Cutting Forces Lab
OBJECTIVE:
To investigate the relationship between the cutting variables: speed, feed, tool material, tool shape, workpiece material, and depth of cut, to the cutting forces produced. The forces that were measured directly were the cutting force, Fc , and the tangential force, Ft . From these and the other variables such as rake angle,, and cutting velocity, Vc, the other forces such as the frictional force between the tool and the chip, F, the normal force between the tool and the chip, N, the shear force, Fs , and the force normal to the shear plane, Fn , will be calculated. Then, all of the velocities and the horsepowers required to make each of the cuts will be calculated.
PROCEDURE:
In part one of the lab, the lathe was set up to make an orthogonal cut on the workpiece which was a piece of aluminum alloy tubing having an outside diameter of 2.4920 inches, an inside diameter of 2.0010 inches, and therefore a mean diameter of 2.246 inches. The thickness of the wall of the tube, which is also the depth of the cut, was 0.491 inches. A tool force dynamometer was mounted in the tool holder for the purpose of measuring the cutting force, Fc , and the tangential force, Ft . By keeping the feed rate constant at 0.0051 inches, and then varying the RPM of the lathe, different chip thickness and therefore different forces were produced.
In part two of the lab, the RPM was held constant while the feed rate was varied. Once again, the lathe was set up to make an orthogonal cut on the same aluminum tube. The tool force dynamometer was again used to measure both the cutting forces and the tangential forces that were produced. From these two measured forces and all of the other pertinent variables, the remaining necessary calculations will then be made.
CALCULATIONS:
By knowing the cutting force, Fc , the tangential force, Ft , and that the rake angle, = 5, the other cutting forces can be calculated using the following relationships for each of the situations that were explored in the lab as follows:
The respected velocities could then be calculated using the following relationships:
The horsepowers that were required for each of the cutting operations were determined using the following relationships:
In order to calculate Hpu and the correction factor, c, so that a comparison can be made against the values that are found in the notes, the following relationship was used:
PRESENTATION OF DATA:
CHIP RPM FEED t2 rc Fc (N) Ft (N) Fs (N) Fn F (N) N (N) # (t1) (N) 1 90 0.0051 0.0125 0.408 452 665 158.3 788.3 701.9 392.32 2 140 0.0051 0.0153 0.333 520 731.5 255.32 860.4 774 454.27 3 215 0.0051 0.016 0.319 639 795 360.56 954.1 847.7 567.28 4 330 0.0051 0.0167 0.305 743 812.3 466.79 997 874 669.38 5 140 0.0012 0.0035 0.343 218 278.3 113.18 334.9 296.2 192.92 6 140 0.0021 0.0068 0.309 347 415 205.8 500.3 443.7 309.51 7 140 0.0045 0.0115 0.319 445 632.4 175.96 753 668.8 388.19 8 140 0.0073 0.0223 0.327 770 1012.6 407.64 1205 1076 678.82 9 140 0.102 0.025 0.408 1346 1332 732.13 1750 1339 1224.8 CHIP RPM FEED t2 rc Vc Vf Vs Phi # (t1) (FT/MIN) (FT/MIN) (FT/MIN) 1 90 0.0051 0.0125 0.408 52.92 21.589 55.385 22.85 2 140 0.0051 0.0153 0.333 82.32 27.439 84.473 18.88 3 215 0.0051 0.016 0.319 126.42 40.302 129.299 18.09 4 330 0.0051 0.0167 0.305 194.04 59.27 197.888 17.36 5 140 0.0012 0.0035 0.343 82.32 28.23 84.667 19.4 6 140 0.0021 0.0068 0.309 82.32 25.415 84.01 17.54 7 140 0.0045 0.0115 0.319 82.32 32.215 85.745 21.98 8 140 0.0073 0.0223 0.327 82.32 26.954 84.358 18.56 9 140 0.102 0.025 0.408 82.32 33.583 86.024 22.85
To obtain the following horsepower values, it was necessary to first convert the appropriate forces from Newtons, N, to pounds force, lbf, so that the units would be correct.
