Data Representation and Modeling for Process Planning

Abstract

Process planning designs the details required for the manufacture of a product according to its design specifications and available manufacturing resources

Appendices

Appendix 1 Database Models for Process Planning

1.1 Data Modeling for External Insert Holder

Figure 28

Fig. 28

Data model external insert holder

1.2 Data Modeling of Insert for Turning

Figure 29

Fig. 29

Data model of insert for turning

1.3 Data Modeling for Internal Insert Holder

Figure 30

Fig. 30

Data model of internal insert holder

1.4 Data Modeling of Insert Holder for Threading

Figure 31

Fig. 31

Data model of insert holder for threading

1.5 Data Modeling of Insert for Threading

Figure 32

Fig. 32

Data model of insert for threading

1.6 Data Modeling of Turning Tool

Figure 33

Fig. 33

Data model of turning tool

1.7 Data Modeling of Threading Tool

Figure 34

Fig. 34

Data model of threading tool

1.8 Data Modeling of Numerical Control Lathe Machine

Figure 35

Fig. 35

Data model of NC lathe machine

Appendix 2 Flowchart of Obtaining Geometry Entities from DXF Representations

Figure 36

Fig. 36

Flowchart of obtaining geometry entities from DXF representations

Appendix 3 Decision-Making Diagrams for Feature Definition Based on Obtained Geometric Entities

3.1 Tangent Line Entity-Based Decision-Making Diagram for Feature Definition

Figure 37

Fig. 37

Tangent line entity-based feature definition diagram

3.2 Circular Entity-Based Decision-Making Diagram for Feature Definition

Figure 38

Fig. 38

Circular entity-based feature definition diagram

Appendix 4 Structure of ManufFeature Java Class

Appendix 5 Several Examples of Tolerance Factors Defined in this Chapter

Figure 39

Fig. 39

Example tolerance factors

Appendix 6 Setup Planning and Sequencing Algorithms

6.1 Nomenclatures

n :

Number of manufacturing faces within a rotational component

$f_{i}$ :

Manufacturing faces, $i = 1,2, \cdots ,n$

K ₀ :

Set of manufacturing faces that exist on the stock

K _i :

Set of manufacturing faces that exist after the work-piece was machined in the ith setup

X :

Set of manufacturing faces that are suitable for location or clamping

${\mathbf{X}}{(}{\mathbf{K}}_{i} {)}$ :

Set of manufacturing faces that are suitable for location or clamping after the work-piece has been machined in the ith setup

C :

Set of manufacturing faces that are cylindrical surfaces

P :

Set of manufacturing faces that are plane surfaces

O :

Set of manufacturing faces that are cone surfaces

A ₁ :

Set of manufacturing faces that can be machined from the left side of the component

A ₂ :

Set of manufacturing faces that can be machined from the right side of the component

A ₃ :

Set of manufacturing faces that can be machined from either the right side or left side of the component

${\mathbf{T}} = [t_{ij} ]$ :

Adjacency matrix of the tolerance factor graph, $i,j = 1,2, \ldots ,n$

6.2 Mathematical Formulation

Set of manufacturing faces:

$$ {\mathbf{F}} = \left\{ {f_{1} ,f_{2} , \ldots ,f_{n} } \right\} $$

Stock geometry vector:

$$ \begin{aligned} {\mathbf{K}} &= \left\{ {k_{1} ,k_{2} , \ldots ,k_{n} } \right\}\\ k_{i} &= \left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if}}\,{\text{face}}\,f_{i} \,{\text{exists}}\,{\text{on}}\,{\text{the}}\,{\text{stock}}} \hfill \\ 0 \hfill & {{\text{otherwise}}\quad i = 1,2, \ldots ,n} \hfill \\ \end{array} } \right. \end{aligned}$$

