The Modelling Of Basing Holes Machining Of Automatically Replaceable Cubical Units For Reconfigurable Manufacturing Systems With Low-Waste Production

Article is devoted the decision of basing holes machining accuracy problems of automatically replaceable cubical units (carriers) for reconfigurable manufacturing systems with low-waste production (RMS). Results of automatically replaceable units basing holes machining modeling on the basis of the dimensional chains analysis are presented. Influence of machining parameters processing on accuracy spacings on centers between basing apertures is shown. The mathematical model of carriers basing holes machining accuracy is offered.


Formulation of the problem
It is possible to present a design of the carrier in the form of a cube ( Figure 1) where on each basilplane is available basing holes Т n , Т (n+1) , Т (n+2) , Т m . On two non-adjacent holes, for example, (Т n , Т (n+2) ) and (Т (n+1) , Т m ) there is a carrier basing on a working position, under the two non-adjacent holes and a basil-plane ( Figure 2).
For raise of efficiency of the automated machining the carrier with the details installed on lateral basil-plane is resurface on a working position. Thus there is an interleaving of a complete set of basing holes and a basil with conservation of the theoretical scheme of basing [1]. Resurfacing the carrier provides change of attitude of a detail. In XOY-system group of holes Т n , Т (n+1) , Т (n+2) , Т m dimensional communications define: A ij н -not recut spacings on centers between holes (i¹j=1, 2,3,4, m), A ij п -recut spacings on centers. Each processed holes Т ij possesses a set of parameters A ij н , A ij п , L xij , L yij , B ij ( Figure  2) which define an arrangement of each hole concerning a basil of carrier G. The parameters influencing accuracy of a mutual bracing of holes are spacings on centers A ij н , A ij п , the set tolerance of hole -Т Δт i .

Figure 1 -Design of the carrier
So accuracy of hole Т n machining is defined by sizes L n in OX, OY -directions ( Figure 3). In an OX axis direction the arrangement of hole Т n is characterized: nominal size L n , size L (n) р = = L n + Δ L n , where ΔL n -a deviation of size L n . The data set of sizes forms a dimensional chain of hole Т n machining. The closing chain link is size L (n) р , increasing a deviation ΔL n , reducing -face value L n .  At calculation of link L (n+1) accuracy for holes Т n+1 will observe a chain of sizes В n (n+1) , A n (n+1) , L n , L (n+1) (Figure 4). Sizes L n , В n (n+1) -have the set rating values and limits deviations ΔL n , ΔВ n (n+1) . Link A n (n+1) -defined (face value is not known), is known its limiting deviation ΔA n (n+1) .

Figure 3 -Dimensional chain
At closing link L (n+1) theoretical values and limiting deviations t L (n+1) are set. It is necessary to count magnitude of required link A n (n+1) face value. At calculation of link L (n+2) accuracy holes Т n+2 will observe a chain from sizes В n (n+2) , A n (n+2) , L n , L (n+2) , and also a chain which is switching on sizes A n (n+1) , A n (n+2) , A (n+1) (n+2) . Link A n (n+2) -defined (face value is not known), is known its limiting deviation ΔA n (n+2) . Thus, for maintenance of carrier basing accuracy of basing holes Т n , Т (n+1) , Т (n+2) , Т m machining it is necessary to stand equal in limits of maximum deviations recut spacing on centres sizes A (n+1)(n+2) , A (nm) , that is possible if equality in tolerance limits of sizes L ij and spacings on centres А ij between basing holes is stood. For hole Т m it is sizes A (n+2) m , A (n+1) m , A (nm) , L m .

Method of investigation
Let's make an auxiliary dimensional chain concerning each closing link and we will write down the additional equation defining rating value of an unknown making link. Also considering, that machining of holes begins, for example, with aperture Т n , sequence of holes Т n , Т (n+1) , Т (n+2) , Т m machining accuracy calculation can look like: 1) machining of hole Т n , machining of hole Т n+1 , machining of hole Т m ; 2) machining of hole Т n , machining of hole Т n+2 , machining of hole Т m ( Figure  5). The simplified record of dimensional chains for each alternative sequence of machining can look like: 1) Т n , Т n+1 → Т m ; 2) Т n , Т n+2 → Т m . In both cases hole Т m is closing. It allows, using results of calculations to define alternative of hole Т m machining (a chain 1 or 2), providing the highest accuracy of its positioning concerning next holes Т n , Т (n+1) , Т (n+2) in each basil G.
The arrangement of hole T m of relative holes T n , T n+2 is defined by rating values of closing links A (n+2) m , A (nm) and sizes L (n) , L (n+2) in OX, OY -directions: (2) where L (n) -rating value of distance of hole Т (n) to edge of a basil of the carrying agent, Δ (n) -value of a deviation of hole Т (n) taking into account elastic deformations of the tool and a carrier, tLa limit deviation on manufacturing of holes Т (n) and Т (n+2) , L (n+2) -rating value of distance of hole Т (n+2) to edge of a basil of the carrier, Δ (n+2) -value of a deviation of hole Т (n+2) taking into account elastic deformations of the tool and a carrier basil, tL -a limit deviation on manufacturing of hole Т (n+2) .
The interconnection of sizes A (n+2)m and A (nm) is being out through a system gear ratio ξ = 2 equalarrangement holes of settlement chain T n , T n+2 T m . Deviation closing links A (n+2) m and A (nm) are defined by relationships: (4) Let's mark out ΔА nm -a deviation of a closing size A (nm) , ΔА (n+2) m -a deviation of a closing link A (n+2) m , ΔB -a deviation of carrier basil size В ij , tL -a maximum deviation on machining of hole Т m , tL (n+2) -a maximum deviation on machining of hole Т (n+2) , tL n -a maximum deviation on machining of Т (n) .
(10) Let's mark out ΔА nm -a deviation of a closing size A (nm) ; ΔА (n+1) m -a deviation of a closing link A (n+1) m ; ΔB -a deviation of size В ij of a carrier basil; tL -a maximum deviation on machining of aperture Т m ; tL (n+1) -a maximum deviation on machining of hole Т (n+1) ; tL n -a maximum deviation of hole Т (n) .
Let's define displacement (correction) е a design value of closing links A ((n+1) m) Р and A (nm) Р concerning their face values A (n+1) m and А nm :

Conclusions
In production conditions of low-waste RMS carrier is constructive conferred a basing redundancy property under the condition of variable spatial position in the work area in order to enable the simultaneous advance of the tool to multiple parts disposed on the lateral faces of its body G i . This allows: 1. Reducing metal consumption of machine tool systems and obtaining a number of technical effects that simplify the organization of the production process.
2. Reducing waste of the production concerning to traditional production forms of organization. 3. In order to enable the accuracy of spatial arrangement of parts on the RMS carrier in this study were obtained dependences of basing parameters on its manufacturing precision parameters of basing holes of its body. Thus, оn carrier basing accuracy the essential agency renders mutual bracing accuracy of basing holes on each basil. Oscillations of basing holes mutual bracing accuracy are caused by alternativeness of machining concerning each carrier basil dimensional chains.
4. The carrier machining algorithmic sequence where each subsequent hole is machining taking into account a lapse of the previous hole machining and maximum deviations of spacings on centres between them is offered.
5. The machining process mathematical model, allowing to count accuracy of basing holes spacings on centres taking into account at stage of their manufacturing lapse of machining process is offered.
6. Results of modelling are confirmed by calculations of carrier basing accuracy and results of its one basil basing holes T n , T n+1 , T n+2 , T m , machining.