1

REPORT

as partial requirement

for

the course on

KINEMATICS OF MECHANISMS

ME 3310, A’16

DESIGN PROJECT TITLED:

DESIGN OF PEANUT BUTTER EXTRUDING CAM AND FOLLOWER PISTON

MECHANISM

Submitted by:

Group 19

Robert Boulanger - rdboulanger@wpi.edu

Constantine “Tino” Christelis - cschristelis@wpi.edu

Yuxin Gao - ygao3@wpi.edu

Nathaniel O’Connor - njoconnor@wpi.edu

Submitted to:

Prof. Onal Cagdas

DEPARTMENT OF MECHANICAL ENGINEERING

WORCESTER POLYTECHNIC INSTITUTE

WORCESTER, MA 01609-2280

10/9/2016

Project Score: TOTAL: _______ out of 100%

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Abstract

The goal of this project aims to design a cam and follower mechanism to pump 0.4 cc of

peanut butter onto cookies moving along a conveyor belt at a constant speed. Using our

understanding of mechanisms from our studies in ME 3310, discussions with Professor Onal,

and research on designs relevant to our purpose, we have developed a design that would satisfy

the necessary task specifications. Our final design utilized a kick period of 50 degrees, followed

by 180 degrees of constant velocity, a sniff period of 50 degrees, and finally 80 degrees of

constant velocity return.

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Table of Contents

Abstract 2

Table of Contents 3

Authorship Page 5

Introduction 6

Background 6

Goal Statement 8

Task Specifications 8

Ideation and Design 9

Design 1 9

Figure 1. Design 1 SVAJ Plot in Dynacam10 9

Design 2 9

Figure 2: Design 2 SVAJ Plot in Dynacam10 10

Design Comparison 10

Figure 3: Initial Design Comparison 11

Design 3 11

Figure 4: Velocity Calculations in Mathcad15 12

Figure 5: Design 3 SVAJ Plot in Dynacam10 12

Figure 6: Design 3 Displacement Plot in Dynacam10 13

Figure 7: Design 3 Velocity Plot in Dynacam10 13

Figure 8: Design 3 Acceleration Plot in Dynacam10 14

Figure 9: Design 3 Jerk Plot in Dynacam 10 14

Figure 10: Design 3 Cam Profile in Dynacam10 15

Package Design 16

Figure 11: Piston Diameter Calculation in Mathcad15 16

Figure 12: Final Design Kinetostatic Force in Dynacam10 16

Figure 13: Spring Calculations in Mathcad15 17

Figure 14: Design of Nozzle in SolidWorks2015 18

Figure 15: Design of Package in SolidWorks2015 18

Figure 16: Cross-Section View of Package in SolidWorks2015 19

Analysis of Final Design 20

Figure 17: Final Design Φ and ⍴ Plot in Dynacam10 20

Conclusion 21

Bibliography 22

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Appendices 23

Appendix 1: Design 1 Continuity Check, Boundary Conditions, and Segment Overview 23

Appendix 2: Design 1 Pressure Angle and Radius of Curvature 28

Appendix 3: Design 2 Continuity Check, Boundary Conditions, and Segment Overview 29

Appendix 4: Design 2 Pressure Angle and Radius of Curvature 31

Appendix 5: Design 3 Continuity Check, Boundary Conditions, and Segment Overview 32

Appendix 6: Design 3 Polynomial Functions 35

Appendix 7: Design 3 Pressure Angle and Radius of Curvature 37

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Authorship Page

Section Author Editor

Abstract Rob Boulanger Nathaniel O’Connor

Introduction Yuxin Gao Nathaniel O’Connor

Rob Boulanger

Background All All

Goal Statement Rob Boulanger All

Task Specifications Rob Boulanger

Yuxin Gao

All

Design 1 Nathaniel O’Connor Tino Christelis

Design 2 Tino Christelis All

Design Comparison All All

Design 3 Tino Christelis Nathaniel O’Connor

Package Design Tino Christelis

Yuxin Gao

Nathaniel O’Connor

Analysis of Final Design Tino Christelis All

Conclusion Nathaniel O’Connor Rob Boulanger

Bibliography Rob Boulanger N/A

SolidWorks Modeling Tino Christelis N/A

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Introduction

One of the most advanced cookie manufacturers in the world provided fresh cookies to