Fixturing vector:

$$ \begin{aligned} {\mathbf{X}} =& \left\{ {x_{1} ,x_{2} , \ldots ,x_{n} } \right\}\\ x_{i} =& \left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if}}\;{\text{face}}\;f_{i} \;{\text{is}}\;{\text{suitable}}\;{\text{for}}\;{\text{locating}}\;{\text{or}}\;{\text{clamping}}} \hfill \\ 0 \hfill & {{\text{otherwise}}} \hfill \\ \end{array} } \right.\\ &\left( {i = 1,2, \ldots ,n} \right) \end{aligned}$$

Cylindrical vector:

$$ \begin{aligned} {\mathbf{C}} =& \left\{ {c_{1} ,c_{2} , \ldots ,c_{n} } \right\} \\ c_{i} =& \left\{ {\begin{array}{ll} 1 \hfill & {{\text{if}}\;{\text{face}}\;f_{i} \;{\text{is}}\;{\text{a}}\;{\text{cylindrical}}\;{\text{surface}}} \hfill \\ 0 \hfill & {{\text{otherwise}}} \\ \end{array} } \right.\\ &\left( {i = 1,2, \ldots ,n} \right) \end{aligned}$$

Plane vector:

$$ \begin{aligned} {\mathbf{P}} = &\left\{ {p_{1} ,p_{2} , \ldots ,p_{n} } \right\} \\ p_{i} =& \left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if}}\;{\text{face}}\;f_{i} \;{\text{is}}\;{\text{a}}\;{\text{plane}}\;{\text{surface}}} \hfill \\ 0 \hfill & {{\text{otherwise}}} \hfill \\ \end{array} } \right.\\ &\left( {i = 1,2, \ldots ,n} \right) \end{aligned}$$

Cone vector:

$$ \begin{aligned} {\mathbf{O}} = &\left\{ {o_{1} ,o_{2} , \ldots ,o_{n} } \right\}\\ o_{i} = &\left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if}}\;{\text{face}}\;f_{i} \;{\text{is}}\;{\text{a}}\;{\text{cone}}\;{\text{surface}}} \hfill \\ 0 \hfill & {{\text{otherwise}}} \hfill \\ \end{array} } \right.\\ &\left( {i = 1,2, \ldots ,n} \right) \end{aligned}$$

Tool approach vector:

$$ \begin{aligned} {\mathbf {A}} &= \left\{ {{a}_{1} ,{a}_{2} , \ldots ,{a}_{n} } \right\}^{\text{T}}\\ a_{i}& = \left\{ {\begin{array}{*{20}l} {[1,0]} \hfill & {{\text{if}}\;f_{i} \;{\text{can}}\;{\text{be}}\;{\text{machined}}\;{\text{only}}\;{\text{from}}\;{\text{the}}\;{\text{left}}\;{\text{side}}} \hfill \\ {[0,1]} \hfill & {{\text{if}}\;f_{i} \;{\text{can}}\;{\text{be}}\;{\text{machined}}\;{\text{only}}\;{\text{from}}\;{\text{the}}\;{\text{right}}\;{\text{side}}} \hfill \\ {[1,1]} \hfill & {{\text{if}}\;f_{i} \;{\text{can}}\;{\text{be}}\;{\text{machined}}\;{\text{either}}\;{\text{from}}\;{\text{the}}\;{\text{left}}\;{\text{side}}} \hfill \\ {} \hfill & {{\text{or}}\;{\text{from}}\;{\text{the}}\;{\text{right}}\;{\text{side}}} \hfill \\ \end{array} } \right. \end{aligned} $$

Tolerance factor (Relative tolerance):

$$ {\mathbf{T}} = [t_{ij} ],\quad t = \frac{1}{{\sum\nolimits_{i = 1}^{m} {\frac{1}{{t_{i} }}} }} $$

6.3 Setup Planning and Sequencing Algorithm

Appendix 7 Tolerance-Grade Conversion Table with Corresponding Machining Processes

7.1 IT-Numbers Based on Tolerance Coefficients

Grade	Tolerance coefficient	Grade	Tolerance coefficient
IT5	7	IT11	100
IT6	10	IT12	160
IT7	16	IT13	250
IT8	25	IT14	400
IT9	40	IT15	640
IT10	64	IT16	1,000

