Aspects about plastic materials calendaring
The objective of the present paper is to provide a calender roll manufactured which do not involve the drawbacks involved in prior art and which allows to determine de roll-separating force.
Keywords: plastic materials, calender, calendered sheet
The calendaring process is based on
2. Theoretical aspects about isothermic flow between two rolls
Since the polymeric materials used for calendering are often in the melt state, the analysis of calendering process is based on the theory of isothermic flow in the gap between rotating rolls for Newtonian and non-Newtonian fluids.
Regarding the driving of materials to be calendered, it can be said that only the workpieces which do not exceed a certain thickness can pass through the calendar's rolls.
In figure 1, it is considered a piece of material with spherical shape fed from the top of the gap between the rolls on which two pairs of forces are acting, pressure forces and , respectively, and friction forces and , respectively.
In order to drag the material into the gap between the rolls, the sum of the components of the friction forces and on the vertical axis must be higher than the sum of pressure forces and .
Fig. 1. Schematic representatio 636u201g n of the fluid flow into the gap between two rolls
In this case, it can be written
where is the material weight.
The gripper angle is the sum of angles and , respectively. For rolls with equal diameters and then and .
If the material weight is neglected, Eq. (1) can have the form
The friction force can be written as a function of the pressure force and the friction coefficient
By substituting Eq. (3) into Eq. (2), the following condition can be written
The friction coefficient is defined as the tangent of the sliding angle . Thus, from Eq. (4) the gripping condition is obtained as follows:
As can be seen from Eq. (5), the gripper angle should be bigger than twice of the sliding angle.
Fig. 2. Schematic representatio 636u201g n of stationary flow between two rolls
Firstly, the theoretical analysis of the material flow was done by Gaskel  and, then, updated by many other researchers. Based on this theory, it is assumed a stationary and isotherm flow state. Also, it is assumed that the fluid is Newtonian, incompressible and, thus, the elastic component can be neglected.
In figure 2, it is illustrated a calender with two rolls with the same size and the same peripheral roll velocity. The origin of the rectangular coordinate system is placed on the axis of symmetry of the gap between the rolls (see Fig. 2). The Z axis is placed along the rolls.
For a fluid with constant density in time and flow space, for two-dimensional flow, the general equation of the flow continuity
can be reduced at
The distribution of the material flow velocities for different flow sections ca be obtained by substituting the pressure gradient
into the following equation
in which the variable is replaced by .
After substituting the variable with , the Eq. (10) can be written as follows:
Hence, for any point, the relative velocity is function of coordinates and , and of parameter .
From Eq. (11), for , it can be seen that . Hence, for the point in which the material flow is loosing the contact with the roll surface as well for the symmetrical point in respect with -axis, the material flow velocity on the flow cross section is constant and equal to the peripheral roll velocity. Based on Eq. (12), in the first point the flow pressure is zero, while in the second point the flow pressure has a maximal value.
Fig. 3. Steady-state flow in the gap between the rolls
The profiles of material flow velocity for different flow cross sections are shown in Fig. 3. For the profile of flow velocity is plane. Since for the flow pressure reaches a maximum, in the range of the pressure gradient is negative and causes a convex flow. Hence, the profile of material flow velocity is convex and the mean flow velocity of the melt polymer is bigger than the peripheral roll velocity.
In the range of the value of pressure gradient is positive and the profile of material flow velocity is concave, in which case the mean flow velocity is smaller than the peripheral roll velocity.
A comparison of the mean flow velocity of the melt polymer and the peripheral roll velocity is leading to the conclusion that the neutral zone which is defined by , divides the flow space into two distinct zones:
The delay zone, for ;
The acceleration zone, for .
On the X axis, in the range of , there is a point for which the material flow velocity is equal to zero. The position of this point can be determined from Eq. (11) if and
From Eq. (13) it can be seen that is function of parameter.
In the range of an inverse flow zone appears, in which case, the material flow velocity has positive values close to the roll surfaces, elsewhere it has negative values.
The polymer recycling into the inverse flow zone has good influences on the homogenization process.
Currently, calenders are working with friction. The peripheral roll velocities for the two rolls and respectively, are different (). In which case, the coordinate of the plane for which the shear stress is equal to zero, is no longer zero (see Fig. 3).
In order to derive the expression of flow velocity, the methodology for the rolling machine without friction is used.
The material flow velocity has the form:
If the friction effect is neglected, , the Eq. (14) is reduced to Eq. (11).