the local people for several years. To offer better service to their customers, this company plans

to make a new flavored cookie by spreading peanut butter on it. The company does not want the

rate of cookie production reduced by this additional process. Therefore, 600 cookies should

receive a coating of peanut butter per minute. The cookies’ centers are spaced 40-mm apart on a

constant-velocity conveyor. 0.4 cc of peanut butter will be applied to each cookie as a 1-mm

thick square patch when the cookie passes by a nozzle. The factory doesn’t want to change the

previous production line, so this mechanism should be able to fit around the existing conveyor

belt. We need to design a simple cam and follower-piston mechanism to work as a pump to

finish the task.

Background

The product that this project design surrounds is peanut butter. Peanut butter is a food

paste and spread made primarily from ground dry roasted peanuts (Wiki, 2016). The peanuts are

crushed down and added into a mixer with powdered sugar. After the mixture is stirred into a

sticky and smooth paste, peanut oil is added and mixed until the viscosity is just right (Baidu

Encyclopedia, 2016). The normal viscosity of peanut butter under room temperature (70F) is

250,000 cps (Viscosity Table, vp-scientific.com). In this project, the CAM mechanism will pump

peanut butter onto the cookies as they pass by the nozzle on the conveyor belt.

One design on the market that performs a function similar to what we are looking for is

used for spread sauce on sandwiches. The cycle functions similarly to our project problem in that

the product is moving at a constant rate along the conveyor belt and needs to be applied the sauce

on each of product fast and continuously and maintain constant distance between each piece of

product before and after getting sauce. The amount of sauce output can be controlled and

changed (GS Italia - Linea Panini, https://youtu.be/uqBpNBV3-pw). But this design uses

computer-controlling system, not CAM mechanism as asked of us.

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During our research, we found a patent for a piston on a cam follower used for a

hydrostatic pump (Cunningham, 1974). It describes using a low friction material for the bearing

for the cam follower. It is shaped in such a way that the low friction bearing locks around the

piston. This patent is essentially one of the first designs for a similar application to our project.

In order to gain a better understanding of cam analysis, we referenced a brief paper

detailing optimal cam and follower designs which analyzed polynomial curves using F.E.M. in

ANSYS 10 to determine the best way to minimize the effects of impact and high contact loads

(Al-Shamma, 2010). For the purposes of this project, we did not need to perform such in depth

analysis, but it gave us a general idea about conditions to avoid and how to properly size our cam

relative to the follower to reduce stress and deflection.

Before we began drafting our first designs, we performed preliminary calculations that

would help us later on in the design and analysis process. Given the number of cookies being

produced per unit of time (600 cookies/min), we can divide this by 60 to get cookies per second

(10 cookies/sec), which then gives us one cookie every 0.1 second. This means that the entire

cycle must be completed and repeated every 0.1 second. With the cam performing one cycle

every 0.1 second, we found the necessary angular velocity of the cam by dividing 2π by 0.1

second. This gave us an angular velocity of 62.832 rad/s.

In talking with Professor Onal, we were able to better understand the principles of

mechanism which would be completing this task. One such principle being the principle of

maximizing mechanical advantage by increasing eccentricity of the cam-follower, and that

regulations regarding maximum Φ angles are actually a bit looser than we originally thought.

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Goal Statement

Design a cam and follower mechanism to pump peanut butter onto cookies moving along

a conveyor belt.

Task Specifications

● The motion of pump will be achieved by machine composed of cam, follower, spring and

piston.

● The roller follower has diameter of 20mm and mass of 0.5kg.

● The nozzle is a 1mm*20mm rectangle.

● Peanut butter should be pumped on 600 cookies per minute.

● Peanut butter pumped on per cookie is 1mm thick square.

● Peanut butter pumped on per cookie is 0.4cc.

● Cam undergoes a constant angular velocity of 62.832 rad/s.

● Cycle of operation is performed in 0.1 sec

● Pumping the peanut butter onto the cookie occurs within 0.05 sec of the cycle

● Cam design reflects that the kick velocity is 3 times the steady state velocity, and the

sniff velocity is -4 times the steady state

● Cookies must maintain a separation of 40-mm between the center of each piece, both

before and after receiving peanut butter.

