Pizza Cutter Devin E. Simpson Design Project I BE 3320

Stress Analysis of a Simple Machine:

Pizza Cutter

Devin E. Simpson

Design Project I

BE 3320

Jeffrey Ortego

Department of Biological & Agricultural Engineering

Louisiana State University Stress Analysis of a Simple Machine: Pizza Cutter 2

Introduction

The objective of the BE 3320 Design Project I was to utilize previous knowledge and existing skills of Autodesk Inventor in combination with newly learned techniques in order to build a simple machine and perform a stress analysis.

A simple machine is a basic mechanical device used to direct a force. We use simple machines in our everyday lives whether it’s in school, at work or back home. Many kitchen utensils used for cooking and prepping are machines that we come across regularly. Thus, the machine I decided to replicate and analyze for the purpose of this project was a pizza cutter.

Pizza cutters are common household items that are used to make the task of dividing a whole pizza into slices much simpler. While there are various types of pizza cutting mechanisms and utensils, the pizza wheel is the most common. The pizza wheel is made up of four main components: a handle, a wheel, a connecting piece and a pin to allow the wheel to rotate. When a human force is applied to the handle in a particular direction pushing the machine forward, the wheel will rotate and create a division in the pizza due to the sharp edges and material of the wheel.

Design Strategy

My approach to beginning the drawings was focusing on the main components. In this case, the two major components also happened to be the larger components. The first of which was the handle. I drew this component to be long enough to accommodate being held by an adult. The average hand with for an adult male is 3.30”, therefore the handle is a comfortable 7” in length. Both sides of the Stress Analysis of a Simple Machine: Pizza Cutter 3 handle were rounded using the fillet tool in order to make gripping the handle much easier. At the left end of the handle, the rest of the components will be attached including the wheel. Because of this, I used the arc tool to make the end with a similar radius to that of the wheel. As a result, it will provide more support and allow the wheel to rotate without getting caught on the handle.

The next main component was the cutting mechanism, which is the wheel.

Thinking practically, the size of the wheel needed to be large enough to slice a large pizza efficiently in a short amount of time. I drew the wheel with a diameter of 2” and a 0.3” opening in the center for the pin to hold it in place.

Following this, I drew the connecting bar to connect the handle to the wheel.

I chose to design this component toward the end because it will be the middle piece in the assembly. Both ends of the connector will be attached to other components of the machine; therefore the ends need to match in shape and size in order to be properly constrained in the assembly. This connector also needed to be thick enough to support the wheel, since it will be the main component holding the two ends of the assembly together.

Lastly, I drew the pin to attach the wheel to the connector and hold the two in place, while still allowing the wheel to rotate. In the assembly, the pin and the wheel are attached using a mate constraint that way the wheel is still able to rotate while attached.

Three of the four components are made of stainless steel in order to be long lasting and durable. The handle of the pizza cutter is made of PMMA plastic.

Stress Analysis of a Simple Machine: Pizza Cutter 4

Stress Analysis

To analyze the stress on the pizza cutter, two forces were applied to the machine. The first force was placed inward on the end of the handle to represent the force as a result of a hand pushing the cutter. The second opposing force was placed upward against the blade as it is slicing the pizza. In order to determine the magnitude of these forces, I tested two scenarios. The first scenario with the forces being applied by a normal, yet relatively strong male adult and the second scenario being an unreasonably strong adult in order to see what the maximum allowable force would be before the pizza cutter would break. According to the International

Encyclopedia of Ergonomics and Human Factors, based on a study on industrial workers, it was concluded that hand forces should not exceed 45N, which is approximately 10lbf1. However, it was mentioned that hand forces can exceed this amount as long as it is not for an extended period of time. Thus, because the use of a pizza cutter typically requires less than five minutes and is not a repetitive activity

(such as those performed by industrial workers), I decided to increase the hand force along the handle to 30lbf for test 1. The opposing force along the wheel is

10lbf in test 1 because it is smaller but still significant. The forces chosen for test 2 had much larger magnitudes, which was done so that a significant difference in the results was able to be seen when performing the stress analysis. With the forces chosen, I ran two simulations.

Stress Analysis of a Simple Machine: Pizza Cutter 5

Table 1. Forces (lbf) applied to the pizza cutter during the two tests

Force 1 (Handle) Force 2 (Wheel)

Test 1 - Success 30lbf 10lbf

Test 2 - Failure 130lbf 50lbf

During test 1, the pizza cutter was able to withstand the forces applied. When looking at the displacement view, the maximum displacement in the Z-direction would be 0.3753”. Whereas the forces applied during test 2 caused the pizza cutter to be displaced 1.262” in the Z-direction, which is more than three times the displacement in test 1. Thus, the scenario in the first test is more practical and will not cause the machine to fail.

