A THREE Axis CNC ROUTER DESIGN

by

Alexander D. Sprunt

SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING IN PARTIALFULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

BACHELOR OF SCIENCEAT THE

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

JANUARY 2000__~~X (j'T-)(D

@ 2000 Alexander D. SpruntAll rights reserved

The author hereby grants to MIT permission to reproduce and todistribute publicly paper and electronic copies of this thesis document in whole or in part.

S ig nature of A uthor ........................................................ ................ .................................Dep rtment of Mechanical Engineering

January 14, 2000

C e rtified by ............................ { .... ......... ..................................................................Alexander H. Slocum

Margaret MacVicar Faculty FellowProfessor of Mechanical Engineering

Thesis Supervisor

A ccepted by .......................................... ............................................................................Ernest George Cravalho

MASSACHUSETTS INSTITUTE Professor of Mechanical EngineeringOF TECHNOLOGY Chairman, Undergraduate Thesis Committee

JUN 2 8 2000 ACIEARCHIVES

LIBRARIES1

A THREE Axis CNC ROUTER DESIGN

by

Alexander D. Sprunt

Submitted to the Department of Mechanical Engineeringon January 14, 2000 in Partial Fulfillment of the

Requirements for the Degree of Bachelor of Science inMechanical Engineering

ABSTRACT

A preliminary design of a low-cost, three-axis, computer numerically controlled (CNC)router was completed with the goal of bringing the advantages of numerically controlledmachine tools to the woodshop. To reduce cost, a novel single rail design wasemployed. The number of custom parts was kept to a minimum and, where necessary,every effort was made to minimize manufacturing cost. The novel features of the designinclude vacuum clamping, the ability to cut joinery at miter angles from 0* to 90*, andforce controlled cutting. Many of the components are used quite aggressively(particularly with regard to stiffness), but the accuracy goal of ±0.005" in X and Y and+0.010" in Z was met.

Thesis Supervisor: Alexander H. SlocumTitle: Margaret MacVicar Faculty Fellow Professor of Mechanical Engineering

3

List of Symbolsball screw lead

angular velocityMioad mass of the load being moved

Jtrans inertia of the transmissionFload external loadNot optimal transmission ratio

x a length (context sensitive)

r constant for ball screw selection - accounts for external loadc constant for ball screw selection - accounts for trajectory shapeCbuckle buckling constantkwhi, shaft whip constant

E Young's modulus

P mass density

I 2nd Moment of inertia (for beam bending, etc.)AX Cross-sectional areate Cycle time (ball screw selection)a Acceleration time (ball screw selection)b Deceleration time (ball screw selection)s, Shaft whip safety factorSb Shaft buckling safety factord Ball screw diameter

Wd Heat dissipation in motor armature coilRa Motor coil resistanceK, Motor torque constant

T, Torque i

F, Force i

J Inertia i

L Life constant for calculating linear guide life {1 05 or 5-1 04}C Load capacity (bearing and ball screw life)dalong Distance between two trucks along a linear guidedaco,, Distance between two trucks perpendicular to a linear guiden Bearing life equation coefficienta Angular acceleration

PO Outside pressure

4

P Inside pressure

Pam Atmospheric pressure

Q Volumetric flow rate

Cd Coefficient of discharge

91 Reynold's Number

t Thickness

v Velocity

P Viscosity

T Temperature

R Ideal gas constant

Ai Area i

q7 Efficiency

#8 An angle for ball screws

0 An angle

G Shear modulus

3, Displacement i

3 Friction force

Fn Normal force

P, Static coefficient of friction

Nholes Number of holes in the optical table

All units are in Systeme Internationale unless otherwise noted.

5

IntroductionThis thesis describes the preliminary design of a low-cost router table that brings thebenefits of computer numerical control (CNC) tools to the woodshop. The routerintroduces entirely new capabilities such as full three-dimensional shaping to the shop inaddition to obviating the need for several conventional woodworking implements such asjoinery jigs and conventional table routers. Tiresome and repetitive tasks can also beautomated for superior output and increased throughput.

Cost reduction was accomplished using a novel, single rail, design that minimizes partcount and eases assembly. There are relatively few custom parts, and those requiredwere designed with attention to manufacturability.

During the course of the project, numerous safety, performance, and ease of useadvantages were developed for a force controlled cutting system that could easily beimplemented using the hardware that was the principal focus of this thesis.

Naturally, there is a balance between cost and performance. With that in mind, areasonable set of specifications was chosen and the design effort was focused onmaximizing the potential of the available hardware.

6

Specifications and FeaturesFootprintWork VolumeRouterAccuracyFeed Rate

3' x 4'6" + computer2'6" x 5' x 10"3 hp, 8-22 krpm, '/2" collet±0.005" for the Y and X Axes, ±0.010 for the Z-Axis20 fpm

Vacuum ClampingVacuum Chip RemovalJoinery CapableForce Controlled Cutting

Table 1

The specifications and features were developed in consultation with Ken Stone, Directorof the MIT Hobby Shop. The last two features were added midway through the projectand will be described in detail later. See the Appendix for competitive benchmarkingdata.

