Dynamic Model of the Weighing Process of an Industrial

Combination Scale: Model Development and Simulative Analysis of

the Product Impact Force

Felix Profe

, Lucas Kostetzer

and Christoph Ament

Chair of Control Engineering, University of Augsburg, 86159 Augsburg, Germany

CADFEM Germany GmbH, 85567 Grafing bei München, Germany

Keywords: Dynamic Model, Weighing Process, Combination Scale, Model Development, Simulation, Impact Force.

Abstract: This work shows a weighing product model that characterizes the processes of product impact during the

weighing procedure of a combination scale. Unfortunately, the product impact force does not exist as a sen-

sor quantity and is difficult to measure. Another complicating factor in developing a product model is the

large variety of products and their fall behaviour. Even with identical product properties, falling comprises

strong stochastic influence. With the help of a discrete element method simulation model it was possible to

directly calculate the product impact force. More than 20 different products were tested. The simulation can

reproduce the random fall behaviour. Based on these analyses, a real-time capable product model was de-

rived. The model is able to generate impact curves based on portion weight, particle weight, impact time,

drop height, and impact duration. Impact duration and time of impact of an individual particle are changing

based on random variables. Due to simplifications, restitution coefficient and particle shape is not consid-

ered. With larger particles there are deviations in comparison of simulation and product model. Due to the

low computational effort, the model could be used, for example, as a system input for a real-time capable

model of a weighing station.

https://orcid.org/0009-0005-7026-9018

https://orcid.org/0000-0003-3820-233X

https://orcid.org/0000-0002-6396-4355

1 INTRODUCTION

This work shows a weighing product model that

could represent the processes of product impact

during the weighing procedure of a combination

scale (CS). Due to the low computational effort, the

model could be used, for example, as a system input

for a real-time capable model of a weighing station.

1.1 Combination Scale

Figure depicts a CS. According to Oehring and

Thiele (1989) CS are particularly suitable for frozen

products, in the confectionery industry and for salad

products. For these products, a desired final weight

(target weight) can be achieved more precisely (and

without large overestimation) by suitably combining

pre-portioned partial quantities. In principle, all

common weighing products can be filled with CS,

but there is no major advantage with free-flowing

and granular products. CS have a larger number of

individual weighing stations from which a computer

determines the optimum combination for the speci-

fied nominal filling weight. Figure 1 shows the CS

components attached to a frame. A distribution cone

is located at the top centre.

Figure 1: Combination scale (left) and section of a weigh-

ing station with linear feeder, feed bucket and weigh

bucket (right) according to Profe and Ament (2022).

150

Profe, F., Kostetzer, L. and Ament, C.

Dynamic Model of the Weighing Process of an Industrial Combination Scale: Model Development and Simulative Analysis of the Product Impact Force.

DOI: 10.5220/0012187800003543

In Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2023) - Volume 2, pages 150-157

ISBN: 978-989-758-670-5; ISSN: 2184-2809

Around the distribution cone, linear feeders (LF)

are arranged in a circle towards the outside. Feed

buckets (FB) are located below the LF, followed

below by weighing buckets (WB), both buckets in

red. Finally, chutes and a funnel are attached below.

The piece goods are fed from above and supplied

to the WB via distribution cone, LF, and FB. The

weight of the partial quantity is determined when the

product is in the WB. Each WB is connected to a

load cell (Profe and Ament, 2022).

1.2 Challenges and Application of

Product Model

A detailed model description of the weighing pro-

cess is of high relevance for the development and

improvement of weighing systems. A model can be

used for example for digital twins, virtual experi-

ments to understand the cause-effect relationship,

control systems (e.g. as an observer), and, in general,

to generate virtual data (Profe and Ament, 2022).

Figure 1 shows the block diagram of the system

weighing station. The output is the weighing signal

from the associated load cell. The system weighing

station includes WB, which is connected to a load

cell. The system input corresponds to the product

impact force (PIF).

The PIF is the force created by the partial quan-

tity falling out of the FB and hitting the WB (weigh-

ing station). A detailed knowledge of the PIF is

important for fast and accurate weighing.

