experimental and numerical investigation of external...

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:03 72

175503-8484-IJMME-IJENS © June 2017 IJENS I J E N S

Experimental and Numerical Investigation of External

Geneva Wheel Mechanism with Four Slots

Manufacturing from Polycarbonate Material Ali Abdul Hadi Tuama

Baghdad University/Engineering College/Mechanical Department

Email: [email protected]

Dr. Majid Habeeb Faidh-Allah

Asst. Prof. (Applied Mechanics)

Baghdad University/Engineering College/Mechanical Department

Email: [email protected]

Abstract-- With a view to achieve the aim of this search, the

experimental works are divided into three parts. The first part of

the experimental work described the manufacturing of Geneva

wheel mechanism and photo-elasticity rig made of (ACRYLIC

FIBERS) used in the photo-elasticity test to apply appropriate

force, fixed Geneva wheel in the test device and to calculate the

distribution of stresses in the areas where a failure occurs. The

second part was the calibration of band factor of a polycarbonate

material type (PSM-5) by pure bending four points because this

material over time is damaged and also affects storage. The third

part of the experimental work described the manufacturing of

Geneva wheel using photo-elastic material (PSM-5) to calculate

the stresses in the model and compare them with Ansys results.

The photoelasticity method is used for measuring the maximum

stress in the Geneva wheel for a different load. The results

showed that the 2-D and 3-D FE model using ANSYS software

gave a very good prediction for the principal stresses in Geneva

wheel. When the results of the 2-D and the 3-D FE model

compared with the results of photoelasticity technique, the

absolute maximum error percentage was (7.04%) and (7.33%)

with respect.

Index Term-- Geneva wheel mechanism, four slots, mechanical

properties, Ansys version 16.1, photo-elasticity technique.

1. INTRODUCTION

Geneva wheel applied in both low and high-speed

machinery, packaging, conveyors, moving films in motion-

picture projection, automatic machinery and automated liquid

filling of bottles. Some researches deal with the Geneva wheel

as a design such as J. Lee and F. Huang [1]. They proposed a

systematic design procedure of curved slots Geneva

mechanisms. They depend on the theory of conjugate surfaces

to present mathematical equations for the pressure angle, slot

profile and cutter’s location for industrialization. For

evaluating the combined structural performance and

kinematics of the mechanism, they established the degree of

wear and maximum contact stress as the "performance index".

They investigated a variety of different design parameters the

performance indices. The indices were used as the objective

function in order to find the optimum design. Iulian Stanasel

and Florin Blaga [2], used an integrated virtual prototype

CAD_CAE_CAM to present the design and implementation of

digital manufacturing. They determined the dimensions of the

elements in the Geneva mechanism and they used the data in

the CAD application for making 3D models. They transferred

the new model to the CAM module that performs the tool

paths. Finally, they obtained the CNC program for the

implementation of a machine tool with iTNC 530 Heidenhain

equipment. Jung-Fa Hsieh [3], proposed a simple method for

the design of curved slots Geneva mechanisms. Using

conjugate surface theory, he proposed a new approach to

derive an analytical description of the curved slots profile

without and with offset feature. Also, he presented analytical

formulae for the principal curvatures of the curved slots and

the pressure angle of the Geneva mechanism. He demonstrated

the effectiveness of an appropriate offset angle in eliminating

the singular points and double-points on the profile of curved

slot. Finally, he fabricated a Geneva mechanism for

demonstrating the feasibility of the proposed approach. David

B. Dooner et al. [4], studied a kinematic of a Geneva

mechanism and a gear train for achieving sporadic motion.

They eliminated using the acceleration, jump at the beginning

of motion and its final stage in Geneva wheel. They replaced

the circular path for the driving pin with a classical Geneva

wheel drive with an epitrochoidal course. Popkonstantinovic

et al. [5], presented at several 3D computer models of the

Maltese cross (Geneva) mechanism. They examined Maltese



cross mechanisms project contain using three types of a 3D

computer model of the Maltese cross mechanism. The aim of

their study was developing the present and acquiring novel

skills and abilities of solving a mechanical systems computer

modeling problem. Also, they presented "the importance of

the strong co-relation among classical mechanical engineering

and up to date modern methods of optimization and modeling

using computer graphics which play a key role in the project.

