Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
2. Figure 2 shows a simplified model to simulate a recording head flying over a rough disk surface in computer hard disk drives. The head has mass m and is supported by a suspension with stiffness k₁. Moreover, the moving disk surface will generate an air bearing lifting the head slightly above the disk surface (e.g., in the order of 20 nm). The air bearing is simplied as a linear spring with stiffness k2 and damping coefficient c. Let x(t) be the roughness of the disk surface and serve as the input excitation to the head/suspension system. Moreover, y(t) is the relative displacement of the head to the disk. In real hard disk drive applications, we want to keep y(t) almost constant, so that the head can follow the disk surface to perform read/write operations. (a) Show that the equation of motion is mi+cy + (k1 + k2) y = −mä – k₁x (2) 1 (b) Derive the frequency response function. Plot the magnitude and phase of the frequency response function. In plotting the frequency response function, let's define k1 k1 + k2 W₁ = W2= m m (3) Describe the motion of the head in the following three frequency ranges: 0 < w< W1, W1

2. Figure 2 shows a simplified model to simulate a recording head flying over a rough disk surface in computer hard disk drives. The head has mass m and is supported by a suspension with stiffness k₁. Moreover, the moving disk surface will generate an air bearing lifting the head slightly above the disk surface (e.g., in the order of 20 nm). The air bearing is simplied as a linear spring with stiffness k2 and damping coefficient c. Let x(t) be the roughness of the disk surface and serve as the input excitation to the head/suspension system. Moreover, y(t) is the relative displacement of the head to the disk. In real hard disk drive applications, we want to keep y(t) almost constant, so that the head can follow the disk surface to perform read/write operations. (a) Show that the equation of motion is mi+cy + (k1 + k2) y = −mä – k₁x (2) 1 (b) Derive the frequency response function. Plot the magnitude and phase of the frequency response function. In plotting the frequency response function, let's define k1 k1 + k2 W₁ = W2= m m (3) Describe the motion of the head in the following three frequency ranges: 0 < w< W1, W1

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
See similar textbooks
icon
Related questions
Question
2. Figure 2 shows a simplified model to simulate a recording head flying over a rough disk surface in computer hard disk drives. The head has mass m and is supported by a suspension with stiffness k₁. Moreover, the moving disk surface will generate an air bearing lifting the head slightly above the disk surface (e.g., in the order of 20 nm). The air bearing is simplied as a linear spring with stiffness k2 and damping coefficient c. Let x(t) be the roughness of the disk surface and serve as the input excitation to the head/suspension system. Moreover, y(t) is the relative displacement of the head to the disk. In real hard disk drive applications, we want to keep y(t) almost constant, so that the head can follow the disk surface to perform read/write operations. (a) Show that the equation of motion is mi+cy + (k1 + k2) y = −mä – k₁x (2) 1 (b) Derive the frequency response function. Plot the magnitude and phase of the frequency response function. In plotting the frequency response function, let's define k1 k1 + k2 W₁ = W2= m m (3) Describe the motion of the head in the following three frequency ranges: 0 < w< W1, W1 <ww2, and w₂ <w. (c) If we want to design the disk drive so that the head can follow the disk surface for a wide frequency range, how should we choose k₁, k2, and m? 10 0 Acceleration Charge q(t) 10 Voltage -20 a(t) Hbag(s) Hamp(s) v(t) -30 Figure 3: Block diagram of an airbag sensor -50 -60 01 02 5 10 20 F-0.5 Hz Figure 4: Magnitude of Gamp (w) F-33 kHz
Transcribed Image Text:2. Figure 2 shows a simplified model to simulate a recording head flying over a rough disk surface in computer hard disk drives. The head has mass m and is supported by a suspension with stiffness k₁. Moreover, the moving disk surface will generate an air bearing lifting the head slightly above the disk surface (e.g., in the order of 20 nm). The air bearing is simplied as a linear spring with stiffness k2 and damping coefficient c. Let x(t) be the roughness of the disk surface and serve as the input excitation to the head/suspension system. Moreover, y(t) is the relative displacement of the head to the disk. In real hard disk drive applications, we want to keep y(t) almost constant, so that the head can follow the disk surface to perform read/write operations. (a) Show that the equation of motion is mi+cy + (k1 + k2) y = −mä – k₁x (2) 1 (b) Derive the frequency response function. Plot the magnitude and phase of the frequency response function. In plotting the frequency response function, let's define k1 k1 + k2 W₁ = W2= m m (3) Describe the motion of the head in the following three frequency ranges: 0 < w< W1, W1 <ww2, and w₂ <w. (c) If we want to design the disk drive so that the head can follow the disk surface for a wide frequency range, how should we choose k₁, k2, and m? 10 0 Acceleration Charge q(t) 10 Voltage -20 a(t) Hbag(s) Hamp(s) v(t) -30 Figure 3: Block diagram of an airbag sensor -50 -60 01 02 5 10 20 F-0.5 Hz Figure 4: Magnitude of Gamp (w) F-33 kHz
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY
SEE MORE TEXTBOOKS