PMD Topic 1 Design Philosophy

8/18/2019 PMD Topic 1 Design Philosophy

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© 1994 by Alexander H. Slocum

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Precision Machine Design

Topic 1

Introduction to the design process forprecision machines

Purpose:

This lecture provides an introduction to the machine designprocess, with emphasis on overall design philosophy, casestudies, and concept selection methods.

Outline:

• Design methodology

• Functional Requirements, Design Parameters, &Preliminary calculations

• Conceptual designs

• Importance of sketching designs

• Conceptual design: Decision making methods

• Machining center design case study

• Coordinate measuring machine design case study

"Enthusiasm is one of the most powerful engines of success.When you do a thing, do it with all your might. Put your whole

soul into it. Stamp it with your own personality. Be active, beenergetic, be enthusiastic and faithful and you will accomplishyour object. Nothing great was ever achieved withoutenthusiasm"

Ralph Waldo Emerson


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Basic precision machine design philosophy

• Designs should be made as mechanically good as isreasonably possible.

• Increases in performance are then obtained via measurement,mapping, and servo control:

C o s t

Mechanical system

Simple servomechanism

Mapped servomechanism

Metrology frame based

servomechanism

Difficulty = Environment × Load × Range × SpeedAccuracy

• Make the design hospitable to measurement:

• Make room for sensors.

• Design in alignment surfaces.

• Minimize Abbe errors.

•

Use modular elements whenever possible:

• Create a “platform concept” that is upgradeable merelyby substituing new components.

• Choose bearings, actuators, sensors, and controller asinterdependent components.

• Design the machine as if you had to use it.


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Organize your thought process

• Design is like a giant box of Legos™

• You need to empty the box on the floor and spread theLegos™ out in order to find the best parts for yourspaceship.

• While looking for a cool wing, you may discover a betterengine!

So:

• Organize your brain to be a collector and analyzer of information.

• Organize your thoughts to be a digester of information and asynthesizer of new designs.

• Organize your mind to be an n-dimensional holographiccomparator.

• Provide it with systematic and random search, compare,and synthesizing capabilities.


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• Imagine that your mind is a vast three dimensional array of cubes which are designed to hold information:

Knowledge

Wisdom

Imagination

• With time, the number of cubes that are filled withinformation grows.

• When you read about a new type of bearing, you file theinformation in a knowledge cube.

• New methods for using bearings may be filed in animagination cube.

• Past experiences with the bearing may be filed in awisdom cube.

• Random or systematic search patterns through the array of cubes allows you to think of solutions to problems.

• During the search for solutions:

• Often you will discover that there is a collection of cubesthat do not have the contents you need.

• Thus you may discover the need for a new invention.


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How to keep informed

• Catalogs.

• One must keep things in perspective and not develop catalogitis.

• Catalogitis: "design is the gospel according tocatalogs, and thou musteth use stock parts."

• The use of standard versus nonstandard parts must beconsidered carefully.

• Before specifying a part, a designer should also check alisting of companies (e.g., in the Thomas Register) .

• Trade magazines and their "Bingo cards" (used to ordermanufacturers' product literature).

• A small personal library of reference books.

• Societies that exists for engineers.1

• Standards used that pertain to the products being designed.2

• Networking:

• You must build a network of friends and associates whocan help you to keep informed, and vice versa.

• You must be able to function effectively in a team.

1 For example, the American Society for Precision Engineering in Raleigh, NC (919)839-8444, and the Japan Society of Precision Engineering.2 For example, a designer of rotary tables or spindles should keep a copy of Axis of Rotation: Methods for Specifying and Testing , ANSI Standard B89.3.4M-1985, andTemperature and Humidity Environment for Dimensional Measurement, ANSI StandardB89.6.2-1973. A catalog of standards is available from the American Society of Mechanical Engineers, United Engineering Center, 345 East 47th St., New York, NY10017.


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Whenever you obtain a new piece of information

• Search through your mind and see if this new piece cancombine with any existing pieces to make something useful.

• Take note during the search if the information can be usefulto someone else whom you know has a problem that needssolving.

• Networking is one of the most powerful assets of aninformation-based society.

• Always look for new applications and opportunities.

• Opportunity always knocks, but one needs to do a careful

MFT (mental Fourier transform) to see where the peaks are!


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Resulting Overall design strategy

1 ) Carefully establish your database and networks as statedabove.