Han Jiguang Yu Kang [6], presented the analysis method of

the combined Geneva mechanism. If the groove number of the

Geneva wheel is a constant the kinematics coefficient of the

Geneva mechanism is a stable for both inner and outer Geneva

mechanism. The elliptic crank using as the drive cranks of the

Geneva wheel is equivalent to the mechanism that contains a

variable length and speed along the elliptical moving crank.

Therefore the kinematics coefficient of the Geneva mechanism

is able to be changed. The combined Geneva mechanism is put

forward based upon the kinematics coefficients. They

proposed the calculation method of the extreme kinematics

coefficient. In the end, they gave the design example.

This search has studied the experimental and numerical

solutions for the design of four slots external Geneva wheel

mechanism under different conditions. The experimental work

used the photo-elastic method in order to predict the stresses

in Geneva wheel. While the ANSYS software used for

numerical prediction of stresses in Geneva wheel. Finally, the

comparison between the experimental and numerical results

was made.

2. EXPERIMENTAL WORKS

The experimental works are divided into three parts. The

first part of the experimental work described the

manufacturing of Geneva wheel mechanism and photo-

elasticity rig made of (ACRYLIC FIBERS) used in the photo-

elasticity test to apply appropriate force. The second part was

the calibration of band factor of a polycarbonate material type

(PSM-5) by pure bending four points. The third part of the

experimental work described the manufacturing of Geneva

wheel using photo-elastic material (PSM-5). The photo-

elasticity method is used the Photo-elasticity machine test

shown in Figure 1. The parts of the photo - elasticity machine

were shown in Figure 1 and Table 1. The dimension of this

unit is length 750 mm, width 400 mm and height 550 mm.

Approximate weight is 15 kg and the power supply is 220 v

with 50 Hz monophasic and Structure of anodized aluminum,

The light source, two fluorescent tubes of 30 cm and 8 w.

Double effect polarizing filters (linear polarization and

circular Polarization) of 30 x 30 cm and protected by

methacrylate sheet. Double effect polarizing glasses.

2.1 Geneva wheel Mechanism and Photo-elasticity Rig

The static experimental investigation of this work has been

performed on test rig which is manufactured from an

ACRYLIC SHEET material design by AUTOCAD Software

and cutting by (CNC) MACHIN as shown from Figure. 2 and

Figure 3. And design mechanism for four slots external of

Geneva wheel by same material of rig (ACRYLIC SHEET).

The purpose of the mechanism to provide applied forces on

slot of

Geneva with a different crank angle (α) is (0, -10, -13,-45) and

Geneva angle (β) as indicated in Figure 4.

2.2 Calibration of Band Factor

The constant Band factor (ƒ) is specification of the material,

independent of its geometric shape. Then, in order to

determine it is just necessary to use a test piece of determinate

form and stratify an adequate head in such way that the

tensions status at any point is known. Maxwell equation 1, to

determine the difference in the principal stresses. [E.J. Hearn

vol. 2].

σ1 – σ2 = (n ƒ) / h (1)

Where:

σ1 and σ2 are maximum and minimum principal stresses,

respectively.

n: is a number of fringes.

ƒ: is the band factor.

h:is the thickness of the prototype.

There are several methods to find band factor we used four

bending .In pure bending test, to calculate the band factor (ƒ)

we use this method called four point bending experiments in

the Laboratory in University of Kufa / College of Engineering

/ Mechanical Engineering Department as shown in Figure 5,

and 6 and Table 2, also we used the following equations:

σX (y) = 6P a2 y / h w3 (2)

ƒ = (6P a2 / w2). [|Y| / n(y)] (3)

Where a2, y, h, w2, and w3 are the dimensions as shown in Fig.