3. The roll-separating force
Based on the laboratory experiments a empirical equation, which relates the material proprieties and the parameters of machine calendering to the roll-separating force, has been derived
is the apparent viscosity of plastic melt;
the diameter of the roll calender
roll rotation, expressed in rot/second
the calendered sheet width;
the calendered sheet thickness;
The roll-separating force developed by dragging the material in the gap between the rotating rolls is very big. Its values are direct proportional to the material viscosity and inverse proportional to the gabsize between the rolls (see Eq. (17)).
Experimental measurements have shown values of (140÷180) KN for sheet thickness of 0,15 mm, and of (140÷180) KN for sheet thickness of 0,025 mm.
The roll-separating forces are sufficient to cause the calendering rolls to deflect affecting sheet profile adversely. The bending deflection at the mid span has a maximum, and affects the sheet thickness uniformity ,  and .
The roll-separating forces are acting on that portion of the roll that has contact with the material flow. The pressure flow reaches a maximum in the inert zone (see Fig. 4).
Fig. 4. Roll deflection caused by the roll-separating forces
The resultant roll-separating force, , deviates from the axial plane with angle. The roll bending takes place in the -direction. The angle is a function of gripper condition, material properties, material flow temperature, gapsize between the rolls, and the peripheral roll velocity.
In case of calendering with more than two rolls, interactions between rolls appear.
For example, in case of four-rolls calender arranged in shape, the roll 3 will be deformed under the action of two equal roll-separating forces in positive and negative direction, and it will influence the uniformity of the calendered sheet. The correction of this deficiency can be done by using a gripping hydraulic device or pre-tension device.
In this paper, the calculation of the roll deflection is done considering the roll as a beam uniformly loaded and supported at both beam head.
The maximum value of deflection is given by the relation [ ]:
is the Young modulus;
- the moment of polar inertia of the roll cross section;
- the roll-separating force per unit length.
Fig. 5. Correction methods for roll deflection:
(a) roll crowning; roll crossing; (c) roll bending.
The dependence of roll deflection on the distance from the barrel roll center in axial direction can be determined by the following equation:
The profile of the gap between the two rolls as well as the variation of the sheet thickness across the sheet width can be determined using Eq. (19).
In case of materials without elasticity, the sheet thickness is equal to the minimum gapsize between the rolls. In case of elastic materials, one must take into account the material elasticity.
In order to manufacture the plastics foil and sheet with uniform thickness, the compensation of the roll deflection is absolutely necessary.
There are three available means of adding correction: (1) roll crowning; (2) roll crossing, especially the last roll is correcting by roll crossing; and (3) roll bending.
It is seen that, additional compensation of the roll deflection is accomplished by uniform distribution of the temperature along the barrel roll. This method is based on the thermal expansion. The main drawback of this method is the change of material viscosity along the roll, which leads to a non-uniform distribution of the roll-separating force.
The most common method for the roll deflection compensation is based on roll crowning. More specifically, the roll has the maximum diameter at the mid-span and is higher than the end diameter with (0,25 - 0,75)mm (see Fig. 5.a).
Rubber industry has traditionally used rolls with generating parallel line coated with a layer of soluble glass, which is particularly machined to obtain the crowned barrel roll.
All different dimensions of rolls can be obtained since the soluble glass layer can be easily replaced and grinded if the modification of the roll profile is necessary, in which case manufacture of the rolls is highly advantageous.
Generally speaking, the roll deflection compensation by roll crowning did not led to good results. The roll deflection is a function of the material properties and the machining parameters. Under these circumstances, a roll with a certain degree of crowning is valid only for one calendering technology and for initially specified calendering parameters. Despite of these inconveniences, the roll crowning is used especially in connection with other compensation methods.
The roll crossing
The roll crossing is done by rotating the axis, skewing one roll with respect to another (see Fig. 5.b). Practically, the roll crossing process is done by moving the bearings counter-current.
The minimum gapsize at the mid-span of the roll barrel is kept constant while it increases at the roll ends. The effect is similar to that obtained by roll crowning. By roll crossing correction of 0,2 mm can be obtained.
In case of the roll crossing, the profile of gapflow between the rolls was defined by Gooch 
represents the displacement of the roll end in horizontal plane.
The profile obtained with eq. (20) is a parabola and do not exactly match up to the profile obtained by roll bending under the action of roll-separation forces.
For a given correction at the roll ends of roll, , the profile of the flow gap obtained by Eq. (20) can be approximate by the following equation
Normally, only the last pair of rolls is corrected by roll crossing.
The most recent compensation method is the roll bending. By roll bending correction of 0.05 mm can be obtained.
The roll bending can be done by means of additional bearings fixed on the two gudgeons sprindles prolonged outside the main bearings of the rolls (see Fig. 5.c).
The additional bearings are loaded via the hydraulic cylinders in the same direction and sense of roll-separation forces.
