Slicing Cuts on Food Materials Using Robotic-Controlled Razor Blade

Table 2

Area external force.

	Normal force only	Tangential force only
Slicing angle	𝛼
External force	𝑃
Components	𝑃𝑛=𝑃cos𝛼	𝑃𝑡=𝑃sin𝛼
Pressure	𝑝𝑛 where 𝑃𝑛=∫^𝑎−𝑎∫^∞−∞𝑝𝑛𝑑𝑠𝑑𝑣	𝑝𝑡 where 𝑃𝑡=∫^𝑎−𝑎∫^∞−∞𝑝𝑡𝑑𝑠𝑑𝑣
Stresses at point A(x, y, z)	[𝜎^𝑛]=𝜎^𝑛𝑥𝜎^𝑛𝑦𝜎^𝑛𝑧𝜏^𝑛𝑥𝑦𝜏^𝑛𝑦𝑧𝜏^𝑛𝑥𝑧=∫^𝑎−𝑎[𝜎^𝑛𝑙]𝑑𝑣	[𝜎^𝑡]=𝜎^𝑡𝑥𝜎^𝑡𝑦𝜎^𝑡𝑧𝜏^𝑡𝑥𝑦𝜏^𝑡𝑦𝑧𝜏^𝑡𝑥𝑧=∫^𝑎−𝑎[𝜎^𝑡𝑙]𝑑𝑣
	Its expression is shown in Appendix A.3	Its expression is shown in Appendix A.3
Stresses	[𝜎]=[𝜎^𝑛]+[𝜎^𝑡]
Stress tensor expression	⎡⎢⎢⎣𝜎^𝑥𝜏𝑥𝑦𝜏𝑥𝑧𝜏𝑥𝑦𝜎𝑦𝜏𝑦𝑧𝜏𝑥𝑧𝜏𝑦𝑧𝜎𝑧⎤⎥⎥⎦=⎡⎢⎢⎣𝑞𝑞^𝑛𝑓1(𝑦,𝑧,𝑎,𝑤)𝑞𝑡𝑓4(𝑦,𝑧,𝑎,𝑤)𝑞𝑡𝑓5(𝑦,𝑧,𝑎,𝑤)𝑡𝑞𝑓4(𝑦,𝑧,𝑎,𝑤)𝑞𝑛𝑓2(𝑦,𝑧,𝑎,𝑤)𝑞𝑛𝑓6(𝑦,𝑧,𝑎,𝑤)𝑡𝑓5(𝑦,𝑧,𝑎,𝑤)𝑞𝑛𝑓6(𝑦,𝑧,𝑎,𝑤)𝑞𝑛𝑓3(𝑦,𝑧,𝑎,𝑤)⎤⎥⎥⎦  *