7

ConfigurationAn optical table was selected as the machine's base with the intention of mounting thetable nearly vertically to meet the footprint specification. The optical table provides aninexpensive, lightweight, precision surface that is essentially pre-configured for vacuumclamping (see Vacuum Clamping section).

Three initial configurations were considered, one open (Configuration A, Figure 1) andtwo closed (Configurations B and C, Figures 3 and 2). A structure is closed if itscomponents form a loop, and open if they do not. For example, a "U" shape is an openstructure, while an "0" shape is closed.

Of the closed configurations, the one with the longer axis fully supported (B) was clearlysuperior. Open structures are inherently more compliant than closed structures, but arealso simpler and less expensive, so once a preliminary spreadsheet analysis of thestructure's stiffness established that it could be stiff enough, an open structure waspursued.

Figure 1: Configuration A (Open) Figure 2: Configuration

Fon

Figure 3: Configuration B (Closed)

8

Now

A-Axis --...

Fixed Supports toelevate the Y-Axis -~

Figure 4: More complete view of configuration A

Reflection on the strengths of configuration A created configurations D and E (SeeFigures 5 and 6). Configurations D and E placed the linear guide for the long axisdirectly on the optical table that serves as the machine's base. This change eliminatedthe need to transfer a reference surface more than a foot up from the optical table.Placing the long axis directly on the optical table also removed any problems from theaxis twisting along the unsupported span.

9

-1

Optical Table

Figure 5: Configuration D

10

Figure 6: Configuration E

The names of the axes will now be defined (See Figure 5 and 6). The Y-Axis is thelongest axis (over 60") and its linear guide is mounted directly to the optical table. TheX-Axis (30") extends across the plane of the optical table orthogonally to the Y-Axis.The Z-Axis (over 10") is orthogonal to the plane of the optical table. The rotation axesare named A, B, and C in order based on which linear axis their rotation axis is parallelto. For example, an A-Axis will revolve around a rotational axis that is parallel with theX-Axis, while a B-Axis will revolve around an axis parallel to the Y-Axis, and so on.

11

The essential difference between Configurations D and E is that Configuration D placesthe Z-Axis at the end of the X-Axis instead of placing the X-Axis on the Z-Axis as inConfiguration E. Configuration D thus enables the router to go into and cut deepcavities. By cantilevering so much mass, however, Configuration D will have a lowerfirst natural frequency. It is important that the first natural frequency be above 30 Hz., orthe machine will tend to ring. Ringing can damage the work piece and make themachine uncontrollable. Further consultation with the Director of the MIT Hobby Shoprevealed that Configuration D had few advantages over configuration E becausewoodworking rarely requires cutting into deep cavities. Such activity is largely confinedto mold and pattern making specialties, which represent only a tiny fraction of allwoodworking activity.

Consultation also revealed the great utility of having a joinery cutting capability. Joineryis cut on the edges of boards (See Figure 7), however, and neither configuration had theability to work edges longer than the Z-Axis.

Figure 7: Router cutting joinery

Two methods were developed for relieving this edge length limitation. One was tocreate a manual B-Axis that could cut joinery on boards mounted to a second opticaltable that was perpendicular to the primary machine base (See Figure 6). The otheroption was to create a manual A-Axis. The router motor would be rotated 90* and drivento an extension to the end of the Y-Axis (See Figure 4). With either of these options,joinery could be cut in the edges of pieces as long as the Y-Axis.

Using an A-Axis had the obvious advantages of involving fewer parts, requiring lessassembly work, and being able to cut joinery into longer edges. There were twopossible locations for the rotational joint of the A-Axis. The joint could be integrated withthe casting for connecting the X-Axis with the Z-Axis (the entire X-Axis linear modulewould rotate along with the router head) or the joint could be built into the mount for therouter. The tradeoff between the two options was rather complex. The choice affectedthe length of the Y-Axis, the weight of the router mount (and thus the machine's naturalfrequency), how constant the machine's stiffness was, and the ease with which therouter bit could be driven beneath the level of the optical table when making joinery.Because of these considerations, as well as various geometric and manufacturingconstraints, the A-Axis was integrated with the router mount.

12

ExperimentsCutting ForcesBefore any analysis could be done to determine the structure's deflection during cutting,the magnitude of the cutting forces had to be determined. To this end, severalexperiments were done with the apparatus diagramed in Figure 8.

Wood

Router Spring Scale

Figure 8: Cutting force experimental apparatus cross section

A number of different cuts were made in different types of wood, with different size bits,and at different feed rates. No force over 31 N was ever observed, and cuts with forcesgreater than 27 N resulted in an unacceptably bad surface finish. With this in mind, thedisplacements due to cutting forces were evaluated by simultaneously applying 50 N toeach axis while the machine was in a worst case configuration. The worst case wasdetermined to be when the Y-Axis was set to mid-travel, the Z-Axis was at the highextreme travel, and the X-Axis was set to the far extreme travel. This configurationmaximized the applied moments and minimized the structure's ability to resist them.