Figure 2: System Weighing station with product impact

force as input and weighing signal as output.

For this purpose, a model approach for a so-

called Product Model will be presented in this paper.

Models of weighing stations were presented in the

publications of Eckstein and Ament (2019) and

Profe and Ament (2022). However, these models

work without a product model although this could

increase the weight acquisition speed or the accuracy

of results. Wente (1992) and Gilman and Bailey

(2005) presented force curve models of weighing

stations, but in these models, there is no specific link

to the weighing goods of a CS. A product model has

not yet been used because the impact force does not

exist as a sensor quantity. PIF is even difficult to

measure directly. Only the system response (weigh-

ing signal) is available. Another complicating factor

in developing a product model is the large variety of

products to be weighed and the varying fall behav-

iour of the product. Even with identical product

properties, falling comprises strong stochastic influ-

ence. In this work the PIF is determined with the

help of the Discrete Element Method (DEM).

2 DEM SIMULATION MODEL

A direct measurement of the PIF was not carried out

on a real test setup, due to the challenges to generate

controlled and reproducible data. Instead, a virtual

model was created (see Figure 2). The model con-

sists of LF, FB and WB. It is a section of a CS.

There is product in LF, FB and WB. In contrast to

the real scale, the product falls directly into LF (see

product input in Figure 2) instead of the distribution

cone. The flaps of FB and WB are able to open and

close the respective buckets.

Figure 3: Virtual simulation model of a weighing station.

Table 1: Timing of LF, FB and WB within a weighing

cycle.

Table 1 depicts the sequence of the processes

running in parallel in the virtual model. The pro-

cesses start in the third row with opening and closing

of WB. Shortly after the WB flaps are closed again,

new product falls into WB. Parallel to WB, FB

opens with a time delay. The flaps of FB start to

open at the moment when WB flaps are fully open.

After the FB flaps are closed, new product can be

added. Therefore LF starts to vibrate. FB is filled

Dynamic Model of the Weighing Process of an Industrial Combination Scale: Model Development and Simulative Analysis of the Product

Impact Force

151

again. The whole process is then repeated and starts

with WB opening again.

2.1 Result Evaluation Methods

The PIF is analysed in the vertical direction. The left

side of Figure 3 shows the mesh of the WB flaps on

which the impact force evaluation is performed.

Parallel to the evaluation of the force, the total parti-

cle mass in the WB is determined over time. For this

purpose, an evaluation block is placed over WB (see

right side of Figure 3). Particles with a velocity of

less than 0.1 m/s belongs to the WB mass. This

allows an objective assessment of how long the

particles take to settle down (analysis of fall behav-

iour).

Figure 4: Mesh of the WB flaps for evaluation of force

(left). Borders of cubic WB evaluation block in blue

(right).

2.2 Mathematical Models

The simulations in this work were performed using

DEM. According to Ansys Inc. (2023) DEM is a

numerical technique for predicting the behaviour of

bulk solids. The equations of motion for every

individual particle are numerically integrated over

time. For this process the total force on a particle

needs to be known. The total force is the resultant of

contact forces (between particles and with boundary)

and body forces (e.g. gravity). When considering the

PIF, the contact force models play an important role.

According to Walton and Braun (1986) Hysteric

Linear Spring was used as normal force model. It

does not use viscous damping terms. Energy is dissi-

pated only upon contact with the boundary or other

particles. The contact force law is defined as follows

(Walton and Braun, 1986):

𝐹





=

min



𝐴

,𝐵



𝑖𝑓 ∆𝑠



0

max



𝐵,𝜆 ∙

𝐴



𝑖

𝑓

∆𝑠



0

(1)

𝐴

= 𝐾



∙𝑠





(2)

𝐵= 𝐹



∆

𝐾



∙∆𝑠



(3)

∆𝑠



= 𝑠





𝑠



∆

(4)

𝐹





and 𝐹



∆

are the normal elastic-plastic con-

tact forces at the current time t and at the previous

time 𝑡∆𝑡. ∆𝑡 is the timestep size. 𝑠





and 𝑠



∆

are

the normal overlap values at the current time t and

the previous time 𝑡∆𝑡. ∆𝑠



is the incremental

contact normal overlap at time t. A positive value

means an approach and a negative value a separa-

tion. The index n stands for normal force. 𝜆 is a

dimensionless small constant with the value 0.001

(Ansys Inc., 2023).

The equivalent stiffness 𝐾



for loading and 𝐾



for unloading are formed as follows:

𝐾



⎩

⎪

⎨

⎪

⎧

𝐾

,



𝐾

,

𝐾

,





𝐾

,

(5)

𝐾



𝐾



𝜀



(6)

𝜀 is the coefficient of restitution. 𝐾

,

is the

contact stiffness of particle 1 and 𝐾

,

is the con-

tact stiffness of particle 2 in case there is an interac-

tion between two particles. 𝐾

,

is the contact stiff-

ness of a particle in general and 𝐾

,

is the contact

stiffness of the boundary. Figure 4 shows the

underlying series connection between particle and

boundary with 𝐾

,

and 𝐾

,

defined in (5). 𝐾

,

and 𝐾

,

are calculated of the Young's modulus 𝐸



or 𝐸



and the particle size L:

𝐾

,

=𝐸



∙𝐿

(7)

𝐾

,

=𝐸



∙𝐿

(8)

Figure 5: Series connection of contact stiffnesses between

particle and boundary.

The following values were used in the simula-

tions: WB as boundary has a 𝐸



100 000 MPa. The particles have a 𝐸



of 100 MPa.

Due to the series connection (Figure 4 and (5)), we

see that 𝐸



has almost no influence, since it is many

times greater than 𝐸



. It follows that in this case the

ICINCO 2023 - 20th International Conference on Informatics in Control, Automation and Robotics

152

stiffness of the particle, 𝐾

,

has a large influence

on the impact force and the stiffness of WB 𝐾

,

small one assuming 𝐾

,

is much stiffer than 𝐾

,

The following modules of the simulation soft-

ware Ansys Rocky 2023 R1 were used for evaluation:

Boudary Collision Statistics, Contacts Overlap

Monitor, and SPH Density Monitor.

3 REAL-TIME CAPABLE

PRODUCT MODEL

With the help of the DEM simulation model pre-

sented in the previous section, reality was approxi-

mated in order to analyse the fall behaviour and the

impact curves. The virtual model serves as a substi-

tute for real experiments due to the effort required

for experiments. However, the DEM simulation

model is very complex and not real-time capable due

to the higher computational effort. Therefore, a

simpler approach is now presented: The so-called

Product Model. It is a model with lower complexity.

This means that some assumptions have to be made.

First, air resistance is not considered (neither in

DEM simulation nor in Product Model). Second, the

impact has no rebound (𝜀 = 0). Third, the Product

Model uses point masses. Fourth, the impact surface

is plane and horizontal (no slanted flaps). Fifth, 𝐸



or 𝐸



is not relevant. Sixth, there is no interaction

between particles. Seventh, each particle generates a

rectangular pulse on impact according to Wente

(1992).

3.1 Mathematical Model

Figure 6: Free falling of two masspoints due to gravity

(left). Force curve of rectangular impact pulse and static

weight force (right).

Figure 5 (left) shows two mass points. 𝑚

,

is the

mass of the i-th point or particle. 𝑚

,

is the mass

of the i+1-th mass point. In total there are n different

mass points. The two mass points shown are

dropped from heights ℎ



and ℎ



from rest (initial

velocity = 0). Just before impact, the i-th mass point

has the impact velocity (Stronge, 2018):

𝑣





2∙𝑔∙ℎ



(9)

g is the acceleration due to gravity at 9.81 m/s.

By integration of Newton's axiom the pulse I is

obtained (Stronge, 2018) by:

𝐼=𝐹



𝑡 ∙𝑑𝑡





=𝑚

,

∙𝑣

,

𝑚

,

∙𝑣

,

(10)

𝐹



𝑡 is the contact force of particle i. Index 1

means immediately before impact and index 2

means after impact. Due to the assumption 𝜀=0,

the particle is completely decelerated ( 𝑣

,

=0).