2 ) Remember Maudslay's maxims:

l . Get a clear notion of what you desire to accomplish, then you will probably get it.

2 . Keep a sharp look-out upon your materials: get r i d of every pound of material you can do without. Put yourself to the question, "what business has i t there?" Avoid complexities and make everything as simple as possible.

3 . Remember the get-ability of parts.

• Stated by Henry Maudslay in the 1700's, they are thefoundation of concurrent engineering.

3 ) Know your customers. Talk to them directly, in addition tolistening to marketing and maintenance and manufacturing.


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Recognize that there are three types of design:

• Scaled design:

• An existing design does the job well, and just needs tobe scaled for the new application.

• For example, a ballscrew size change for a largermachine.

• Evolutionary design:

• An existing design is pretty good, but fundamentalimprovements can be made.

• For example, a ballscrew evolves into a planetaryrollerscrew.


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• Revolutionary design:

• A totally new approach is used to achieve the samefunction, but with better performance.

• For example, a linear electric motor instead of ascrew-type transmission.

Carriage

Linear motor

magnet assembly

Rail

Linear

motor coil


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But be careful not to jump to quickly!

•

INA introduced ballscrew-like shaft with a helical gothicarch lead.

• Instead of small balls rolling on a large shaft (at highspeed), it uses four ball bearings:

•

The inner races are rounded to mate with thegothic arch groove, and the axes of rotation areinclined to the shaft.

• The result is an order-of-magnitude lower rollingelement velocity, and no need for lost contact duringrecirculation.

• This actuator is half the cost of a linear motor systemand can run at nearly the same speed!

• It is perfect for the actuation of grinding tables ateither creep-feed or reciprocal grinding speeds;However, it still has the issue of shaft rotationalinertia.


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The Result of all the above is the Design Process

• A good designer:

• Carefully budgets time and resources.

• Defines what she wants to accomplish (functionalrequirements).

• Defines the resources available (materials, parts thatcan be used).

• Creates solutions ranging from a “safe” solution to aneat, wild WOW solution.

• Evaluates the physics and feasibility of solutions thatcan be created within the context of the allowable timeand budget!

• Updates the schedule and budget• Embodiment and Details: Makes the design happen in a

timely, orderly, well-documented manner.

• Implements the design (competes) and then reflects onwhat went right and wrong.

Functional Requirements, Design Parameters, &Preliminary calculations

•

Before you start “designing”, you have to get your box of Legos in order.

• You are designing a deterministic machine, sodeterministically:

•

Determine what the machine must do (FunctionalRequirements, Frs)

• Start thinking about what elements (Design Parameters, DPs)could enable you to satisfy the FRS.

•

Identify the physics that govern the performance of the DPs.


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Functional Requirements (FRs) & DesignParameters (DPs)

• From the overall strategy, the functional requirements can bedeveloped (sketches of the design strategy can be helpful).

• Design Parameters: Physical attributes that satisfy FRs.

Physics of the problem

• It is often useful to list the physics involved next to thefunctional requirements (simple models can help).

Example:

Basic FRs Initial DPs

Easy to do Impressive WOW

Dominantphysics

Fast travelspeed

0.25m/s .5 m/s 1 m/s F=ma

Γ =Fr

V=at

V=rω

x=0.5at2

Frontscooper

Forklifttype (raise

only)

Raise andcurl

Raise, curl,extend

M=Fl

σ=Mc/I

Climb peak wheelsclosespaced

Tracks Jump! Friction

F=FNµ

Notflippable

Low centerof gravity,wide stance

Outriggers BIG wheels,noprotrudinghardware,drives upsidedown

ΣM=0

basicstability


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Conceptual design

• Conceptual design can affect a machine's:

• Accuracy.

• Repeatability.

• Resolution.

• Frictional qualities.

• Difficulty of design.

• Difficulty of manufacture.

• Operating cleanliness.

• Cost.

• Safety.

• Ruggedness.

• Availability.

• Any overlooked item will come back to haunt you, so get it

right the first time!


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There are several methods for generating conceptualdesigns:

FIRST get the design team to identify the Functional Requirements!, Then:

• Individual thought:

• Often the most creative.

• Rohrbach's 635 method:

• First individual, and then group analysis anddiscussions, offers the best of both worlds.

• Group brainstorming:

• Greatest breadth of resources applied collectively.


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Individual thought is often the most creative.

