11.2.2 Process Force Calculation The calculation of milling forces is based on a material removal simulation that also calculates complex cutter work piece engagement conditions and therefore the chip geometry. Based on the chip geometry the milling forces are calculated using a standard model presented in [3]. While other methods for cutter work piece engagement simulations are introduced in [12, 13, 14, 15] the dexel representation used in this work enables an efficient computation of the engagement condition. Especially in applications of milling with industrial robots the accuracy of the dexel based method is considered to be appropriate. In order to increase the calculation accuracy [16] recommends the usage of a multi-dexel model for the representation of the work piece (cf. Figure 11.4). Figure 11.4: Dexel representation of a work piece in three directions in space. Thereby the description of a single dexel is done by line equations, Here, is a point on the line, is the line direction, is the scaling factor and the p d t s starting point in space. The work piece is modeled using a multi-dexel representation compromising dexel directions in and The discretization of x, y z. the work piece is defined by the dexel distances and In order to receive a dx, dy dz. sufficient accuracy of the force calculation the relation between the dexel kd discretization and the tool radius is considered, R . During a simulated milling operation the tool moves through the work piece in discrete time steps The incremental size of the time step is ti. dt. In every time step the material removal is calculated, whereis the ti=1,…, nint tooth passing time calculated by with the number of revolution and the number of teeth n 11.2.2.1. Calculation of the Chip Geometry The material removal simulation calculates a point cloud representing the outer volume of a single chip from which the discrete chip geometry is extracted. The chip geometry is described by the angular discretized chip thickness with h(φ,z) the entry and exit angles As the chip thickness varies along the cutting φin, φout.
11.2.2 Process Force Calculation The calculation of milling forces is based on a material removal simulation that also calculates complex cutter work piece engagement conditions and therefore the chip geometry. Based on the chip geometry the milling forces are calculated using a standard model presented in [3]. While other methods for cutter work piece engagement simulations are introduced in [12, 13, 14, 15] the dexel representation used in this work enables an efficient computation of the engagement condition. Especially in applications of milling with industrial robots the accuracy of the dexel based method is considered to be appropriate. In order to increase the calculation accuracy [16] recommends the usage of a multi-dexel model for the representation of the work piece (cf. Figure 11.4). Figure 11.4: Dexel representation of a work piece in three directions in space. Thereby the description of a single dexel is done by line equations, Here, p is a point on the line, d is the line direction, t is the scaling factor and s the starting point in space. The work piece is modeled using a multi-dexel representation compromising dexel directions in x, y and z. The discretization of the work piece is defined by the dexel distances dx, dy and dz. In order to receive a sufficient accuracy of the force calculation the relation kd between the dexel discretization and the tool radius R is considered, . During a simulated milling operation the tool moves through the work piece in discrete time steps ti. The incremental size of the time step is dt. In every time step ti=1,…, nint the material removal is calculated, whereis the tooth passing time calculated by with the number of revolution n and the number of teeth 11.2.2.1. Calculation of the Chip Geometry The material removal simulation calculates a point cloud representing the outer volume of a single chip from which the discrete chip geometry is extracted. The chip geometry is described by the angular discretized chip thickness h(φ,z) with the entry and exit angles φin, φout. As the chip thickness varies along the cutting
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