Process capability improvement of an engine connecting rod machining process

Abstract

Statistical process control is an excellent quality assurance tool to improve thequality of manufacture and ultimately scores on end-customer satisfaction. SPCuses process monitoring charts to record the key quality characteristics (KQCs)of the component in manufacture. This paper elaborates on one such KQC of themanufacturing of a connecting rod of an internal combustion engine. Here thejourney to attain the process potential capability index (C_p) and the process performance capability index (C_pk) values greater than 1.33 is elaborated by identifying the rootcause through quality control tools like the cause-and-effect diagram andexamining each cause one after another. In this paper, thedefine-measure-analyze-improve-control (DMAIC) approach is employed. Thedefinition phase starts with process mapping and identifying the KQC. The nextphase is the measurement phase comprising the cause-and-effect diagram and datacollection of KQC measurements. Then follows the analysis phase where theprocess potential and performance capability indices are calculated, followed bythe analysis of variance (ANOVA) of the mean values. Finally, the processmonitoring charts are used to control the process and prevent any deviations. Byusing this DMAIC approach, standard deviation is reduced from 0.48 to 0.048, theC_p values from 0.12 to 1.72, and the C_pk values from 0.12 to 1.37, respectively.

Introduction

One of the major manufacturing processes in engine manufacturing is that ofconnecting rod manufacturing. This paper implements thedefine-measure-analyze-improve-control (DMAIC) approach to improve the capability ofconnecting rod manufacturing process by reducing the thickness variations from anominal value.

Process mapping and identifying key quality characteristics (KQCs) is carried out inthe ‘definition phase’, while estimation of process capability indicesis carried out in the ‘measure phase’. The one-way analysis of variance(ANOVA) method of investigation to test for the differences between themanufacturing data is employed in the ‘analysis phase’. Finally, theprocess monitoring chart (PMC) for the thrust face thickness is employed in the‘improve and control phase’.

Statistical process control studies form the basic tool for obtaining the requiredprocess capability confidence levels. The various process capability indices aredefined as follows:

$$C_{\mathrm{P}}=\frac{\mathrm{USL}-\mathrm{LSL}}{6\sigma }$$

(1)

$$C_{\mathrm{PKU}}=\frac{\mathrm{USL}-\mathrm{\mu }}{3\sigma }$$

(2)

$$C_{\mathrm{PKL}}=\frac{\mathrm{\mu }-\mathrm{LSL}}{3\sigma }$$

(3)

$$C_{\mathrm{PK}}=min\left\{\frac{\mathrm{USL}-\mathrm{\mu }}{3\sigma },\frac{\mathrm{\mu }-\mathrm{LSL}}{3\sigma }\right\}$$

(4)

where USL and LSL are the upper and lower specification limits,μ = process mean, andσ = standard deviation.

The term C_p denotes the process potential capability index, and similarly, the termC_pk denotes the process performance capability index. C_p gives an indication of the dispersion of the product dimensional valueswithin the specified tolerance zone during the manufacturing process. Similarly, theindex C_pk denotes for the centering of the manufacturing process with respect tothe mean of the specified dimensional tolerance zone of the product. C_pk gives us an idea on whether the manufacturing process is performing atthe middle of the tolerance zone or nearer the upper or lower tolerance limits. Ifthe manufacturing process is nearer the lower limit, then the process performancecapability index is given by C_pkl, and if the manufacturing process is nearer the upper limit, then theprocess performance capability index is given by C_pku. As a measure of precautionary safety, the minimum value between thetwo is taken as the value of C_pk.