CHIP # Wc (Hp) Ws (Hp) Wf (Hp) 1 0.163 0.0597 0.1032 2 0.2916 0.1469 0.1447 3 0.5503 0.3176 0.2327 4 0.9822 0.6293 0.3529 5 0.1223 0.0653 0.057 6 0.1946 0.1178 0.0768 7 0.2496 0.1028 0.1468 8 0.4318 0.2343 0.1976 9 0.7548 0.429 0.3063
By assuming a value for the feed factor, c, of c = 1 (this is the value that you would use for a feed rate of 0.012 irp), the following values for HPu were calculated:
ASSUME THAT C = 1.0 (from notes for a feed rate of 0.012 ipr) CHIP# Wc HPu Q 1 0.163 0.1025 1.59 2 0.2916 0.1181 2.47 3 0.5503 0.1448 3.8 4 0.9822 0.1685 5.83 5 0.1223 0.2101 0.582 6 0.1946 0.1908 1.02 7 0.2496 0.1145 2.18 8 0.4318 0.122 3.54 9 0.7548 0.1525 4.95
If you then assume a value for the Hpu of Hpu = 0.3 (the value from the notes for Aluminum alloys with BHN 50 - 100), the following values for the feed factor correction, c, were calculated:
ASSUME THAT HPu = 0.3 (from notes the value for Aluminum Alloy) CHIP# Wc 0.3Q C 1 0.163 0.477 0.342 2 0.2916 0.741 0.394 3 0.5503 1.14 0.483 4 0.9822 1.75 0.561 5 0.1223 0.175 0.699 6 0.1946 0.306 0.636 7 0.2496 0.654 0.382 8 0.4318 1.062 0.407 9 0.7548 1.485 0.508
CONCLUSION:
By assuming a value of c = 1, the HPu values that were calculated were all lower than the recommended value that is found in the notes for Aluminum alloys. This tells me that the value that is found in the notes is probably on the high side purposely so that any calculations that are done using it will error on the conservative side.
When the value for HPu that is in the notes for Aluminum alloys is used, the values that are calculated for the feed correction factor, c, are all close to the values that are found in the notes. I believe that the values that were calculated for both c and HPu are close enough to the values found in the notes, allowing for experimental error, to call the experiment a success.
GRAPHS:
Surface Texture
OBJECTIVE:
The objective of this portion of the lab was to investigate the relationship of the cutting variables to the surface texture (roughness) on the workpiece that is produced. The experiment was performed on two different types of material. The two types of specimens were brass and a cold rolled steel.
PROCEDURE:
A one inch diameter bar of each type of material was mounted in the chucks of two lathes. A 0.0015 deep cut was made on each of the two pieces of stock. The RPM on both lathes was held constant, while the feed rate was varied. The surface roughness on each test piece was then measured after the cut was made at each of the respected velocities using a profilometer. The profolimoter had previously been calibrated against a standard. The RPM on the lathe with the steel test specimen was held constant at 255. On the lathe with the brass test specimen, the RPM was held constant at 1000.
GRAPHS:
CONCLUSIONS:
During cutting operations, the tool leaves a spiral profile on the workpiece called the feed mark as it travels across the surface that is being machined. As a direct result of this, the higher the feed rate and the smaller the nose radius of the tool, the more pronounced the feed marks will be. Two ways to combat the effects of this undesirable surface finish would be to decrease the feed rate, or to increase the nose radius of the cutting tool.
In order to make any kind of meaningful comparison on the surface textures between the two materials you would want to have the speed the same on both lathes, and then make passes on both materials at the same feed rates. If this were to be done, then the comparison could be somewhat meaningful. Since we did not do this, what could be said in general is that even though the materials and the speeds were different, the test specimen that was turned at the higher RPM (steel) has the better/smoother surface finish of the two materials. It should also be noted at this time that the lab calls for a comparison to be made between the values of Ra that were recorded during the lab and those that are in the class notes. Since I could not seem to locate the values that were to be compared against in the notes or the text, no comparison was made.