7.2 Machining Processes Corresponding to IT-Numbers

Appendix 8 Summary of Knowledge Tables for Calculating Machining Parameters

8.1 Material Classifications According to ISO 513

Material	Description
PI	Carbon steels non-alloyed
	Carbon cast steels
	Carbon tool steels
	Low alloyed steels
PII	Alloyed and medium alloyed steels
	Low and medium alloyed steels
	Alloyed tool steels
	Ferritic and martensitic corrosion-resistant steels
MI	Austenitic and Ferritic-Austenitic corrosion-resistant, heat-resistant, and creep-resistant steels
	Nonmagnetic and abrasive resistant steels
MII	Special creep-resistant Ni, Co, Fe, and Ti-based alloys
MIII	Heat-treated steels with hardness 48–60 HRC
	Hardened ingot-mould iron with hardness 55–85 HSH
KI	Grey cast iron alloyed and non-alloyed
	Nodular cast iron
	Malleable cast iron
KII	Non-ferrous metals
	Al alloys
	Cu alloys

8.2 Insert Grades According to ISO 513

Chemical vapour deposition (CVD)					Physical vapour deposition (PVD)		Uncoated
320P	210K	525P	530P	535P	816	836	S10	S20	HF7	HF10
TiC/TiCN/TiN Multi-layer coated					TiN coated

8.3 Basic Cutting Speed in Turning

M	Turning	Tool Materials/cutting speed,νc15 (m-min-1)
		Type	Grade
			320P	210 K	525P	530P	535P	816	S10	S20	836	HT7	HF10
PI	Fine turning	S	340	290	280	–	–	220	210	180	–	–	–
		C,W	340	290	280	–	–	220	210	180	–	–	–
		T	340	290	260	–	–	220	190	170	–	–	–
		D	330	270	260	–	–	210	190	170	–	–	–
		V	330	270	260	–	–	200	190	160	–	–	–
		R	340	290	280	–	–	220	210	180	–	–	–
	Finishing	S	300	250	245	240	–	–	–	–	–	–	–
		C,W	300	250	245	240	–	–	–	–	–	–
		T	290	240	230	225	–	–	–	–	–	–	–
		D	280	240	230	225	–	–	–	–	–	–	–
		V	290	230	220	210	–	–	–	–	–	–	–
		R	300	250	245	240	–	–	–	–	–	–	–
	Semi-roughing	S	235	195	180	175	–	–	–	–	–	–	–
		C,W	235	195	180	175	–	–	–	–	–	–	–
		T	225	185	170	165	–	–	–	–	–	–	–
		D	225	185	170	165	–	–	–	–	–	–	–
		V	215	175	160	155	–	–	–	–	–	–	–
		R	235	195	180	175	–	–	–	–	–	–	–
	Roughing	S	165	–	135	130	120	–	–	–	–	–	–
		C,W	165	–	135	130	120	–	–	–	–	–	–
		T	155	–	125	125	110	–	–	–	–	–	–
		D	155	–	125	125	110	–	–	–	–	–	–
		V	155	–	125	125	110	–	–	–	–	–	–
		R	165	–	135	130	120	–	–	–	–	–	–
PII	Fine turning	S	260	225	210	–	–	165	155	135	–	–	–
		C,W	260	225	210	–	–	165	155	135	–	–	–
		T	260	225	195	–	–	165	140	125	–	–	–
		D	240	210	195	–	–	155	140	125	–	–	–
		V	240	210	195	–	–	150	130	115	–	–	–
		R	260	225	210	–	–	165	155	135	–	–	–
	Finishing	S	230	190	180	175	–	–	–	–	–	–	–
		C, W	230	190	180	175	–	–	–	–	–	–	–
		T	220	180	170	165	–	–	–	–	–	–	–
		D	220	180	170	165	–	–	–	–	–	–	–
		V	220	180	165	160	–	–	–	–	–		–
		R	230	190	180	175	–	–	–	–	–	–	–

