Sally Miller PUPS 3

2/21/2016 Problem (Opportunity!): Think of the machine you want to design, build and own as the term project in this class. 1. State the problem to be solved, what else exists, and why you think you should design a new machine (even if just for fun). (1 pt) I’m going to build a mini desktop mill with a work area of about 300 mm x 300 mm x 150mm. There are a variety of desktop mills on the market (such as the Roland Modela and Othermill) However, they cost a few thousand dollars, and I know I can make one much, much cheaper. The challenge will be to make one with similar tolerances! My main use case will likely be engraving of wood, plastic, glass, or stone, but I’d like it to have 3 axes so I can also make molds to cast small silicone parts if I want. Since my main use case will be an engraver, I might end up making a 2 axis machine—that’s a little up in the air still. I’m planning on making a mount/clamp to hold a variable speed dremel. I think making a secure clamp will be one of the biggest challenges to maintain my required tolerance. 2. State the Functional Requirements and specifications for your machine, with the understanding that other than three stepper motors and the Arduino control board and stepper motor drivers, each student has to scrounge up their own materials. (1 pt)

Functional Requirements

Design Parameters

Analysis References Risk Counter Measures

300mm x 300mm x 150mm

Fit on a desk

Accuracy: 1mm/300mm

Accurate engravings that don’t show warpage

Stiffness Strength

FUNdaMENTALs, Machinery’s HB

Play in dremel clamp

Use foam or some malleable material in between rigid clamp and dremel

Spindle speed:

Optimal for 1/16”

http://mdm.boschwebservices.com/files

Clearing chips Fan? Or manual chip clearing?

1000-3000rad/s

and 1/32” bit

/r00682v-1%20r19397v3.pdf

Test to see if this is a problem

a. Remember to also consider important details

i. Safety is a critical part of design to be considered from the beginning! ii. Seals, bellows, wires, cutting chips, fixturing…

3. Embody the FRs in a FRDPARRC table for your machine (where a lot of the entries of course will be blank, but as your design progresses you can fill them in). (1 pt). See above 4. What are the forces the machine has to withstand? (1 pt)

a. If a cutting machine, think of the power of a similar machine, the speed of the spindle, and diameter of the tool to estimate forces…

Dremel Specs: 3000 Series Variable Speed Rotary Tool Cost: ~$60 (Amazon.com) Amperage: 1.2 A Voltage: 120 V Speed: Variable (5000-32,000 RPM)

Operating Instructions: http://mdm.boschwebservices.com/files/r00682v-1%20r19397v3.pdf

Engraving tool diameter: 1/16”=1.6 mm 𝑃𝑜𝑤𝑒𝑟 = 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 ∗ 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 = 1.2𝐴 ∗ 120𝑉 = 144 𝑊

𝑃 = 𝜏 ∗ 𝜔𝑠𝑝𝑖𝑛𝑑𝑙𝑒

144 𝑊 = 1000 𝑟𝑎𝑑/ sec∗ 𝜏

𝜏 =144

1000= 0.144 𝑁 ∗ 𝑚

0.144 𝑁 ∗ 𝑚 = 𝐹𝑐𝑢𝑡 ∗𝐷𝑡𝑜𝑜𝑙

2= 𝐹𝑐𝑢𝑡 ∗

0.0016 𝑚

2

𝐹𝑐𝑢𝑡 =2 ∗ 0.144 𝑁 ∗ 𝑚

. 0016 𝑚= 180 𝑁

This is the max force.

But how much power does it actually take to cut the material?

5. Given the desired accuracy of the machine, what is the required stiffness? (1 pt) Accuracy: 1 mm/300 mm

𝐾 =𝐹

𝛿 where F is the applied force, 𝛿 is the deflection, and K is the bending stiffness.

I’m assuming that the deflection is 0.1 mm because I know there will be tolerance considerations for the bearings, actuators, and structure, and so I am including a large safety factor into my analysis.

