Matrixes from Axiomatic Model

All discussed effects produce a complex grinding process model. This axiomatic model, however, is simplified and based on existing models. The main application is fine grinding of ductile material, leaving exemptions, special process variants and

Fig. 7.32 Low scrap rate (diagram follows Fig. 7.30)

other applications open. Experimental data, sensitivity analyses and empirical data could enhance the axiomatic grinding process model a lot.

Relations between the functional requirements and design parameters can now be expressed through matrixes according to Eq. 7.7. Figure 7.36 shows the matrix for tool properties, Fig. 7.37 for the grinding system, and Fig. 7.38 for the cooling lubricant properties. A known interdependence is marked with “x”, an enlarging or positive effect of the parameter on the functional requirement on the left by “+”, a minimizing or negative effect by “—”, and a known bilateral effect by “±”. Equations are given where known and important. The contradictory dependencies would need sensibility analyses to determine the dominant trend.

The matrixes Figs. 7.36, 7.37 and 7.38 are not exhaustive. They do not display linear relationships, but rather general dependencies that have to be put into equations. For example, the functional requirement “Reduce mechanical impact on workpiece” is a function, but not a sum, of grit size, grit concentration, equivalent wheel diameter, wheel speed, workpiece speed, depth of cut (Eq. 7.15), and also grit friability, wheel width, grinding mode, and lubrication ability of the cooling

Fig. 7.33 Low tool costs (diagram follows Fig. 7.30)

lubricant. The impact of each of the parameters can be found by sensitivity analyses.

Reduce mechanical impact on workpiece

= f(max. undeformed chip thickness (7.10), grit friability, wheel width, grinding mode, lubrication ability of the coolant)

(7.15)

Fig. 7.34 Low dressing tool wear (diagram follows Fig. 7.33)

Fig. 7.35 Low auxiliary costs (diagram follows Fig. 7.30)

Bond properties	(l) A)|3|ise|e puo0					X			X
GT Лрлцэприоэ ieeL| PUO0							+
(1) eoueisisej 1ВЭЦ puoa							+
(l) |виэ1вш Bmpuoq JO eOUBJSISeJ 1В01ШЭЦ0									X
Tool properties	(l) Bujoueieq |веіщ						X				X
(I) JOjAeqeq Bujduiep |eeq/v						X				X
(I) sq Ч1Р! М 1ЭЭЧМ				■		‘		‘		+1
(l) Jeieuiejp |веіщ
(l) jeiemejp |eeqM bg	■			CO4 r^, +1	CO4 r^, +	+l!		+i °? CD I"- Sw’ +	+ll	+1
(l) uojsnjiojd								+
(l) qidep ejod uee|/|							+
(l) Aijsojod |веіщ			+				+
(l) |oo) uo ujeued						X
(i) qiBueJis puo0	X	X	X	X	X	X		X	X	X
(l) uojiejiuesuos	‘			+1	+	+1		+1	+1	+1
^ (1) 8|ВМЭ1ВШ jo eouBis|sej |во|швчо		+				+			X	+
Grit properties	(і) Aimqeui lug	+	+	+	X		X		X	X	X
(l) sseupjeq		+			X	+				+
Ш Лцлцэпр — uo3 ;eeq Buqeoo							+
(l) esueisjsej ;eeq		+				+	+			+
ПТ Ацлцэприоэ ieeq jug							+
(i) ezjs iug	+			+1	‘	+1		+1	+1	+1
or snjpej eBpe Bupino lug					+
(i) edeqs ijjg								X
		Make chip formation effective	Do not lose tool sharpness	Transport chips	Reduce mechanical impact on workpiece	Control workpiece surface grooves	Control workpiece surface pattern	Take away heat	Reduce heat generation	Suppress chemical reactions	Be cost-effective