M	Turning	Tool Materials/cutting speed,νc15 (m-min-1)
		Type	Grade
			320P	210 K	525P	530P	535P	816	S10	S20	836	HF7	HF10
PII	Semi-roughing	S	175	145	135	130	–	–	–	–	–	–	–
		C,W	175	145	135	130	–	–	–	–	–	–	–
		T	170	140	130	125	–	–	–	–	–	–	–
		D	170	140	130	125	–	–	–	–	–	–	–
		V	160	130	120	115	–	–	–	–	–	–	–
		R	175	145	135	130	–	–	–	–	–	–	–
	Roughing	S	125	–	100	95	90	–	–	–	–	–	–
		C,W	125	–	100	95	90	–	–	–	–	–	–
		T	115	–	95	90	85	–	–	–	–	–	–
		D	115	–	95	90	85	–	–	–	–	–	–
		V	115	–	95	90	85	–	–	–	–	–	–
		R	125	–	100	95	90	–	–	–	–	–	–
MI	Fine turning	S	230	–	–	180	–	100	–	–	80	60	45
		C,W	230	–	–	180	–	100	–	–	80	60	45
		T	210	–	–	170	–	85	–	–	80	60	45
		D	210	–	–	170	–	85	–	–	70	55	40
		V	200	–	–	160	–	80	–	–	70	55	40
		R	230	–	–	180	–	100	–	–	80	60	45
	Finishing	S	–	160	–	140	–	100	–	–	80	–	–
		C,W	–	160	–	140	–	100	–	–	80	–	–
		T	–	155	–	135	–	90	–	–	75	–	–
		D	–	150	–	135	–	90	–	–	75	–	–
		V	–	150	–	130	–	90	–	–	70	–	–
		R	–	160	–	140	–	100	–	–	80	–	–
	Semi-roughing	S	–	120	110	105	–	85	–	–	55	–	–
		C,W	–	120	110	105	–	85	–	–	55	–	–
		T	–	115	100	95	–	80	–	–	50	–	–
		D	–	115	100	95	–	80	–	–	50	–	–
		V	–	105	95	90	–	75	–	–	45	–	–
		R	–	120	110	105	–	85	–	–	55	–	–
	Roughing	S	–	–	–	80	–	50	–	–	43	–	–
		C, W	–	–	–	80	–	50	–	–	43	–	–
		T	–	–	–	75	–	45	–	–	38	–	–
		D	–	–	–	75	–	45	–	–	38	–	–
		V	–	–	–	75	–	45	–	–	38	–	–
		R	–	–	–	80	–	50	–	–	43	–	–

M	Turning	Tool Materials/cutting speed,νc15 (m-min−1)
		Type	Grade
			320P	210 K	525P	530P	535P	816	S10	S20	836	HF7	HF10
MII	Finishing	S	–	–	–	–	–	50	–	–	45	40	35
		C,W	–	–	–	–	–	50	–	–	45	40	35
		T	–	–	–	–	–	45	–	–	40	35	30
		D	–	–	–	–	–	45	–	–	40	35	30
		V	–	–	–	–	–	40	–	–	35	30	25
		R	–	–	–	–	–	50	–	–	45	40	35
	Semi-roughing	S	–	–	–	–	–	35	–	–	30	27	20
		c,w	–	–	–	–	–	35	–	–	30	27	20
		T	–	–	–	–	–	30	–	–	25	20	18
		D	–	–	–	–	–	30	–	–	25	20	18
		V	–	–	–	–	–	25	–	–	20	15	12
		R	–	–	–	–	–	35	–	–	30	27	20
	Roughing	S	–	–	–	–	–	30	–	–	25	20	18
		c,w	–	–	–	–	–	30	–	–	25	20	18
		T	–	–	–	–	–	25	–	–	20	18	15
		D	–	–	–	–	–	25	–	–	20	18	15
		V	–	–	–	–	–	25	–	–	20	18	15
		R	–	–	–	–	–	30	–	–	25	20	18
MIII	Finishing	S	–	50	–	–	–	50	–	–	35	45	30
		c,w	–	50	–	–	–	50	–	–	35	45	30
		T	–	45	–	–	–	45	–	–	35	40	20
		D	–	45	–	–	–	45	–	–	35	40	20
		V	–	40	–	–	–	40	–	–	30	35	20
		R	–	50	–	–	–	50	–	–	35	45	30
	Semi-roughing	S	–	35	–	–	–	35	–	–	22	30	18
		c,w	–	35	–	–	–	35	–	–	22	30	18
		T	–	30	–	–	–	30	–	–	18	25	15
		D	–	30	–	–	–	30	–	–	18	25	15
		V	–	25	–	–	–	25	–	–	15	20	10
		R	–	35	–	–	–	35	–	–	22	30	18
KI	Fine turning	S	–	250	–	210	–	170	–	–	145	140	125
		c,w	–	250	–	210	–	170	–	–	145	140	125
		T	–	230	–	200	–	160	–	–	135	135	120
		D	–	230	–	200	–	160	–	–	135	135	120
		V	–	225	–	195	–	155	–	–	130	130	115
		R	–	250	–	210	–	170	–	–	145	140	125