Friction With Clamping SurfaceBecause

3 = F,(1)

it was necessary to determine the static coefficient of friction between the aluminum topof the optical table and the wood work piece. Machinery's Handbook gave a range of0.2 to 0.6 for "wood on metals (clean)"', but prudence demanded experimentalverification. To that end, a block of wood was placed on a sheet of steel (the surfacematerial for the optical table), and the angle of the sheet with respect to the horizontalsteadily increased until the block was just about to slip (See Figure 9). The test wasperformed with the wood grain both parallel and perpendicular to the direction of travel,but the difference proved to be negligible.

Green, Robert E., ed. Machinery's Handbook. 25 ed. New York: Industrial Press, 1996. p. 190.

13

mg cos(O)

mg

The block will start to slipwhen 3 = mg sin(9),which implies thatPsmg cos(9) = mg sin(O)

Figure 9: Block on an incline with force vectors

P, = mgsin(9) = tan(O)mg cos(9)

The result after averaging several runs wasessentially at the midpoint in the range provided

that p,=0.38 (See Table 2), whichby Machinery's Handbook.

Run Orientation Angle Ps1 19 deg 0.3442 Parallel 20 deg 0.3643 21 deg 0.3844 20 deg 0.364

22 deg21 deg21 deg22 deg

0.4040.3840.3840.404

Average: 0.379

Table 2

(2)

is

5678

14

Linear GuidesBecause it was the fastest way to obtain a rough estimate of the necessary size, thelinear guides were selected first based on expected bearing life. Estimates of the likelyforces and moments were input into a spreadsheet along with the relevant parametersfor a number of different manufacturers' rails. Due to the unusually complex loading thetrucks were to undergo, the standard equivalent forces definition component of thebearing life equation,

equivaent Fvertical I + IFhorizontal I + C ro I Fr0 1quzvan (~ roll-capacity)(3)

was inadequate, so after consulting with the manufacturer, a slightly modified versionwas used:

F -I~v Iroll IFequivalent =|Fvertica I + |Fhorizontal I + C +roll i

q roll-capacity

Fyaw

rpitch

Irpitch

Fpitch-capacity

~yaw~ >+ Ia

yaw-capacity(4)

roll

Truck

Figure 10: Definition of torques and forces

Life = (equivale" L10

n = 33

roller

ball(5)

Bearings with sufficient life (5 years of 8-hour days at maximum speed with a 50% dutycycle) were then checked to see if they could withstand the occasional shock of a 200lbf. impact load at the spindle. Combinations with two trucks on one rail, two trucks ontwo rails, and four trucks on two rails were also examined.

15

dacross

daiong

Figure 11: Diagram view of two rail - four truck

J~roll I + +tc IF.yawl 6Fequivalent = Fverticai I + IFhorizontal )+ " (+)

4 2 dacross dalong dalong

dacross

Figure 12: Diagram of two rail - two truck configuration

roll Ipitch yaw

equivalent =- \Fvertical r + - + (7)2 across 2 tch-capacity yaw-capacity

dalong

Figure 13: Diagram of one rail - two truck configuration

+1pitch I +1yaw C yIroll IFequivalent = 2 (Fvertical I + Fhorizontal j) + + 2 i) (8)

2daong rol-aact

The results of the bearing life analysis were used to size the rails that went into the firstsolid model. Finite element Analysis (FEA) of that model suggested that the dominantconstraint would be stiffness.

The cornerstone to successfully determining the stiffness of the machine's structure wasa simple method of modeling the linear guide trucks. The truck's torsional compliancewould be the principal source of the Abbe (angular) errors, which tend to dominate in anopen structure. Successive iterations (See Figure 14) of a finite element model of just atruck and a rail were used in conjunction with roll data (roll being the most compliant

16

mode) supplied by STAR Linear Systems to find an equivalent Young's Modulus for thenecessary trucks. The Young's Modulus could then be input into the FEA program.

0.18

0.16

0.14

0.120

0.10

0.08

8 0.06

0.04

0.02L

0.002000 2500 3000 3500 4000 4500

Young's Modulus (Pa)

Figure 14: Iteration towards an effective equivalent Young's modulus

In the future, it might be better to model the truck as two parts (See Figure 15). After all,the trucks themselves are by no means monolithic. The center section would be"mushy" to approximate the compliance of the balls or rollers, while the outer sectionwould be one to one and half times the stiffness of steel. The stiff outer sections wouldensure that the loads were transmitted evenly to the compliant interior of the block. If, asis now the case, the entire block is given a low Young's modulus adjacent parts mustprovide the stiffness necessary to spread the loads throughout the block, a stiffness,which is in fact already present in the block. Using the stiffness of adjacent parts is notalways desirable or feasible, and it is a great frustration to accommodate a design to theanalysis tool.

