An arrangement for producing a three-dimensional product by successive fusing together of selected parts of powder layers applied to a work table is previously known from, for example, U.S. Pat.  No.  4,863,538.  The arrangement comprises a work table on which said three-dimensional product is to be built up, a powder dispenser which is arranged so as to distribute a thin layer of powder on the work table for forming a powder bed, a radiation gun for delivering energy to the powder, fusing together of the powder then taking place, means for guiding the beam emitted by the radiation gun over said powder bed for forming a cross section of said three-dimensional product by fusing together parts of said powder bed, and a control computer in which information about successive cross sections of the three-dimensional product is stored.  The three-dimensional product is built up by fusing together selected parts of successive powder layers applied.  The control computer is intended to control deflection means for the beam generated by the radiation gun over the powder bed according to an operating scheme which reproduces a predetermined pattern.  When the operating scheme has fused together a desired area of a powder layer, a cross section of said three-dimensional product has been formed.  A three-dimensional product is formed by successive fusing together of successively formed cross sections from powder layers applied successively by the powder dispenser. 
An arrangement for producing a three-dimensional product where measurement of the surface structure and the surface temperature of the three-dimensional body produced is permitted during the manufacturing procedure is known from SE 0001557-8.  By using the arrangement described therein, increased correspondence of the shape of the three-dimensional bodies produced in relation to the intended shape is made possible. 
In order to meet industrial requirements in the manufacture of three-dimensional models, it is important to achieve a sufficiently high manufacturing rate.  This is especially the case if an arrangement as described above is to be used for series production.  Attempts have been made using increased sweep speed with a corresponding increase in power of the beam.  In the process for manufacturing the three-dimensional products, however, it has been found that surface stresses in the manufactured product give rise to shape deviations and also internal stresses in the product which can give rise to the initiation of crack formation.