surface variation and mating surface rotational error in assemblies taylor anderson ugs june 15,...

Surface Variation and Mating Surface Rotational Error in Assemblies

Taylor AndersonTaylor AndersonUGSUGS

June 15, 2001June 15, 2001

Introduction

Periodicity in surface variation

Characterization of surfaces

Quantifying assembly variation

Conclusions

outline

introduction

Every product manufacturer in the world is chasing the product quality “Holy Grail”

Effective Product Lifecycle Management must include variation analysis and tolerance management

ADCATS and others are working to make this as painless as possible

component variation

Size or location variation

Form or shape variation

Feature orientation variation

Surface roughness variation

real-world surface variation

All real surfaces contain SOME variation.

Surface variation can cause assembly variation.

Surface variation can propagate through assemblies.

assembly variation

Component size variation

Component feature location variation

Component form or shape variation

accumulation of variation

Geometric variations propagate through an assembly as imperfect shapes and surfaces contact each other.

propagation of variation

F

F

FK

K

K

F

F

XX

Y

Y

Assembly joints (contacts) have:

Kinematic degrees of freedom

Feature variation degrees of freedom

Feature variation propagates along kinematically constrained degrees of freedom

K

research objectives

1. Characterize surface variation

2. Correlate rotational error magnitude due to surface variation

Many manufacturing processes are periodic

Milling, turning, machined molds, etc.

Many factors affect periodicity

Spindle speeds / feed rates

Vibration and/or deflection of: cutting tool

material being cut

fixturing assemblies

machine tool

periodicity in surface variation

Surface variation can be characterized as a sum of several sinusoids.

periodicity in surface variation

Surface Profile

extracting periodic information

Sum of periodic variations appears in nature– Vibratory systems

– Optics

– Signal processing

– Acoustics

– others…

time

signal amplitude

sampling interval

signal processing

distance

surface variation amplitude

sample length

surface variation

t

y y

Fourier analysis method

T

Fixed sampling interval

Fixed sampling rate

Store ( t , y ) pairs

– Time coordinate

– Amplitude coordinate

Time Variation Frequency Spectrum

AutoSpectrum

Surface

Fourier analysis method

C.L.1 C.L.2

/ C.L.

wavelength is not enough…

Scalable when rotation is less than 5 degrees. (small angle theorem)

C.L.1

C.L.2

<max rotation depends on / C.L.

C.L.1 C.L.2

dimensionlessparameter

non-dimensionalizing rotation

Characteristic Length = C.L.Characteristic Length = C.L.

Tolerance ZoneTolerance Zone




= actual rotational error


ArcTanArcTan (( ))ZoneZone

C.L.C.L. ==




= standardized rotational error





is dimensionless

(standardized)

(actual)

Video microscope

Collect simulated surface data Collect real surface data

Known sinusoidal inputs Manufactured surfaces

Surface generation program

Analyze rotational error

Interpret results

research methodology

Simulation Application

theoretical surface simulation

Inputs

Assembly Simulation

Random sinusoidal inputs for:Form variation (wavelength, amplitude, phase)Waviness variation (wavelength, amplitude, phase)Roughness variation (wavelength, amplitude, phase)

Simulated Surfaces 200 data points per sample

4000 samples per Monte Carlo simulation

manufactured surface analysis

Raw Data

Digital Enhancement

Assembly Simulation

Wavelength / Characteristic Length

Max

Rot

atio

n M

agni

tude

/ B

eta

0.5 1.0 10.0

/ / C.L.C.L.

max rotational error vs. / C.L.

0.5 1.0 10.0

longer wavelengths



Max

Rot

atio

n M

agni

tude

/ B

eta

0.25

0.50

0.66

0.80

1.00

1.20

3.00

5.00

Zone #1: / C.L. < 0.5Zone #2: / C.L. > 0.5 and / C.L. > 1.0 Zone #3: / C.L. > 1.0

0.5 1.0 10.0



Max

Rot

atio

n M

agni

tude

/ B

eta

phase distribution assumption

Probability that a given C.L. will encounter a given phase is uniformly distributed.

Goal is statistical understanding of the distribution of rotational errors for various values of /C.L.