Figure 15: Future block with a compliant inside and a stiff outer shell

2 Bamberg, Eberhard. Ph.D. Thesis MIT Mechanical Engineering Department

17

Iterative Steps

Desired Output based on data suppliedby STAR Linear Systems

The Router MotorConsultation with the Director of the MIT Hobby Shop established the requirement for avariable speed (8-22 krpm) 3 hp. router motor with a " collet. It was tentativelyassumed that an existing router would be bought off the shelf, and after being stripped ofvarious unnecessary elements, bolted to the rest of the machine.

There are two major varieties of routers available today: pneumatic and electric.Pneumatic routers were attractive because they don't burn out and because they arelighter than electric routers. Unfortunately, after consulting manufacturers of pneumatictools such as Sioux, Campbell-Hausfeld, and Beaver, it was found that pneumaticrouters over 1 '/2hp do not exist. The higher power would require excessive flow rates atstandard shop air pressures.

The catalogs of major electric router manufacturers Sears, Porter-Cable, Bosch, andDeWalt were therefore surveyed to determine reasonable characteristics for 3 hp.routers. It was conservatively estimated that such a router would weight 8 kg. andrequire a cylindrical envelope 5 " in diameter and 6" high.

These parameters were used in the solid model to fix associated dimensions and toaccurately assess the machine's natural frequencies.

18

Concept RefinementPerhaps it has already become obvious, but it is very difficult to write a linear narrativeabout a non-linear design process.

Version OneVersion One is the first in a series of solid model implementations of Configuration Ewith a manual A-Axis (See Figure 5). A single size 55 roller rail with a long style runnerblock creates the Y-Axis. The Z-Axis is composed of a single size 55 ball rail with asingle truck. An integrated linear module was chosen for the X-Axis. The decisionwhich rails to use for the first two (Y and Z-Axes) was made principally on the basis ofbearing life and impact loading requirements. An integrated linear module was used forthe X-Axis despite its expense because it was unlikely that a better combination ofstiffness, compactness, and light weight could be designed in a short period of time.The specific model chosen was a STAR Linear Systems MKK 2080. The MKK 2080 hadsufficient life and was the largest model before a substantial step-up in size and weight.

X-Axis

Z-Axis

Truck

Y -A xis

Shoulder

Figure 16: Version 1, note the shoulders for mounting the linear guides.

19

For the finite element analysis, the runner blocks were represented by materialsoptimized to have the same torsional stiffness (See the Linear Guides section). Theintegrated linear module was approximated by a rectangular cross-section beamcontrived to have the same second moments of inertia that the manufacturer supplied forthe selected linear module. Until a bracket could be designed, the part that serves as aproxy for the router was given the stiffness of steel, but a high enough density to ensureit would have twice the mass of the expected router. The factor of two was used toprovide a safety margin and to account for the weight of the mount.

This version showed promise, but was extremely short lived. The natural frequency ofthe first mode, 23 Hz., was unacceptable but not by so much as to be without hope.Furthermore, the casting to which the Y-Axis runner block and the Z-Axis rail weremounted would be quite difficult to manufacture because of the required interior grinding.

Version TwoTwo approaches were taken to overcoming the deficiencies of Version One.was to replace the single Y-Axis rail with two smaller rails (See Figure 17). Onof bearing life, size 35 ball rails were selected. The single rail for the Z-Axisreplaced with two rails to see if doing so had any advantages.

The firstthe basiswas also

Figure 17: Version Two, multiple rails and runner blocks used for both the Y and Z-axes

20

Despite the cost, complexity, and other penalties, two small rails (in this configuration)proved to have no structural advantage over one larger rail. The natural frequencyactually dropped to 20 Hz.

In hindsight, this test was probably a little unfair. The Young's Modulus of the blockswas calibrated for roll moment loading (the blocks' weakest mode), while they wereactually loaded in compression.

Version ThreeThe second approach to solving Version One's problems was putting two trucks on asingle rail for the Y-Axis. To ease manufacture, the casting was simplified by removingthe troublesome overhang and using special assembly fixtures instead of shoulders formounting the linear guides. To increase its stiffness, the casting was closed byattaching a plate to the back side.

Figure 18: Version Three, note the inclusion of the ball screws and the cleaner Y-to-Zcasting

This version had an acceptably high natural frequency, but the displacements due toanticipated cutting forces were too high. The major sources of these displacementswere torsional deflection of the Z-Axis truck and bending of the X-Axis linear module.

Because the ball screw sizes had been determined by this point (See Ball ScrewSelection Section), a more complete model was created to include them, while the finiteelement analysis was still done on a more primitive model to reduce the computing time.The ball screws were mounted directly "above" the linear guides in an effort to minimizethe torque they would apply to the block and to keep the castings as simple as possible.

21

The more complete model revealed an even larger problem than the unacceptably highdisplacements, however.

