CapacitorProduction

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The Problem: In the manufacturing of the ceramic capacitors (a device capable of holding an electric charge), the first step in the process is the mixing of the raw materials to produce the ceramic powder to be utilized in the manufacturing process. This synthesized ceramic powder is then mixed with an organic binder prior to being cast into greenware tapes for the manufacture of the capacitors. Adding organic binder is similar to adding water to cement mix in order to be able to pour the cement. In this case, the binder is mixed with the powder and allows the powder to be cast into greenware tapes. The greenware tapes, after drying, have the consistency and thickness of a 5 ¼ inch floppy disk. They are then made conductive by coating with a metallic ink, stacked, and cut into strips. The strips are then processed through a series of ovens that first slowly removes the organic binder and then sinters (bakes) the ceramic power into a hard, solid strip of ceramic material. These solid strips are later cut into the individual capacitors. The problem is to determine some of the parameters for the powder manufacturing process.
Areas of Application:
Problem solving
Basic arithmetic skills
Rates and ratios
Materials Included:
	Problems dealing with the mixing, heating, and the manufacturing of greenware tapes.
Background Information and Assumptions:
The process involved in the manufacture of the ceramic powder is made up of a series of steps and needs to be done in the most time effective manner. 
The ceramic powder is produced by the following process: 
Three different raw materials, X, Y and Z , are first combined as powders in a large container in a ratio by weight of 10 : 3 : 1. 
The 20 kilogram batches of the raw materials are mixed for a period of 4 hours.
This 20 kilogram mixture is then heated in an oven at a temperature of 600° C for a period of 8 hours to produce the ceramic powder, XYZ. 
The resulting material has consistency of chalk. Thirty (30) kilogram batches are ground up into powder to obtain particles with a specific maximum size during a 4 hour process. 
The particle size is determined by a screening process with about 85% of the ground material being acceptable. (The non-acceptable material can be used if it is re-ground to the proper size.) 
Organic binder is then added to the acceptable ground powder in a ratio of 8 : 1 by weight (powder to binder) and mixed for 8 hours to produce the powder-binder mixture that is then cast into the greenware tapes for further processing.
The fabrication process for the greenware tapes requires 2.5 kilograms of ceramic powder per finished block. There are 1,000 blocks of greenware tapes produced every 24 hours. The process engineer also wants to produce enough extra powder so that if a problem occurs (oven or mixing unit breaks down, raw powder or organic binder shipment is one day late), the process can continue to run for 24 hours without a stoppage.
Goal:
To make this process work in the most effective manner, the process engineer must determine the amount of raw materials and binder, the number of raw material mixers, the number of ovens, the number of grinders, and the number of powder-binder mixing units that are required to ensure a continuous 24 hour operation.
Requirements:
Determine the amount of each of the raw materials, X, Y, and Z that must be available for a week to ensure the process can run continuously and efficiently.
Determine the amount of organic binder that must be available for a week to ensure the process can run continuously and efficiently.
Determine the number of ovens and mixing units, both powder and powder-binder, that must be available to continually produce ceramic materials for producing the 1,000 blocks each day. (Remember that breakdowns do occur and you need to include this factor in your final result. You’ll need to make an assumption about the number of breakdowns per week. You can assume that a repair can be completed within one operation cycle, .i.e. 8 hours for an oven). 
List all assumptions you have made about the process and indicate how they have effected you conclusions, such as machine breakdown and machine maintenance.
If time allows, a flow diagram of the process for the materials would be interesting to develop.
Additional information that might be useful. 
Since all the ceramic powder is manufactured using the same process, it can be assumed that all the powder is the same and can be divided up and/ or mixed together at any step in the process. This will not effect the results.
 