Literature survey

The literature survey of process capability improvements using the DMAIC approachis discussed in this section. Schilling (1994) emphasizedhow process control is better than the traditional sampling techniques. Duringthe same era, Locke (1994), in his paper titled‘Statistical measurement control,’ emphasized the importance ofprocess charts, cause-and-effect considerations, and control charting. Afterprimitive studies on statistical quality control, Lin (2004) had shed some light on process capability indices for normaldistribution. Tong et al. (2004) suggested that a DMAICapproach is useful for printed circuit board quality improvement. They alsoproved how design of experiments is one of the core statistical tools forsix-sigma improvement. Subsequently, Li et al. (2008) onceagain proved the importance of DMAIC approach to improve the capability ofsurface mount technology in a solder printing process. Hwang (2006) discussed the DMAIC phases in detail with application tomanufacturing execution system. Gentili et al. (2006)applied the DMAIC process to a mechanical manufacturing process line, whichmanufactures both professional and simple kitchen knives. Sahay et al. (2011) once again brought the DMAIC approach into use toanalyze the manufacturing lines of a brake lever at a Connecticut automotivecomponent manufacturing company. Singh (2011)investigated the process capability of polyjet printing for plastic components.In his observation, he traveled the improvement journey of the process ofcritical dimensions and their C_pk value attainment greater than 1.33, which is considered to be anindustrial benchmark. In recent studies conducted by Lin et al. (2013), they focused on turbine engine blade inspection as it is akey aspect of engine quality. They elaborated on the accurate yield assessmentof processes with multiple characteristics like the turbine blade manufacturingprocess. Kumaravadivel and Natarajan (2013) dealt with theapplication of the six-sigma methodology to the flywheel casting process. Theprimary problem solving tools used were the process map, cause-and-effectmatrix, and failure modes and effects analysis (FMEA). Sharma et al. (2013a), b in their papers adoptedthe DMAIC approach to solve the bolt hole center distance and crankpin borehoning operations of the connecting rod manufacturing process. Chen et al.(2013) discussed the application of ANOVA methodologyto find significant parameters that affect the part's quality indices withrespect to plastic injection molding.

A careful study from the above literature reveals that the DMAIC approach is thebest methodology for problem solving tools to improve the manufacturing processcapability levels. Hence, this paper focuses on the application of DMAICapproach for process capability improvement of the crankpin bore honingoperation of an engine connecting rod manufacturing process.

Definition phase

The definition phase starts with the correct mapping of the machining processflow of the connecting rod.

Process mapping

The process flow chart for the machining line of the connecting rod machiningcell consisted of the following machining operation sequence shown inFigure 1. Table 1describes the machining operations of the connecting rod manufacturing cell.

Figure 1

Process flow chart. Refer to Table 1for the corresponding descriptions of the operations.

Table 1 Machining operations of the connecting rod manufacturing cell

Identifying KQCs

The acceptable thrust face thickness variation of the connecting rod forgings waslimited from 0.5 mm to a maximum of 1 mm. The forgings from thesetolerance limits resulted in a thrust face ‘unclean’ problem andwere subsequently rejected. This caused costly repair and rework. Hence, in thisregard, this research aims at improving the connecting rod manufacturing processby reducing the thrust face thickness variations early in the stages of themachining process line so that these variations are not carried to thesubsequent machining operations down the manufacturing line. Hence, thrust facethickness was of the main concern and identified as a KQC, whose value is equalto 27.000^{(+0.500/0.000)} mm. Figure 2depicts a diagrammatic view of this key process characteristic (KQC).

Figure 2

Thrust face thickness.

Measurement phase

In this phase, the thrust face thickness data of 30 nominal consecutive readingsis collected and plotted on the process monitoring chart. This data collectionwas performed in four iterations. In each iteration, the data set of thrust facewidth measurement readings is taken and analyzed for C_p and C_pk values and followed by the suitable corrective action. Thecorrective action was decided based on the cause-and-effect diagram. After thecorrective action was implemented, the next iteration was performed. Thisprocedure was continued until the C_p and C_pk values are greater than or equal to 1.33, i.e., up to4σ quality level as decided by the management of the enginemanufacturing plant.

Cause-and-effect diagram

The key process characteristic identified was the thrust face thickness which isequal to 27.000^{(+0.500/0.000)} mm whose machining tolerance zone isequal to 0.500 mm. The C_p value, i.e., the process potential capability index, {C_p = (USL − LSL)/6σ}, wasnominally equal to 0.2, which was far below the acceptance level limit greaterthan 1.33 for the above KQC. The first part of the measurement phaseinvestigation was to track down and differentiate the common causes and specialcauses involved. For doing so, the cause-and-effect diagram was employed, asshown in Figure 3.

Figure 3

Cause-and-effect diagram showing the variables affecting the thrustface thickness.

Machine setup

The machine employed was a vertical grinding machine which consisted ofin-process sensors which sensed the amount of material removed during thegrinding process. Figure 4 shows a picture of themachine loading and unloading platform.

Figure 4

Machine loading and unloading platforms.

Process failure modes and effects analysis

A FMEA sheet for thrust face thickness is shown in Table 2. From the causes enumerated in the cause-and-effect diagram, thefailure modes and effects analysis was performed keeping in view the KPC understudy. The risk priority numbers which were above 100 (as per the decision ofthe management) were considered to be the criteria for implementing thecorrective action. It can be noticed that the highest risk priority number (RPN)is for in-process sensing gauge malfunction, followed by improper grinding wheeldressing and worn-out fixture rest pads. Hence, to mitigate these causes, anecessary action plan was devised. After performing the necessary action, thepotential process FMEA was once again performed, and the risk priority numberswere recalculated until they attained a RPN below the 100 level mark.

