# Is the belt speed accurate on your conveyor belt scale system?

The accurate weighing of bulk material on a conveyor is highly dependent on accurate speed sensing.

Continuous belt weighing is the process of determining the mass flow rate of bulk material being transported on a conveyor belt. It involves the determination of the instantaneous weight of the material on the belt and the linear speed of the belt. These two variables, determined separately, are brought together to produce flow rate or total weight.

In many cases, people have found that the conveyor belt speed used by their belt scale system controller does not match the belt speed when checked by another method. The reported difference has sometimes been as much as 5%. This can have a significant impact on the accuracy of the mass flow rate of the material.

There can be several factors that contribute to belt speed errors, including but not limited to:

- incorrect scale factors used to convert the speed sensor signal to the belt speed
- faulty speed sensors or speed sensor installation
- an error in the comparison method used to check the belt speed reported by the controller.

This article will focus on the first factor: incorrect scale factors used to convert the speed sensor signal to belt speed.

#### Background

Many belt scale systems include two sensors: the load sensor, or the weighbridge, and the speed sensor. The signal sent from each sensor is sampled multiple times per second by the controller, or integrator. The integrator calculates the instantaneous rate output using this formula:

where:

*r* = instantaneous rate

*l* = instantaneous belt load sampled from load sensor

*s* = instantaneous belt speed sampled from the speed sensor.

The instantaneous rate output from the controller is one of the process variables of interest to the plant operator. The controller integrates the calculated instantaneous rate values over time to determine the total amount of product that has passed across the scale. Total production across the scale is another process variable that may be of interest to the plant operator.

From the above formula, it is reasonable to conclude that any error in the conveyor belt speed compounds any error with the load signal. The first way to resolve a belt speed issue is to acquire the belt speed accurately prior to addressing any load sensor accuracy issues.

There are many types of speed sensors used on conveyor belt scales. The speed sensor is commonly coupled to the shaft of a non-drive pulley in contact with the conveyor belt at all times. The output signal is a square wave voltage pulse measured in hertz (Hz).

The belt scale system controller reads the frequency signal and rescales it to represent belt speed. The scale factor is called the ‘speed constant’. Instructions on how to program the speed constant will be located in the manufacturer’s user manual. The pulley circumference and the pulses per revolution (PPR) are the two variables that influence the speed constant. The PPR is listed on the nameplate for the speed sensor.

#### Pulley circumference

So the question is: what should be used for the pulley circumference?

Belt scale manufacturers recommend using the diameter of the coupled pulley to calculate the circumference. One may interpret this statement to mean the pulley diameter that is measured at one end of the pulley or whatever diameter is listed on the conveyor specification sheet or drawing. But this may not always be accurate.

To ensure accuracy, we have to consider these points:

- Some non-drive conveyor pulleys are crowned to help track the belt. The diameter of the pulley is larger in the centre than it is at the ends (see Figures 1 and 2). The pulley circumference should be based on using the largest pulley diameter.
- One manufacturer’s standard ‘hydro-crowned’ pulley is tapered 1/8″ per foot of width on the diameter, or 1/4″ maximum. The nominal pulley diameter is given at both ends and the pulley will have a larger diameter in the centre.
- The machined-crown pulleys from another manufacturer use 1/8″ x 8″ that tapers off the radius each end on pulleys wider than 24″. The nominal pulley diameter is given at the centre and the pulley will be smaller at the ends.
- A belt manufacturer recommends using the ‘pitch line diameter’ for calculating the pulley circumference. The pitch line diameter is further explained to be the measurement taken at the centroid of the belt when it is wrapped around a pulley.
- The above belt manufacturer further explains that the centroid of the belt is where the belt is neither in compression nor tension when it is wrapped around a pulley. Since the belt carcass cannot stretch or compress, consider using the centre line of the carcass as the centroid distance. The calculation parameters are shown in Figures 1, 2 and 3.

Let’s quantify the accuracy error by using the above points in an example.

#### The effect of belt thickness

For example, consider the following parameters:

- Coupled pulley details: 406 mm diameter (16″) by 965 mm wide (38″), machined crown, lagging 9.525 mm thick (3/8″).
- Belt details: 914 mm wide (36″), two-ply, 38.5 N/mm (220 PIW), 4.76 mm (3/16″) by 1.58 mm (1/16″) SBR covers, with an overall thickness of 8.7 mm (11/32″).
- The speed sensor is a 256 PPR encoder.

*Figure 1: Bottom cover contact.*

When the speed sensor is coupled to a pulley in contact with the belt bottom cover (Figure 1), the belt centroid distance from the bottom cover (shown in Figure 2) is:

*Figure 2: Belt cross-section dimensions.*

When the speed sensor is coupled to a pulley in contact with the top cover, as per Figure 3, the belt centroid distance from the bottom cover is:

*Figure 3: Top cover contact.*

#### Speed constant based on the pulley only

If the belt scale commissioning agent uses the circumference at the end of the pulley, then the circumference measurement may be based on as little as 400 mm (15¾″) diameter for the pulley details given above when the lagging thickness is also ignored.

The speed constant is defined by:

where:

*k _{s}* = speed constant (pulses per metre)

*k*= encoder PPR (pulse per revolution)

_{e}*d*= pulley diameter (mm)

Therefore, the speed constant for the example is:

#### Effect of the belt

The pitch line diameter is given by:

where:

*d _{pl}* = pitch line diameter

*d*= nominal pulley diameter

_{p}*t*= lagging thickness

_{lagging}*d*= belt centroid distance

_{c}When the installation is as per Figure 1 and the pulley is in contact with the bottom cover:

The speed constant is therefore:

This is a 7.7% difference from using the pulley alone for the calculation. The difference is even greater when the pulley is in contact with the thicker top cover:

The speed constant in this case is therefore:

This is a 9.2% difference from using the pulley alone for the calculation.

So in these cases, any error in the weighing will be have an additional 7.7% or 9.2% error multiplier caused by using only the pulley diameter in determining the speed constant.

#### Physical checking is necessary

The above analysis shows how much the reported belt speed can be affected by the method chosen for the calculation of the speed constant. In the real situation, it may not be practical to gather all the details needed to accurately calculate the circumference based on using the pitch line diameter. Hence, for most belt scale installations, it is prudent to have another method of checking the belt speed to compare with the belt speed detected by the controller.

It will be necessary to make adjustments to the speed constant in the controller, based on a secondary speed check as needed, to get the belt speed right prior to working on load sensor signal accuracy differences.

*Image credit: ©stock.adobe.com/Sved Oliver*

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