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Dr.-Ing. Eduard Davydenko and Prof. Dr.-Ing. habil. Walter Gnilke


This paper represents a small portion of the work done in the area of shoe calendering development by Andritz Küsters. The theoretical part of the study includes a mathematic-physical model of the calendering process. An example of the optimization of shoe calendering parameters for folding boxboard shows the effectiveness of the new mathematical model. The results of pilot calender trials for the Andritz shoe calendar, the PrimeCal X, are also presented and discussed.


Calendering methods with an extended nip have already been used for nearly 15 years, but are much less common than traditional soft calenders for this application. Only a few studies have dealt with the physical process of new calendering technology, and this was a primary reason for undertaking the study. The mathematical models for the optimization of the calendering effect are less well known for these applications. The purpose of the present work was to establish the relationship between the paper properties and calendering conditions based on a new mathematical model.


Figure 1 – Shoe calender nip

Figure 2 – Mechanical model of shoe calendar nip

The functional principle of a shoe calender is shown in Figures 1 and 2. The shoe calendar consists of a heated roll, and the PrimeRoll X with a flexible belt and concave shoe. The paper web is calendered in the extended nip created by the thermal roll and the belt. For this installation, the PrimeRoll X, which houses the concave shoe, is located in the bottom position with the thermal roll installed directly above. The surface temperature of the thermal roll can be adjusted, along with the incoming moisture, the amount of steam for re-moisturizing the web, the shoe length, the compressive stress in the nip, and the pressure distribution in the nip in machine direction.


In our study of the paper behaviour in a shoe calender nip, we focus on visco- and plasto-mechanical, thermo-dynamical and lubrication processes. The use of VEHD-theory (visco -elastic-hydrodynamic theory) appears to be very effective in this application. Based on VEHD-theory, the deformation behaviour of visco-elastic layers under compression, hydrodynamic lubrication theory of elastic glide bodies, and the heat transfer from the heated roll to the web can be linked in one model. This enables the calculation of pressure distribution in the nip, the temperature fields in the web, and the thickness of lubrication oil film between the shoe and belt.

For this model, a balanced combination of force components was studied on two -dimensional deformation field with the Voigt-Kelvin-body being used for describing of paper behaviour under compression. The heat transfer and the temperature distribution are described based on Fourier differential equation. The Fourier-rows proved to be an effective mathematical tool to describe the deformation, the oil film lubrication, and the heat transfer.



Figure 3 – Thermodynamic conditions in a shoe calendar nip

Figure 3 illustrates the thermodynamic conditions in a shoe calender nip based on the observation of a pilot calender. The purpose of the study is to estimate the temperature distribution across the board thickness. The heat transfer, which occurs from the heated roll to the web, increases as compressive pressure is increased in the nip. Due to a free definition of the shoe length and variable adjustment of line load, the shoe calender enables us to control the dwell time and the compressive pressure in the nip independently of each other. This is in comparison to a conventional soft calender where the shoe length defines the dwell time in nip, not the line load. The determining factor of shoe calendering is the heat transfer from the heated roll to the web. The thermal softening of the paper surface is very important for the final results of calendaring on the sheet. 

In this study, it was found that, the thermal energy Qt (J/m²) which occurs to the web can be used as characteristic parameter best describing the calendering conditions in a shoe calender nip. The parameter Qt takes into consideration the shoe length, the calender speed and the surface temperature of the heated roll in a wide range of practical parameters.


In order to establish the empirical relations between the paper parameters and calendering conditions, a simplified model of the calendering process can be considered as a black box. Our statistical model of calendering process (Figure 4) was created based on a general statistical model.

Figure 4 – Statistical model of the calendering process

The influence (predictors) – incoming moisture, line load, temperature, etc. and output variables (responses) – smoothness, bulk, outgoing moisture, etc. will be defined.

We assume that through the effect of calendering, via a change of incoming parameters, a reproducible change of the output parameters will occur. Additionally, there will be some random disturbances that overlap the calendering process. These process disturbances can be caused by random quality variations of the uncalendered paper, reproducibility of calendering conditions and measurement errors.

Extensive tests on a pilot calender were required in order to determine the impact of variations of process parameters on the finished board quality. In this study, the different parameters of the calendering process and their interactions were estimated regarding the quality parameters of folding boxboard. As a result of correlation analysis an optimal parameter combination was obtained for the best calendering result.

Table 1 shows a typical dataset for the calendering trials with a PrimeCal X in the case of folding boxboard. The tests cover a wide range of temperature, compressive pressures, steam amounts, shoe length and calender speeds. With the help of experiment design, the number of test points for the factors x1-x4 can be reduced to 45 without any loss of information.

Table 1 - Dataset for the calendering trials at PrimeCal X for folding boxboard


The calendering trials were performed on a pilot shoe calendar, PrimeCal X, at Andritz Küsters facilities. Figure 5 shows the basic principle of the pilot calender. The pilot calender consists of three nips with each nip including a steam shower. The shoe calender can be operated at linear loads from 50 kN/m to 1500 kN/m. The roll surface temperature can be adjusted from 50 °C to 300 °C. The speed of the paper web ranges between 80 m/min up to 1400 m/min. The web width is in the range of 800-900 mm.

