## Posted tagged ‘number’

### Red Marbles, Blue Marbles

August 24, 2011

Problem: you have two jars, 50 red marbles, 50 blue marbles. you need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. (when picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar) you can arrange the marbles however you like, but each marble must be in a jar.

### Solution

Chance! chance is easy if you know how to do the formula. we know that we have two choices to make. first we’ll pick a jar, and each jar will have a 1/2 chance of being picked. then we’ll pick a marble, and depending how we stack the marbles, we’ll have a (# of red marbles in jar)/(# of total marbles in jar) chance of getting a red one.

for example, say we put all the red marbles into JAR A and all the blue ones into JAR B. then our chances for picking a red one are:

1/2 chance we pick JAR A * 50/50 chance we pick a red marble
1/2 chance we pick JAR B * 0/50 chance we pick a red marble

do the math and you get 1/2 chance for a red marble from JAR A and a 0/2 chance for a red marble from JAR B. add ‘em up and you get the result = 1/2 chance for picking a red marble.

think about it for awhile and see if you can figure out the right combination. we had a 50/50 (guaranteed) chance in picking a red marble from JAR A, but we didn’t have to have 50 red marbles in there to guarantee those fantastic odds, did we? we could’ve just left 1 red marble in there and the odds are still 1/1. then we can take all those other marbles and throw them in JAR B to help the odds out there.

let’s look at those chances:

1/2 we pick JAR A * 1/1 we pick a red marble
1/2 we pick JAR B * 49/99 we pick a red marble

do the math and add them up to get 1/2 + 49/198 = 148/198, which is almost 3/4.

we can prove these are the best odds in a somewhat non-formal way as follows. our goal is to maximize the odds of picking a red marble. therefore we can subdivide this goal into maximizing the odds of picking a red marble in JAR A and maximizing the odds of picking a red marble in JAR B. if we do that, then we will have achieved our goal. it is true that by placing more red marbles into a jar we will increase the chances of picking a red marble. it is also true that by reducing the number of blue marbles in a jar we will increase the odds also. we’ve maximized the odds in JAR A since 1/1 is the maximum odds by reducing the number of blue marbles to 0 (the minimum). we’ve also maximized the number of red marbles in JAR B. if we added any more red marbles to JAR B we would have to take them out of JAR A which reduce the odds there to 0 (very bad). if we took any more blue ones out of JAR B we would have to put them inJAR A which reduce the odds there by 50% (very bad).

it wasn’t really a good proof, but QED anyway 😛

### METALLURGY

August 23, 2011

Definition:

The Process of producing components from metallic powder parts made by powder metallurgy may contain non-metallic constituents to improve the bonding qualities and properties.

Number and variety of products made by powder metallurgy are continuously increasing:

1. Tungsten Filaments for Lamps
2. Contact Point relays
3. Self lubricating bearings
4. Cemented carbides for cutting tools etc.

Characters of Metal Powders:

• Shape:

It is influenced by the way it’s made. The shape may be spherical (atomization) (Electrolysis) flat or angular (Mechanical crushing). The particle shape influences the flow characteristics of powders.

• Particle Size (Fineness) and size distribution:

Particle Size and Distribution are important factors which controls the porosity, Compressibility and amount of shrinkage. Proper particle size and size distribution are determined by passing the powder through a standard sieves ranging from 45 to 150 micrometer mesh.

• Flowability:

The ability of the powders to flow readily and conform to the mould cavity. The flow rate helps to determine to possible production rate.

• Compressibility:

It’s defines as the volume of initial powder (Powder loosely filled in cavity) to the volume of compact part. Depends on particle shape & size distribution.

• Apparent Density:

The Apparent density depends on particle size is defined as the ratio of volume to weight of loosely filled mixture.

• Green strength:

It refer to strength of a compact part prior to sintering. It depends on compressibility and helps to handle the parts during the mass production.

• Purity:

Impurities affects sintering & Compacting Oxides & Gaseous impurities can be removed from the part during sintering by the use of a reducing atmosphere.

• Sintering ability:

It is the ability which promotes bonding of particles by the application of heat.

Powder Metallurgy Process steps:

Manufacture of Metal Powders:

Methods:

• Mechanical pulverization:

Machining, Drilling or Grinding of metals is used to convert them to powders.

• Machining:

It Produces coarse particles (Flack form) especially Magnesium powders.

• Milling or Grinding:

It suitable for brittle materials.

• Shorting:

The process of dropping molten metal through a Sieve or small orifice in to water. This produces Spherical particles or larger size. Commonly used for metals of low melting point.

• Atomizing:

In this molten metal is forced through a nozzle, and a stream of compressed air, stream or Inert gas is directed on it break up into five particles. Powders obtained in irregular in shapes. Atomization commonly used for aluminium, Zinc, Tin, Cadmium and other metals of low melting point.

• Electrolytic deposition:

It’s used mainly for producing iron and copper powders. These are dense structure with low apparent density. It consists of depositing metal on cathode plate by conventional electrolysis processes. The Cathode paltes are removed and the deposited powder is scraped off. The powder is wasted, dried, screened & oversized particles are milled or ground for fineness. The powder is further subjected to heat treatment to remove the work hardening effect.

