Method and apparatus for producing a primary roll of material

Method for producing a first primary roll having a predetermined lateral surface defined by a diameter D.sub.f, said primary roll being made of material wound around a spindle, said material being used to produce smaller secondary rolls of material, said method comprising steps of:

• (a) calculating a portion S.sub.f of said lateral surface, which is covered by said spindle;
• (b) calculating a portion S.sub.p of said lateral surface, which represents remaining unusable material wound around said spindle;
• (c) calculating a portion S.sub.a of said lateral surface, which represents an error margin determined by an operator;
• (d) calculating a portion S.sub.i of said lateral surface, which represents material needed to produce said smaller secondary toils of material;
• (e) calculating a time varying compression factor K1 which is derived from a compression factor K where K=((sum of lateral surfaces of material of a previous second primary roll used to produce previous secondary rolls)/(sum of lateral surfaces of material of said previous secondary rolls));
• (f) calculating D.sub.f where:
• ##EQU8## (g) winding up material around said spindle to produce said first primary roll until a diameter of said first primary roll reaches said diameter D.sub.f ;
• whereby loss of material is reduced by taking into account said compression factor K1 which varies with respect to time.

Apparatus for producing a first primary roll having a predetermined lateral surface defined by a lateral diameter D.sub.f, said primary roll being made of material wound around a spindle, said material being used to produce smaller secondary rolls of material, said apparatus comprising:

• means for calculating a portion S.sub.f of said lateral surface, which is covered by said spindle;
• means for calculating a portion S.sub.i of said lateral surface, which represents material needed to produce said smaller secondary rolls of material;
• means for calculating a time varying compression factor K1 which is derived from a compression rate K of a previous second primary roll used to produce previous secondary rolls with respect to said previous secondary rolls;
• (d) means for calculating D.sub.f where:
• ##EQU9## (e) means for winding up material around said spindle to produce said first primary roll until a diameter of said first primary roll reaches said diameter D.sub.f ;
• whereby loss of material is reduced by taking into account said compression factor K1 which varies with respect to time.

Apparatus for producing a first primary roll having a predetermined lateral surface defined by a lateral diameter D.sub.f, Said primary roll being made of material wound around a spindle, said material being used to produce smaller secondary rolls of material, said apparatus comprising:

• means for calculating a portion S.sub.f of said lateral surface, which is covered by said spindle;
• means for calculating a portion S.sub.p of said lateral surface, which represents remaining unusable material wound around said spindle;
• means for calculating a portion S.sub.a of said lateral surface, which represents an error margin determined by an operator;
• means for calculating a portion S.sub.i of said lateral surface, which represents material needed to produce said smaller secondary rolls of material;
• means for calculating a time varying compression factor K1 which is derived from a compression rate K where K=((sum of lateral surfaces of material of a previous second primary roll used to produce previous secondary rolls)/(sum of lateral surfaces of material of said previous secondary rolls));
• means for calculating D.sub.f where:
• ##EQU10## means for winding up material around said spindle to produce said first primary roll until a diameter of said first primary roll reaches said diameter D.sub.f ;
• whereby loss of material is reduced by taking into account said compression factor K1 which varies with respect to time.