REDESIGN OF THE LOWER CURVE PORTION OF THE BELT TRACK FOR

THE 1.5” PITCH, 60°, JORGENSEN HINGED STEEL BELT (MILLENIUM)

CONVEYOR.

By

Gregory D. Michalak

A Report Submitted For

MT-4901, CAPSTONE PROJECT

In Partial Fulfillment of the

Requirements for the Degree of

Bachelor of Science in Mechanical Engineering Technology

Milwaukee, Wisconsin

November, 2006

ABSTRACT

The purpose of this project is to fulfill the requirements for the degree of

bachelor’s of science in mechanical engineering technology. The project I chose to do

was the design of a part for a Jorgensen Conveyors Inc. Conveyor. This part would take

the place of 4 pieces currently welded together.

The purpose of this part is that it is part of the track for the belt to travel in. It is

positioned at the lower curve section of the conveyor where the belt transitions from the

horizontal to the 60° incline. See the Appendix for a drawing of this type of conveyor and

where this part would be located.

The manufacturing processes chosen to make this into one piece was the die

casting process.

Using the NADCA (North American Die Casting Association) Product Design for

Die Casting OEM Design Sourcebook and the help of my advisor for this project,

Professor Dave Gerow, a part was designed that can be casted using the popular die

casting process.

After the design was complete, aluminum alloy ANSI C443.0 was chosen as the

material for the purpose of this project and a structural static analysis using FEA was

performed on the part to ensure that it would be able to perform its intended function

under normal operating conditions. After concurrently using the solid modeling package

Solidworks student edition 2006 w/ CosmosWorks, the part was geometrically optimized.

Because the material used in this analysis has a ductility greater than 5%, which is

considered ductile, the failure theory used for this analysis was the ductile theory of Von-

Mises. Using the Von-Mises Stress, called the effective stress, the maximum value

1

according to Cosmosworks was 6443 PSI for the upper curve and 5851 PSI for the lower

curve. Since both values are below the yield strength of 17,000 PSI, the part according to

the theory will not yield. The smallest factor of safety for the upper and lower curve was

2.2 and 2.4 respectively.

This design according to my analysis will not fail. Further study will be taken as

to possible other materials to be used. The problem with die casting is that there are not

many materials to choose from and most are considered brittle (less than 5% ductility).

The design can be casted because of the features I put into the part which are: draft,

rounds, and uniform wall thicknesses. A cost analysis of this design compared to the

welding of four materials will be done at a future time. If it is proved that it cost more to

cast this piece than to weld four pieces together, other manufacturing processes will be

looked at such as: sand casting and investment casting.

Thanks to this project, I have gained more confidence in myself to perform finite

element analysis.

2

ACKNOWLEDGEMENTS

I would like to acknowledge Jorgensen Conveyors Inc. for giving me this

opportunity to fulfill my requirements for MT-4901.

I would also like to give acknowledgements to Professor Dave Gerow of MSOE

for his help with my project. He gave me much advice as to the design of the casting and

how to go about performing the FEA correctly. He also showed me how to verify

complicated designs using strength of materials theory that I didn’t know how to do

before.

3

TABLE OF CONTENTS

List of figures Pages 5-14

Introduction & Background Page 15

Discussion

Explanation of Casting Design Pages 16-17

Explanation of the FEA analysis Pages 18-20

Conclusion Pages 21-22

Bibliography Page 23

Appendix See attachments

4

LIST OF FIGURES

Figure A. Current pieces that are welded together for the lower curve piece

Figure B. The four pieces welded together to the inside of the conveyor casing

Skirt

Hot rolledM1044bar stock

5

Figure C. Front isometric view of initial casting design

Figure D. Front isometric view of final casting design

Direction belt moves in casting

Ribs designed into front of casting

skirt Upper curve and lower curve respectively

Bosses @ the bottom of the casting add material to the very bottom of the piece in case the belt would completely lose its tension and fall.

6

Figure E. Back isometric view of initial casting design

Section is cored out to reduce mass. In the final design ribs are employed to reinforce the wall of the skirt.

Buckling is evident here. Upper curve bends up while skirt portion bends down.

