Loss in Weight Feeder Calculations

Optimize gravimetric feeding rates, refill cycles, and material usage

Figure 1: Simulated Weight vs. Time (Gravimetric Cycle)

Refill Cycle Schedule (Next 5 Cycles)

Cycle #	Start Time (min)	Refill Trigger Time (min)	Weight Consumed (kg)	Status

What are Loss in Weight Feeder Calculations?

Loss in weight feeder calculations are the mathematical foundation of gravimetric feeding systems used in industrial processing. Unlike volumetric feeders that dispense material based on speed and volume, a loss-in-weight (LIW) feeder continuously weighs the material in its hopper and adjusts the discharge speed to maintain a precise mass flow rate (e.g., kg/hr or lbs/hr).

These calculations are critical for industries such as plastics compounding, food processing, pharmaceuticals, and chemical manufacturing. Accurate calculations ensure consistent product quality, reduce material waste, and prevent process downtime caused by improper refill timing or capacity planning.

Engineers and operators use these calculations to determine the gravimetric feed rate, the refill frequency, and the usable capacity of the system. Understanding the relationship between the target feed rate and the hopper's weight loss over time is essential for tuning the PID controllers that manage the feeder's motor speed.

Loss in Weight Feeder Formula and Explanation

The core principle of a loss-in-weight system is measuring the negative rate of change of weight ($\Delta W$) over a specific time interval ($\Delta t$). The fundamental formula for the actual feed rate is:

Feed Rate (F) = (W_start – W_end) / (t_end – t_start)

Where:

• W_start = Weight of material at the beginning of the sample.
• W_end = Weight of material at the end of the sample.
• t_elapsed = Time duration of the sample.

Key Variables Table

Variable	Meaning	Common Unit	Typical Range
Target Rate	Desired mass flow output	kg/hr or lbs/hr	0.5 – 5000+
Usable Capacity	Weight available between refill limits	kg or lbs	10% – 90% of Hopper
Bulk Density	Mass per unit volume of material	kg/m³ or lbs/ft³	200 – 1500
Refill Interval	Time between refill cycles	Minutes	5 – 60 mins

Practical Examples of Feeder Calculations

Example 1: Plastic Extrusion Line

A plastics manufacturer needs to feed polyethylene pellets into an extruder at a rate of 120 kg/hr. They have a hopper with a total capacity of 50 kg. To maintain accuracy, they set the refill trigger at 20% and stop refilling at 90%.

• Usable Capacity: 50 kg × (0.90 – 0.20) = 35 kg.
• Time Between Refills: 35 kg / 120 kg/hr = 0.291 hours.
• In Minutes: 0.291 × 60 = 17.5 minutes.

Interpretation: The operator must ensure the central vacuum system can refill the hopper every 17.5 minutes. If the refill system takes longer than the "gravimetric hold" period allows, the feeder may run empty.

Example 2: Micro-Ingredient Dosing

A bakery line doses a vitamin premix at 2.5 kg/hr. The hopper is small, holding only 5 kg.

• Usable Capacity: 5 kg × 0.70 (70% swing) = 3.5 kg.
• Time Between Refills: 3.5 kg / 2.5 kg/hr = 1.4 hours (84 minutes).

Interpretation: This low feed rate allows for a long time between refills. However, with such a slow rate, the resolution of the weigh scale becomes critical. The loss in weight feeder calculations must account for scale sensitivity to detect small weight changes over short intervals.

How to Use This Loss in Weight Feeder Calculator

1. Enter Target Feed Rate: Input the required mass flow for your process (e.g., 50 kg/hr).
2. Define Hopper Capacity: Enter the maximum weight rating of your feeder's hopper.
3. Set Refill Limits:
   • Refill Stop Level: The high point where refilling stops (usually 80-90%).
   • Refill Trigger Level: The low point that signals a refill request (usually 20-30%).
4. Input Density (Optional): Enter material bulk density to see volumetric data.
5. Analyze Results:
   • Check Time Between Refills to ensure your upstream material handling system can keep up.
   • Review the Refill Batch Size to size your refill valves or vacuum receivers correctly.

Key Factors That Affect Loss in Weight Results

Several physical and mechanical factors influence the accuracy of loss in weight feeder calculations and performance:

• Material Bulk Density: Variations in density (e.g., fluffy powder vs. pellets) change the volume required to meet the target weight. If density drops, the screw speed must increase.
• Refill Phase Disturbance: During refill, the feeder cannot weigh the material loss (since weight is being added). It enters "volumetric mode" based on recent history. Long refill times reduce overall accuracy.
• Vibration and Noise: External vibrations can cause the load cells to read incorrectly. Filtering algorithms in the controller are used to smooth the weight signal.
• Feeder Screw Geometry: The design of the screw (single, twin, spiral) affects the consistency of the flow. Inconsistent flow leads to noisy weight data.
• Venting: Proper venting is crucial. If air is trapped during refill, it can aerate the material, causing it to flush through the screw like a liquid (flooding), destroying accuracy.
• Minimum Throughput: Running a large feeder at a very low rate (e.g., <5% of capacity) often leads to poor results because the weight loss per second is too small for the load cell to resolve accurately.

Frequently Asked Questions (FAQ)

What is the difference between volumetric and gravimetric feeding?

Volumetric feeding relies on the speed of the screw (RPM) to dispense material, assuming density is constant. Gravimetric feeding (Loss-in-Weight) measures the actual weight change and adjusts the speed dynamically to maintain a set mass flow, compensating for density changes.

Why is the "Refill Time" important?

During refill, the feeder operates blindly (volumetrically). The shorter the refill time, the sooner the feeder returns to gravimetric control, ensuring higher overall accuracy.

What is a typical turndown ratio for a LIW feeder?

Most manufacturers specify a 10:1 or 20:1 turndown ratio. This means a feeder designed for 100 kg/hr can typically run accurately down to 5-10 kg/hr.

How do I calculate the required refill rate?

The refill device (e.g., vacuum loader) must supply material significantly faster than the feeder consumes it. A common rule of thumb is that the refill rate should be at least 10 times the maximum feed rate.

Can I use this calculator for liquid loss-in-weight?

Yes, the math is identical. Simply treat the "Hopper Capacity" as the tank capacity and ensure units (kg/hr) are consistent.

What happens if the bulk density changes?

In a gravimetric system, the controller detects that weight is not leaving fast enough (or too fast) and adjusts the screw speed automatically. This calculator shows how density affects the volumetric rate (L/hr).

What is "Gravimetric Mode" vs "Volumetric Mode"?

Gravimetric Mode uses live weight data to control speed. Volumetric Mode uses a fixed speed (usually the average of the last few minutes) during disturbances like refilling.

Why does my feeder read negative weight?

This usually indicates a calibration error, a mechanical bind on the load cell, or upward forces (like air pressure) acting on the hopper.

Active