• Do leisurely things (e.g., long walks) that you know inspirecreative thought.

• Get out of traffic and take alternate routes.

• Sketch ideas and the ideas principal components.

• Cut out the principal components and pretend they aremodular elements.

• Like toy building blocks, try different combinations of components to make different machines.

• Pit one machine idea against another and imaginestrategies for winning.

• Take the best from different ideas and evolve them intothe best 2 or 3 ideas that you can think of.


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Rohrbach's 635 method:

• Six people write down their three best ideas and circulatethem to the other five for comments.

• The people then get together to discuss their ideas.

• A written record is made of who first had the idea, sopersonality conflicts are more easily avoided.

• It tends to generate a collective mind, so everybody knowswhat everyone else has been thinking.

• The group mind then works together in a more efficientmanner when brainstorming.


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Group brainstorming:

• A means to often solve personal creativity deadlocks.

• A means to make sure something hasn't been overlooked.

• Group personality factors must be considered:

• Shy individuals getting run over.

• Aggressive individuals driving.

• An individual's personality often has nothing to do withcreativity.

• Careful to avoid conflicts over the issue of who first thoughtof the idea.

• The people in the group must be willing to take praise orscolding as a group.

• Formal methods exist.

• Psychologists have generated established rules to makethe process work successfully.3

Have the meeting over the hardware! or in the shop!

3 G. Pahl and W. Beitz, Konstruktionslehre, Springer-Verlag, Berlin, 1977.Translated and published as Engineering Design, Design Council, London, 1984, pp. 87-88.


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Importance of sketching designs

• The ability to sketch approximate scale drawings of aconcept is invaluable.

• Sloppy disproportionate sketches send a signal tomanagers that the design will also be sloppy.

• Design sketches of ideas and major components allow one tobuild and compare models of ideas.

• A matrix of ideas can be laid out and "what-if"scenarios can then be performed.

• "Moving" components (a piece of paper) from design to

design allows for rapid real-time evolution.


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• The ability to sketch a stick figure of a design and label theerror motions is invaluable.

• Knowing where the errors are signals that you

understand the physics of the design.

• The ability to tell which error motions cause critical errorsat the tool point is invaluable.

• Knowing what the critical errors are signals that youunderstand the details of the design.

• A stick figure helps to:

• Define the sensitive directions in a machine.

• Locate coordinate systems.

• Set the stage for error budgeting.

• It helps to prevent the designer from locking in on a shapetoo early.

Y carriage

Z carriage

Wheel/

Workpiece

Spindle

(rotor in bearings)

Column

Bed

Reference

Y

Z

X

400

315

1700

425

1700

100

Table

450

300

400 545700

330

115

240

110

100

300

215

Sensitive for surface

and profile grinding

Sensitive for profile

grinding


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Sketching example: A surface grinder:

Table

Wheel

Y axis column Y axis carriage

Z axis carriage

Z axis linear motion bearings

Z axis Ballscrew

Y axis motor

Z

X

Y

Bed


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Preliminary calculations

• Past the hand sketch, and before the computer sketch, todetermine feasability, and to guiode initial FEA.

• Spreadsheets provided with this course to aid in the design of precision machines:

Spreadsheet Purpose

AHP.XLS To apply the Analytic Hierarchy Process to selection of the "best"concept

BALLSCRW.XLS To determine equivalent load rating for ballscrew selection

BEAMBEND.XLS To determine slope, bending, and shear deflections of a simply

supported beam loaded by its own weight.

BIMAT.XLS To determine thermal deformations in a bi-material beam

BOLTJDES.XLS To design bolted joints

CYLNDEXP.XLS To calculate the radial displacement of a pressurized cylinder

HERT.XLS To determine Hertz contact stresses between bodies in pointcontact.

HERTZTAN.XLS To determine tangential stiffness and contact stress between twobodies (e.g., for friction drive design)

KINCOUP.XLS To design three groove kinematic couplings

KINSLIDE.XLS To analyze of errors in a kinematically supported carriage (slide)

RAILDES.XLS To design bolted "boxway" bearing rails

RAILFND.XLS To determine characteristics of a bolted rail on elastic foundation

SCREWPOW.XLS To calculate power to turn a screw

CLD.XLS To design a constrained layer damper

THERMERR.XLS To determine temperature gradient induced errors in a simplysupported beam

TMDDES.XLS To design tuned mass dampers


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Error Budget Spreadsheets provided with this course to aid inthe design of precision machines:

Spreadsheet Name User Input Output to User

CShelp.XLS Location (position andorientation) of coordinatesystems for tool and work.

none

CS_inp.XLS none. Ideal location of tool in work.

