An Axtrusion Based Lathe

Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.

An Axtrusion Based Lathe

Roger Cortesi


Purpose:

To design the most accurate lathe possible wit the Axtrusion prototype hardware and minimal other components.


High Level Functional Requirements

• Use Axtrusion prototype hardware

• Require a minimal of donated equipment

• Easy to assemble and test on granite surface plate

• As accurate as possible while meeting above constraints


Axtrusion Prototype Hardware

Linear M otorPerm anent M agnets

Carriage

W ay

Top PrecisionSurface

Side PrecisionSurface

Linear M otor CoilTop OutboardPorous GraphiteAir Bearings

Top InboardPorous GraphiteAir Bearings

Side PorousGraphite AirBearings

One Axtrusion carriage has been assembled and testedA second granite way has been built.A second carriage casting is available. It has not been machined


Initial Machine Concepts

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B C

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W ork p iece B ase is 2 "h ighe r than T oo l B ase

A B

CD

E

F

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B

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E F

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EF

The first concept show with the tool closest to the work piece (top) and furthest from the work piece (bottom).Motion error estimates were performed for the tool in both positions. Moving the tool to the furthest from position added about 4 microns of error in the X and Z directions.

Two more concepts that require that the ways be secured on a surface plate.


Spindle Selection

• The workpiece spindle will have to be donated (or built by students).

• Therefore our choices are limited in this matter.• For the initial machine design I arbitrarily selected

a mid sized belt driven spindle from Setco™. • This seemed to be a representative sample of the

spindles that would be available to us.


Data Used in Motion Error Model

Carriage Error MotionsPosition Accuracy in Direction of Travel 1.3 micronsCarriage Pitch 12 micro-radiansCarriage Yaw 12 micro-radiansCarriage Roll 5 micro-radians

Spindle Error MotionsRadial Runout 5 micronsAxial Runout 5 micronsSpindle Abbe Errors 33 micro-radians

S p ind le R unou tD is tance

F orew ardB earings

R earw ardB earings

N om ina l S p ind leC en te r L ine

B earing S pac ingThe sketch to the left shows how spindle Abbe error is estimated from the spindle runout data. The value for runout is applied in opposite direction at the front and rear bearings. This yields a formula for the angular displacement of the spindle centerline of:

cingBearingSpa

RunoutAngle

2

Carriage Error Data is from the Axtrusion Prototype. Roll data is estimated by removing errors due to the linear motor from the pitch and yaw data. The remaining errors are due to way straightness. These errors should be similar among pitch, yaw, roll.


Estimated Motion Errors

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B C

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FA

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E F

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EF

RSS Sumw/ grinding spin w/o grinding spin

Lathe x z x zVersion 1 23.8 9.5 21.2 8.1Version 1a 33.2 18.9 31.4 18.3Version 2 20.0 9.1 16.8 7.6Version 3 na na 18.7 7.6

1

1a

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Accuracies above are in microns and DO NOT include Thermal and Dynamic Errors.

Values for “w/o grinding” have the errors associated with the tool spindle removed.


Minimizing Thermal Errors

• To fit the linear motor on the prototype carriage the cooling coils were remove.

• The linear motor coil is a major heat source in the machine.

• The carriage structure is magnesium with an of • All these factors require that the “thermal

centerline” of the Axtrusion carriage be used


Axtrusion Carriage Thermal Centerline

G ran ite W ay

A xtrus ion C arriage

T herm a l C en te rlines

P os ition E ncoderE nd V iew S ide V iew

The location of the thermal centerlines for the Axtrusion carriage is determined by the location of the way surfaces and location of the position encoder for the carriage.

Locating Tooling, Spindles etc. on these centerlines will minimize thermal errors.


Improved Thermal Concepts

The initial machine concepts are modified to improve their thermal performance.

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A B

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F

This concept is improved by moving the grinding spindle to the thermal centerline of its carriage.This concept improves its thermal performance

by moving the tool post to the thermal centerline of its carriage. This action moves the tool tip away from the yaw COM, therefore greater error motions would occur.


Dynamic Errors

Frequency [Hz] Equivalent RPM Q factor362 21,720 48

487.0 29,220 5608.0 36,480 33

Modal Data from the Prototype Axtrusion Carriage

Input

OutputQ cuttingdynamic FQF

Cutting forces on the machine are amplified by the Q factor when the machine is operating at resonant frequencies to form a much greater dynamic forces.

These dynamic forces are then applied as static force to the machine and resulting displacements calculated and entered as the dynamic errors for the machine.

34 N is estimated to be the dynamic cutting forces on the machine.This is for finish cut on a 12mm diameter Aluminum part at max surface speed

Calculation next slide…


Wtool 3mm Width of tool

MRR Depth Feed Nspin Wtool MRR 14.4mm

3

s Metal Removal Rate

Pspin pal MRR Pspin 7.9W Power Requided for Turning the Part

FcutPspin

Speed Fcut 0.7N Estimate of the cutting forces on the finish pass

Q 48 Q Factor for Estimating Dynamic Cutting Forces. Q factor from Modal Analysis of Axtrusion Prototype. Note this Q factor is for a frequency of 362 Hz. To excite this mode would require the spindle Spinning at 21.7 THOUSAND RPM. This is the equivalent of working a part in Aluminum that is between 1.5 and 2 mm in diamater at the maximum surface speed

Fdyn Q Fcut Fdyn 34N Fdyn 7.6lbf The Dynamic Cutting Forces

rev 2radEstimating the Cutting Forces for a metal working lathe.RPM

rev

min

pal 0.55Ws

mm3

An estimate for the unit power requriements for metal removal for Aluminum and Magnisum Alloys (Marks Standard Handbook for ME's)

Dwp 12mm Diameter of Work PieceThese values are from the Mark's Standard Handbook for ME's

Depth 0.02in Depth of Cut on finishing passThese values are for the FINISHING PASS on a small partFeed 0.2

mm

rev Feed Rate

Speed 670m

min Surface Speed of Cut

NspinSpeed

Dwp Nspin 2828.5RPM Spindle Speed to Achieve Surface Speed


Quick Check of Carriage Compliance Under the Estimated Dynamic Cutting Force

Tool Force

2 Air Bearings2 Air BearingsCenter of Stiffness

LtLb

Fdyn 35N m 106m rad 10

6rad

Ltool 500mm This the approximate moment arm on between the tool tip and COM of the carriages.

Kbrg 80N

m appoximate stiffness of one of the carriage's air bearings.

Lbrg 275mm approximate bearing spacing on the carriages

Krot 4 0.5 Lbrg 2 Kbrg Krot 6.1 106

N mrad

The rotational stiffness of the carriage, using 4 bearings at 1/2 the bearing spacing from the carriage COM.

carriageFdyn Ltool

Krot carriage 2.9rad This a conservative estimate for the

rotational errors in the carriage due to dynamic forces

So as an estimate these dynamic errors will add about 3 to 5 microns in each direction.


Version 4 of the Lathe

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T oo l B ase is 4 " H ighe rthan W ork p iece B ase

RSS Sumw/ grinding spin w/o grinding spin

Lathe x z x zVersion 1 25.0 11.0 22.4 9.6Version 1a 33.2 18.9 31.4 18.3Version 2 20.0 9.1 16.8 7.6Version 3 na na 18.7 7.6Version 4 na na 17.5 7.8

An Axtrusion Based Lathe

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