● All designs and peanut butter pump must be OSHA and FDA compliant

● Cam operates on a forced-closed system

● Functions for displacement, velocity, and acceleration are continuous, jerk is finite

● The spring has a negligible mass and is continuously under some magnitude of

compression

● Spring should have infinite life under fatigue

● Peanut butter is only assumed compressible under constant velocity

● Peanut butter undergoes no displacement during “kick” and “sniff” periods

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Ideation and Design

Design 1

Our first design was created in such a way that both the kick and sniff were to be short

durations of constant velocity. The longer constant-velocity portions of the piston movement

were for 140 degrees of cam rotation, while the constant-velocity kick and sniff were 20 degrees

each. The four constant velocity segments were each connected with 10 degree segments of

acceleration. This was done under the initial assumption that the kick and sniff were required to

have a certain constant-velocity duration. Polynomials were chosen for all 8 segments of this

design in order to make sure all boundary conditions were met. Polynomials we required for the

constant velocity segments, so the acceleration portions had to have the same boundary

conditions as the beginning and end of those segments.

Figure 1. Design 1 SVAJ Plot in Dynacam10

Design 2

Our second design approached the kick and sniff steps from a different angle. Instead of

assuming the kick and sniff velocities to be constant for a long duration, the assumption was

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made that the kick and sniff velocities were speed minimums that the follower should surpass for

a short amount of time. This assumption allowed us to treat the kick and sniff periods as

polynomials, with boundary conditions at their ends and mid-beta. Halfway through the

kick/sniff (mid-beta), a velocity condition was set to be at least 3 times or four times great for the

kick and sniff respectively. The “extrusion” of peanut butter for this design was assumed to be

proportional to total displacement, resulting in having the first two and last two beta segments

each adding to 180 degrees of cam rotation.

Figure 2: Design 2 SVAJ Plot in Dynacam10

Design Comparison

To fairly compare the two designs, each of the design’s maximum values that we wanted

to compare was divided by that designs maximum displacement. This allowed us to compare the

designs regardless of the fact that each design called for the follower to move different lengths.

The calculations, considerations, and results from this process are shown below (note that in the

figure, “Design 3” actually refers to “Design 1”).

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Figure 3: Initial Design Comparison

Design 1 ended up minimizing velocity relative to our other designs, but had a

significantly higher acceleration. This higher acceleration was due to the kick and sniff requiring

a much shorter duration to reach their constant velocity, rather than just peaking at a high

velocity during the entire kick duration. The velocity was lower, but not nearly as significantly

lower because it still needed to cover a similar displacement over the kick and sniff periods.

Regardless of the design, this mechanism would be required to operate for millions of

cycles without experiencing wear and fatigue. Since we wanted to focus on the long term life of

this mechanism, we decided that a lower acceleration would be better suited for this kind of

application.

And so, we decided that Design 2 would be the best approach to this problem, and used

the designs beta values, function type, and boundary conditions as a template for the next

iteration of design.

Design 3

The first design change that would have to be made for the next iteration would be a

correction of the beta values, as it was learned late into the design process that peanut butter is

NOT displaced during the kick and sniff periods. This meant that the follower’s constant velocity

movement had to be recalculated, as it went from being done in 120 degrees to having a cycle

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length of 180 degrees. Assuming a 10mm displacement of peanut butter was desired, the new

velocity required for this movement was calculated using the below functions.

Figure 4: Velocity Calculations in Mathcad15

With the velocity conditions calculated, the boundary conditions for all the polynomials

were determined and entered into Dynacam10. Below are screenshots of the resulting SVAJ

plots. Full details on boundary conditions and polynomial coefficients are available in the

Appendix.