Classroom Time:
Left to the individual Teacher.
Assessment:
Left to the individual Teacher.
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The ceramic powder manufacturing process involves several steps starting with the mixing of the raw materials in preparation for the casting of greenware tapes. There are a series of machines that are essential for this production. In order for the process to be efficient both materials and machines must be available. If any of these are not available, the process is delayed.
The process involved in the manufacture of the ceramic powder is made up of a series of steps and needs to be done in the most time effective manner. 
The ceramic powder is produced by the following process: 
Three different raw materials, X, Y and Z , are first combined as powders in a large container in a ratio by weight of 10 : 3 : 1. 
The 20 kilogram batches of the raw materials are mixed for a period of 4 hours.
This 20 kilogram mixture is then heated in an oven at a temperature of 600° C for a period of 8 hours to produce the ceramic powder, XYZ. 
The resulting material has consistency of chalk. Thirty (30) kilogram batches are ground up into powder to obtain particles with a specific maximum size during a 4 hour process. 
The particle size is determined by a screening process with about 85% of the ground material being acceptable. (The non-acceptable material can be used if it is re-ground to the proper size.) 
Organic binder is then added to the acceptable ground powder in a ratio of 8 : 1 by weight (powder to binder) and mixed for 8 hours to produce the powder-binder mixture that is then cast into the greenware tapes for further processing.
The fabrication process for the greenware tapes requires 2.5 kilograms of ceramic powder per finished block. There are 1,000 blocks of greenware tapes produced every 24 hours. The process engineer also wants to produce enough extra powder so that if a problem occurs (oven or mixing unit breaks down, raw powder or organic binder shipment is one day late), the process can continue to run for 24 hours without a stoppage.
Limitations in the Manufacturing Process:
Sufficient amounts of raw materials X, Y, and Z and binder must be available to keep the process running continuously for a week.
Sufficient quantities of machines (mixers, ovens, grinders, powder-binder mixers) must be available to keep the process running continuously for a week.
Fifteen percent of all sieved material does not meet required particle size.
A repair can be completed within one operation cycle, .i.e. 8 hours for an oven.
All operation times must be met. 
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Problem #1:
	Determine the amount of each of the raw materials, X, Y, and Z that must be available for a week to ensure the process can run continuously and efficiently.
Problem #2:
Determine the amount of organic binder that must be available for a week to ensure the process can run continuously and efficiently.
Problem #3:
Determine the number of ovens and mixing units, both powder and powder-binder, that must be available to continually produce ceramic materials for producing the 1,000 blocks each day. 
Problem #1 Suggestions & Solutions:
Since the manufacturer must produce 1,000 blocksper day for a week, and each block contains 2.5 kilograms of powder, the amount of powder needed per week for completed blocks is:
Since the powder is produced from three raw materials X, Y, and Z in a ratio of 10:3:1, the amount of X is:
Since the powder is produced from three raw materials X, Y, and Z in a ratio of 10:3:1, the amount of Y is:
Since the powder is produced from three raw materials X, Y, and Z in a ratio of 10:3:1, the amount of Z is:
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In addition, a one day supply is needed on-hand to ensure continuous operation in case a shipment is delayed. Therefore, the extra amounts of X, Y, and Z needed are one seventh of the amounts needed per week as calculated above.
The amount of additional X required for one extra day is:
The amount of additional Y required for one extra day is:
The amount of additional Z required for one extra day is:
Therefore, the total amount of raw materials needed for one week production plus raw material for an extra day is:
The amount of X required is:
12,500 + 1,786 = 14,286 kilograms
The amount of Y required is:
3,750 + 536 = 4,286 kilograms
The amount of Z required is:
1,250 + 179 = 1,429 kilograms
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However, when the manufacturing process is initiated, additional material must be included. The reason for this is that 15 % of the material after the first grinding is unacceptable because of particle size. The assumption is made that after the initial start-up, this material can be recycled into the grinding process. Therefore, an additional 15% of X, Y, and Z is required for all batches on the first day of operation.
The amount of additional X required for the first 2,500 kilograms (1,000 blocks/day at 2.5 kilograms/block) is:
1,786 kilograms*15% = 268 kilograms of X
The amount of additional Y required for the first 2,500 kilograms (24 hours) is:
536 kilograms*15% = 81 kilograms of Y
The amount of additional Z required for the first 2,500 kilograms (24 hours) is:
179 kilograms*15% = 27 kilograms of Z
The total for the first week of operation, which include the amount of raw materials for one week, the extra day supply of raw materials, and the additional raw materials for the first cycle to compensate for the 15% loss (remember, after the first day of operation, we assume that the unacceptable 15% is then recycled), is:
The amount of X required is:
12,500 + 1,786 + 268 = 14,524 kilograms
The amount of Y required is:
3,750 + 536 + 81 = 4,367 kilograms
The amount of Z required is:
1,250 + 179 + 27 = 1,456 kilograms
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Problem #2 Suggestions & Solutions:
Since in one week we will produce 17,500 kilograms of XYZ powder, the amount of binder needed is 1/8 (ratio of binder to powder) of 17,500 kilograms. 
However, since the requirement states that there must be an extra one-day supply of materials on hand, we must also include an extra one-day supply of binder. The extra amount of binder, therefore, is:
Therefore, the total amount of binder necessary to have on hand for one week production is:
2,188 + 313 = 2,501 kilograms of binder
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Problem #3 Suggestions & Solutions:
In order to determine the number of pieces of equipment needed for operation, we must first determine the flow of material through the manufacturing process. This is depicted in the flow chart below that identifies both the amounts of material held by the machines (ovens, powder mixing units and powder-binder mixing units) and the time required for each operation. 
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Since we must process 2,500 kilograms of powder per day, and the first step of each cycle (the mixing of powders X, Y, and Z) requires 4 hours, we can run 6 cycles in a 24-hour period. The next step after defining the flow diagram is to develop a process chart to help identify the equipment needed for each of the six process cycles. The process chart will be based upon the amount of time, as well as the amount of material, that is needed for each step in the process. 
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As an example, each cycle in the 24-hour period would process:
The mixing process of this first batch of material takes four hours and is then immediately put into an oven for eight hours. The second batch is then mixed for four hours in the same mixer. However, when this batch is completely mixed, a new oven is required since the first oven is only half-way through its eight-hour cycle. The third batch, when completed mixing, can be put into the first oven, since the first batch has completed that heating cycle. Extending this discussion through the process for all six batches, the following process chart can be created.
	