𝐾 =1.45 𝑁

0.0001 𝑚= 14500 ∗

𝑁

𝑚

6. Assume the structural loop length of your machine is three times the sum of the distances each axis must travel, to get a feel for the structural loop: (2 pts) 3*(0.3m+0.3m+0.15m)=2.25m Spreadsheet for all calculations for #6: Cantilevered beam

Assuming curcular cross section w/ outer dimension 1/5 the length, wall thickness 1/20 the diameter

δ 0.0001 m

F 1.45 N

E 2E+11 Pa

L 0.000551918 m

Assuming L=2.25m, b=b, h=2b, t=b/10

b 0.031548736 m

L 2.25 m

Curved Beam

Assuming L=2.25m, b=b, h=2b, t=b/10

r 0.01733125

R 0.716197244

a. What is the size of a cantilever beam (tube cross section) whose length is the length of the structural loop?

i. State your assumptions on proportions.

Assuming the base is b, height is 2b, wall thickness is b/10, and length is 2.25m, which is the assumed length of the structural loop, b for aluminum (E=69 GPa) is 41 mm and b for steel (E=200 GPa) is 32 mm.

ii. Assume tube outer dimension is 1/5 the length, and wall thickness 1/20 the diameter.

This doesn’t make sense. All dimensions are given. The length of the beam is the structural loop, the outer dimension is ¼ the structural loop, and the thickness is 1/20 the diameter. Nothing is unknown. However, I did the analysis assuming the length of the structural loop to be unknown. For steel, L is 0.5 mm, and for aluminum, L is 1.6 mm. Not very helpful!

b. What is the size of a C-shaped (curved beam 180 degree segment) (tube cross section) whose length is the length of the structural loop?

i. State your assumptions on proportions. Updated 2/25/16

Assuming radius r and thickness r/5, for aluminum r=2.3 cm and for steel r=1.7 cm.

ii. Assume tube outer dimension is 1/5 the length, and wall thickness 1/20 the diameter. from above, this isn’t very useful. Reference: http://www.eis.hu.edu.jo/ACUploads/10526/CH%204.pdf

c. If the mass of the machine is N x the mass of the tube, what is a first order estimate of the natural frequency of your machine as a function of N (plot it).

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10 12 14 16

Nat

ura

l Fre

qu

ency

(H

z)

N (mass of machine = N x mass of tube)

Natural frequency of machine as a function of its mass (assuming structure made from Al)

Ref: http://teaching.ust.hk/~mech300/mech300_7_2_beam.pdf

7. Sketch stick figures for different strategies you now envision for solving the problem. (1 pt)

a. Use the basic starting FRDPARRC and enter more detail for each strategy

Strategy 1

Functional Requirements

Design Parameters

Analysis References Risk Counter Measures

300mm x 300mm x 150mm

Fit on a desk

Accuracy: 1mm/300mm

Accurate engravings that don’t show warpage

Stiffness Strength

FUNdaMENTALs, Machinery’s HB

Play in dremel clamp

Use foam or some malleable material in between rigid clamp and dremel

Spindle speed: 1000-3000rad/s

Optimal for 1/16” and 1/32” bit

http://mdm.boschwebservices.com/files/r00682v-1%20r19397v3.pdf

Clearing chips Fan? Or manual chip clearing? Test to see if this is a problem

Strategy 2

Functional Requirements

Design Parameters

Analysis References Risk Counter Measures

300mm x 300mm x 150mm

Fit on a desk

Accuracy: 1mm/300mm

Accurate engravings that don’t show warpage

Stiffness Strength

FUNdaMENTAL, Machinery’s HB

- Play in dremel clamp

- Longer structural loop

Use foam or some malleable material in between rigid clamp and dremel

Spindle speed:

Optimal for 1/16”

http://mdm.boschwebservices.com/files/r0068

Clearing chips Fan? Or manual chip clearing?

1000-3000rad/s

and 1/32” bit

2v-1%20r19397v3.pdf

Test to see if this is a problem

b. Apply Error Apportionment for different strategies

8. Create geometric error budgets for “top” strategies. (2 pts) I don’t have a good understanding of how the error budget works. I’ve attached the best I could come up with, but I’d like to go over this again in class (or outside of class). The error apportionment makes sense to me, but at this point I can’t do anything useful with the error budget spreadsheet. I know you don’t like attachments, but in this case I can’t help it. See attached error budget on main 2.70 webpage. Peer Review: