Jiadong Zhang

1
Sensitivity Analysis of Pico Femto Sliders
Research Review, 2002

• Researcher Jiadong Zhang
• Advisor Frank Talke

2


Outline

• Background and Motivation
• Implementation
• Sensitivity Study Using Monte Carlo Analysis
• Future Work
• Summary

3


Background
Motivation

• High storage density, low spacing
• 100 Gbit/in2 ---gt 5nm
• Requirements for hard disk drive
• small and stable spacing between slider disk
• high airbearing stiffness
• low sensitivity of spacing on disk velocity and
  skew angle
• Sensitivity of flying behavior is important

4


Implementation

step 1
step 1
step 2
step 3
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Solver CMRR Simulator V3.0
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Slider Design and Modeling


Sensitivity Study
Using Monte Carlo Analysis
slider I (pico) air bearing step 150
nm cavity depth 770 nm
slider II (pico) air bearing step 260
nm cavity depth 2.5 ?m
slider III (femto) air bearing step 105
nm cavity depth 540 nm
7
Flying Height vs Disk Velocity
slider I
slider III
slider II
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Sensitivity Study using Monte Carlo Analysis

• Select independent variables
• Pivot Point Position
• Pre-load
• Pitch Static Attitude
• Roll Static Attitude
• Air bearing Step Height
• Cavity Depth
• Assuming the independent variables have
• normal distribution

selected independent variables and tolerances for
slider I
same tolerances were chosen for slider I, II
III

• Calculate the distributions of FH, Pitch angle
  Roll angle

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Monte Carlo Analysis Results of Slider I
Roll Angle Nominal -1.0746 ?rad Mean
-1.0275 ?rad STD 5.7702 ?rad
Flying Height Nominal 14.0807 nm Mean
13.8559 nm STD 0.5839 nm
Pitch Angle Nominal 45.9059 ?rad Mean
45.9962 ?rad STD 1.5288 ?rad
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Monte Carlo Analysis Results of Slider II
Roll Angle Nominal -2.6884 ?rad Mean
-2.5244 ?rad STD 4.7516 ?rad
Flying Height Nominal 3.9383 nm Mean
3.7435 nm STD 0.6850 nm
Pitch Angle Nominal 156.0938 ?rad Mean
156.1735 ?rad STD 5.0248 ?rad
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Monte Carlo Analysis Results of Slider III
Roll Angle Nominal -0.8996 ?rad Mean
-0.9797 ?rad STD 5.5885 ?rad
Flying Height Nominal 5.3372 nm Mean
5.2272 nm STD 0.3330 nm
Pitch Angle Nominal 24.9528 ?rad Mean
24.6880 ?rad STD 1.3444 ?rad
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Characteristic Values of Resulting Distributions
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Monte Carlo Analysis Results of Slider Iwhen
only air bearing step height varies
Roll Angle Nominal -1.0746 ?rad Mean
-1.0770 ?rad STD 0.0097 ?rad
Flying Height Nominal 14.0807 nm Mean
14.1091 nm STD 0.1066 nm
Pitch Angle Nominal 45.9059 ?rad Mean
45.9488 ?rad STD 0.1740 ?rad
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Monte Carlo Analysis Results of Slider Iwhen
only cavity depth varies
Roll Angle Nominal -1.0746 ?rad Mean
-1.0744 ?rad STD 0.0046 ?rad
Flying Height Nominal 14.0807 nm Mean
14.1006 nm STD 0.3683 nm
Pitch Angle Nominal 45.9059 ?rad Mean
45.9011 ?rad STD 0.0735 ?rad
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Monte Carlo Analysis Results of Slider IIwhen
only air bearing step height varies
Roll Angle Nominal -2.6884 ?rad Mean
-2.5924 ?rad STD 0.3494 ?rad
Flying Height Nominal 3.9383 nm Mean
3.8989 nm STD 0.1080 nm
Pitch Angle Nominal 156.0938 ?rad Mean
155.7502 ?rad STD 1.0609 ?rad
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Monte Carlo Analysis Results of Slider IIwhen
only cavity depth varies
Roll Angle Nominal -2.6884 ?rad Mean
-2.6733 ?rad STD 0.2488 ?rad
Flying Height Nominal 3.9383 nm Mean
3.9591 nm STD 0.4278 nm
Pitch Angle Nominal 156.0938 ?rad Mean
156.2534 ?rad STD 1.3959 ?rad
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Monte Carlo Analysis Results of Slider IIwhen
only pre-load varies
Roll Angle Nominal -2.6884 ?rad Mean
-2.6898 ?rad STD 0.1496 ?rad
Flying Height Nominal 3.9383 nm Mean
3.9392 nm STD 0.1115 nm
Pitch Angle Nominal 156.0938 ?rad Mean
156.1030 ?rad STD 1.8959 ?rad
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Monte Carlo Analysis Results of Slider IIwhen
only pivot point position varies
Roll Angle Nominal -2.6884 ?rad Mean
-2.6986 ?rad STD 1.3690 ?rad
Flying Height Nominal 3.9383 nm Mean
3.9338 nm STD 0.1424 nm
Pitch Angle Nominal 156.0938 ?rad Mean
156.1268 ?rad STD 0.8746 ?rad
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Conclusions

• The resulting distributions of FH, pitch angle
  and roll angle are nearly Gaussian
• The design of the air bearing geometry is one of
  the key issues which affect the sensitivity of
  flying behavior. The design parameters in the
  high pressure areas are especially important
• Increased attention must be exercised to control
  the manufacturing tolerances when the slider
  flying height decreases
• FH, pitch angle and roll angle are nonlinear
  functions of air bearing step height
• FH, pitch angle and roll angle are almost linear
  functions of cavity depth

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Future Work
step 1
Optimize the air bearing design so that
satisfies the strict multi-objected goals.
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Optimization of Slider
Air Bearing Design

• Characteristic of optimization of slider air
  bearing
• design
• Large number of design variables
• Operating parameters
• Geometry variables of ABS contour
• Nonlinear nature of Reynolds equation

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Optimization of Slider
Air Bearing Design

• Traditional optimization algorithms
• Not suitable for large number of variables
• Gradient-based, expensive
• Only insure local optimum
• Global optimization algorithms
• Simulated Annealing (SA)
• Genetic Algorithm (GA)
• DIRECT algorithm

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Simulated Annealing
(SA)

• An analogy of metal annealing process
• The solution first evolves at a given control
  
• value T
• (1) through a large number of randomly
• generated solutions
• (2) by taking acceptance probability
• The solution then repeatedly evolves according
• to an annealing scheme (T )

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Genetic Algorithm (GA)

• Inspired by Darwin's theory of evolution
• Starts with a set of solutions called population
  
• Two solutions (Parents) are selected from the
  current
• population to reproduce new solutions
  (Offspring)
• (1) Crossover
• (2) Mutation
• All the new solutions form a new population
• The above steps are repeated until certain
  conditions
• are satisfied

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DIRECT algorithm

• DIviding RECTangles, a global deterministic
  algorithm
• based on the Shubert algorithm
• Main Idea
• Finding all the potentially optimal
  hyper-rectangles
• Dividing the hyper-rectangles to find the minima

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Summary

• Sensitivity analysis has been performed on Pico
  Femto sliders
• The resulting distributions of FH, pitch angle
  and roll angle are nearly Gaussian
• Increased attention must be exercised to control
  the manufacturing tolerances when the slider
  flying height decreases
• FH, pitch angle and roll angle are nonlinear
  functions of air bearing step height
• FH, pitch angle and roll angle are almost linear
  functions of cavity depth
• Optimization of slider air bearing design will be
  implemented using global optimization algorithms