	Day 1 - 480 KG of mix goes into each batch 1 through 6
	
	
	
	
	Day 2 & beyond - 418 KG of mix goes into each batch 1 through 6
	
	
	First Calculations - Assume no Downtime or Losses
	
	
	
	
	
	
	
	0
	4 hrs
	8 hr
	12 hrs
	16 hrs
	20 hrs
	24 hrs
	
	
	
	
	
	
	
	
	
	Mix 1
	20 kg each
	1
	2
	3
	4
	5
	6
	
	4 hr cycle
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	Bake 600 C
	20 kg each
	5 day 2
	1
	 
	3
	 
	5
	
	8 hr cycle
	
	6 day 2
	 
	2
	 
	4
	 
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	Grind
	30 kg each
	4 day 2
	5 day 2
	6 day 2
	1
	2
	3
	
	4 hr cycle
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	2nd Mix
	30 kg each
	3 day 2
	 
	5 day 2
	 
	1 day 1
	 
	
	8 hr cycle
	
	2 day 2
	4 day 2
	 
	6 day 2
	 
	2 day 1 >
	
	
	
	
	
	
	
	
	
	
	
	418 kg/cycle
	
	
	
	
	
	
	2500 kg per day
Based upon the discussion and the above chart, we can now calculate the number of pieces of equipment that are required for continuous 24-hour operation. In all calculations regarding the number of machines required, the calculated value is always rounded up to the next whole number since a part of a machine does not exist.
In the first mixing step, each mixer can process 20 kilograms of material. As a result, the number of mixers needed is:
	
In the baking cycle, each oven can hold 20 kilograms of material. However, since the oven cycle is 8 hours, we will need twice as many ovens as mixers or:
Once the material has been baked, it goes into the grinding cycle. Since each grinder can process 30 kilograms of material, the number of grinders needed
	
After the material is ground, it is mixed with binder in the powder-binder mixer, which also holds 30 kilograms of powder. However, this process takes 8 hours. So, the number of powder-binder mixers is equal to the twice number of grinders, or:
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The values for the amounts of equipment that were calculated above do not include the fact that on the start-up run additional material needs to be processed to compensate for the fact that 15% is lost prior to mixing powder with binder. We know from previous calculations that on the first day 15% more than 2,500 kilograms of powder is needed.
2,500 kilograms*1.15 = 2,875 kilograms
Since we are running 6 cycles, each cycle will start with 480 kilograms of raw materials. We therefore need to have sufficient equipment to carry out the first 24-hour cycle. Using the same arguments as before, the number of powder mixers is:
Likewise, the number of ovens needed is twice the number of mixers, or 48, and the number of grinders needed would be:
However, the number of powder-binder mixers remains the same because even in the first 24 hours, only 2,500 kilograms results from the grinding process (15% lost is recycled into the next cycle), or 28 powder-binder mixers. 
	
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In the real world, nothing runs perfectly, and machines do break down and need maintenance. In order for the process to run continuously, the process engineer must plan ahead for such situations. From past experience, it is known that 5% of machines breakdownor need maintenance per week. This must be taken into account. Going back to the first calculations on the number of machines required for continuous operation and assuming that an additional 5% is required, the number of machines needed is 
The number of powder mixers needed is:
21 mixers*1.05 = 23 mixers
The number of ovens needed is:
42 ovens*1.05 = 45 ovens
The number of grinders needed is:
14 grinders*1.05 = 15 grinders
The number of powder-binder mixers needed is:
28 powder-binder mixers*1.05 = 30 powder-binder mixers
If we assume that all of the machines were individually tested in operating efficiently prior to the initial start-up process, we will then assume that there are no breakdowns in the initial 24-hour cycle. Therefore, there is no need to buy additional equipment, except for the number of powder-binder mixers, since the number of machines needed for the initial 24-hour cycle is greater than that required to compensate for a 5% breakdown/maintenance rate. The manufacturer would need to purchase one additional powder-binder mixer because the number of machines needed was not affected by the first 24-hour cycle.
8 hrs
4 hrs
8 hrs
4 hrs hrshrs
15%
85%
Binder
Castings
Powder-Binder Mixer (30 kgms/batch)
Oven (20 kgms/batch)
Ceramic Grinder (30 kgms/batch)
Raw Material Mixer (20 kgms/batch)
X:Y:Z (10:3:1) (2,500 kgms)