Calculation of radial material removal and the thickness of the layer with the current roughness when grinding brittle non-metallic materials

OBRABOTKAMETALLOV Vol. 23 No. 3 2021 TECHNOLOGY Fig. 3. Hole grinding diagram where D x r – increment of the amount of material removal due to brittle fracture; ζ – the parameter depending on the shape of the abrasive grains, the properties of the processed material and the law of grain distribution over the depth of the working layer of the tool is calculated according to formula [19]: +χ+β ζ = θ 2 ( ) 1 x m . Then the dependency (5) will take the form: ( ) ( ) +χ+β − +χ − β + D − + − − β = + D − + + + + D 1 1 1 2 ( ) ln(1 ) ( ) ( ) m j p j j m m j p j j j p H r y H G H r y H G H r ( ) +χ − + + D − + + 1 1 ( ) m j p j j G H r y H +χ+β − +χ+β β +χ+β   + D − + + + D     θ +   + D + + D     θ 2 2 1 ( ) 3 ( ) 1 ( ) ( ) 1 ( ) x x x m j p j j j p m j p j p m H r y H H r G H r H r . After arithmetic operations: +χ+β − +χ +χ − − β D − − − β = D − + + + D − + + D 1 1 1 2 1 1 ( ) ln(1 ) ( ) ( ) ( ) m p j m m m p j p j j p r y G r y G G r y H r +χ+β − +χ+β β +χ+β   D − + + D     θ +   + D + + D     θ 2 2 1 ( ) 3 ( ) 1 ( ) 1 ( ) x x x m p j j p m j p j p m r y H r G H r H r . (6)