When the Z-Axis was driven to the bottom of its range, the X-Axis linear moduleinterfered with the Y-Axis ball screw. Fixing these problems resulted in a completeredesign of the main casting in Version 4.

X-Axis linear moduleinterference with the Y-Axis Ball ScrewY-Axis ball screw

X-Axis Linear Module

Figure 19: Version Three, note how X-Axis linear module interferes with the Y-Axis ballscrew

Version FourThe main casting was completely redesigned, resulting in a number of improvements.Solving the interference problem while keeping the height (and thus the moment ofinertia) of the casting to a minimum meant placing the Z-Axis rail on the side of thecasting directly above the Y-Axis rail (See Figure 21). This change had numerousadvantages. It reduced the distance from the center of the Y-Rail to the point of closestapproach to the router. That distance plus the 30" that the router must be able to travelto meet the specification determines how much moment is applied to both the Y and Z-rails, so reducing the length was advantageous. The natural frequency improved aswell. This change also simplified the casting connecting the Z-Axis to the X-Axis to aplate.

FEA revealed that the structure's displacements due to the expected cutting forces werestill unacceptably high. The primary sources of this problem were bending in the X-Axislinear module and torsion about the Z-Axis.

Several attempts were made to solve this problem. The roller block on the Z-Axis waschanged into a long style block, and steel stiffeners were added to the linear module.These measures were partially successful. The deflection in the Y direction, which hadalways been the most troublesome, was reduced to only 103% of the allowableaccuracy. A high price was paid for this rather limited success, however. The additionalmass of the stiffeners pushed the structure's first natural frequency down to a dubiouslyacceptable 26 Hz.

22

Figure 20: Version Four, view 1, note the redesigned casting

Figure 21: Version Four, view 2, note the stiffeners on the X-Axis linear module

23

Version FiveStronger measures were taken in the hopes of finally resolving the natural frequency andcutting force displacement issues.

Slightly increasing the width of the casting connecting the Y-Axis to the Z-Axis andmoving the Z-Axis rail all the way down created enough space to replace the long truckon the Z-Axis with two standard length slimline trucks, while increasing the height of thecasting only slightly.

The shape of the stiffeners was optimized and aluminum was used instead of steelbecause of its lower density. The new stiffener shape came from tapering a triangle two-thirds (See Figure 22) down the length of the linear module.The mounting structure for the router motor was also replaced with a lighter structuremade of aluminum in an effort to create more natural frequency margin.

RedesignedStiffener -

Z-Rail moved allthe way down

Figure 22: Version 5

The changes were effective. The displacements were reduced to acceptable levels andthe natural frequency was increased to 41 Hz. Because the model is a simplification, the

24

calculation of the first natural frequency was done without accounting for the mass ofseveral components (e.g. the motors for the X-Axis and Z-Axis as well as other pieces oftransmission hardware). The addition of these components will effect the naturalfrequency, but due to their light weight and proximity to the Y-Axis, the effect should notoverwhelm the available margin.

25

Force ControlDuring the experiments to measure the cutting loads the router would experience, it wasdiscovered that a person naturally performs force control when working with a router. Asthe cutting forces vary due to the heterogeneity of the wood, the operator compensatesto maintain surface finish.

Torque (and thus force) sensing can be accomplished at almost no additional cost bymeasuring motor current. The drive system's losses due to friction are minimal so theycan be neglected, and motor current is already an output from the servo controller.

Using force control has advantages other than improving surface finish. Because themachine is monitoring the cutting forces, it could alert the operator when the specifiedtolerance can no longer be met. With this in mind, the operator could plan a roughingcut with high forces, and then come back in to finish the work with a less aggressive cutthat applied lower forces to the machine.

There are safety advantages as well. With knowledge of the size of the work piece'sclamping face (either input by the operator or obtained by other means) and theavailable clamping pressure, the controller could set a hard limit on cutting force in orderto prevent work piece slippage.

26

Ball Screw SelectionThe leads and the diameters of the ball screws were selected by matching the inertia ofthe transmission (the ball screw being the primary component) with the equivalent inertiaof the relevant stage and load forces while simultaneously applying the shaft whipconstraint.

N 2 Mla3N2 t + M +r ~,(9)o trans

whereF 2 t2

r= !"" " (10)r M load

and1 1 (1

C =-+a 1-b

is the equation for minimizing the heat dissipation. Naturally, when there is no externalload,

N2t oad, (12)

which results in inertia matching.

whip E (13)s, A~px4

is the shaft whip constraint. Combining (9) with the shaft whip constraint, the definitionof N,

No,, = ,z (14)

the definition of lead,

2 =- -(15)

the second moment of inertia,

I= , (16)64

the cross-sectional area,

AX = 2 ,(17)*4

and the moment of inertia,

3 J. Park and S. Kim, "Optimum Speed Reduction Ratio for D.C. Servo Drive Systems," International

Journal of Machine Tools Manufacturers, Volume 29, Number 2, 1989.