For test 1, which was a success, the maximum 1st principle stress was

16.75ksi. Between the two materials, PMMA plastic and stainless steel, the ultimate tensile strength range was approximately 11ksi to 78ksi. Thus, 16.75ksi is a reasonable stress value for the entire assembly since it is within that range. The safety factor obtained from the report for this successful simulation range from

0.37ul to 15ul.

Images and the full reports generated by Inventor for both simulations can be found in the appendix on pages 16-25.

Biological Impact

During its use, a pizza cutter will come into contact with two biological materials at one time. The handle will be in contact with the human hand acting as Stress Analysis of a Simple Machine: Pizza Cutter 6 the driving force, while the wheel will be in contact with the pizza. The impact of skin coming in contact with the handle when applying a force will not have a significant impact on the skin, except minor discomfort due to the texture of the material. However, this is why the handle is the only component made of plastic.

Often times, pizza cutters will have a grip or plastic that is form fitting to the hand for a smooth fit. In fact, the force exerted by the human on the pizza cutter handle is reduced due to the circular design of the cutting mechanism. This allows the human to put less force into cutting than they would a knife because it causes the human wheel to produce it’s own force. This force is considered to be a centripetal force, which is the inward force between the pizza and the wheel.

Error

While Autodesk Inventor’s stress analysis add-in is fairly accurate, the solutions and values calculated are still approximate values. In addition, there are many human errors that can result impact the accuracy of the results but even a single error can change your results as well. For this project, the drawing of the individual parts was fairly simple. However, assembling the parts together proved to be more challenging. Due to the roundness of several components, it was difficult to properly constrain all components. Because of this, prior to running the simulations I had to manually bond together the handle and the connecting component. When it came time to run the simulation, I received a window with the following warning, “The deformation is large compared to the model size. Please verify that load and constraint settings are properly scaled.” This was an issue that I Stress Analysis of a Simple Machine: Pizza Cutter 7 was unable to resolve, however, I was still able to run the simulation. Thus, this error may have altered the results I received.

Stress Analysis of a Simple Machine: Pizza Cutter 8

References

1 "Recommended Maximum Force For Human Hand - Human Ergonomics."

MEADinfo. Accessed September 30, 2016. Stress Analysis of a Simple Machine: Pizza Cutter 9

Appendix

I. Drawings

A. Shaded Assembly Drawing (pg. 10)

B. Assembly Drawing (pg. 11)

C. Handle Drawing (pg. 12)

D. Wheel Drawing (pg. 13)

E. Connector Drawing (pg. 14)

F. Pin Drawing (pg. 15)

II. Stress Analysis

A. Failed Stress Analysis Autodesk Inventor Report (pg. 16-19)

B. Failed Stress Analysis Image, Z–Displacement (pg. 20)

C. Successful Stress Analysis Autodesk Inventor Report (pg. 21-24)

D. Successful Stress Analysis Image, Z–Displacement (pg. 25)

Stress Analysis of a Simple Machine: Pizza Cutter 10

Shaded Assembly Drawing

Stress Analysis of a Simple Machine: Pizza Cutter 11

Assembly Drawing

Stress Analysis of a Simple Machine: Pizza Cutter 12

Handle Drawing

Stress Analysis of a Simple Machine: Pizza Cutter 13

Wheel Drawing

Stress Analysis of a Simple Machine: Pizza Cutter 14

Connector Drawing

Stress Analysis of a Simple Machine: Pizza Cutter 15

Pin Drawing

Stress Analysis of a Simple Machine: Pizza Cutter 16

Stress Analysis Report Failure

Overview: Force 1 (Handle) = 130lbf, Force 2 (Wheel) = 50lbf

Analyzed File: Pizza Cutter Assembly.iam Autodesk Inventor Version: 2016 (Build 200138000, 138) Creation Date: 9/29/2016, 6:55 PM Simulation Author: dsimps6 Summary:

Project

Part Number Pizza Cutter Assembly Designer dsimps6 Cost $0.00 Date Created 9/27/2016

Status

Design Status WorkInProgress

Physical

Mass 0.328674 lbmass Area 33.0398 in^2 Volume 4.00057 in^3 x=2.99288 in Center of Gravity y=2.82073 in z=-0.217156 in

Note: Physical values could be different from Physical values used by FEA reported below.

