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hw6_spring_09_soln

# hw6_spring_09_soln - EML 6267 Assignment#6 Spring 2009...

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Unformatted text preview: EML 6267 Assignment #6 Spring 2009 Please remember to put your name on your assignment. Due: Monday, 3/23/09 1. (20 pts.) Complete problem 5 from chapter 4 of the text. List the K t and K n values for the Fourier approach. Please use plot limits of zero to 25000 rpm and zero to 6 mm. For the Fourier approach, we must determine the corresponding cutting force coefficients: ( ) ( ) 404 . 68 tan 1 tan 1 = = = β n K and 1947 404 . 1 2100 2 = + = t K N/mm 2 . Using these values, the stability lobe diagram was determined using e_4_5.m. The plot in Fig. s.4.5 is very similar to the average tooth angle approach result shown in Fig. s.4.4.d. 0.5 1 1.5 2 2.5 x 10 4 1 2 3 4 5 6 Ω (rpm) b lim (mm) Figure s.4.5: Stability lobe diagram ( j = 0 to 4). 2. (20 pts.) Complete problem 6 from chapter 4 of the text. We determine the constant force axial depth from: ( ) ( ) 8 . 5 42 tan 2 180 60 10 tan 2 = ⋅ = ⋅ = π γ φ p d b mm. 3. (60 pts.) The textbook provides the derivation for the six cutting force coefficients k t , k te , k n , k ne , k a , and k ae when the radial depth of cut is equal to the tool diameter (slotting). Determine expressions for the four coefficients k t , k te , k n , and k ne for arbitrary radial depths of cut (i.e., arbitrary start and exit angles). Perform the following steps: a) (10 pts.) Expressions for the mean x and y direction forces as a function of φ s , φ e , N t , b , f t , and the force model coefficients are provided in Eqs. 4.7.15 and 4.7.16. Organize these equations in slope-intercept form (similar to Eqs. 4.7.18 and 4.7.19). in slope-intercept form (similar to Eqs....
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hw6_spring_09_soln - EML 6267 Assignment#6 Spring 2009...

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