Figure 5: Design 3 SVAJ Plot in Dynacam10

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Figure 6: Design 3 Displacement Plot in Dynacam10

Figure 7: Design 3 Velocity Plot in Dynacam10

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Figure 8: Design 3 Acceleration Plot in Dynacam10

Figure 9: Design 3 Jerk Plot in Dynacam10

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The next step was to physically size the cam. With a total piston displacement of 15mm,

a cam prime radius of at least 4 times this displacement is ideal. To be safe, a prime radius of

70mm was chosen (10mm longer than the minimum requirement). While increasing the

eccentricity of the follower-cam system produces a greater mechanical advantage, and thus

lowers motor torque requirements, we decided not to add such a feature to the system. The

rationale behind this decision was that the small increase in mechanical advantage would not be

worth the trouble of an added layer of tolerance and thus possibility for error in the machining

and assembly of the package. The visual representation of the cam-follower system showing

these final design parameters is shown below.

Figure 10: Design 3 Cam Profile in Dynacam10

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Package Design

With the cam design finalized, the other aspects of the mechanism could be determined.

Given the volume of peanut butter that must be displaced, and given that the follower moves

(and displaces peanut butter) 10 mm, we were able to calculate the piston diameter.

Figure 11: Piston Diameter Calculation in Mathcad15

The most important part of the mechanism, second to the cam itself, is the spring. The

spring is placed between a grounded surface and the follower, ensuring that the cam-follower

system is “force closed”. First, the preload the spring exerts on the follower had to be

determined. This was estimated by changing the preload value in the “dynamics” tab of

Dynacam10 until all forces present on the follower throughout the cam cycle were greater than

zero. What this means, is that the follower is constantly forced into contact with the cam,

regardless of how much force the cam is exerting on the follower as it is equalized by the spring.

Figure 12: Final Design Kinetostatic Force in Dynacam10

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For our chosen cam design, the required preload force was approximately 150 Newtons.

This means that a spring must apply 150 Newtons of force on the follower, keeping it tangent

with the cam, when the system is static. To do this, said spring must not be at its free length, but

rather be compressed a small, arbitrary amount. We chose a deflection of 5mm. From here, we

could calculate the required spring constant, and choose a spring from the tables in Appendix D

of Norton’s “Design of Machinery”. It should be noted that the spring constant was not the only

constraint, as springs have other parameters that must be taken into consideration. These

parameters include maximum deflection, maximum load, and under what deflection the spring

will work free. As a general design precaution, higher wire diameters were more appealing, as

springs will generally have longer life spans the thicker the wire diameter.

Figure 13: Spring Calculations in Mathcad15

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0.4cc of peanut butter will be pumped by a cylinder-shaped piston, and come out through

the rectangle-shaped outlet. According to calculation, an outlet of 1mm*20mm is best to meet

the demand. We designed a nozzle that adapts the cylinder-shaped input port to the rectangle-

shaped outlet.

Figure 14: Design of Nozzle in SolidWorks2015

With the cam, follower, piston, spring, and nozzle all fully defined, we have a complete

system of parts ready for packaging. In an ideal design, linear bearings would be positioned

along the length of the piston-follower, supporting its weight, taking all shear forces delivered

from the cam, and generally keeping it concentric with the peanut butter cylinder. However, due

to the scale of the system, these components were not modeled, but their presence should be

assumed. Below is a model of the complete package for the system, as well as a cross-section

labeled diagram.

Figure 15: Design of Package in SolidWorks2015

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Figure 16: Cross-Section View of Package in SolidWorks2015

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Analysis of Final Design

With the cam completely defined, analysis was required to check for acceptable pressure

angles and curvature radii. Large pressure angles are unideal, as a large pressure angle means the

cam surface is starting to put force on the follower at an angle non-collinear with the followers

allowed axis of motion. The smaller the pressure angles, the less force is “wasted”, and the less

torque is required by the motor driving the cam. As calculated by Dynacam10 and shown below,

pressure angles never exceed +/- 10 degrees, which is more than substantial.

Radius of curvature is another important aspect of cam analysis. If the radius of curvature

is ever smaller than the radius of the follower and concave, then the follower is unable to follow

the cam surface through the rotation, as it physically could not be tangent to such a surface. If

radius of curvature is smaller than follower radius and is convex, then the follower will move

unpredictably over the cusp, and possibly damage the cam surface. The Dynacam10 screenshot

from below shows that we have minimum concave and convex radius of curvature values of

~933mm and ~46mm respectively. Both of these values are over four times greater than the

follower radius, which makes our design not only functional, but also highly optimal since ρ

values are recommended to be at least 3 times greater than the follower radius (Norton, pg.459).