Thus, for each individual particle, the impact pulse

can be set up as follows:

𝐼



=𝑚



,

∙𝑣



(11)

For simplicity, the integral of the impact force of

a single particle is modelled as a rectangle with

𝐼



=𝐹

,

∙∆𝑡



(12)

where ∆𝑡



is the duration of a single particle

impact. Thus the impact force is:

𝐹

,

𝐼



∆𝑡



(13)

The moment of impact of an individual particle

results from the fall time:

𝑡





2∙ℎ



𝑔

(14)

Figure 5 (right) shows the rectangular force

curve over the course of time. After the impact has

occurred, the force 𝐹



𝑡 switches to the static

weight fraction 𝐹

,

The curve of the total impact force is given by

the sum of all particle forces according to Wente

(1992):

𝐹𝑡



= 𝐹



𝑡











(15)

3.2 Model Parameters

Figure 6 shows the inputs and outputs of the Product

Model. Using the target weight 𝑚



and the

piece weight 𝑚



, the number of particles is calcu-

lated with

𝑛=

𝑚



𝑚



(16)

Dynamic Model of the Weighing Process of an Industrial Combination Scale: Model Development and Simulative Analysis of the Product

Impact Force

153

Figure 7: input and output parameters of the

Product Model.

The number of pieces is rounded if the target weight

is not a multiple of the piece weight. ∆𝑡



speci-

fies the duration of the single pulse. With this ap-

proach, all single pulses are equal. Thus applies:

∆𝑡



=∆𝑡







(17)

∆𝑡



is the time step size and ℎ



is the

mean drop height of the particles.

In order to represent the randomly occurring fall

behaviour, the drop height of the individual particle

is modelled as a normal distributed random variable:

ℎ



~𝒩ℎ



,𝜎





(18)

ℎ



determines the fall time 𝑡



of the individual

particle. The difference between the shortest and

longest fall time (total time duration) is set by the

standard deviation 𝜎



. It is assumed that the

majority of impact curves have the same total dura-

tion. However, there are differing impact situations.

Therefore 𝜎



is also a random variable. It ap-

plies:

𝜎



~𝒩𝜇



,𝜎





(19)

𝜇



=𝛾

,

(20)

𝜎



𝛾

,

𝛾

,

(21)

𝛾

,

is the lower limit of 𝜎



and

𝛾

,

is the upper limit. 𝜎



is cut off for

smaller values than 𝛾

,

𝜎



=𝛾

,

𝑖𝑓 𝜎



 𝛾

,

(22)

4 PRODUCT EXPERIMENTS

Experiments were conducted with both models –

DEM simulation model and Product Model. The

sweet marshmallow like product in Figure 7 on the

left side is the original product. It looks like Santa

Claus. From now on the product will be called

Marshmallow (MM) or just product in this paper.

The product has dimensions of 55 mm  23 mm 

16 mm and an average piece weight of 5.832g. The

density is 300 kg/m³.

Figure 8: Original sweet marshmallow (MM) like product

(left) and simplified particle model (right).

Table 2: Piece weight 𝑚



and piece number n depending

on SF.

SF Piece Number n

Piece Weight

𝑚



0.1 1000 0.1%

0.3 37 2.7%

0.4 16 6.4%

0.7 3 34.3%

1.0 1 100.0%

In the simulation, a simplified representation is

chosen (Right side of Figure 7). The product is a

cuboid with a chamfer at each of the four corners. In

the Product Model, only the piece weight of the

product is of interest, since the masses are point

masses. In the following investigations, the size and

thus also the piece weight is changed with a scaling

factor (SF). For this purpose, the length 𝑙, width 𝑤,

and depth 𝑑 of the original MM product are changed

respectively. Thus the scaled volume 𝑉



defined:

𝑉



=𝑆𝐹



∙𝑙∙𝑤∙𝑑

(23)

Table 2 shows the piece weight 𝑚



and piece

number n as a function of SF for selected sizes.

4.1 Overview of Studies

Virtual experiments are carried out with the aid of

the DEM simulation model. The Product Model was

derived on the basis of these findings.