Figure F. Deformation Plot of original casting due to the loading on the upper curved portion.

7

Figure G. Back isometric view of final casting design

Figure H. Deformation Plot of final casting due to the loading on the upper curved

portion

Ribs designed into back of the casting

Skirt wall reinforced with ribs.

Not as much deformation as in the first design.

Welded on this edge

Welded on these edges

8

Figure I. Upper curve boundary conditions of final casting design for FEA

(front isometric view)

Figure J. Upper Curve boundary conditions of final casting design for FEA

(back isometric view)

9

Figure K. Lower Curve boundary conditions of final casting design for FEA

(front isometric view)

Figure L. Lower Curve boundary conditions of final casting design for FEA

(back isometric view)

10

Figure M. Stress analysis plot of upper curve of final design

Max. stress for upper curve section of final design

11

Figure N. Stress analysis plot of lower curve of final design

Max. stress for lower curve section of final design

12

Figure O. Point load deformation of upper curve (scaled to 300)

Figure P. Distributed load deformation of upper curve (same scale, 300)

Not a realistic deformation. Loads never act at a single point but are distributed over an area.

Much betterRepresentation of the loads acting on the upper curve.

13

Figure Q. Split lines shown on upper curve

Figure R. Resultant Reaction force for entire model for upper curved portion of the

analysis

Separate surfaces created. Intersections of these separate surfaces is where the forces were applied.

14

Figure S. Resultant reaction force for entire model for lower curve portion of the analysis

Figure T. A section of a 1.5” pitch conveyor belt

Figure U. Side view of the 1.5” pitch section of the belt

Rollers of the belt

1.5” pitch distance

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INTRODUCTION & BACKGROUND

Jorgensen Conveyors Inc., headquartered in Mequon, Wisconsin, designs and

manufactures conveyors and material handling equipment.

In an attempt to save costs, a design for assembly project has been identified that

could save the company money. The current lower curve portion of the 1.5” pitch

Jorgensen conveyor is welded into an assembly using four parts. As shown in Figure A

on page 5, one of the pieces is a sheetmetal part (called the skirt) that Jorgensen forms in

a brake press but the material, 14 gage sheetmetal, is purchased from Award

Manufacturing at $.80/in. The other 3 pieces are hot rolled bar stock M1044 and are

purchased from Central Steel & Wire Company at a cost of $.45/in. As of 2006, it cost

Jorgensen $1.07/in. to weld (includes labor, materials, and tools). According to Jorgensen

Conveyors it costs $33.00 to manufacture that piece.

The objective of this design is to design a part that costs less than the current costs

to produce the curved piece for the belt track.

The constraints of this design are:

1) The dimensions of the part cannot be changed except for the wall thickness

2) The ability of the part to withstand the 325 lb force from the belt tension

3) That the part cost less than the current cost now to produce this assembly

During the design process, two designs were compared using FEA. The initial

design shown in Figures C & E on pages 6 & 7 had no ribs designed into any

portion of the part, and the final design does have ribs designed into it.

This report will focus on the final design and the reason for this decision.

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DISCUSSION

Explanation of the casting design

The reason for the shape of the part is that in this area the belt transitions from

moving horizontal to an incline angle of 60°. If this part was not part of the conveyor

assembly, the belt would rise up due to the 325 lbs of tension on the belt and would

interfere with the casing of the conveyor and would not move. As shown in Figure D on

page 6, the belt moves in a clockwise direction with the rollers making contact with the

upper curve of the casting when moving up the incline and then when it comes around the

headshaft and transitions back down the incline the rollers make contact with the lower

curve of the casting design.

For the casting design I followed these rules according to the NADCA(north

American die casting association)[1]:

1) Uniform wall thickness

In both designs as shown in Figures C&D on page 6, a wall thickness of 0.156” is

maintained throughout the part.

2) Fillets and rounds at intersections between perpendicular surfaces

In Figures C &D on pgs. 6 & 7 the part has fillets and rounds where any two

perpendicular surfaces intersect. According to NADCA, fillets and rounds reduce the

stress concentration between those surfaces. A corner will have a much higher stress

concentration than a fillet or round will [1]. If there is too large a fillet or radius

according to Degarmo, Black, & Kohser, then this may create a hot spot [3]. This corner

is thicker in cross section than the wall thickness of the casting. These areas because they

are thicker tend to cool slower and tend to be areas of abnormal shrinkage[3]. When the

17

differences are large, the hot spot areas are likely to contain defects such as porosity or

voids, and the part is likely to fail in these areas[3].