M	Turning	Tool Materials/cutting speed,νc15 (m-min−1)
		Type	Grade
			320P	210 K	525P	530P	535P	816	S10	S20	836	HF7	HF10
KI	Finishing	S	–	220	–	185	–	145	–	–	125	–	–
		C, W	–	220	–	185	–	145	–	–	125	–	–
		T	–	210	–	175	–	135	–	–	115	–	–
		D	–	210	–	175	–	135	–	–	115	–	–
		V	–	200	–	160	–	125	–	–	105	–	–
		R	–	220	–	185	–	145	–	–	125	–	–
	Semi-roughing	S	–	175	–	150	–	120	–	–	105	–	–
		C,W	–	175	–	150	–	120	–	–	105	–	–
		T	–	165	–	140	–	110	–	–	95	–	–
		D	–	165	–	140	–	110	–	–	95	–	–
		V	–	155	–	130	–	100	–	–	85	–	–
		R	–	175	–	150	–	120	–	–	105	–	–
	Roughing	S	–	130	–	115	–	90	–	–	80	–	–
		C,W	–	130	–	115	–	90	–	–	80	–	–
		T	–	120	–	105	–	80	–	–	70	–	–
		D	–	120	–	105	–	80	–	–	70	–	–
		R	–	130	–	115	–	90	–	–	80	–	–
KII (Al) HB 100	Finishing	S	–	–	–	–	–	800	–	–	–	680	–
		C,W	–	–	–	–	–	800	–	–	–	680	–
		T	–	–	–	–	–	800	–	–	–	680	–
		D	–	–	–	–	–	750	–	–	–	600	–
		V	–	–	–	–	–	700	–	–	–	550	–
		R	–	–	–	–	–	800	–	–	–	680	–
	Semi-roughing	S	–	–	–	–	–	600	–	–	–	480	–
		C,W	–	–	–	–	–	600	–	–	–	480	–
		T	–	–	–	–	–	600	–	–	–	480	–
		D	–	–	–	–	–	550	–	–	–	450	–
		V	–	–	–	–	–	500	–	–	–	400	–
		R	–	–	–	–	–	600	–	–	–	480	–
	Roughing	S	–	–	–	–	–	400	–	–	–	350	–
		C,W	–	–	–	–	–	400	–	–	–	350	–
		T	–	–	–	–	–	400	–	–	–	350	–
		D	–	–	–	–	–	350	–	–	–	320	–
		V	–	–	–	–	–	300	–	–	–	280	–
		R	–	–	–	–	–	400	–	–	–	350	–

