CONCLUSIONS

Cycle Time ReductionTo reduce the cycle time the following possibilities could be explored:•Consider the possibility of using a different material such as nylon to produce the gears. Cooling time and subsequently total cycle time is reduced for this material due to difference s in its thermal properties.•Consider using a water cooled mold for the production of the gears. This will allow the part to cool to a suitable ejection temperature much sooner and cycle time will be reduced as a result. •Increasing the injection rate only slightly reduces the cycle time and would only be appropriate if the increased injection rate yields other positive characteristics.

Strength VariationAlthough the presence of weld lines did not significantly impact the strength of the gears, conditions should be avoided that would make it possible for the weld line to extend completely through an individual tooth. These conditions include low melt temperatures and flow rates. An additional indication that the weld line was not the cause for this variation was that failure typically occurred in the fast injection side of the gear. A Wiebul distribution further confirmed these findings and will be used to recommend operating conditions.

Although it was not possible to related the failure of a single tooth engagement with the failure from a multiple tooth engagement, equations that would predict the failure torque were generated that predicted the failure under each individual loading conditions. The most notable parameters included in these equations are the loading conditions derived from the Lewis Formula, the melt temperature, and the injection flow rate. These equations were very accurate in predicting the failure torques.

Verification TechniquesCommercial Software (MoldFlow)Using the calculated pressures, the reliability of MoldFlow remains questionable. However, these uncertainties are minimal and can easily be attributed to limitations of the software package. Also the program accurately determines cool times and fill times. The program was also useful in determining the impact of moving the sprue to the center of the gear and it indicated that #####.

Tensile TestingThe most significant difference between tensile testing and gear teeth testing was the significance of the weld line. The weld line was greatly decreased the load that the tensile specimen was capable of withstanding. However, as it relates to the impact of injection flow rate and melt temperature, tensile testing does demonstrate similar behaviors to those found in the gear teeth testing.

Expert EvaluationEvaluations made by each one of our experts did not correlate with one another to a significant degree. This indicates that this is at best an imperfect method of part quality verification.

ME 495 Section 8 Tuesday, 2:30 – 5:30 pm

Brad Fetters, Prashanth Gururaja, John Kelly, and Joshua Martin

Design of an Injection Molded Gear Procedure SECTION INSTRUCTORChinar Aphale

PROFESSORWilliam Schultz

University of Michigan

PEAK TORQUE PREDICTION EQUATION

Weld Line and Tooth Location EffectsTooth Location EffectThe tooth location effect was found by testing each gear’s teeth at several locations on the gear. We chose to test each gear once at each of the following locations: near a weld line, on the fast injection side of the gear, and on the slow injection side of the gear. This was done for single tooth tests and multiple tooth tests. Although the effects were small given the error in the results, we determined that the weakest location on the gears was the fast injection side. It was then determined that the data for the fast injection side would be used in the torque prediction equation. The reason for this is that the gear is presumably useless once the teeth in one location have been broken.

Weld Line EffectThe weld lines do not have a significant effect. Table # below shows our peak torque results for single and multiple gear teeth tested at weld lines and places other than at weld lines with error representing a 95% confidence level. The table shows that for the gears, the presence of weld lines does not adversely effect the gear strength. In fact, for the single tests it resulted in a slightly higher average torque than the rest of the gear. This a result is from two factors. First, for many of the tests that we did, the weld lines did not extend all the way to the edge of the gear. Second, the weld lines are oriented parallel with the applied bending stress. In spite of this analysis, we recommend that flow rates lower than 20ccs and temperature below 195 C not be used as there is some indication that this could cause the weld lines to extend completely through the gears.

Melt Temperature, Flow Rate, and Single/Multiple Tooth Test EffectsTo illustrate the effects of temperature, flow rate, and single/multiple tooth tests, we produce Figure # below. The figure shows the average peak torque of the gears for three tested melt temperatures, three tested flow rates, and single and multiple tooth fracture tests. In this figure, the shade of data indicates the flow rate and the type of line and data point indicate the fracture test. The error for each of these data points representing a 95% confidence is 50 lb-in.

Melt Temperature EffectWe determined that melt temperature has a second order curvature effect on the gear strength. This is illustrated in Figure # as each of the curves indicate a similar curvature due to temperature variation. Although there is significant error in the data, the melt temperature has a consistent trend of yielding lower peak torque values at a melt temperature of 205 C. Another observation from this plot is that 195 C has a lower deviation across flow rates. After determining that melt temperature had a second order effect on the peak torque, we proceeded to determine a specific relationship. We did this by plotting the overall average values of peak torque for each temperature setting. We then fit a curve to the data to determine the relationship seen in (#). We will use this relationship to form an overall equation for peak torque that includes other variables.

