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# (Solved): Background: A number of investigators have modified the basic Taylor Tool Life Equation to evaluate ...

Background: A number of investigators have modified the basic Taylor Tool Life Equation to evaluate the effects of other machining variables such as feed and depth of cut on tool life. A modified tool life equation developed by Bhattacharyya and Ham [1] has been used to predict the expected tool life for both ferrous and non-ferrous materials for a wide range of machining conditions. It can be expressed as:

Where V is cutting speed

T is tool life

f is feed rate

d is depth of cut

a and b are material/cutting condition constants

and C is a constant

Sen and Bhattacharyya performed a series of machining studies on ductile irons where the speed, feed and depth of cut parameters were estimated during turning studies using high speed steel cutting tools. From these studies, two different tool life predictive equations were developed, one for small depths of cut and the other for large depths of cut as follows:

VT.28f.40d.40=324

Where V is cutting speed measured in surface m/min

f is feed rate measured in mm/rev

and d is depth of cut measured in mm

These tool life expressions can also be used to evaluate the influence of expected casting dimensional variability on tool life variations. For turning operations, dimensional variability, from casting to casting or batch to batch, causes direct variations in the actual depth of cut. Oversized castings cause the effective depth of cut during initial rough turning to increase. Similarly, undersized castings will decrease the effective depth of cut during initial rough turning operations. Calculate expected tool life variations during turning based solely on the expected dimensional variation of castings for two different sets of casting dimensional assumptions:

Condition 1: batch-to-bach variation in the nominal diameter of the rough castings prior to machining

Condition 2) a change in the variability of casting diameter for a lot of castings (normally distributed) but no shift in nominal dimensions.

To do these assessments we will be using typical values for the dimensional variability, typical machining depths of cut, and typical cutting conditions (f=0.18 mm/rev and V=115 m/min)

For Condition 1: Estimate the tool life variation due to expected casting dimensional variability when turning a round casting using a nominal turning depth of cut of 1.5 mm. Determine the expected tool life variation during rough turning due to an expected ductile iron casting feature diameter nominal dimensional shift of +/- 0.08 mm. Assume that all of the castings in one batch are oversized by 0.08 mm and all of the castings in the other batch are undersized by 0.08 mm

For Condition 2: Estimate the tool life variation due to expected casting dimensional variability for two batches of castings assuming that the nominal diameter of each batch of castings is the same, but that one batch of castings has more dimensional variability than the other. Assume that both batches of casting have the same nominal dimension but the two batches of casting each have a different +/- 3 sigma dimensional variability: +/- 0.04mm and +/- 0.02 mm. Assume that the dimensional variation for each batch is normally distributed. Will dimensional variability in and of itself cause variations in tool life?