27

Jtrans 32 (18)

yields the equations:

d= 512M 22 d 7&dX Sw E ii7 (19)

whip

and

2 = p7rxd (20)8 Mioad

The results of applying these-equations with a shaft whip safety factor (sw) of 0.8 to themachine's three axes are show in Table 3.

Y-Axis Z-Axis X-Axisdiameter (d) 46.92 mm 16.12 mm 17.83 mmlead (1) 48.59 mm/rev 2.83 mm/rev 12.49 mm/rev

Table 3The buckling criterion,

Fuke, Cbuckle (21)'bukle 64sbx2

was then applied to these results. All met the constraint, but ball screws are naturallynot available in exactly these sizes, so after checking against packaging constraints andavailability, the following values were settled on:

Y-Axis Z-Axis X-Axisdiameter (d) 50 mm 16 mm 16 mmlead (e) 20 mm/rev 5 mm/rev 10 mm/rev

Table 4In the future, a better way to do this would be to plot dissipated heat,

cR il 2m2 2 rW a lv load N2 am + 1 + , (22)Wd K2 t [ Moa N 2 N2

over a reasonable range of diameter and lead values using a 3-D plotting program.Then, after applying the buckling and shaft whip constraints, the available lead anddiameter combinations could be plotted as points on the graph so that the powerminimizing combination could be selected more graphically and intuitively.

Finally, the candidates were tested to ensure sufficient life. The relevant life equation is:

Life[hours]= .0 (23)Fnlen, 2c o

When all the candidates proved to have sufficient life, ball screw selection was complete.

28

Vacuum ClampingEffective work piece clamping is naturally a must for this application. The safety andaccuracy of the machine depend upon it. At the same time, the clamping mechanismmust be flexible to accommodate a variety of work pieces and have a low profile so thatit does not interfere with the machine's operation. The clamping must also be quicklyand easily done. Clamping a work piece is not a value adding process.

Vacuum clamping offered a number of advantages. The operator need only set thepiece on the machine's base and open a few valves. Accommodating irregular partswould not be a problem. There need only be one flat surface of sufficient size.

This concept fit well with using an optical table for the machine's base. Optical tablesalready have holes through which the vacuum could be drawn. The optical table couldalso be easily partitioned internally (See Figure 23). By sub-dividing the table, amanifold of valves can limit how much of table vacuum is drawn through.

Optical Table

Internalpartitions

Holes to drawvacuum through

X

Figure 23: Partitioned optical table base

The power necessary for the vacuum pump was calculated with the equation

Power = (P, - P )Q.

The flow was determined using the orifice equation:

P0 d T=293K

t I

Pi

Figure 24: Orifice diagram and variable definitions

29

.- .- .- .- .-. . . -.. . . ... - -.

(24)

)0

Q = A.,Cd P-p

I d9i n <86.78

2.23745+64 t (25)

1 d9" > 86.78

1.5+13.740 t t

where

9, = pvd (26)

and

P + PP = ' . (27)

while the pressure was set by the magnitude of the cutting forces as determinedexperimentally (gravitational loads are supported by the fences).

Because of the piecewise nature of the orifice equation, the problem was solvediteratively using a seed velocity from the Bernoulli Equation (See Figure 25).

Bernou:iill veioty 93 -- Cd velcQt

Figure 25: Iterative process for determining flow rate

After setting the internal pressure to 40% of atmospheric pressure, the maximum flow(for input into equation 24) was determined by multiplying the flow through one orifice bythe number of holes in one sixth of the optical table (the standard hole pattern is 00.25"on 1" centers).

The clamping force on any particular work piece is calculated using the equations:

F, = N ,, Ahoe (atm - i)Aclamp face

Aoptical table

Famp = 3 = pF, (29)

Parts with clamping faces as small as 10" x 10" can be held, and assuming that themaximum open area on the board would be one sixth of the total area, the necessaryhorsepower of the pump, neglecting the pump efficiency is 9.5 hp.

One weakness of using vacuum clamping is that while the clamping force scales withwork piece size, the magnitude of the cutting forces which the clamping force must resistdo not. One solution to this problem is to make lighter, lower force, cuts on smaller workpieces. Another is to provide fixtures to aid in the clamping of small work pieces. The

30

fixtures would have large clamping faces (possibly coated with a high friction material)that could in effect increase the size of the small part's clamping face (See Figure 26).

Work Piece

Fence

Optical Table

Fixture

- Friction Material

Figure 26: Clamping fixtures for small work pieces

31

Servo MotorsThe input torque has several different components. The largest is the torque required toovercome gravitational and cutting forces. Once those forces were estimated byexperimentation and calculation, they were input into the equation:

Fexternal - (Fgravity + F,,,,,,g )(30)

After consultation with manufacturer's catalogs, an efficiency (q) of 90% was used. Thenext major torque component is that due to the friction from the pre-loaded ball nut.