Simulation: 1 General objective and settings: Design Objective Single Point Stress Analysis of a Simple Machine: Pizza Cutter 17

Simulation Type Static Analysis Last Modification Date 9/29/2016, 6:53 PM Detect and Eliminate Rigid Body Modes No Separate Stresses Across Contact Surfaces No Motion Loads Analysis No

Mesh settings: Avg. Element Size (fraction of model diameter) 0.1 Min. Element Size (fraction of avg. size) 0.2 Grading Factor 1.5 Max. Turn Angle 60 deg Create Curved Mesh Elements No Use part based measure for Assembly mesh Yes

Material(s)

Name Stainless Steel Mass Density 0.289018 lbmass/in^3 General Yield Strength 36259.4 psi Ultimate Tensile Strength 78320.4 psi Young's Modulus 27992.3 ksi Stress Poisson's Ratio 0.3 ul Shear Modulus 10766.3 ksi Pizza Cutter Blade Part Name(s) Pizza Cutter Connector Pizza Bolt Name PMMA Plastic Mass Density 0.0429192 lbmass/in^3 General Yield Strength 7092.35 psi Ultimate Tensile Strength 11574 psi Young's Modulus 397.403 ksi Stress Poisson's Ratio 0.355 ul Shear Modulus 146.643 ksi Part Name(s) Pizza Cutter Handle

Force: 1

Load Type Force Magnitude 130.000 lbforce Vector X -54.020 lbforce Stress Analysis of a Simple Machine: Pizza Cutter 18

Vector Y 64.924 lbforce Vector Z 98.826 lbforce

Force: 2

Load Type Force Magnitude 50.000 lbforce Vector X 27.576 lbforce Vector Y 23.161 lbforce Vector Z -34.687 lbforce

Contacts (Bonded)

Name Part Name(s) Pizza Cutter Blade:1 Bonded:1 Pizza Cutter Connector:1 Pizza Cutter Connector:1 Bonded:3 Pizza Bolt:1 Pizza Cutter Connector:1 [M]: Bonded:2 Pizza Cutter Handle:1

Results

Reaction Force and Moment on Constraints

Reaction Force Reaction Moment Constraint Component Component Name Magnitude Magnitude (X,Y,Z) (X,Y,Z) 26.4448 lbforce -3.58006 lbforce ft 112.126 58.3842 lbforce Fixed Constraint:1 -88.0852 lbforce 49.3974 lbforce ft lbforce ft -64.1395 lbforce -30.9161 lbforce ft

Result Summary

Name Minimum Maximum Volume 4.00078 in^3 Mass 0.328682 lbmass Von Mises Stress 0 ksi 82.2341 ksi 1st Principal Stress -74.155 ksi 72.5682 ksi 3rd Principal Stress -137.747 ksi 17.3802 ksi Displacement 0 in 1.71627 in Safety Factor 0.0862458 ul 15 ul Stress XX -113.244 ksi 18.0739 ksi Stress Analysis of a Simple Machine: Pizza Cutter 19

Stress XY -14.6259 ksi 13.1795 ksi Stress XZ -27.7264 ksi 27.936 ksi Stress YY -77.0201 ksi 30.7627 ksi Stress YZ -19.4422 ksi 14.1826 ksi Stress ZZ -107.317 ksi 65.0236 ksi X Displacement -0.0929706 in 0.250321 in Y Displacement -0.0486236 in 0.536644 in Z Displacement -0.100285 in 1.62624 in Equivalent Strain 0 ul 0.191809 ul 1st Principal Strain 0 ul 0.154551 ul 3rd Principal Strain -0.213107 ul 0.0000189722 ul Strain XX -0.176952 ul 0.0337434 ul Strain XY -0.0498689 ul 0.0449371 ul Strain XZ -0.0945368 ul 0.0952516 ul Strain YY -0.0381287 ul 0.0473638 ul Strain YZ -0.0662907 ul 0.0483575 ul Strain ZZ -0.133343 ul 0.122929 ul Contact Pressure 0 ksi 228.148 ksi Contact Pressure X -49.8649 ksi 55.6802 ksi Contact Pressure Y -18.1068 ksi 37.6424 ksi Contact Pressure Z -92.7032 ksi 218.198 ksi Stress Analysis of a Simple Machine: Pizza Cutter 20