3) Draft of 1°on surfaces where the die and casting surfaces would separate from each

other

According to NADCA, draft is highly desirable on surfaces of the part parallel to

the direction of withdrawl of the die from the casting because it allows the casting

to release easily from the die surfaces [1].

4) Ribs at the back end of the part that is cored out

In Figure G on page 8, ribs are designed into the part. The function of these ribs is

to keep strength in that portion of the casting while removing mass from it. As shown in

figures F & H on pages 7& 8, the ribs help reduce deformation in the skirt portion of the

part. The ribs are spaced approximately 1.5” apart, the distance the pitch of the belt is.

Pitch is the distance between the centers of two adjacent rollers and is shown in Figures T

& U on page 15.

5) Bosses added to increase strength at very bottom of part

The function of the bosses in Figure D on page 6 is to create a safety

mechanism built into the part in case the belt would lose its tension and

fall partly onto the bottom of the part. A Jorgensen conveyors belt could

weigh anywhere from 30 to 100 lbs or more for a 1.5” pitch conveyor.

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Explanation of the Fea analysis

The Von - Mises criteria for ductile materials was used as a theoretical way to

verify that this part would not fail under normal operating conditions. The material

chosen for this design was aluminum die casting alloy C443.0. This material was chosen

mainly because it was one of the few with ductility greater than 5%.

The Von-Mises criterion was the chosen criterion used in this analysis over the

Maximum Principal Stress criterion and Tresca Criterion because it provides the best

correlation. The Tresca criterion provides good correlation, but is more conservative than

the Von-Mises criterion. The Maximum Principal Stress criterion produces

unconservative results for some loading conditions, and should not be used for ductile

materials [2].

A static linear analysis was chosen for this part because the part is fixed in space,

the loads acting on the part don’t vary with time, and the material behaves in a linear

fashion. The load put on both the upper and lower curves of the part is the chain pull of

the belt which is a constant 325 lbs.

Their were two separate analysis done: one for the upper curved portion of the

part when the belt is moving up the incline and the other when the belt is transitioning

from the incline to the horizontal. The reason for the two separate analysis is that their

cannot be tension in both the upper and lower portions of the belt if it’s to move; their has

to be slack in one portion of the belt for it to move.

For the upper curved analysis when the belt is transitioning from the horizontal to

the incline approximately 5 rollers will be in contact with the part. I approximated this

because each roller is spaced 1.5” between centers of the adjacent roller. I then divided

19

the 325 lb chain pull by 5 to give each roller an approximate force of 65 lbs acting

upward on the curve. Then I divided this force by the number three because this is how

many vectors I placed at each location. Spreading this force to three vectors distributed

the load better than a point load. A point load would not represent the surface of the

roller. Also, when a point load was applied at each location the deformation plot was not

representative of what the actual deformation should look like. You can see the difference

in the deformation in Figures O & P on page 13.

For the lower curve analysis when the belt is transitioning from the incline to the

horizontal approximately 7 rollers will be in contact with the part. The 325 lbs of force

was divided by 7 to give each roller an approximate force upwards on the surface of 47

lbs. I then divided this number by three, the number of vectors placed at each area. An

explanation as to why three vectors were chosen was given above.

In order to properly apply the loads to the part as they would be applied in the real

world, the areas where the loads were applied to were broken into separate surfaces using

datum points, planes, and split lines in Solidworks student edition 2006 w/ cosmosworks.

The split line function in solidworks allows you to split up an area into several areas. The

vertex of these intersecting areas is where you can apply loads to [4]. In Fig. Q on page

14 it shows that the upper surface was broken into individual surfaces.