£Fpre-loadoad - F = (31)404~ain,8)

tan(p)= (32)ball-circle

Fpre-load - (33)10

The sum of the external torque and the torque due to pre-loading is the requiredcontinuous torque of the motor.

The intermittent torque requirement is the sum of the continuous torque and theacceleration torque. The acceleration torque is found with the equation:

Facceleration = equivalent a , (34)where

Jequivalent = Mload 2 + Jball scre (35)

The maximum operating speed of the motor was calculated with the equation

2 = -. (36)

These calculations were performed for the three axes, and the results are summarized inTable 5.

Y-Axis Z-Axis X-AxisExternal Torque 4.95 Nm 0.18 Nm 0.11 NmPre-Load Torque 1.69 Nm 0.08 Nm 0.09 NmContinuous Torque 6.64 Nm 0.25 Nm 0.20 Nm

Acceleration Torque 1.26 Nm 0.05 Nm 0.02 NmIntermittent Torque 8.61 Nm 0.30 Nm 0.21 Nm

Maximum Operating Speed 952.2 rpm 3808.8 rpm 1904.4 rpm

Table 5These results were used to select motors in Table 6 for the three axes.

32

Speed-Torque CurveI

TORQUEDDM-030/F-4050

0 1000 2000 3000 4000SPEED (R.P.M.)

DDM-005N-1003

ContinuousTorque

IntermittentTorque

TORQUE15.8 (Nm)

13.6

11.3

9.0

6.8

4.5

2.3

0

6.90 Nm 13.60 Nm

TORQUE(Nm)

_0.9

0.7

Y-Axis

Z-Axis&

X-Axis

Legend:

0-5

-0.2

0

1.00 Nm

SPEED (R.P.M.)

= Intermittent Operating Region= Continuous Operating Region= Drive Operation with 115 VAC RMS Input Voltage

Table 6

33

0.35 Nm

Error Budget

Structure (Gravity)Structure (Cutting)Ball Screw LeadBall Screw Windup (Cutting)Ball Screw Windup (Gravity)Ball Screw Axial (Cutting)Ball Screw Axial (Gravity)Ball Nut (Cutting)Ball Nut (Gravity)Ball Screw Fixed Support (Cutting)Ball Screw Fixed Support (Gravity)Parallelism P_ (Y-Axis)Parallelism P_1 (Z-Axis)Parallelism P_1 (X-Axis)A_3 (Y-Axis)A_3 (Z-Axis)A_3 (X-Axis)H (Y-Axis)H (Z-Axis)H (X-Axis)Y-to-Z CastingZ-to-X PlateOptical TableTotalRMS (of non-zero values)

Average of Total and RMS

Goal

X Y

61.01 pm 102.31 pm

127.00 pm 127.00 pm

Z Comments

Accuracy grade 5

0.68 pm35.91 pm

7.00 pm0.42 pm0.00 pm1.29 pm0.00 pm0.14 pm0.00 pm0.15 pm0.00 pm

22.00 pm8.00 pm0.00 pm

15.00 pm15.00 pm0.00 pm0.00 pm0.00 pm0.00 pm2.00 pm1.00 pm0.00 pm

108.59 pm13.42 pm

7.70 pm70.08 pm15.40 pm0.04 pm1.09 pm0.35 pm8.69 pm0.04 pm0.97 pm0.04 pm0.97 pm0.00 pm8.00 pm

12.50 pm0.00 pm0.00 pm

15.00 pm0.00 pm

15.00 pm0.00 pm

10.00 pm20.00 pm

0.00 pm185.85 pm

18.76 pm

0.42 pm31.62 pm

5.00 pm0.04 pm0.09 pm0.47 pm1.04 pm0.14 pm0.32 pm0.15 pm0.34 pm

22.00 pm0.00 pm

12.50 pm0.00 pm0.00 pm0.00 pm

15.00 pm0.00 pm

15.00 pm2.00 pm1.00 pm

101.60 pm208.74 pm26.29 pm

117.51 pm

254.00 pm

Table 7

The errors due to structure, both gravity and cutting, were determined using FEA.Software compensation is used to filter out 95% of the gravity loading and 80% of theball screw lead error. Budget items "Ball Screw Lead," "Parallelism," "A3," "H," and"Optical Table Flatness" were taken from the relevant manufacturers' catalogs. Ballscrew windup was calculated with equation

gshaft windup = ,xdG ,

(37)

which reflects the axial stiffness of the ball screw back through the encoder. Ball screwaxial deflection was calculated with equation

4xFaxial = 2 .

rrd E(38)

The errors due to ball nut and ball screw mount deflections were accounted for usingstiffness data supplied by the manufacturer. The errors due to the Y-to-Z and Z-to-X

34

.... W

HHHHHHHHH

Accuracy ClassAccuracy ClassAccuracy ClassAccuracy ClassAccuracy ClassAccuracy ClassAccuracy ClassAccuracy ClassAccuracy Class

0.004" optical table

transition castings were calculated by programming a 10 arc second per meter grindingerror on each surface and evaluating the displacement of the router bit.