Peak Torque = 0.356T2 - 144T + 14700 (#)

Flow Rate EffectThis can be seen from Figure #. With the flow rate, the data does not follow any outstanding trends.

Single/Multiple Tooth Test EffectNext, we determined the relationship between single and multiple tooth tests. Overall, multiple tooth test fail at a load of 180 ± 60 lbs while single tooth tests fail at a load of 140 ± 60 lbs. The substantial error shown for these values represents a 95% confidence level. Though several teeth contribute to the strength during the multi tooth test, the added contribution is only a fraction of a single tooth strength. In fact, we found a multiplier relating multiple to single tooth tests that is 1.3 ± 0.4. On average, the multiple tooth tests give a peak torque 1.3 times the peak torque for single tooth test with the same setup. But, the 95% confidence level error of 0.4 shows that in many cases one may find that the single tooth test would yield a higher torque than the multiple tooth. To further investigate the relationship between the single and multiple tooth tests, we created a correlated each of the tests with one another. Interestingly, the single and multiple tooth tests were not highly correlated (correlation coefficient = 0.1). This means that getting a high peak torque for one single or multiple tooth test, does not mean that other tests (single or multiple tooth) will result in a relatively high peak torque.

Obtaining the Torque Prediction Equation

ANALYSIS OF GEAR VERIFICTION TECHNIQUESReliability of Quality ControlCurrent method for quality control involves expert evaluation. Using our team of expert evaluators each of 45 gears were evaluated for clarity, color, smoothness, and appearance under a polariscope. Evaluations of each expert were correlated against those of his/her colleague to determine reliability. Maximum clarity correlation coefficient was 0.32, maximum color correlation coefficient was 0.05, maximum smoothness correlation coefficient was 0.48, and maximum polariscope coefficient was 0.28. Assuming experts have abilities similar to those used in this experiment, expert evaluation is not an ideal method for quality control as demonstrated by lack of correlations in the evaluations.

Dog Bone ApplicabilityThe weld lines are very important when they are oriented perpendicular to the applied stress. This was first proved using an analysis of variance (ANOVA) on all of the tensile specimens. The specimens were separated by those injected from one end and the those injected from both ends. The specimens that were injected from both ends had a weld line near the middle of the part. ANOVA for these specimens yielded an F value much larger than Fcrit (F=210, Fcrit=3.9) meaning that the difference between the two groups is very significant. Similarly, the P value for this was 5E-25 which corresponds to nearly 100% confidence that the weld lines are significant. Also, we found the peak load for those without weld lines is 340 ± 20lb-in while those with weld lines in 290±50lb-in. This shows that the specimens without weld lines provide a higher peak load and more importantly, a lower deviation in the peak load. The error presented in these values represents twice the standard deviation of the samples taken.

MoldFlow ApplicabilityWe were asked to check for the applicability of MoldFlow in your gear manufacturing process. In any fluid flow, pressure is one of the most important properties. Thus, we used the pressure drop in the gates to validate MoldFlow. We found that MoldFlow did not accurately predict pressure drop for each run. However, the errors in MoldFlow’s calculations were consistent for each injection rate. Therefore, we believe that MoldFlow can be applied to your gear production so long that the error can be determined with comparison to simple engineering analysis calculations. Discrepancies in MoldFlow results are due to imperfections in the mesh size and its 2.5-D format instead of 3-D. Also MoldFlow stops calculations when the specified ejection temperature is reached, whereas the injection molder machine ejects the gear after a specified time. After comparing estimates of fill time with MoldFlow’s calculations, we found that MoldFlow can accurately predict fill time. MoldFlow’s calculations are within the uncertainty of our estimates and consistently off from the mean of our calculations for each injection rate. Variation with temperature and material are minimal.   [C2]Can put in recommendations?

Wiebull Approach to Variation of Gear Strength

INJECTION PROCESS BEHAVIORSPrediction of Cool TimeCooling time is governed by the following partial differential equation (pde):

However, a 1-D Assumption can be made because the diameter of the gear is much larger than the thickness and the equation becomes:

Using a Fourier series to construct f(x), the initial temperature distribution, this pde yields the following solution:

Using symmetry, the position of the centerline of the gear is the point x=0. The temperature at different times is given in Figure### when the initial polymer temperature was 140º C and the mold temperature was 40º C. The glass transition temperature (TG) for polystyrene is 105º C. However, it would not be wise to eject the part immediately after this temperature is reached but a lower ejection temperature, 90º C, would eliminate any potential problems. Cooling times for a number of different polymer starting temperatures is given in Table #### for an ejection temperature of 90º C. Even though the polymer melt temperatures were 195, 205, and 210 degrees C, significant heat loss occurred in the sprue and as a result, initial temperatures of 140 and 150 degrees C are more appropriate.