First, a comparison of PIF is made between

DEM simulation and Product Model at a target

weight of 50g (SF=1 and SF=0.3). Subsequently,

the target weight is increased to 100g at SF=0.4.

There the duration of PIF is compared. Then 𝜀 is

increased from 𝜀=0.1 to 𝜀=0.7. Finally, the maxi-

mum PIF is examined as a function of SF.

In the case of the Product Model, the tests on 𝜀

cannot be carried out, since the model does not in-

clude this property.

ICINCO 2023 - 20th International Conference on Informatics in Control, Automation and Robotics

154

4.2 DEM Simulation Setup

The model-specific parameters of the simulations

are given below. If not explicitly mentioned, these

settings are used for all simulations. Static friction

𝜇



and dynamic friction 𝜇



have the same

value in this work (𝜇



=𝜇



=𝜇). 𝜇=0.7

is used between particles. From particle to boundary

(in our case, among others, the WB flaps) 𝜇=0.3.

Both are default settings. If not otherwise men-

tioned, 𝜀=0.1.

Figure 9: Comparison of the impact curve depending on

NSF.

To save calculation time, a Numerical Softening

Factor (NSF) of 0.01 was used instead of the default

value NSF=1. All stiffness parameters (e.g. in (1) -

(3)) are multiplied by NSF (Lommen, Schott and

Lodewijks, 2014). This can result in overlapping

bodies, which in our case has a large effect on the

impact force (see Figure 8). A lower NSF is more

suitable for the presented application due to the load

cell and its elastic spring effect. Global deformations

prolong the contact period, reduce the maximum

contact force and transfer significant energy into

structural vibrations according to Stronge (2018).

Figure 10: Convergence analysis of the maximum force of

the impact curve depending of sample time.

The stiffness is used to determine the time step

size of the calculation. For NSF=1 the time step size

is 5.87e-7s and for NSF=0.01 the time step size is

5.87e-6s. In addition, the output time step size (sam-

ple time) has to be defined separately. Figure 9

shows a convergence analysis of the sample time. It

has no influence on the calculation accuracy, but on

the output accuracy. For reasons of calculation time,

memory requirements and accuracy, 30µs was cho-

sen as sample time.

4.3 Product Model Setup

For the Product Model ∆𝑡



=500µ𝑠 is chosen.

The value was fitted from the impact duration of a

single particle in DEM simulation results.

5 RESULTS

In the following, the PIF is converted into a weight

value with:

𝑃𝐼𝐹𝑡



=

𝐹𝑡





𝑔

(24)

This allows a better view of the ratio of the maxi-

mum value of PIF to the static weight.

5.1 Comparison SF=1

Figure 10 shows the first comparison between

simulation and Product Model (50g MM, SF=1). 7

pieces fall onto WB flaps. Product Model generates

exactly 7 small impacts. In the simulation model

there are more than 7 impacts. The maximum force

is between 4kg and 5kg.

Figure 11: Falling of 50 g MM with SF=1. Comparison of

simulation and Product Model with a root mean square

error (RMSE) of 464.098g.

5.2 Comparison SF=0.3

Figure 12: 50g MM with SF=0.3. Comparison of Product

Model and simulation with RMSE = 94.301g.

2,000

4,000

6,000

8,000

10,000

7891011

PIF [g]

Time [ms]

Comparison NSF (SIM01699)

NSF = 1 NSF = 0.01

0.00

10.00

20.00

30.00

40.00

50.00

0.E+00 1.E-04 2.E-04 3.E-04

Maximum PIF [N]

Sample Time [s]

Convergence Analysis

0 204060

PIF [kg]

Time [ms]

SF=1 - 50g (Comparison)

DEM (SIM01759) Product Model

0 5 10 15 20

PIF [kg]

Time [ms]

SF=0.3 - 50g (Comparison)

DEM (SIM01743) Product Model

Dynamic Model of the Weighing Process of an Industrial Combination Scale: Model Development and Simulative Analysis of the Product

Impact Force

155

Figure 11 shows a comparison between simulation

and Product Model with SF=0.3. The maximum

force is between 2kg and 3kg. The duration of the

highest peak is about 10ms.