M	Turning	Tool Materials/cutting speed,νc15 (m-min−1)
		Type	Grade
			320P	210 K	525P	530P	535P	816	S10	S20	836	HF7	HF10
KI	Finishing	S	–	220	–	185	–	145	–	–	125	–	–
		C, W	–	220	–	185	–	145	–	–	125	–	–
		T	–	210	–	175	–	135	–	–	115	–	–
		D	–	210	–	175	–	135	–	–	115	–	–
		V	–	200	–	160	–	125	–	–	105	–	–
		R	–	220	–	185	–	145	–	–	125	–	–
	Semi-roughing	S	–	175	–	150	–	120	–	–	105	–	–
		C,W	–	175	–	150	–	120	–	–	105	–	–
		T	–	165	–	140	–	110	–	–	95	–	–
		D	–	165	–	140	–	110	–	–	95	–	–
		V	–	155	–	130	–	100	–	–	85	–	–
		R	–	175	–	150	–	120	–	–	105	–	–
	Roughing	S	–	130	–	115	–	90	–	–	80	–	–
		C,W	–	130	–	115	–	90	–	–	80	–	–
		T	–	120	–	105	–	80	–	–	70	–	–
		D	–	120	–	105	–	80	–	–	70	–	–
		R	–	130	–	115	–	90	–	–	80	–	–
KII (Al) HB 100	Finishing	S	–	–	–	–	–	800	–	–	–	680	–
		C,W	–	–	–	–	–	800	–	–	–	680	–
		T	–	–	–	–	–	800	–	–	–	680	–
		D	–	–	–	–	–	750	–	–	–	600	–
		V	–	–	–	–	–	700	–	–	–	550	–
		R	–	–	–	–	–	800	–	–	–	680	–
	Semi-roughing	S	–	–	–	–	–	600	–	–	–	480	–
		C,W	–	–	–	–	–	600	–	–	–	480	–
		T	–	–	–	–	–	600	–	–	–	480	–
		D	–	–	–	–	–	550	–	–	–	450	–
		V	–	–	–	–	–	500	–	–	–	400	–
		R	–	–	–	–	–	600	–	–	–	480	–
	Roughing	S	–	–	–	–	–	400	–	–	–	350	–
		C,W	–	–	–	–	–	400	–	–	–	350	–
		T	–	–	–	–	–	400	–	–	–	350	–
		D	–	–	–	–	–	350	–	–	–	320	–
		V	–	–	–	–	–	300	–	–	–	280	–
		R	–	–	–	–	–	400	–	–	–	350	–

8.4 Feed Rate and Cutting Depth in Turning

Material	Feed rate, f r (mm-rev−1)				Cutting depth, a p (mm)
	Fine turning	Finishing	Semi-roughing	Roughing	Fine turning	Finishing	Semi-roughing	Roughing
PI,II	0.05–0.1	0.1–0.2	0.2–0.4	0.4–0.8	0.2–1.0	0.8–2.0	1.5–4.0	4.0–10.0
MI	0.05–0.1	0.1–0.2	0.2–0.4	0.4–0.8	0.2–1.0	0.8–2.0	1.5–4.0	4.0–10.0
MII	–	0.1–0.2	0.2–0.3	0.3–0.4	–	0.05–1.5	1.5–2.5	2.5–3.5
MII	–	0.08–0.2	0.2–0.3	–	–	0.8–1.5′	1.5–2.5	–
KI	0.05–0.1	0.1–0.2	0.2–0.4	0.4–0.8	0.2–1.0	0.8–2.0	1.5–4.0	4.0–10.0
KII	–	0.1–0.2	0.2–0.4	0.4–0.8	–	0.8–2.0	1.5–4.0	4.0–10.0

8.5 Durability Correction Factor (P, M, K Types)

T min	K VT	T min	K VT
10	1.10	30	0.84
15	1.00	45	0.76
20	0.93	60	0.71

8.6 Work-Piece Hardness Correction Factor

8.6.1 P Type

HB	K VHB	HB	K VHB
120	1.18	220	0.90
140	1.12	240	0.86
160	1.05	260	0.82
180	1.00	280	0.80
200	0.95	300	0.77

8.6.2 M Type

HB	K VHB	HB	K VHB
<150	1.40	270–300	0.72
150–180	1.18	300–330	0.68
180–210	1.00	330–360	0.66
210–240	0.87	360–390	0.62
240–270	0.79

8.6.3 K Type

HB	K VHB	HB	K VHB
Grey/nodular/malleable cast iron		Heat resistant/special cast iron
160–200	1.26	200–300	0.50
200–240	1.00	300–360	0.40
240–280	0.80	360–450	0.30
280–330	0.60

