Nipped or contacting rolls are widely used for the following:

Papermaking:

• Pressing
  
• Dewatering
  
• Calendering
  

Converting:

• Embossing
  
• Texturizing
  
• Laminating
  
• Calendering
  
• Printing
  
• Transporting
  

Nipped rollers are also used abundantly in board machines, paper finishing, printing, tanning and textile machinery.

Crowning 1

Crowning 2

Crowning 3

Crowning 4

Crown computation typically accounts for the following influences:

• Line contact force between nipped rolls
  
• Deflection caused by the moment due to overhung bearings
  
• Deflection due to gravity
  
• Pull due to clothing or belting tension
  
• Uneven thermal expansion across the roll
  

Since the deflections are usually small, the linear theory of elasticity is applicable. The deflection due to each influence is computed independently. The total deflection will be the algebraic summation of these deflections.

In a large number of applications it is desirable to cover one of the mating rolls with a layer of polymeric material of natural or synthetic origin. The nip between such rolls, which are often called the rubber covered rolls, is considerably 'softer'. Unlike the 'harder' rolls which develop a Hertzian contact, these rolls contact over a wider region, and the contact pressure is more evenly distributed.

The compression of the rubber layer is a two-dimentional elasticity problem and has been extensively studied. See "Deformation of Contacting Rollers with Compliant Coatings", Ph.D. Thesis by Balbir Singh, University of Pennsylvania, 1979. Using this analysis, the stresses in the contact region are computed. Felt rolls are also handled with this theory.

The crown curve of nipped rolls without any cover is the sum of the deflection curves of the two rolls as computed by the 2nd order beam deflection equation. This is valid because the contact is assumed incompressible.

In the case of the rubber covered rolls, the nip is elastic, i.e., its compression is not negligible. Also the thickness of the rubber cover varies from midspan to the ends due to crowning. As a result the spring constant of the nip is a variable, and the deflection curve of this beam is a fourth order equation akin to the equation of a beam on an elastic foundation. Details are available in the above cited thesis.

Usually, the line load in the nip is desired to be uniform, a constant pli. In unique cases it may be desirable to taper off the load at the two ends, thus creating a varying nip. These cases are solved analytically for the non-covered rolls, but require an iterative approach for the covered rolls.

Rolls are crowned for a given uniform nip line load, and must be operated at that load to ensure a uniform nip. In specific applications, rolls can be skewed to emulate the effect of crowning. Again, the validity of this approximation is ensured by the fact that the deflections are small.

Skewing is an inexpensive way to provide the capability to vary the "effective crown" in operation by just moving the support bearings.

These rolls are complex in design, and are critical by the fact that the shaft is quite slender and therefore stressed and prone to vibrate. These rolls must not be used without any covering.

1. SIMPLE CROWNED ROLLS

Crown Calculation

• for given uniform or any other line load
  
• for varying roll EI
  
• accounted for bearing overhang
  
• provide crown table

Crown Correction

• take nip impressions
  
• roll measurements
  
• nip pli and crown in use
  
• compute crown correction
  

2. CROWN PROFILE CORRECTION FOR RUBBER ROLLS

Develop Nip Spring Constant

• procure rubber properties
  
• experimentally develop a few points of compression
  
• compute relation between load and deflection
  
• compute nip psi footprint
  

Crown Calculation

• Use above developed spring constant
  
• Compute crown curve
  

3. PLI CALCULATION FOR GIVEN END LOADS

When rolls are operated at other than design loading

• Procure roll drawings and crown specification
  
• Rubber properties
  
• Take nip impression
  
• Compute crown curve as above
  
• Compute pli deviation
  

4. ROLL GRINDING SUPPORT

• Provide midspan crown and degree of cosine curve
  
• Provide crown table
  
• Geometry conversion and N-C table or cam to suit roll grinder
  

5. SKEWED ROLLS

• One or two sided skews
  
• Develop pli table for various skews
  
• Design bearing supports and skewing arrangement
  

6. ROLL DESIGN

• Mechanical design of rolls
  
• Stresses and deflections
  
• Roll drive design
  
• Roll bearing design and bearing life calculations
  
• Roll loading means
  
• Wedges or other methods of setting gaps
  
• Gap/penetration measurement
  

7. ZERO CROWN ROLLS

• Analyze the application
  
• Mechanical design of rolls
  
• Stresses, deflections and critical speeds
  
• Roll drive, loading, gap setting, etc.
  
• Assembly procedure and support