• Chemical reduction:

It’s used for producing iron, Copper, Tungsten, Molybdenum, Nickel & Cobalt powder process consists of reducing the metal oxides by means of carbon monoxide or Hydrogen. After reduction, the powder is usually ground & Sized.

Forming to shape:

1. The process of mixing the powders is called Blending.
2. The Loose powders are formed in to shape by compacting.

### METALLURGY

August 23, 2011

Definition:

The Process of producing components from metallic powder parts made by powder metallurgy may contain non-metallic constituents to improve the bonding qualities and properties.

Number and variety of products made by powder metallurgy are continuously increasing:

1. Tungsten Filaments for Lamps
2. Contact Point relays
3. Self lubricating bearings
4. Cemented carbides for cutting tools etc.

Characters of Metal Powders:

• Shape:

It is influenced by the way it’s made. The shape may be spherical (atomization) (Electrolysis) flat or angular (Mechanical crushing). The particle shape influences the flow characteristics of powders.

• Particle Size (Fineness) and size distribution:

Particle Size and Distribution are important factors which controls the porosity, Compressibility and amount of shrinkage. Proper particle size and size distribution are determined by passing the powder through a standard sieves ranging from 45 to 150 micrometer mesh.

• Flowability:

The ability of the powders to flow readily and conform to the mould cavity. The flow rate helps to determine to possible production rate.

• Compressibility:

It’s defines as the volume of initial powder (Powder loosely filled in cavity) to the volume of compact part. Depends on particle shape & size distribution.

• Apparent Density:

The Apparent density depends on particle size is defined as the ratio of volume to weight of loosely filled mixture.

• Green strength:

It refer to strength of a compact part prior to sintering. It depends on compressibility and helps to handle the parts during the mass production.

• Purity:

Impurities affects sintering & Compacting Oxides & Gaseous impurities can be removed from the part during sintering by the use of a reducing atmosphere.

• Sintering ability:

It is the ability which promotes bonding of particles by the application of heat.

Powder Metallurgy Process steps:

Manufacture of Metal Powders:

Methods:

• Mechanical pulverization:

Machining, Drilling or Grinding of metals is used to convert them to powders.

• Machining:

It Produces coarse particles (Flack form) especially Magnesium powders.

• Milling or Grinding:

It suitable for brittle materials.

• Shorting:

The process of dropping molten metal through a Sieve or small orifice in to water. This produces Spherical particles or larger size. Commonly used for metals of low melting point.

• Atomizing:

In this molten metal is forced through a nozzle, and a stream of compressed air, stream or Inert gas is directed on it break up into five particles. Powders obtained in irregular in shapes. Atomization commonly used for aluminium, Zinc, Tin, Cadmium and other metals of low melting point.

• Electrolytic deposition:

It’s used mainly for producing iron and copper powders. These are dense structure with low apparent density. It consists of depositing metal on cathode plate by conventional electrolysis processes. The Cathode paltes are removed and the deposited powder is scraped off. The powder is wasted, dried, screened & oversized particles are milled or ground for fineness. The powder is further subjected to heat treatment to remove the work hardening effect.

• Chemical reduction:

It’s used for producing iron, Copper, Tungsten, Molybdenum, Nickel & Cobalt powder process consists of reducing the metal oxides by means of carbon monoxide or Hydrogen. After reduction, the powder is usually ground & Sized.

Forming to shape:

1. The process of mixing the powders is called Blending.
2. The Loose powders are formed in to shape by compacting.

### INDUCTIVE CHARGING

August 23, 2011

In the future all electronic devices will be wirelessly powered. Small, battery-powered gadgets make powerful computing portable.

The battery charger should be capable of charging the most common battery types found in portable  devices today.  In addition, the charging  should be  controlled from the base station and a bidirectional communication system between  the pickups  and base  station  should be developed.

Inductive Power Systems:

Inductive Power Transfer (IPT)  refers to the concept of transferring electrical power between two isolated circuits across an air gap.  While based on the work and concepts developed by pioneers such as  Faraday and Ampere, it  is  only recently that IPT has been developed into working systems.

Essentially, an IPT system can be divided into two parts;

• Primary and
• Secondary.

The primary side of the system is made up of a resonant power supply and a coil. This power supply produces a high frequency sinusoidal current in the coil.  The secondary side (or ‘pickup’) has a smaller coil, and a converter to produce a DC voltage.

Working of Inductive Power Transfer:

In this system communications signals are encoded onto the waveform that provides power to the air gap. Communication from the primary side to the secondary is implemented by switching the power signal at the output of the resonant converter between its normal level  and a lower level which is detectable by the pickup but still provides enough power to control the pickup microcontroller. This process is called Amplitude Shift Keying (ASK). This is achieved by varying the output voltage of the buck converter which provides an input DC voltage to the resonant converter.

Communication from the secondary to the primary is achieved by a process called Load Shift Keying (LSK).  This involves varying the loading on the pickup.   Any load on the pickup will reflect a voltage on the primary circuit proportional to the load.  Therefore a variation in the load on the pickup can be detected by the charging station.

The communications system must provide two discrete levels of voltage reflected onto the primary side,  to represent the on and off states for digital communications. The difference must be easily detected on the primary side to provide a robust communications channel. Signals are decoded by simple filters and comparators which feed a  digital signal to the microcontrollers.