Fig. 7.36 Axiomatic matrix for the grinding tool (“+”: enlarging or positive effect, “—”: minimizing or negative effect, “±”: enlarging and minimizing effects are known, “x”: effect with unclear tendency)

others	(S) JeMoa eipujds цбпощ) бииоциош sseoojd										X
(S) бицооэ ашцэе|/|										X
(S) A6.10U0 бШЦеШ |Bj J0}B|/|							+
(s) Ацлірприоо еэц |ВЫ0)Б|/|							+
(S) 6u;duie|o |ео;иецо0|/|
Dressing process	6lljSS0jp snonuiiuoo	X	X								X
ISJ s0|oAo 6ujss0.jp Miq 0iun|OAdM ‘ЦЭВ|/|	X		X	X	X			X		X
(S) рэв ino 6ujss0.jp jo qid0Q	X		X	X	X					X
(S) РЬ 0\ЄЛ p00dS 6UjSS0JQ	X		X	X	X			X		X
r (S) (S) PBiA р00^ 6UjSS0jp |BjXV	X		X	X	X			X		X
(s) PSA 6UjSS0jp 6ujjnp P00ds |004M
(s) 0ШП|ОЛ pUOUIBja										+
(s) АщепЬ ljj6 pUOUIBjp 6UjSS0JQ										+1
(s) J9||OJ UJOj риошвіа	X		X	X	X			X		X
Grinding parameters	(S) °UBJ lAIdU						X
(S) 0рош 6u;pujj6 имоа	+			+		+		+	+	+
(S) b оіузл p00ds								X
(s) ‘в (ПО (O 4ldsa	+			(7-8)	S					+1
(s) 4lBd Bujpuuo
(S) мл pe©ds 0O0jcbjJOM	+			(7-8)	, *9	+|ії		± (i. a.7- 8)	+,S	+1
(S) Iflldd sipujds 1ЭЭЧМ
(S) ss0oojd d0).s-!t|n|/y										X
(s) ’л pssds 1ЭЭЧМ				(7-8)	+?		+	+i 00		+1
		Make chip for­mation effective	Do not lose tool sharpness	Transport chips	Reduce mechanical impact on workpiece	Control workpiece surface grooves	Control workpiece surface pattern	Take away heat	Reduce heat generation	Suppress chemical reactions	Be cost-effective

Fig. 7.37 Axiomatic matrix for the grinding system (“+”: enlarging or positive effect, “—”: minimizing or negative effect, “±”: enlarging and minimizing effects are known, “x”: effect with unclear tendency)

Cooling lubricant properties

Cooling lubricant supply

Lubrication ability (C)

Lubricant viscosity (C)

Degeneration stability (C)

Coolant properties kw. cw(C)

Haet capacity (C)

Cooling lubricant and additives (C)

Maintenance (C)

Needle nozzle (C)

Cleaning nozzle (C)

Coolant cooling (C)

Filtering system (C)

Coolant exchange intervals (C)

Make chip formation effective

—

Do not lose tool sharpness

Transport chips

+

Reduce mechanical impact on workpiece

—

Control workpiece surface grooves

Control workpiece surface pattern

—

Take away heat

+

X

Reduce heat generation

±

Suppress chemical reactions

—

X

Be cost-effective

—

—

X

X

X

X

—

Fig. 7.38 Axiomatic matrix for the cooling lubricant enlarging or positive effect, minimizing or negative effect, “±”: enlarging and minimizing effects are known, “x”: effect with unclear tendency)

7.3 Axiomatic Grinding Process Model 211

The matrix can be helpful in clarifying how the system components and parameters in grinding are intertwined [LINK12c]. The functional requirements that are related most to process sustainability can be discussed with the matrix.

Sustainability needs to consider the four dimensions of technology, economics, environment, and society. Specific sustainability indicators cover these dimensions, depending on the framework and user. Figure 7.39 lists the most useful indicators for common grinding processes [LINK13]. These indicators are connected to functional requirements of the axiomatic grinding process model from Figs. 7.36, 7.37 and 7.38.

The matrixes Figs. 7.36, 7.37 and 7.38 highlight where research is needed on better process understanding and quantitive equations for grinding.