Single Station Manufacturing Cells

What is a single station manufacturing cell?(Mikell P. Groover 2018)

It is an automated production machine capable of operating unattended for longer than one work cycle. A worker is not required except for periodic tending of the machine.

Main questions to answer:

  1. How many workstations are needed to satisfy demand?

  2. How many machines can be assigned to one worker in a machine cell or cluster?

A machine cluster or cell is a collection of machines serviced by one, or more workers.

Formulas for single station automated cells

Let \(SC\) represent part storage capacity. Then, the unattended time of a machine is \(UT\):

\[ UT=\sum_{k=1}^{SC} T_{ck} \tag{1}\]

Where \(k\) is the part type manufactured, and \(T_{ck}\) is the cycle time for part \(k\).

Unattended time must provide enough time for:

  1. An operator to tend multiple machines.

  2. Scheduled tool changes.

  3. Shift fitting.

  4. Lights-off operation.

Storage capacity devices

Automated example.

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Manual example

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Zero storage capacity

In this case we calculate the cycle time of the work center as:

\[ T_c=T_m+T_s \tag{2}\]

where \(T_c\) is the cycle time of the work center, \(T_m\) is the machine processing time, and \(T_s\) is the worker’s service time.

SC=1

In this case the cycle time of the work center is:

\[ T_c=MAX \{T_m,T_s \}+T_r \tag{3}\]

and \(T_r\) is the re positioning time of the pallet changer that includes the movements to put a finished part away and raw work parts into position in front of the work head of the machine.

if \(T_s>T_m\) we have machine idle time. If \(T_s \ge T_m\) we have 100% machine utilization.

What happens when \(SC >1\)?

CNC machines

CNC stands for “Computer Numerical Control.” CNC machining is a manufacturing process where computer software is pre-programmed to tell a machine how to move factory tools and machinery. Once the programming is put into the machine, it will operate on its own. The speed and position of machinery and tools are run through software. A CNC machine operates like a robot.

Examples of CNC machines

  1. CNC Mills. The most basic ones operate on a three axis system.

  2. Lathes. These machines cuts pieces in a circular direction. This process is done with indexed tools. They carry all cuts out with incredible precision and high velocity. A two-axis system is most common.

  3. Plasma cutters. Speed and heat are needed when we need to make precision cuts in metal. To achieve this, compressed air gas is combined with electrical arches.

  4. Wire electrical discharge machines. Also known as “EDMs.” They use electrical sparks to mold pieces into specific shapes.

  5. Sinkler electric discharge machines. Also known as “sinker EDMs.” Operate like wire EDMs but work materials are soaked in a dielectric fluid to conduct electricity and then mold pieces into specific shapes.

  6. Water jet cutters. Often used to cut granite and metal with high pressured water that can be mixed with sand or other materials. They allow for more cutting power without adding heat.

  7. CNC drilling machines. They use multi-point drill bits to create circular holes. Drill bits are ofter feed perpendicularly to the work surface to create vertical holes. They can also be programmed to make angular holes. (Leveillee 2020)

Basics of CNC machining

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Types of CNC machines

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Analysis of single station cells

To determine the number of single station cells required we need to define the workload per time period under consideration, and divide this workload by the time available for one cell in the time considered.

The number of work stations needed are:

\[ n=\frac{WL}{AT} \tag{4}\]

where \(WL\) is the workload or total timer needed to produce a quantity of units during the period of interest. \(AT\) is the available time per workstation, and \(n\) the number of work stations.

\(WL\) can also be obtained as:

\[ WL=\sum_{j}^{}Q_jT_{cj} \tag{5}\]

where \(Q_j\) is the number of units of part type \(j\), and \(T_{cj}\) is the corresponding cycle time.

To have a better estimate of the number of work stations needed we can add setup time and defect rates:

\[ WL=TT_{su}+ \sum_{j} \frac{Q_jT_{cj}}{(1-q_j)} \tag{6}\]

where the total setup time is expressed as the sum of all setup times for parts of type \(j\) ,

\(TT_{su}=\sum_j T_{suj}\)

\(Q_j\) is the number of good pieces of type \(j\) produced.

\(q_j\) is the fraction defect rate of part \(j\).

The available time per cell is calculated as follows:

\[ AT=H_pA \tag{7}\]

Where \(AT\) is the available time per cell [=] time per cell , \(H_p\) is the amount of time for the cell during the period [=] time per cell , and \(A\) is availability :

\[ A= \frac{MTBF-MTTR}{MTBF} \tag{8}\]

where \(MTBF\) and \(MTTR\) are mean time between failure and mean time to repair.

Thus, Equation 4 can be calculated considering quality, availability and setup times.

Design of machine clusters (manufacturing cells with multiple machines manned by one operator)

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A machine cluster is a collection of two or more machines producing parts or products with identical cycle times and serviced by one worker. A machine cell is a collection of machines that produce a family of parts or products. The conditions to organize machines in a manufacturing cluster are:

  1. The cycle time of the machine is greater than its service time requiring worker’s attention.

  2. The cycle time of all machines in the cluster is the same.

  3. Machines serviced by one person are close to each other.

  4. The work rules of the plant and the union permit the worker service more than one machine.

Let,

\(T_m\) be the machine processing time. A part of the machine cycle time.

\(T_s\) be the machine service time, where a worker is required.

Then, machine cycle time is:

\[ T_c=T_m+T_s \] {#eq-machine cycle time}

This equation assumes that workers are always available when needed.

If there are more than one machine served by the worker, he or she will need to move from machine to machine to serve the equipment. This time is called re-positioning time $T_s$. Therefore, the time needed to service \(n\) machines is \(n(T_s+T_r)\).

The system will be balanced when worker’s time and machine cycle time are equal:

\[ T_m+T_s=n(T_s+T_r) \tag{9}\]

and the number or machines needed is:

\[ n=\frac{T_m+T_s}{T_s+T_r} \tag{10}\]

\(n\) has to be an integer. Thus, we have the following cases:

\[ n_1= \biggl \lfloor \frac{T_m+T_s}{T_s+T_r} \biggr \rfloor \tag{11}\]

and,

\[ n_2= \biggl \lceil \frac{T_m+T_s}{T_s+T_r} \biggr \rceil \tag{12}\]

When the number of machines is \(n_1\) we have worker with idle time. When the number of machines is \(n_2\) we have machine idle time. Which selection is better?

Selecting machinery when we have cost estimates

Let \(C_L\) and \(C_m\) be labor and machine cost rates respectively [=] money per time (e.g., dollars per minute). Then we can estimate the number of machines in a cost per unit basis.

When we consider \(n_1\) the cost per work unit during a cycle can be estimated as1:

\[ C_{pc}(n_1)= \biggl( \frac{C_L}{n_1} + C_m \biggr) (T_m+T_s) \tag{13}\]

When we consider $n_2$, the cycle time of the machine cluster will be the time it takes for the worker to service all \(n_2\) machines: \(n_2(T_s+T_r)\) . Thus, an estimate of the of cost per unit is:

\[ C_{pc}(n_2)=(C_L+n_2C_m)(T_s+T_r) \tag{14}\]

References

Leveillee, Charles. 2020. “What Is a CNC Machine? An Overview of CNC Machining Prototech Asia.” http://https%253A%252F%252Fprototechasia.com%252Fen%252Fwhat-is-a-cnc-machine.
Mikell P. Groover. 2018. Automation, Production Systems, and Computer-Integrated Manufacturing. Fifth Edition. Pearson.

Footnotes

  1. We assume that one unit is produced by each machine during a cycle.↩︎