Stress Analysis Failure

Figure 1. Z Displacement of the pizza cutter handle due to the applied forces in Test II Stress Analysis of a Simple Machine: Pizza Cutter 21

Stress Analysis Report Success

Overview: Force 1 (Handle) = 30lbf, Force 2 (Wheel) = 10lbf

Analyzed File: Pizza Cutter Assembly.iam Autodesk Inventor Version: 2016 (Build 200138000, 138) Creation Date: 9/29/2016, 6:48 PM Simulation Author: dsimps6

Project

Part Number Pizza Cutter Assembly Designer dsimps6 Cost $0.00 Date Created 9/27/2016

Status

Design Status WorkInProgress

Physical

Mass 0.328674 lbmass Area 33.0398 in^2 Volume 4.00057 in^3 x=2.99288 in Center of Gravity y=2.82073 in z=-0.217156 in

Note: Physical values could be different from Physical values used by FEA reported below.

Simulation: 1 General objective and settings: Design Objective Single Point Simulation Type Static Analysis Last Modification Date 9/29/2016, 6:47 PM Stress Analysis of a Simple Machine: Pizza Cutter 22

Detect and Eliminate Rigid Body Modes No Separate Stresses Across Contact Surfaces No Motion Loads Analysis No

Material(s)

Force: 1

Load Type Force Magnitude 30.000 lbforce Vector X -12.466 lbforce Vector Y 14.983 lbforce Vector Z 22.806 lbforce Stress Analysis of a Simple Machine: Pizza Cutter 23

Force: 2

Load Type Force Magnitude 10.000 lbforce Vector X 5.515 lbforce Vector Y 4.632 lbforce Vector Z -6.937 lbforce

Fixed Constraint: 1

Constraint Type Fixed Constraint

Contacts (Bonded)

Name Part Name(s) Pizza Cutter Blade:1 Bonded:1 Pizza Cutter Connector:1 Pizza Cutter Connector:1 Bonded:3 Pizza Bolt:1 Pizza Cutter Connector:1 [M]: Bonded:2 Pizza Cutter Handle:1

Results

Reaction Force and Moment on Constraints

Reaction Force Reaction Moment Constraint Name Magnitude Component (X,Y,Z) Magnitude Component (X,Y,Z) 6.95112 lbforce -0.795258 lbforce ft Fixed Constraint:1 26.17 lbforce -19.6147 lbforce 13.4159 lbforce ft 11.3126 lbforce ft -15.8687 lbforce -7.16784 lbforce ft

Result Summary

Name Minimum Maximum Volume 4.00078 in^3 Mass 0.328682 lbmass Von Mises Stress 0 ksi 18.9772 ksi 1st Principal Stress -17.1127 ksi 16.7466 ksi Stress Analysis of a Simple Machine: Pizza Cutter 24

3rd Principal Stress -31.7877 ksi 4.01086 ksi Displacement 0 in 0.396062 in Safety Factor 0.37373 ul 15 ul Stress XX -26.1332 ksi 4.17093 ksi Stress XY -3.37521 ksi 3.04154 ksi Stress XZ -6.39835 ksi 6.44675 ksi Stress YY -17.7738 ksi 7.09908 ksi Stress YZ -4.48666 ksi 3.27293 ksi Stress ZZ -24.7653 ksi 15.0055 ksi X Displacement -0.0214538 in 0.0577672 in Y Displacement -0.0112203 in 0.123841 in Z Displacement -0.023143 in 0.375287 in Equivalent Strain 0 ul 0.0442637 ul 1st Principal Strain 0 ul 0.0356656 ul 3rd Principal Strain -0.0491786 ul 0.0000037938 ul Strain XX -0.0408352 ul 0.00778704 ul Strain XY -0.0115082 ul 0.0103705 ul Strain XZ -0.021816 ul 0.0219811 ul Strain YY -0.00879905 ul 0.0109301 ul Strain YZ -0.0152979 ul 0.0111595 ul Strain ZZ -0.0307715 ul 0.0283682 ul Contact Pressure 0 ksi 52.6495 ksi Contact Pressure X -11.5073 ksi 12.8492 ksi Contact Pressure Y -4.17848 ksi 8.68666 ksi Contact Pressure Z -21.3931 ksi 50.3532 ksi Stress Analysis of a Simple Machine: Pizza Cutter 25

Stress Analysis Success – Z-Displacement View

Figure 1. Z Displacement of the pizza cutter handle due to the applied forces in Test I