Figure ###: Gear thickness temperature as a function of time and position Table ###: Cooling times for different polymer temperatures

Prediction of Fill TimeWe estimate fill time to be ### (or table with injection rates and fill times?). To do this, we simply divided the volume of the gear by the injection rate, for each injection rate. A number of simplifying assumptions were made which allowed us to calculate the fill time easily. We assumed the flow to be Newtonian, fully developed, steady, isothermal (uniform viscosity) and incompressible These assumptions led us to calculate the fill time using lumped analysis instead of differential analysis, using Navier-Stokes equations. Since the amount or volume of polystyrene in each gear is relatively small and the fill time is small compared to the cool time and overall production time, we feel that our assumptions do not compromise accuracy in our calculations of fill time. Our estimates are validated at least by the computational (Mold Flow) model. Also need to consider the shrinkage in the mold

Injection Pressure DropWe estimated the pressure drops inside the gates of the molding machine to verify that the gears can be made safely at the clamping force the machine is capable of producing. Large enough pressure drops will cause air bubbles, flash, or other disfigurements that would significantly weaken the gear strength, and therefore lead to greater variation in gear strength. We calculated the pressure drop Δp for each injection rate and melt temperature by first assuming that the flow of the polystyrene was steady, incompressible, and Newtonian (viscosity not dependent on strain rate of the flow). This allowed us to use Pouiseille flow equations. We obtained polystyrene viscosity information from MoldFlow as a function of strain rate and temperature (polystyrene is non-Newtonian is real life). We chose viscosities at strain rates of 1000s-1. Considering lower strain rates yield pressures greater than 33 MPa, the maximum pressure that a 30-ton injection molder machine cannot exert (those strain rates do not occur in the polystyrene flow). Since the pressure of the flow entering the gear is very small, the pressure drop is very close to the maximum pressure. We exponentially interpolated between temperatures. The maximum pressure drops (13 MPa for 1000/s strain rate) are also well below the normal high pressure range for injection molding machine (~200MPa) [2] . We found that pressure drop increases with injection rate and decreases with melt temperature. As such, the largest pressure drops occurred at the 80cc and 195C runs. While none of the gears produced at this operating condition were anomalously weak, we are uncertain as to the feasibility of operating outside of these conditions.

REFERENCES

[1] Frank P. Incropera and David P. Dewitt. Introduction to Heat Transfer. 4th edition. 2002

[2] Kalpakjian, Serope, Steven r. Schmid. Manufacturing Engineering and Technology.

4th Edition. Prentice Hall, NJ, 2001.

ACKNOWLEDGEMENTS[1] [2]

ADDITIONAL CONSIDERATIONSSprue Location

Alternate MaterialFrom our simulations with the quality control software, we found that using an alternated material such as nylon for the gears could greatly reduce the cycle time. Although nylon has a much higher glass transition temperature and must be processed at a higher temperature, it cools back to the glass transition temperature quicker. This is a result of its higher thermal conductivity and a smaller temperature difference between its glass transition and processing temperatures. Because of this faster cool time, nylon could be used to reduce the overall cycle time for producing the gears assuming it adequately fulfills the strength requirements.

Cooled MoldThe overall cycle time for the injection molding process could be reduced if the mold was cooled more quickly. One could do this by choosing a mold material that has the highest thermal conductivity among materials suitable for injection molds. We researched possible solutions for this using (((((program name))))) and found that ((((material name)))) is suitable for injection molds and has a very low conductivity of ###. Also, one could consider using an advanced cooling system. Possibilities also include adding a water cooling system to the mold. Of course this would be more expensive to purchase and operate, but the time savings could be tremendous. Furthermore, additional costs would be added in producing the mold since several machining steps would be required to produce a serpentine path through which the water could flow and in the process, remove heat from the mold. However, if the mold could be kept at a temperature of 15º C, the cooling times that could be achieved are listed in Table ### corresponding to the initial temperatures used above. Also the time savings is indicated.