Table 2 Process failure modes and effects analysis sheet

Data collection

Data collection of the key process characteristic was performed for 32consecutive machined components. Data collection was performed in fouriterations spanning a period of 3 weeks, i.e., about 2,500 consecutivecomponents. The data is tabulated in Table 3. Thedata in Table 3 was plotted on the process monitoringchart with the number of components in the x-axis and componentdimension on the y-axis and is shown in Figure 5.

Figure 5

Process monitoring charts.

Table 3 Measured dimensions in tabular form

Analysis phase

The analysis phase comprises performing the calculations for the C_p and C_pk values across each iteration. This was followed by one-way ANOVAmethod of investigation to test for the differences between the four iterationsof the data sets.

Calculations of C_p and C_pk

The calculations of C_p and C_pk are tabulated in Table 4. From theprocess monitoring charts and the calculations in Table 4, the following sections are the analysis done for the data set ofeach iteration.

Table 4 Calculations of C _p and C _pk

Iteration 1

The first set of the statistical process capability study is composed of theraw data of the KQC, which depicted the transparent picture of the state ofthe existing problem. Continuous set of readings of the connecting rod aftergrinding operation no. 10 were captured with the help of a dial gauge on ametrological surface plate. Hence, it is seen here in the first iteration ofstatistical process control (SPC) studies that the process is not capable,and the C_p and C_pk values of the characteristic under study are 0.20 and 0.12,which are far less than that for process to be capable, i.e., 1.33. Hence,the next set of data is captured after performing measurement systemanalysis (MSA) studies in iteration 2 of SPC studies for the KPC understudy.

Iteration 2

In this iteration, the data is collected after gauge repeatability andreproducibility (GR&R) was performed for the dial gauge and calibrationof the dial gauge as a part of the measurement system analysis procedure.From the set of data in Table 3, it is seen thatthere is a marginal increase of C_p from 0.20 to 0.28 and C_pk from 0.12 to 0.21. This marginal increase is a positive sign,but still, the process is not capable as both C_p and C_pk are far less than the desired value of 1.33. This calls foranother iteration.

Iteration 3

In this iteration, data is collected after machine preventive maintenanceschedule completion and replacement of grinding shoes of the machine as wellas rest pads of the fixture. From the set of data in Table 4, it is seen that there is a noticeable increase ofC_p from 0.120 to 1.23 and C_pk from 0.21 to 0.99. This increase is a positive sign, butstill, the process is not capable as both C_p and C_pk are far less than the desired value of 1.33. This calls foranother iteration, i.e., iteration 4.

Iteration 4

This iteration tackles the ‘tool wear compensation’ cause. It isa common phenomenon that as any machining operation progresses, there is acalculated wear of the cutting tool responsible for the machining operation.The grinding operation here is no such exception. Hence, here the data wascollected after presetting the value for the tool wear compensation knob at15 μm on the control panel of the machine. This means that afterevery wear out of 15 μm of the grinding shoes, the grinding wheelsurface is lowered by 15 μm in order to compensate for the toolwear so that the dimensions of the product being machined will remainunchanged.

One-way ANOVA method

The one-way ANOVA method of investigation is adopted to test for the differencesbetween the four iterations of data collected.

Procedure describing one-way ANOVA

In general, one-way ANOVA technique is used to study the effect ofk(>2) levels of a single factor. A factor is a characteristicunder consideration thought to influence the measured observations, andlevel is a value of the factor.

To determine if different levels of the factor affect measured observationsdifferently, the following hypotheses are to be tested:

$$H_0:{\mu }_i=\mu \mathrm{all}i=1,2,3,4$$

H₁: μ _i  ≠ μ for somei = 1, 2, 3, 4, where μ _i is the population mean for level i and μ isthe overall grand mean of all levels.

Here we have four levels (i.e., four iterations), and each level consisted of32 measurement readings of thrust face thickness of the connecting rod. Thesum, sum of squares, mean, and variance for each iteration are tabulated inTable 5.

