficient learning aid as well. The

software is also provided with a dialogue box to check for

the insertion of inadequate data by giving a warning

message and assist the user to take necessary corrective

measures if required.

However, the novelty of the present paper is to ascertain

the accuracy of the virtual manufacturing technique being

implemented for gear manufacturing processes. In order to

validate the simulation process, an arrangement is made to

transform virtual objects into reality using the rapid

prototype technique. The dimensions and the tooth profiles

of these actual solid models are then compared with the

virtual gears. It has been observed that dimensions of the RP

gears matches quite well with their ideal values obtained

from software products. This is true for tooth profile as well.

As such validation of the virtual manufacturing techni-

que is always a difficult task. The proposed methodology

can be employed to ascertain the efficacy of any virtual

manufacturing process.

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Documents

Virtual and Physical Prototyping Virtual manufacturing of various types of gears and validation of the technique using rapid prototype