(5).The moment of inertia of the cross-section area of the

beam under four points bending is:

I = (h. w 3) /12 (4)

The maximum bending moment is:

M = P.a2 (5)

The maximum principal stress is:

σ1 = (M. y) / I (6)

The summary of calculation according to eqs. 2 and 3 is

illustrated in Table 3.

2.3 Photo-elastic Model of Geneva Wheel

The photo-elastic model made of a transparent material that

is doubly refracting under loads such as polycarbonate

material type (PSM-5) with thickness (6.5 mm) is used. The

mechanical properties are shown in Table 4. The Geneva



wheel model should be made carefully from the transparent

material according to the mentioned dimensions in Table 5 by

drawing in the AUTOCAD Software to export and cutting by

(CNC) machine as shown in Figure. 7 with a scale of 1:1.

3. NUMERICAL ANALYSIS by ANSYS

This section deals with the finite element modeling of the

Geneva wheel. The finite element models of Geneva wheel are

built with ANSYS Software version 16.1. The element used in

ANSYS is The SOLID187 element is a higher order 3-

Dimensions with ten node element (see Fig. 9). Also, element

use in ANSYS is The PLANE183 is a higher order 2-

Dimensions with eight or six node element (see Fig. 10). This

component has a quadratic displacement conduct and is used

in irregular. Every node in this element has three degrees of

freedom. These grades of freedom are transitioning in the

nodal x, y, and z directions. Two models are used, the first

model is a two-dimensional model and the second one is a

three-dimensional model. The geometry and dimensions of the

Geneva wheel, which used in this work, were taken from the

optimization work of four slots Geneva wheel achieved by

Bushra R. Al-Juwari [7]. The dimensions of the external four

slots Geneva wheel is shown in Figure 11, and Table 5. The

Geneva wheel is drawn by AUTOCAD 2016 Software.

4. PHOTO-ELASTIC TECHNIQUE RESULTS

The dimensions of the Geneva wheel used in this work

were mentioned in Table 5 and these dimensions were the

optimum dimensions that founded by [7]. In other hand, the

material fringe constant for the Polycarbonate (PMS-5) was

calculated in chapter five (f = 11.643KPas/fringe/m) and the

mechanical properties of Polycarbonate (PMS-5) are: modulus

of elasticity = 2.7 GPA. And the Poisson Ratio = 0.36 (from

the data sheet of Polycarbonate (PMS-5)). Experimentally, the

stress distribution in Geneva wheel manufactured by

Polycarbonate (PMS-5) can be shown in Figure. 12. Different

applied load in different crank angle were used to get the

suitable photo-elastic image and larger number of fringes in

order to make the calculation simple. In the same way, two

and three-dimensional finite element models of Geneva wheel

were built using ANSYS software (see Fig. 13 and Fig. 14). In

this numerical model, the mechanical properties of

Polycarbonate (PMS-5) were used in order to compare

between the experimental model (Photo-elastic model) and

numerical model (ANSYS model). The principal stress (σ1) of

experimental and theoretical results was summarized in Table

(6). The error percentage comparison between experimental

and 2-D and experimental and 3-D FE model was illustrated in

Table (7). From these results, the 2-D and 3-D models gave a

very good prediction for calculating the principal stress (σ1)

and stress distribution in Geneva wheel for different crank

angles and different loads.

5. CONCLUSIONS

The 2-D FE model using ANSYS software gave a very

good prediction for the displacement and stresses in

Geneva wheel. When the results of the 2-D FE model

compared with the results of the photo-elasticity

technique, the absolute maximum error percentage was

(7.04%). And the 3-D FE model using ANSYS software

gave a very good prediction for the displacement and

stresses in Geneva wheel. When the results of the 3-D FE

model compared with the results of the photo-elasticity

technique, the absolute maximum error percentage was

(7.33%).