Finally, to convert all of the worst-case assumptions to a more "typical" series of errors,the root-mean-square of all the non-zero errors was averaged with the sum. Theseresults suggest that it might even be possible to tighten the specification for the X and Z-Axes.

35

ConclusionGoing forward, there are still several open issues.

The linear guides and ball screws need contamination protection. The X-Axis linearmodule has integrated seals, but the ball screws and linear guides for the Y and Z-Axesare currently unshielded. Because the ball screws are directly above the linear guides,both might be covered by a single set of bellows.

The addition of vacuum chip removal should not be a problem. Ducting will have to berun from the router bit area back to the base of the machine, but surplus vacuum can beeasily drawn from the clamping system.

The biggest remaining challenge is probably the pivot for the A-Axis. The pivot mountmust be both lightweight and stiff. Lightweight so that it does not unnecessarily erodethe natural frequency margin, and stiff so that it does not add to the error budgetsignificantly. Naturally, the pivot will have to be adjustable, but the locking mechanismwill have to be designed with vibration in mind. It would probably also be a good idea toinclude a potentiometer (or equivalent) so that the controller can measure the angle ofthe pivot. The controller must know the set angle so that it can match it when cuffing atmiter angles other than 00 and 90*.

36

Appendix: Competitive BenchmarkingName The AutoRout Router SeriesCompany AutoRout Inc.Work Volume 5'x5', 5'x8', 5'xlO',5'x12'Feed RateRepeatabilityAccuracySpindle Multiple, 7-12 hpClamping Vacuum, 10-30 hpURL www.autorout.comComment drills, saws, 4th AxisPrice $53,296 Base

Name AXYZ SeriesCompany AXYZ Automation Inc.Work Volume 39"x39"x6" to 150"x99.5"x6"Feed Rate 300 ipmRepeatabilityAccuracySpindle 1.5-7.5 hpClampingURL www.axyz.comCommentPrice

Name RT SeriesCompany BobCAD CAM Inc.Work Volume 8'x4'xlO"Feed Rate 200-1000 ipmRepeatabilityAccuracy 0.005"Spindle Multiple, 3.25 hpClamping Vacuum optionalURL www.bobcadcam.comComment THK or STAR Linear GuidesPrice $15,000-$47,000

Name CNT 1000/900 SeriesCompany CNT Motion SystemsWork Volume 60"x120"x5"Feed Rate 1000 ipmRepeatabilityAccuracySpindle Multiple, 0.5-3 hpClamping Vacuum, 10 hpURL www.cntmotion.comCommentPrice $13,000-$45,000

37

Name Thermwood Router SeriesCompany Thermwood Inc.Work Volume 5'x5' to 5'x20'Feed Rate 1500 ipm

Repeatability 0.002"AccuracySpindle 4-15 hpClamping VacuumURL www.thermwood.comComment Turret head, 5 Axis availablePrice $40,000-$120,000

NameCompanyWork VolumeFeed RateRepeatabilityAccuracySpindleClampingURLCommentPrice

200-600 SeriesGerber Scientific Products

35.4"x31.4"-6'8"x10'600-54 ipm

Vacuumwww.gspinc.com

CNC Mini-RouterMinitech

NameCompanyWork VolumeFeed RateRepeatabilityAccuracySpindleClampingURLCommentPrice

www.minitech.com"Portable"

$9,500

NameCompanyWork VolumeFeed RateRepeatabilityAccuracySpindleClampingURLCommentPrice

CamtoolLarken Automation

24.5"x24.5"x5" to 100"x150"x6"200 ipm

±0.001

1.5-3 hpT-slot or vacuum

www.storm.ca/l-arken/

$7,000 - $30,000

38

Name Shoda NC-1Company Shoda USAWork Volume 0.5m x 1.Om x 0.4mFeed RateRepeatabilityAccuracySpindle Up to 3, 12 hpClamping Vacuum clamping or T-SlotURL www.shodausa.comComment tilting spindle, very industrialPrice

Name ShopBot Personal Robotic 96Company ShopBot Tools Inc.Work Volume 8'x4'x7"Feed Rate 200 ipmRepeatabilityAccuracy 0.01"Spindle bracket for any standard routerClampingURLComment user built from partsPrice www.shopbottools.com

NameCompany Super Tech and AssociatesWork Volume 36"x23.5"x2.375"Feed Rate 150 ipmRepeatabilityAccuracySpindle DeWalt RouterClampingURL www.super-tech.com/root/iCommentPrice

Name DaVinci Production CenterCompany Techno-IselWork Volume 8"x8"x6.8" to 59"x96"xlO.8"Feed RateRepeatabilityAccuracySpindle 0.75 hp to 7.5 hpClamping Vacuum or Clamp barURL www.techno-isel.comCommentPrice

39