K_inp.XLS Compliances betweencoordinate systems.

None.

F&M_inp.XLS Forces and moments applied tocoordinate systems.

Resultant sum forces andmoments.

Temp_inp.XLS Thermal expansion coefficientand temperature differencesbetween coordinate systems.

Thermal expansion errors.

Geo_err.XLS Geometric errors between thecoordinate systems

Sum_err.XLS None Sum of all the errors in eachcoordinate system.

Err_out.XLS Error toggle switch andmapping improvement factors

Ideal and actual location of tool inwork, and the resulting locationerror between the tool and thework in the reference frame


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Conceptual design: Decision making methods

• There are many systematic methods available for evaluatingdesign alternatives.

• Most rely on some sort of weighting of attributes toarrive at a "desirability score".

• The simplest method is a linear weighting scheme:

• Apply a desirability value to each parameter that affectsthe performance of a component in a design.

• Easiest to use provided user bias can be minimized.

• Acceptable when there are only a few design alternativesto consider.

• A linear weighting scheme (a series of +, -, 0 wrt abaseline design) will give equal weighting to attributes.

Design 1(Baseline)

Design 2 Design 3 Design 4

Accuracy 0 + 0 +

Ergonomics 0 - - +

Cost 0 0 + +

Flexibility 0 0 - +

Robustness 0 + - -

Manufacturability 0 + 0 -

Serviceability 0 + + 0

Total + and - 0 3 - 1 2

• Use to identify positive attributes of competing designs thatcan be blended in with the best to make it better.


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Example: Select a linear bearing for a machine tool

• Factors to consider in their selection include:

• Accuracy of motion: Straightness, Smoothness.

• Friction Characteristics: Static µ, Dynamic µ.

• Cost: Purchase, Install, Maintain

• When there are more than several variables, it is oftendifficult to evaluate their relative importance.

• It is like trying to add Newtons to meters, the dimensionscannot be added properly.

• A method is needed to non-dimensionalize the parameters.

Carriage (saddle)

Base

Rail

Keeper

Mt

MtoE1

S1 THREAD

N2HH1

A2

A

S2 SCREW SIZE

S3 SCREW SIZEA1

A3

N1H2

N3

B

E2

E3

T

L

C, CoMl

Mlo

V

R

R

Ru

Ru

R

RRl R

l


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• Thomas Saaty developed the Analytic Hierarchy Process(AHP) to help make complex decisions.

• First determine the relative importance of each

characteristic at each level in the outline of designattributes.

• Next evaluate the relative characteristics of eachcomponent of the design with respect to the most explicitcharacteristic.

• Comparisons are done with experienced personnel from:

• Engineering

• Marketing

• Manufacturing

• Service

• The relative evaluation characteristics' importances aredebated in an open forum.

• The relative importances of the components are debatedin an open forum.

• Egos are diffused, and only rationally justifiablepositions are accepted.

• This is an excellent method to start a project off on a concurrent engineering track


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Step 1: Setting up the AHP Model

• Compare the AHP's construction to a system of water tanks

40%

100%

25% 15% 12% 8% 15% 15% 10%

20% 40%

Level 1

Level 2

Level 3

• The distribution of water is analogous to the distribution of priorities (or weights).

• The desirability (or weight) for each entry with respect toother entries on that level can be equated to:

• The distribution (by percent) of the initial volume of water among the reservoirs on the same level.

• At any level the total percentage of water distributed amongthe reservoirs at that level is equal to 100%.

Select a bearing for a Diamond Turning Machine

Straightness Smoothness Maintain

Accuracy Friction Cost

InstallPurchaseStaticDynamic


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Step 2: Importance of design choices

• The evaluation of a design option is done by determining its"importance" for each Level 3 entry (the lowest level).

• The "importance" of an item with respect to each entry inLevel 3 can be expressed in terms of actual physical values.

• Most often, a numerical scale should be used such as:

Importance Defini tion

1 Equal importance

3 One a little more important than the other (1/3)

5 One is more important than the other (1/5)

7 One is much more important than the other (1/7)

9 Absolute importance (1/9)

Accuracy Friction Cost

Accuracy 1

2 4Friction .5 1 2

Cost .25 .5 1

• The team debates the comparisons and fills out the top row.