Acknowledgements:

I would just like to thank the Departments of

Mechanical Engineering, Baghdad University and

Department of Mechanical Engineering, Kufa

University for supporting tests facilities of this study.



Fig. 1. Photo-elasticity machine test.

Table I Parts of the Photo-elasticity machine.

Number Attributive

1 Framework

2 Translucent spread plate

3 Double effect polarizing filters (linear polarization and circular polarization)

4 Double effect analyzing filters (linear polarization and circular polarization)

5 dial gauge

6 Ten screws to press the test piece correctly

7 Clamps and screws to fasten the test pieces

Fig. 2. 3D AUTOCAD software Geneva mechanism. Fig. 3. Manufacturing of rig test.

Fig. 4. Mechanism of Geneva wheel.



Fig. (5): Pure bending four points. Fig. 6: Calibration of polycarbonate and numbered (n).

Table II

Details of pure bending calibration.

Parameter Symbol Value Unit

Force on sample p 95 N

Bending moment M 1900 N.mm

Moment of Inertia I 4000 mm4

Length a1 20 mm

length a2 20 mm

Width w 20 mm

Thick h 6.5 mm

Length L 200 mm

Table III

Calculation material fringe value.

Fringe

No.

Average distance

y (mm)

Bending stress

𝝈𝒃 (N/mm2)

Material fringe

value(ƒ)

0 10.065 4.780875 0

1 4.375 2.279525 12.075

2 8.125 1.03607 11.2125

Material fringe constant by calibration (kPas/fringe/m) 11.643

Table IV

Mechanical properties of polycarbonate (PMS-5) Property Symbol Unit Value

Modulus of elasticity E GPas 2.7

Passion's ratio ν --- 0.36

Density ρ kg/m3 1000

Table V

Dimensions of four slots Geneva wheel [7]. Dimension Sample Value

Geneva Wheel Radius R 50.8 mm

Driving Pin Diameter d 24.8 mm

Geneva Wheel Tip Thickness t 7 mm

Geneva Wheel Depth W 6.5 mm

Radius of Geneva Wheel Shaft b 6 mm



Fig. 7. Setup manufactures Geneva wheel from polycarbonate.

Fig. 9. Three dimensions element. Fig. 10. Two dimensions element. (SOLID187) used in this work [8]. (PLANE183) used in this work [8].

Fig. 11. Two dimensions of the four slots Geneva wheel



(a) Crank angle (α) = 0o and load = 21 N. (b) Crank angle (α) = 0o and load = 25 N.

(c) Crank angle (α) = -10o and load = 30 N. (d) Crank angle (α) = -10o and load = 35 N.

(e) Crank angle (α) = -13o and load = 30 N. (f) Crank angle (α) = -13o and load = 35 N.

(g) Crank angle (α) = - 45o and load = 8 N. (h) Crank angle (α) = -45o and load =10 N.

Fig. 12. Experimental photo-elasticity technique for different crank angle and different applied load.



(a) Crank angle (α) = 0o and load = 21 N.

(b) Crank angle (α) = -10o and load = 30 N.

(c) Crank angle (α) = -13o and load = 30 N.

(d) Crank angle (α) = -45o and load = 8 N.

Fig. 13. Theoretical principal stress (σ1) of 3- D FE model of polycarbonate

(PMS-5) for different crank angle and different applied load.



(a) Crank angle (α) = 0o and load = 21 N. (b) Crank angle (α) = 0o and load = 25 N.

(c) Crank angle (α) = -10o and load = 30 N. (d) Crank angle (α) = -10o and load = 35 N.

(e) Crank angle (α) = -13o and load = 30 N. (f) Crank angle (α) = -13o and load = 35 N.

(g) Crank angle (α) = -45o and load = 8 N. (h) Crank angle (α) = -45o and load =10 N. Fig. 14. Theoretical Von Misses stress of 3- D FE model of polycarbonate

(PMS-5) for different crank angle and different applied load.



REFERENCES [1] J. Lee and F. Huang, "Geometry Analysis and Optimal

Design of Geneva Mechanisms with Curved Slots"; Proc. Instn Mech. Engrs Vol. 218 Part C: J. Mechanical

Engineering Science, p.p. (449-459), 2004.

[2] Iulian Stanasel and Florin Blaga, "Virtual Manufacturing of Classic External Geneva Mechanism"; Annals of the

Oradea University Fascicle of Management and

Technological Engineering ISSUE #3, December 2013. [3] Jung-Fa Hsieh, "Design and Analysis of Geneva

Mechanism with Curved Slots", Transactions of the

Canadian Society for Mechanical Engineering, Vol. 38, No. 4, P.P. (557-567), 2014.

[4] David B. Dooner, Antonio Palermo and Domenico Mundo,

"An Intermittent Motion Mechanism Incorporating a Geneva Wheel and a Gear Train", Transactions of the

Canadian Society for Mechanical Engineering, Vol. 38,

No. 3, p.p.(359-372), 2014.

[5] Popkonstantinovic, Z. Jeli and Lj. Miladinovic, "3D

Modeling and Motion Analysis of the Maltese Cross (Geneva) Mechanisms", 14th IFTOMM World Congress,

Taipei, Taiwan, October 25-30, 2015.

[6] Han Jiguang Yu Kang, "Analysis and Synthesis of Geneva Mechanism with Elliptic Crank", International Journal of

Hybrid Information Technology Vol.8, No.8, p.p. (253-

260), 2015. [7] Bushra R. Al-Juwari," A Theoretical Study on the External

Geneva Mechanisms", Thesis, Baghdad University, 1996.

[8] ANSYS 2012, "ANSYS Mechanical APDL Structural Analysis Guide", ANSYS, Inc., U.S.A.2001; 14:406-11.

NOMENCLATURE

Latin Symbols:

Symbol Description Units

f Material fringe value (N/mm)/fringe

h Thickness of the

prototype. mm

I Mass moment of inertia Kg.mm2

n Number of fringes. ______

p Load apply N

y Distant measured from

the neutral axis mm

Greek Symbols:

Symbol Description Units

Crank position at any

instant of motion degree

b Bending stress N/mm2

𝜎1 , 𝜎2 Principle stress N/mm2

Table VI

Experimental and theoretical maximum principal stress (σ1).

No. Crank angle

(α) (Deg.)

Load

(N) Fringe no.

Max. Principal stress (σ1) (Map.)

Photo-elasticity

method

2-D

FEM 3-D FEM

1. 0 21 3 9.6186 9.761 10.2

2. 0 25 4 11.883 11.620 12.1

3. -10 30 5 15.560 15.06 15.6

4. -10 35 6 17.824 17.569 18.1

5. -13 30 6 16.412 17.568 17.6

6. -13 35 7 20.089 19.708 20.6

7. -45 8 4 11.883 12.67 13.33

8. -45 10 5 15.560 15.841 16.7

Table VII

The comparison between experimental and theoretical maximum principal stress (σ1) and error percentage.

No.

Crank

angle (α)

(Deg.)

Load

(N)

Max. principal stress (σ1) (Map) Error %

Photo-elasticity

method

2-D

FEM

3-D

FEM 2-D FEM 3-D FEM

1. 0 21 9.6186 9.761 10.2 -1.48046 -6.04454

2. 0 25 11.883 11.620 12.1 2.213246 -1.82614

3. -10 30 15.560 15.06 15.6 3.213368 -0.25707

4. -10 35 17.824 17.569 18.1 1.430655 -1.54847

5. -13 30 16.412 17.568 17.6 -7.04363 -7.23861

6. -13 35 20.089 19.708 20.6 1.89656 -2.54368

7. -45 8 11.883 12.67 13.33 -6.62291 -12.1771

8. -45 10 15.560 15.841 16.7 -1.80591 -7.32648

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