8.7 Optimized Cutting Speed

$$ v_{C} = v_{C15} \times k_{\text{VT}} \times k_{\text{VHB}} $$

(6)

where

$v_{C}$ :

Optimized cutting speed

$v_{C15}$ :

Basic cutting speed

$k_{\text{VHB}}$ :

Hardness correction factor

$k_{\text{VT}}$ :

Durability correction factor

Appendix 9 Structure of Turning ToolOODB Java Class

Appendix 10 Calculation of Production Time and Cost

10.1 Production Time Factor, T_p

$$ T_{p} = T_{m} + T_{i} \times N_{t} + T_{\text{su}} \times N_{\text{su}} $$

(7)

where

$T_{m}$ :

Machining time $\left( {{L \mathord{\left/ {\vphantom {L {\left( {f_{r} \times N} \right)}}} \right. \kern-0pt} {\left( {f_{r} \times N} \right)}}} \right)$

$L$ :

Feature length

$N$ :

Cutting speed in rpm

$f_{r}$ :

Maximum permissible feed in mm/rev

$T_{i}$ :

Time to perform an index

$N_{t}$ :

Number of tools to machine a part

$T_{\text{su}}$ :

Time to perform a set-up

$N_{\text{su}}$ :

Number of tools that must be added to the machine’s magazine

10.2 Production Cost Factor, C_t

$$ C_{t} = C_{i} \times N_{t} + C_{\text{su}} \times N_{\text{su}} + \sum\limits_{i = 1}^{n} {C_{t}^{ (i )} } $$

(8)

where

$C_{i}$ :

Cost of performing an index for a tool, $(P \times T_{i} )$

$C_{\text{su}}$ :

Cost of performing a set-up for a tool, $(P \times T_{\text{su}} )$

$N_{\text{su}}$ :

Number of tools that must be added to the machine’s magazine

$C_{t}^{(i)}$ :

Cost of a tool i

n :

Number of tools required to perform operations

P :

Pay rate

10.3 Rank of Tool Alternatives, Score

$$ {\text{Score}} = \alpha \times C_{t} + \beta \times T_{p} $$

(9)

where

Weighting condition	α	β
Normal condition	0.5	0.5
Cost weighted condition	1.0	0.0
Production time weighted condition	0.0	1.0

Appendix 11 Knowledge Tables and Equation for Calculating the Maximum Power

11.1 Cutting Resistant and Feed Influence Exponent

Material group	$P_{S 1}$[MPa]		$1 - Z$
PI	1,760		0.76
PII	1,770		0.75
MI	2,530		0.75
MII	Ni, Co alloys	2,895	0.76
	Ti alloys	1,860	0.79
MIII	2,060		0.86
KI	Grey cast iron	1,120	0.78
	Malleable cast iron	1,190	0.77
	Nodular cast iron	1,430	0.76
KII	Cu alloys	710	0.76
	Al alloys	508	0.78
	Mg alloy	250	0.78

11.2 Coefficient, $k_{\text{kr}}$

Approach angle	$k_{\text{kr}}$
90	1.00
80	1.015
70	1.02
60	1.04
55	1.06
50	1.08
45	1.10

11.3 Required Motor Power, P

$$ P = \frac{{a_{p} \cdot f_{r}^{1 - Z} \cdot P_{S1} \cdot k_{\text{kr}} \cdot v_{C} }}{42,000}\left[ {\text{kW}} \right] $$

(10)

where

$v_{C}$ :

Optimized cutting speed [m/min] [Refer to Eq. (6)]

$f_{r}$ :

Feed rate [mm/rev]

$a_{p}$ :

Cutting depth [mm]

$1 - Z$ :

Feed influence exponent for different materials machined

$P_{S1}$ :

Specific cutting resistance (cutting force for feed f = 1 mm/rev at kr = 90)

$k_{\text{kr}}$ :

Coefficient representing the approach angle kr influence

Appendix 12 Structure of MachineOODB Java Class