Quantization of tiny time pills in micro encapsulation

illustration of two capsule pills

“Our quality control is awful; we have way too many rejects and customer complaints,” said the technical production superintendent for a micro encapsulation product.

So, what was going on? Two liquid monomers were flow controlled, together with the coated fluid, to a machine that coated the chemical in a small sphere, the process is known as micro encapsulation.

Micro encapsulation is a process in which tiny particles or droplets are surrounded by a coating to give small capsules with many useful properties, according to Wikipedia; “The objective is not to isolate the core completely but to control the rate at which it releases the contents.”

The coating in this application was a polymer which was water soluble. This coated product, the tiny time pills, needed a controlled release, which requires exact monomer flow rates. The monomer in question was pumped by a gear pump, and the volume delivered is directly proportional to the rotational speed (Figure 1).

graph showing gear pump characteristics

Figure 1 This graph shows typical gear pump characteristics for a controlled-release operation.

The pump’s AC 3-phase induction motor was powered by a variable frequency drive (VFD), a device that rectifies the oncoming AC power and transforms it to an output of variable frequency through IGBTs. The speed was set by an incoming voltage signal.

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The flows were accurately measured by mass flow meters. This signal was used to control the mass flow rate to the machine. The signal in question was noisy, so it was filtered to the controller input, which set the required output signal to the VFD.

Do you keep the flows constant? Yes, we don’t change anything. Searching the historically-stored data files, I located an unfiltered signal from the mass meter. A histogram plot of 24 hours of data (sampled frequently) is shown in Figure 2.

graph of monomer flow rate

Figure 2 A view of the 24-hour monomer mass flow histogram shows a quantization error.

A histogram is a plot that places variables in “bins” of various sizes and displays vertical bars that are proportional to the data population in each bin. It’s recommended to plot the diagram with an odd number of bins to show symmetry. If the plot relieved a “missing tooth” or bi-nodal distribution, one would expect a normal distribution in this application. How can this be? The signal to the VFD does not change.

A review of the VFD specifications together with a little arithmetic showed the problem. The VFD speed was set by an analog voltage signal, converted by an analog-to-digital converter (ADC), and has a quantization error, Q = full scale/number output states. For any analog input, noise introduced with the signal can result in the output varying between + and – Q/2, quantization uncertainty or noise. The histogram shows the effect of the quantization error. The VFD output dithers between these two points. This plot has two nodes because of the resolution.

A little arithmetic shows this: The positive displacement pump curve has a slope of 0.1 gal per revolutions per minute (rpm) flow. The motor synchronous speed is 1800 rpm. The adjustable frequency AC drive published specification of 514 frequency divisions, the resolution. The motor is connected to the pump by a speed reducer, the ratio is 7.65; that is 7.65 motor revolutions equals 1 pump revolution.

The monomer density is 9.25 pounds mass per gallon. The two nodes have peaks at 127.8 and 127.4 pounds per minute, the difference is 0.4 pounds per minute. This mass flow divided by density is the volume flow difference, 0.0432 gallons. This flow divided by the flow to speed slope is 0.4324 rpm difference. The speed reducer causes a rotation speed difference of 3.3081 rpm.

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These differences closely agree with the data shown in the histogram plot. This deviation was too wide to manufacture the coating within the required specification. The facility quickly changed the VFD to one with better resolution, which solved the problem.

Robert Heider is a retired engineer with over 50 years’ experience with emphasis on the design of advanced process controls and process development.

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