Figure 17: Final Design Φ and ⍴ Plot in Dynacam10

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Conclusion

Our final design consists of a cam and follower characterized by four polynomial

sections, two of which are constant velocity, and two of which are a kick and sniff that accelerate

the follower. The extending and retracting constant velocities are not equal and opposite, due to

the need to have peanut butter extruded for exactly half of the cycle. The displacement, velocity,

and acceleration functions are all continuous, with a total peanut butter displacement of 10mm.

This cam and follower design satisfies the kick, sniff, and constant velocity requirements

to extrude peanut butter onto cookies at the proper rate and timing. The design meets all of our

task specifications, but there are other ways in which it could be improved and optimized. The

places which are a concern are with the sniff portion, as well as potentially the tolerances of the

cam radius.

An undesired effect that occurred while reiterating design 2 into design 3 is that the sniff

segment became slightly distorted, with the velocity actually falling below the constant retraction

velocity briefly. This should not have any real effect on the outcome of the process, as during the

kick and sniff the peanut butter undergoes no displacement. It does however introduce

unnecessary acceleration to the cam and follower, which in turn will cause fatigue sooner in its

life cycle. In a further iteration of this design, a better polynomial function could be selected in

order to minimize the acceleration during this segment.

An additional concern is with how the design will wear after use and with tolerances

while manufacturing the cam. Since the total displacement is only 10mm, if the cam wears down

enough over thousands of cycles, the device will no longer extrude enough peanut butter onto the

cookies. Also, after many cycles, the spring will begin to fatigue and will no longer hold the

follower to the cam as strongly. If this system were to be manufactured, very strict tolerances

would be required to make sure the cam functions as intended. A future design could fix this

issue by using a larger displacement with a smaller piston. In addition, by increasing the cam

prime radius to a greater value, more control can be had over accurate machining of the cam

surface, resulting in actual follower motion that more accurately fits with what we

mathematically designed.

Besides the minor secondary concerns as described above, this design fulfills all task

specifications and accomplishes the company’s project goal with a highly optimized cam and

follower system.

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Bibliography

Al-Shamma F. Mustafa F. Salimann S. An Optimum Design of Cam Mechanisms with Roller

Follower for Combined Effect of Impact and High Contact Loads. Al-Khwarizmi

Engineering Journal, Vol6, No. 4, PP 62-71. 2010. Retrieved from

http://www.iasj.net/iasj?func=fulltext&aId=2181

Cunningham, S,Firth, D,Wells,J. "Cam Follower Piston". Patented 1974: US3783749

[Michele Scandroglio]. (2011, April, 14). GS Italia - Linea Panini. [Video File] Retrieved from

https://www.youtube.com/watch?v=uqBpNBV3-pw&feature=youtu.be

Norton, R. L. (2012). Design of Machinery – An Introduction to the Synthesis and Analysis of

Mechanisms and Machines. New York, NY: McGraw-Hill.

Peanut Butter. (2016, Oct 7). Retrieved from https://en.wikipedia.org/wiki/Peanut_butter

Viscosity Tables. (n.d.). Retrieved October, 2016, from http://www.vp-

scientific.com/Viscosity_Tables.htm

花生酱. (n.d.). Retrieved October, 2016, from http://baike.baidu.com/item/花生酱

/8544484?fr=aladdin

Programs and Software Used

Mathcad15 - for calculation presentation

Dynacam10 - for cam design and analysis

SolidWorks2015 - for package design and product visualization

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Appendices

Appendix 1: Design 1 Continuity Check, Boundary Conditions, and Segment Overview

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25

26

27

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Appendix 2: Design 1 Pressure Angle and Radius of Curvature

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Appendix 3: Design 2 Continuity Check, Boundary Conditions, and Segment Overview

30

31

Appendix 4: Design 2 Pressure Angle and Radius of Curvature

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Appendix 5: Design 3 Continuity Check, Boundary Conditions, and Segment Overview

33

34

35

Appendix 6: Design 3 Polynomial Functions

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Appendix 7: Design 3 Pressure Angle and Radius of Curvature