• The matrix is diagonal, and determinism is applied to ensureconsistency.

• Check lower diagonal values to make sure the team agreeswith them.

This forms a "fuzzy Logic set" characterizing whatthe team feels are the important judgment factorsfor a design.


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• Priority is approximately the geometric mean of the row.

• Overall priority is normalized with respect to the sum of theindividual priorities.

• The level three normalized priorities are multiplied by thecorresponding level two normalized priorities.

• This yields a normalized weight for the level threecharacteristics.

• For the bearing selection, the spreadsheet output for levels 2& 3 is:

Accuracy Friction Cost Priority N. Prior. Level 2Accuracy 1.000 2 . 000 4 .00 0 2.000 0.571 =57%

Friction 0.500 1.000 2.000 1.000 0.286 =29%Cost 0.250 0.500 1.000 0.500 0.143 =14%Sum 1.750 3.500 7.000 3.500 1.000

Accuracy Straight. Smooth. Priority N. Prior. N. Wght Level 3Straightness 1.000 0 .500 0.707 0.333 0.190 33*57=19%Smoothness 2.000 1.000 1.414 0.667 0.381 67*57=38%Sum 3.000 1.500 2.121 1.000 0.571

Friction Static Dynamic Priority N. Prior. N. Wght Level 3Static 1.000 4 .000 2.000 0.800 0.229 80*29=23%Dynamic 0.250 1.000 0.500 0.200 0.057 20*29=6%

Sum 1.250 5.000 2.500 1.000 0.286Cost Purchase Install Maintain Priority N. Prior. N. Wght Level 3Purchase 1.000 0 .500 0 .50 0 0.630 0.200 0.029Install 2.000 1.000 1.000 1.260 0.400 0.057Maintain 2.000 1.000 1.000 1.260 0.400 0.057Sum 5.000 2.500 2.500 3.150 1.000 0.143

• Note that the total of all the normalized weights is 1.0.

• Each matrix is diagonal (mathematical relationships). Onlyenter numbers in bold

This defuzzifies the qualitative judgments so theycan be applied in a deterministic manner to evaluateoptions.


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Step 3: Results

• Desirability is found by combining the normalized weightswith the relative evaluations of bearing characteristics:

desirability = (level 3 weights) × (bearing desirability values)∑ j = 1

7

• Again, a team discusses and justifies the comparisons, sonovice designers become enlightened.

• For the bearing selection, the spreadsheet output is:

Bearing comparison: Overall Norm

Straight. Smooth. Static mu Dyn. mu Purchase Install Maintain Goodness GoodnessSliding teflon 7 0 . 00 0 7 . 0 0 0 1 . 0 0 0 2 . 0 0 0 5 . 0 0 0 3 . 0 0 0 5 . 0 0 0 0.274 0.27

Rolling balls 6 0 . 00 0 5 . 0 0 0 3 . 0 0 0 5 . 0 0 0 3 . 0 0 0 5 . 0 0 0 5 . 0 0 0 0.283 0.28

Hydrostatic 9 0 . 00 0 9 . 0 0 0 9 . 0 0 0 5 . 0 0 0 1 . 0 0 0 2 . 0 0 0 1 . 0 0 0 0.443 0.44

• To prevent a person from driving the results to theirfavorite without rational discussion:

• Each product in the overall goodness column isnormalized by the sum of the choices' desirability values.


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• The AHP should be used by a group of "experts" fromengineering, marketing, manufacture, maintenance, etc.

• The numbers you generate while practicing alone may

seem arbitrary to you.

• However, they do get you to think about the designcriteria.

• A group will educate members about why designdecisions are made.

• It helps a group to rapidly converge on consensus,because it forces members to focus on one topic at atime.

• It then gives a deterministic means to pull all theelements together for a total decision.


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Case study: Cincinnati Milacron's high speedmachining center (HSMC)

• Designed for high speed hole drilling and near-net-shape

part finishing.

• Speed and reliability were of prime concern.

• Goal was to minimize the number of parts.

• Machine would be used in duplex mode (two machines facingeach other), so a horizontal spindle was required.


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Conceptual designs

• Fully articulated and traveling articulated designs:

• Low rigidity.