5.3 Duration of Impact at 100g

The static weight is increased to 100g with SF=0.4.

Figure 12 depicts a comparison of DEM simulation

and Product Model. The simulation shows a dura-

tion of about 40 to 50ms. There are two peaks. The

first peak is higher than the second. The duration of

PIF at Product model is about 50ms. There is only

one higher peak at about 30ms.

Figure 13: 100g MM with SF=0.4 after 23.88ms (left).

Comparison of simulation and Product Model (right).

5.4 Variation of Restitution Coefficient

PIF in Figure 13 (right) with ε=0.7 is very similar

to PIF with ε=0.1 (left side of Figure 13). ε has an

influence on K



but not on K



according to (5) and

(6). Nevertheless, the rebounding particles change

the PIF of the following particles. Table 3 shows the

deviation of the PIF when changing ε from ε=0.1

to a higher value. In addition, with a higher ε the

particles are longer in motion (comparison of static

weight in Figure 13 left to right). With ε=0.7 the

static weight shows the first particle in rest at about

45ms (see right side of Figure 13). With ε=0.1 this

occurs at about 25ms (Figure 13 left).

Figure 14: PIF and static weight of 50g SF=1 and 𝜀=0.1

(left) and 𝜀=0.7 (right). Due to the rebound, many parti-

cles are still in motion after 70ms with 𝜀=0.7 (blue).

Table 3: RMSE of PIF to 𝜀=0.1.

𝜀

RMSE [g]

0.3 226.419

0.5 267.293

0.7 275.186

5.5 Fluctuation and Variation of SF

Figure 14 shows the ratio of maximum PIF to static

weight as a function of SF. There are large fluctua-

tions, which is caused by the random fall behaviour.

The trend is that PIF gets higher SF increases.

Figure 15: Ratio of maximum force to static weight as a

function of SF.

6 DISCUSSION

Using the DEM simulation model, it was possible to

directly calculate the PIF, which is difficult to meas-

ure with a sensor in an experiment. A large number

of test series with more than 20 different products

could be carried out in the simulations. Likewise, the

random fall behaviour during impact could be simu-

lated. Based on these analyses, a real-time capable

product model was derived. The model could gener-

ate impact curves based on target weight, piece

weight, impact time, mean drop height, and impact

duration. Total impact duration and time of impact

of an individual particle are changing based on ran-

dom variables. Due to simplifications, restitution

coefficient and shape of the particle are not consid-

ered. This means that only one impact per particle is

mapped at a PIF curve. For larger particles, as in the

case of the original size of the test product MM,

there are therefore deviations in comparison of DEM

simulation and Product Model (see Figure 10). If the

buckets are filled to a greater extent, delayed double

peaks occur (see DEM in Figure 12). The Product is

hindered in the FB when falling (behaviour like in

an hourglass). This is also not represented by the

Product Model. However, if the bucket size is se-

lected correctly, this situation should not occur in

practice.

0 10203040506070

PIF [kg]

Time [ms]

SF=0.4 - 100g (Comparison)

DEM (SIM01701) Product Model

0204060

Static Weight [g]

PIF [kg]

Time [ms]

= 0.1 - 50g (SIM01759)

PIF Static Weight

0204060

Static Weight [g]

PIF [kg]

Time [ms]

= 0.7 - 50g (SIM01762)

PIF Static Weight

100

150

0 0.2 0.4 0.6 0.8 1

Max(PIF) / Weight [-]

SF [-]

Ratio Max(PIF) / Static Weight

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In summary this study shows a weighing product

model that could represent the process of product

impact during the weighing procedure of CS. This

paper analysed the PIF isolated from the system.

However, the PIF is dependent on the stiffness of the

system weighing station (see (5) and Figure 4).

Therefore, the weighing station and its effect on the

PIF should be taken into account in future studies.

So far, a comparison has been made from the

Product Model to a virtual test (DEM simulation).

However, it would be very desirable if in future

work a comparison could be made with

measurements on a real weighing station and exam-

ples from literature (with the extended model).

Stronge (2018) shows approaches for impact against

flexible structures.

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