C.L.

C.L.

C.L.

C.L.


Max

Rot

atio

n M

agni

tude

/ B

eta

0.5 1.0 10.0


Max

Rot

atio

n M

agni

tude

/ B

eta

Phase

rotational error vs. / C.L. vs. phase


0.5 1.0 10.0

Max

Rot

atio

n M

agni

tude

/ B

eta

Phase



0.5 1.0 10.0

≤ 0.50

Max

Rot

atio

n M

agni

tude

/ B

eta

Phase



0.5 1.0 10.0

0.50

Max

Rot

atio

n M

agni

tude

/ B

eta

Phase



0.5 1.0 10.0

0.66

distribution for / C.L. = 0.66

0% 100%Phase

Amplitude

Fre

qu

ency

0

66%=0

66% in spike

4

3

2

1

1

2

3

4

+0.72

+0.72

Am

pli

tud

e

Max

Rot

atio

n M

agni

tude

/ B

eta

Phase



0.5 1.0 10.0

0.80


0% 100%Phase

Amplitude

Fre

qu

ency

0 4

2

1

2

3

Am

pli

tud

e

4

3

125%=0

25% in spike

+1.70

+1.70

Max

Rot

atio

n M

agni

tude

/ B

eta

Phase



0.5 1.0 10.0

1.00


0% 100%Phase

Amplitude

Fre

qu

ency

0 4

1

2

3

Am

pli

tud

e

+2.35

2

4

3

1

+2.35

Max

Rot

atio

n M

agni

tude

/ B

eta

Phase



0.5 1.0 10.0

1.20


0% 100%

Amplitude

Fre

qu

ency

0 4

1

2

3

Am

pli

tud

e

+2.32

2

4

3

1

Phase

Max

Rot

atio

n M

agni

tude

/ B

eta

Phase



0.5 1.0 10.0

3.00


0% 100%

Amplitude

Fre

qu

ency

0 4

1

2

3

Am

pli

tud

e

+1.05

2

4

3

1

Phase

Max

Rot

atio

n M

agni

tude

/ B

eta

Phase



0.5 1.0 10.0

5.00


0% 100%

Amplitude

Fre

qu

ency

0 4

1

2

3

Am

pli

tud

e

+0.63

2

4

3

1

Phase

rotational error distributions

Distributions different at every / C.L.

Distributions are highly non-normal

Logical, gradual change in shape

/ C.L. < 0.5 / C.L. = 0.66 / C.L. = 0.8 / C.L. = 1.0

/ C.L. = 1.2 / C.L. = 3.0 / C.L. = 5.0 / C.L. =

/ C.L.

Max

/

0.5 1.0 10.0

conclusions

This graph describes an UPPER BOUND on rotational error at a given value of / C.L.

Given uniformly distributed phase, these distributions describe the STATISTICAL PROBABILITY of a given rotational error at a given value of / C.L.

0

1

3

conclusions

Only SOME values of / C.L. are relevant to assemblies

/ C.L. greater than 0.5

/ C.L. less than 4.0 (higher for some applications)

Translates to geometric form variations

Roughness and waviness may be neglected

conclusions

Characterization using a sum of sinusoids is sufficient

Most easily sampled frequencies are most important

Very high and very low frequencies are actually least relevant

Non-dimensionalized graphs are scalable

May be used for any size geometry

Form variation will dominate rotational error

Variation amplitude and rotation magnitude are linearly correlated within realm of small angle theorem

contributions

Rigorous mathematical relationships between periodic surface variation and rotational errors in assemblies

Surface variation simulation model

Application of Fourier transform to surface periodicity extraction

Three regions of rotational behavior

Non-dimensionalized rotation graphs

Monte Carlo simulation of distributions

Small angle theorem applicability

recommendations

Model new distributions for use in CATS

Fine-tune the frequency spectra extraction

Characterize manufacturing processes

Specify geometric tolerances based on selection of a characterized manufacturing process

Thank You !

surface variation and mating surface rotational error in assemblies taylor anderson ugs june 15,...

Documents

shape variation slide

realworld surface variation

variation analysis

component variation

location variation form

possible slide

propagation of variation

dimensionless parameter