• Large error at tool cause by angular error at joint (Abbeerror).

• Too many degrees of freedom.


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• Scissors jack design:

• Large number of joints.

• Non-uniform transmission ratio:


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• Rectilinear design for a high speed machining center:

• Linear axes are easy to manufacture.

• Configuration lends itself to the use of a single moving wallto prevent chips and coolant from getting into sensitiveareas.

Spindle

Moving wall


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Effects of sealing systems on concept selection

• Greater stiffness and accuracy can be obtained if the duplexrequirement is dropped and the pallet is allowed to be on a

moving axis.

• The spindle is then carried on a 2 degree of freedomstacked axis.

• The work holding table (pallet) has a single degree of freedom.

• With the pallet on a Z axis, the spindle stacked axes onlyneeds a single seal:

• The Y axis can be positioned behind a moving wall.


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Case study: Sheffield's ring bridge coordinatemeasuring machine (CMM)

• Structural configurations for CMMs:

• Fixed table cantilever arm CMM.

• Moving bridge CMM.

• Column type CMM.

• Moving ram horizontal arm CMM.

• Moving table horizontal arm CMM.

• Gantry type CMM.

• Ring bridge type CMM.

• Goodness can be defined by CA factor:

CA =volume × throughput

accuracy × price(1.6.1)

• The CA factors for existing machines and the CA factorcustomers wanted indicated the need for a new CMM design.

Z

Y

X

Workpiece

tableProbe

Ring bridge


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Applying the AHP method to CMM design

• The CA factor is not too helpful for a qualitative comparisonof design concepts.

• Existing design types to be evaluated using the AHP include:

• Fixed table cantilever arm• Moving bridge• Column• Moving ram horizontal arm• Moving table horizontal arm• Gantry• Ring bridge


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• AHP parameters for CMM evaluation:

Accuracy ModularityScanning (contouring) X axis

Abbe (sensors) Yaxis

Abbe (actuators) Zaxis (ram)Abbe (bearings) StructureCenter of stiffness/mass congruence

Dynamic (stiffness) EvolvabilityDynamic (mass) AutomatedDecoupling (part weight) Touch trigger

Different sizesCost

Sale price ErgonomicsMaintain Operator

Labor to produce ServiceComponents to buy Sales

ManufacturabilityBearingsStructureAssembly


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• The importance of the major design criteria were assumed tobe:

Manufac t- Modul - E v o l v - Ergon- Norm.

Accuracy C o s t u r a b i l i t y a r i t y a b i l i t y o m i c s Priority prior ity

Accuracy 1.00 1 . 0 0 3 . 0 0 5 . 0 0 5 . 0 0 5 . 0 0 2.69 0.34

C o s t 1.00 1.00 3.00 5.00 5.00 5.00 2.69 0.34

Manufac t urab i l i t y 0.33 0.33 1.00 1.67 1.67 1.67 0.90 0.11

M o du l a r i t y 0.20 0.20 0.60 1.00 1.00 1.00 0.54 0.07

E v o l v a b i l i t y 0.20 0.20 0.60 1.00 1.00 1.00 0.54 0.07

E r g o n o m i c s 0.20 0.20 0.60 1.00 1.00 1.00 0.54 0.07

Sum 2.93 2.93 8.80 14.67 14.67 14.67 7.88 1.00

• Existing design types evaluated using the AHP gave thefollowing results:

• Column 0.75• Moving table horizontal arm 0.84• Moving bridge 0 .88• Fixed table cantilever arm 1.00• Moving ram horizontal arm 1.01• Ring bridge 1 .05• Gantry 1 .07


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• When one performs a sensitivity analysis by trying differentpriorities in the AHP spreadsheet:

• The accuracy requirement drives the decision towards a

closed frame structure.

• It also implies that the part should not rest on a moving axis.

• The gantry design drives the main mass closer to the centerof mass and stiffness.

• The ring bridge design drives the mass through the bottomportion of the ring.

• If ease of part loading and the ability to program the CMM

in teach mode, the ring bridge may become an equal choice.

• The lighter moving structure of the bridge design wouldmake the gantry machine easier to move by hand.

• Even though the access is more limited.


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• Two designs were done, and cost and ergonomicsconsiderations indicated the ring bridge design was best.

• From the sales literature (Courtesy of Sheffield Measurement, a Giddings & Lewis

Company):

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PMD Topic 1 Design Philosophy