Table ###: Cooling times and time savings for a water cooled mold (15º C)

RESIDUAL STRESS ANALYSISTo allow us to study the residual stresses in the gears, we viewed them with a polariscope. Figure # shows what the gears looked like in the polariscope. The different stress regions are indicated by color bands. The residual stresses are the highest where these color bands are very close together. From observing this photo, one can see that the residual stresses are high specifically near the holes and also in the center of each of the gear teeth. This result is to be expected as stress concentrations occur near holes and other features not found in the the part body.

COST ANALYSISCycle Time ReductionMinimizing cost is a very important concern in any injection molding operation. The primary determinant of cost is the cycle time. Material costs is $0.12 per part but this is a fixed cost. The cost break down per minute can be found in Figure ### where MRO is Maintenance, Repair, and Operations and the cost per minutes is $0.60. Therefore, if the cycle time can be reduced by 10 seconds, which is achievable simply by using a water cooled mold, $0.10 can be saved per part. Over the lifetime of a mold anywhere from 104 to 107 parts can be made with one mold [2], savings could range from $1,000 to $100,000. However, since the conditions in this molding operation are not excessively harsh (lower pressure, temperature, and forces), production runs toward the larger extreme are readily achievable. Since molds typically cost $20,000 to $40,000 and the inclusion of a cooling system would not exceed 20% of this cost, the use of a water cooled mold should be explored.

Figure ###: Injection Molding Cost Breakdown

Molding Machine SelectionAnother possibility would be using a more inexpensive injection molding machine. Using the injection pressure for the calculation, the required clamping force was 10.9 tons. Using this information, it would be inappropriate to use an injection molder that was not capable of withstanding this force. Similarly it would not be necessary to use injection molders capable of withstanding forces of greater than 60 tons which begin at $50,000 [2]. An injection molding machine capable of 30 tons would be more than sufficient for this application and the cost ranges from $25,000 to $45,000 [2].

RECOMMENDATIONS

Cost ReductionsUse the techniques mentioned in the conclusions section to reduce the cycle time of the part. Since the entire process can be broken down into per minute costs, substantial savings can be made by reducing the cycle time by 5 or 10 seconds.

An injection molding machine capable of clamping pressures greater than 15 tons but less the 60 tons should be used for production of these gears. This machine will be less costly to operate but will be able to withstand the pressures that develop during the injection operation.

Reducing Strength VariationUsing the Weibul distributions generated for each of the 9 different molding conditions, an intermediate injection molding temperature and a large injection molding pressure should be used to manufacture the gears are the variations in strength will be lowest under these conditions. The sprue location should not be move to the center of the gear because weld lines will be created on diameters of the gear and consistency of strength will be decreased as a result.

Verification Techniques If the capabilities do not exist to perform verifications using a gear teeth breaker, tensile testing is a reasonable substitute. However, ensure the injection only occurs at one end as weld lines will make the results of such tests unreliable.

The use of the professional molding simulation package, MoldFlow, is valuable, but its limitations must be accounted for. Its usefulness can be found in situations where situations are to be tested that would require the production of new, costly molds, such as moving the sprue to a different location.

Based on the evaluations of our experts, the technique of expert evaluation should no longer be used to validate the injection molded gears. However, if WP’s experts are highly trained and can readily identify what constitutes a successfully produced gear, expert evaluation could be used with care. Other, more reliable, techniques should be used in conjuction with expert evaluaiton nevertheless.

ABSTRACTIn an October 3, 2005 memorandum, Wolverine Plastics (WP) asked us to improve their injection molding process for four inch pitch diameter, polystyrene gears. These improvements include decreasing the cycle time for the process and decreasing the strength variation of the gears. Along with the improvements WP asked that we determine the effects of some of the process parameters. These parameters include the injection flow rate and the melt temperature. WP also suggests that sprue location, weld lines in the parts, and number of engaged teeth during use have an effect on the strength variation. Additionally, WP asked us to test they’re current methods of quality control for applicability. These methods of quality control include standard dog-bone tensile tests and MoldFlow, a simulation software.

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Figure #:Figure #: The 30 Ton Injection Molding Machine

Figure #: Figure #: The important high stress region is along the edge of the gear near the teeth

Initial Temperature (º C)

140 150 195 205 210

Cooling Time (s) 33.8 38.0 53.8 56.8 58.3

Time Savings (s) 10.0 11.0 14.2 14.6 14.8

Initial Temperatur

e (º C)

Cooling Time (s)

140 43.8

150 49.0

195 68.0

205 71.4

210 73.1

Direct Head29%

Indirect Labor21%

Fringe25%

MRO4%

Overhead3%

Material Cost18%