The restraints chosen for this part were chosen by taking into consideration as to

how this part would be fixed in space. The back portion of the piece would be laying flat

against the inside surface of the casing, so an on flat face restraint was applied to this

surface. The vectors are pointing towards where the casing would be because it’s

preventing the part from translating in the positive z-direction (for this part the z-axis is

20

the x-axis). According to Sheppard & Tongue if a restraint prevents the translation of the

system in a given direction, then a force and or moment acts on the system at that

location of the restraint in the opposing direction [5]. The upper edge of the skirt was

given an immovable constraint because this is where a weld will be placed along, so no

translation or rotation will take place along that edge. Finally the curved cutouts, two on

each side, was given fixed constraints because this is also where a weld will be placed

along, so no translation or rotation will take place along those bottom edges. Figures I

thru L on pages 9 & 10 show the restraints by the use of green vectors.

Verification of Analysis

Using cosmosworks the verification was done using the reaction forces provided

in the study. In Figures R & S on pages 14 & 15 it shows that for the upper & lower

curve the reaction force equals the load of 325 lbs applied. (0.14 lbs error for upper curve

& (1.5 lbs error for lower curve)

21

CONCLUSION

The purpose of this project is to fulfill the requirements for the degree of

bachelor’s of science in mechanical engineering technology. The project I chose to do

was the design of a part for a Jorgensen Conveyors Inc. Conveyor. This part would take

the place of 4 pieces currently welded together.

The purpose of this part is that it is part of the track for the belt to travel in. It is

positioned at the lower curve section of the conveyor where the belt transitions from the

horizontal to the 60° incline.

The manufacturing processes chosen to make this into one piece was the die

casting process.

Using the NADCA (North American Die Casting Association) Product Design for

Die Casting OEM Design Sourcebook and the help of my advisor for this project,

Professor Dave Gerow, a part was designed that can be casted using the popular die

casting process.

After the design was complete, aluminum alloy ANSI C443.0 was chosen as the

material for the purpose of this project and a structural static analysis using FEA was

performed on the part to ensure that it would be able to perform its intended function

under normal operating conditions. After concurrently using the solid modeling package

Solidworks student edition 2006 w/ CosmosWorks, the part was geometrically optimized.

Because the material used in this analysis has a ductility greater than 5%, which is

considered ductile, the failure theory used for this analysis was the ductile theory of Von-

22

Mises. Using the Von-Mises Stress, called the effective stress, the maximum value

according to Cosmosworks was 6443 PSI for the upper curve and 5851 PSI for the lower

curve. Since both values are below the yield strength of 17,000 PSI, the part according to

the theory will not yield. The smallest factor of safety for the upper and lower curve was

2.2 and 2.4 respectively.

This design according to my analysis will not fail. Further study will be taken as

to possible other materials to be used. The problem with die casting is that there are not

many materials to choose from and most are considered brittle (less than 5% ductility).

The design can be casted because of the features I put into the part which are: draft,

rounds, and uniform wall thicknesses. A cost analysis of this design compared to the

welding of four materials will be done at a future time. If it is proved that it cost more to

cast this piece than to weld four pieces together, other manufacturing processes will be

looked at such as: sand casting and investment casting.

Thanks to this project, I have gained more confidence in myself to perform finite

element analysis.

23

BIBLIOGRAPHY

[1] North American Die Casting Association.1998. PRODUCT DESIGN FOR DIE CASTING, 5TH ed. Page 26, “Developing the Configuration.”

[2] Howard, William E. March 2004. “Failure Criteria.” Class notes from MT-3601: Finite Element Analysis. Professor Dr. William “Ed” Howard. MSOE, Milwaukee, Wisconsin. Available from author.

[3] Degarmo, Paul E., Black, J.T., Kohser, Ronald A. MATERIALS AND PROCESSES IN MANUFACTURING, 9Th ed. Chapter 13, Fundamentals of Casting, page 292.

[4] Tickoo, Sham. SOLIDWORKS for Designers Release 2005. Chapter 9, Advanced Modeling Tools-III, page 31.

[5] Sheppard, Sheri D., Tongue, Benson H. STATICS, ANALYSIS AND DESIGN OF SYSTEMS IN EQUILIBRIUM, 1ST ed. Chapter 6, DRAWING A FREE-BODY DIAGRAM, page 219.

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APPENDIX

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