The roll-separating forces are uniformly distributed on the barrel roll length, while the loadings of the additional bearings are concentrated.
Under the separated action of the each load, the profiles of the gapflow between the rolls are different. This difference is very small compared to the difference obtained by the roll crossing.
By roll crossing with additional bearings, either similar or contrary effects to that of roll crossing (or contrary effect) can be obtained.
The major feature of the roll crossing is that it can be applied to any roll of calender and is not related to the driving system.
The roll correction is a linear function of hydraulic pressure from the loading cylinders, and, hence, the correction can be precisely adjusted.
Let be the bending momentum applied on each cylinder end. The roll deflection has a maximum value at the mid-span and is defined by
The profile of flow gap between the rolls can be obtained by combining the Eq. (21) and (22).
Generally speaking, the profile obtained by roll bending is different to that obtained by roll crossing. However, only experimental investigation can decide which one is most convenient.
The roll bending can amplify or diminish the correction of the gap profile and it makes possible to be applied in connection to roll crowning.
The major drawback of the calendering process is the assurance of the dimensional uniformity of the calendered sheet.
The material thickness should to be uniform not only along the sheet length but also on the sheet width.
The longitudinal uniformity can be assured by:
(1) reducing the clearance from the bearings by means of mechanical or hydraulic systems; (2) decreasing the clearance from the deflection compensation devices;
(3) decreasing the clearance from the gapsize adjusting device.
The transversal uniformity can be obtained by either roll crossing or roll bending.
The compensation of temperature decreasing at the end of the rolls, which lead to the variation of roll diameter, can be done by grinding the roll barrel or by using rolls with peripheral grooves.
4. Pilot machine calender
In order to simulate the calendering process, to experimentally measure the roll-separation force and to determine how the quality of the roll surface can influence the quality of calendered sheet, in this paper, a pilot three-roll calender arranged in shape is proposed (see Fig. 6).
Figure 6 shows the skeleton diagram of the three-roll calender. The arrangement comprises:
a three-roll calendar;
a spur gearing distribution boxe;
a worm-driving gearmotor.
The calender is made of three-rolls , and supported on the ball roll friction bearings fitted onto the vertical supporting frame.
During the calendering process, the three-rolls are carrying out constant rotational motions.
The rolls driving is done by means of a worm gear-motor via the chain transmition, the spur gearing distribution box, the ball joints and the fast coupling, The worm gear-motor has a redaction ration and the normal speed .
The characteristics of pilot simulation calendering machine are:
Horizontal adjustment stroke:
Vertical adjustment stroke
Maximum sheet thickness
Depending on the thickness preform, the necessary position for the calendering process of rolls and with respect to roll , is adjusted by horizontal feed (withdraw) of roll and vertical feed of , respectively, as follow:
I. Horizontal movement of roll (see fig. 8):
The rolling friction bearings are placed onto the two spur rack bodies, which can slip over the rigid guide machined in the walls.
The spindle micro screw makes the spur rack to move, this movement is simultaneously send forward to the opposite spur rack via two gears fixed on intermediate shaft.
After the necessary distance between the rolls and is appropriate, the feed device is locked with two screws.
II. Vertical movement of roll
Similarly, the rolling friction bearings of the roll are placed into two spur rack bodies, which slid over the vertical rigid guide from the lateral walls.
The rotation movement of the adjustment device' micro screw is transmitted to a worm-driving gear. The two spur racks are simultaneously operated by two gears placed onto the same shaft and thus the vertical movement over the imposed displacement is determined.
After the position of the roll with respect to roll is set up, the adjustment device is locked with two screws.
According to the skeletom diagram (see Fig. 6), the distribution box contains two spur gearings in order to transmit the rotational movement from the gear-motor to each calender roll. The two spur gearings have equal and constant gear reduction ratios and , respectively.
Each gear wheel corresponds to a calender roll, as follows:
- corresponds to ;
- corresponds to ;
- corresponds to .
The gear wheel is the driving wheel, while the gear wheels and are the driven wheel.
The calender driving is made by the worm-driving gearmotor which is a mono-block construction, for which the normal speed is reduced to by worm-driving gear. The cinematic transmission between the gearmotor and the gearbox is assured by chain transmission with two spocket wheels ( ).
In this paper, a pilot calender machine for sheet and foil is presented. Using the pilot calendering machine the simulation of the calendering process can be carry out, and the roll-separating forces during the calendering of foil and sheet with thickness of (0,25-5) mm can be determined. Moreover, the analysis of the way in which the quality of rolls can influence the quality of calendered sheets can be carried out.
The experimental results will be published in a future paper.