Figure 5 - Pilot calender PrimeCal X at Andritz Küsters

For the pilot trials, various dwell times can be examined with the different shoe lengths of 50, 75, 115 and 170 mm, along with an optional shoe at 250 mm and 300 mm length. The paper web is calendered between the thermal roll and the belt. The calendered paper surface is the top side.

Uncoated folding boxboards produced at two paper mills were used for this study. The board grades are denoted as KF(1) and KF(2). The final board grade is the coated folding boxboard GD2 400 g/m². The basic layers consist of secondary fibres B12 and B19. The furnish for the top layer was based on a mixture of a large part of wood free white waste paper fines, a portion of fresh fibres, and LWC. The basis weight of the basic board is 380 g/m².


In this study, 90 test points were performed on the pilot calender PrimeCal X and 30 test points on a conventional soft calender. A dataset of the calendering conditions and board parameters for the calendering trials of folding boxboard is assembled in Table 1.

The calendering results on folding boxboard are shown in Figure 6 for the investigated range of line load, ingoing moisture, and steam amount. The temperature, calender speed, and shoe length are indirectly included in the specific thermal energy Qt.

Figure 6 – Cornerstone diagrams for calendering parameters of folding boxboard KF(1) (L=170 mm)

The desired results for PPS roughness of 3.5-4.5 µm, with a minimal bulk loss and for maximum of bending stiffness can be achieved at line load of 538 kN/m and steam amount of 3.7 g/m². To reach the target for a maximal bending stiffness, an input of thermal energy of a level around 11 kJ/m² will be required. The best results for micro roughness in terms of PPS and gloss can be achieved at 13 kJ/m². An extreme value for PPS-roughness, gloss and bending stiffness could be clearly identified in the 3D- plots for line load and thermal energy in Figures 7-9. Figure 10 shows the contour plot for specific thermal energy Qt in kJ/m² independent of calender speed and surface temperature of the thermo roll at contact length of 170 mm. The marked area between the curves at Qt=11 kJ/m² and Qt=13 kJ/m² show the practically relevant operational window for calender speed and temperature for the best board quality achievable at shoe length of 170 mm.

Figures 11 and 12 compare the shoe calender with a conventional soft calender on the basis of the calendering results for PPS roughness, bulk, and bending stiffness for the board grades KF(1) and KF(2). For the same value of PPS roughness, a higher value for bulk can be achieved on PrimeCal X compared with the conventional soft calender. With the new shoe calendering technology, the bulk loss can be reduced from 15-20% (conventional soft calender) to as little as 4-6% (PrimeCal X). The analysis of the calendering results leads to the conclusion that a remarkable increase in bending stiffness in relation to the PPS roughness can be established with the use of the PrimeCal X. The PrimeCal X provides a better ratio of the bending stiffness to the PPS roughness compared with the conventional soft calender.

Figure 7 – PPS-roughness as a function of line load LL and thermal energy Qt for folding box board KF(1) at a contact length of 170 mm

Figure 8 – Gloss GL TS as a function of line load LL and thermal energy Qt for folding boxboard KF(1) for a contact length of 170 mm

Figure 9 – Bending stiffness BS MD as a function of line load LL and thermal energy Qt for folding boxboard KF(1) at a contact length of 170 mm

Figure 10 – Plot for thermal energy Qt for folding boxboard KF(1) at a contact length of 170 mm

Figure 11 – PPS roughness as a function of bulk for board KF(1) at 430 m/min

Figure 12 - Bending stiffness as a function of PPS-roughness for board KF(1) at 430 m/min

Figure 13 - Bending stiffness as a function of PPS-roughness for board KF(1) at 430 m/min


Based on engineering and scientific methods, a new mathematical model was developed in order to describe the technological process of calendering in a shoe calender nip. The introduced theory of shoe calendering provides useful results for the determination of optimal calender parameters. The effect of calendering is most improved with the increase of specific thermal energy until a maximum calendering result is reached.  However, further increase of thermal energy leads to the deterioration of nearly all quality parameters associated with calendering. A distinct extreme value for PPS-roughness, Bendtsen-value, gloss and bending stiffness could be identified in case of the two different grades of folding boxboard being examined. The calendering of board outside of the optimal range of calendering conditions leads not only to a waste of energy, but also to the deterioration in the paper quality. 

In this study, it was found that the thermal energy Qt (J/m²) which occurs to the web in the shoe calender nip seems to be a useful characteristic number, which takes into consideration the shoe length, the calender speed, and the surface temperature of the thermal roll closely with each other in the wide range of practice-relevant parameters.  An optimal group of settings on the shoe calender can be found with the help of introduced characteristic number Qt with excellent efficiency, requiring less data points than previous trial work. For the default value of calender speed, the optimal shoe length and the surface temperature of the thermal roll can be found. With the optimized shoe length, the board can be calendered at a moderate temperature level (under 220 °C) without any loss on paper quality and production capacity.


Financial support from EU and European Fund for Regional Development is gratefully acknowledged. Special thanks are expressed to our partners from Kappa Smurfit paper mills for their continued support.


Dr.-Ing. Eduard Davydenko
Andritz Küsters GmbH & Co. KG
Eduard-Küsters-Str. 1
D-47805 Krefeld

Prof. Dr.-Ing. habil. Walter Gnilke
Brunnenstraße 16
D-01979 Lauchhammer

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