Table 5 Mean and variance of all four iterations

If x _ij denotes the data from the i th level and j thobservation, then the overall or grand mean is given by

$$\mathrm{\mu }={\displaystyle \sum _{i=\mathrm{l}}^4{\displaystyle \sum _{j=1}^{32}\frac{x_{\mathit{ij}}}{N}}}$$

(5)

where N is the total sample size of all four iterations, i.e.,32 × 4 = 128. Hence, from Equation 5, weget μ = 27.233.

The sum of squared deviations about the grand mean across all Nobservations is given by

$${\mathrm{SST}}_T={\displaystyle \sum _{i=1}^4{\displaystyle \sum _{j=1}^{32}{\left(x_{\mathit{ij}}-\mathrm{\mu }\right)}^2}}$$

(6)

The sum of squared deviations for each level mean about the grand mean isgiven by

$${\mathrm{SST}}_L={\displaystyle \sum _{i=1}^{4}4\times {\left({\mathrm{\mu }}_i-\mathrm{\mu }\right)}^2}$$

(7)

The sum of squared deviations for all observations within each level fromthat level mean summed across all levels is given by

$${\mathrm{SST}}_E={\displaystyle \sum _{i=1}^4{\displaystyle \sum _{j=1}^{32}{\left(x_{\mathit{ij}}-{\mathrm{\mu }}_i\right)}^2}}$$

(8)

From Equations 6, 7, and 8, the values of SST _T , SST _G , and SST _E obtained are 8.694, 0.55289, and 8.084, respectively.

On dividing SST _T , SST _L , and SST _E by their associated degrees of freedom (df), we get the meanof squared deviations, respectively. Hence, the mean of squared deviationsbetween levels is given by

$${\mathrm{MST}}_L=\frac{{\mathrm{SST}}_L}{d{f}_L}=\frac{0.55289}{\left(4-1\right)}=0.184$$

(9)

The mean of squared deviations within levels is given by

$${\mathrm{MST}}_E=\frac{{\mathrm{SST}}_E}{d{f}_E}=\frac{2.94}{\left(128-4\right)}=0.065$$

(10)

Finally, the F statistic is given by the following formula:

$$F_{\mathrm{statistic}}=\frac{{\mathrm{MST}}_L}{{\mathrm{MST}}_E}=\frac{0.98}{0.065}=15.07$$

(11)

On summarizing all the above values in tabular form, the ANOVA table isobtained as shown in Table 6.

Table 6 ANOVA table

An α value of 0.05 is typically used, corresponding to 95%confidence levels. If α is defined to be equal to 0.05, thenthe critical value for the rejection region is F_{critical (α, K − 1, N-K)} and is obtained to be 2.677. Thus,

$$F_{\mathrm{critical}}=2.677$$

(12)

From Equations 10 and 11, it is seen that

$$F_{\mathrm{statistic}}>F_{\mathrm{critical}}$$

(13)

Therefore, the decision will be to reject the null hypothesis. If thedecision from the one-way analysis of variance is to reject the nullhypothesis, then it indicates that at least one of the means(μ _i ) is different from the other remaining means. In order to figure outwhere this difference lies, a post hoc ANOVA test is required.

Post hoc ANOVA test

Since here the sample sizes are the same, we go for Tukey's test forconducting the post hoc ANOVA test. In Tukey's test, the honestlysignificant difference (HSD) is calculated as

$$\mathrm{HSD}=q\sqrt{\frac{{\mathrm{MST}}_E}{n}}=3.63\sqrt{\frac{0.065}{32}}=0.16$$

(14)

where q is the studentized range statistic which is equal to a valueof 3.63, for a degree of freedom of 124 and k = 4. Thedifference between the individual mean values of the four iteration levelscan be summarized in a tabular form as shown in Table 7.

Table 7 Differences of means between any two iterations

In Table 7, the absolute difference is of concern,and so the negative signs are to be ignored. Also in Table 7, it is seen that the difference of μ₁ − μ₄ = 0.16, which is equal with that of the HSD inEquation 14. Hence, it is concluded that the mean set of data betweeniteration 1 and iteration 4 is statistically significant when compared tothe rest. Thus, it is concluded that among all the different causesenumerated in the cause-and-effect diagram, the most influencing cause isthe tool wear compensation correction for the measurement data of iteration4.

Improve and control phase

In this phase, the process monitoring charts are regularly employed formonitoring of the thrust face thickness of the connecting rod. In addition,gauge calibration is done periodically as a part of measurement system analysis,and properly calibrated gauges are used at the work place.

Result and discussion

As part of standardizing the process, the following activities were carried out:

• 1. The tool wear compensation knob which does not have any graduations was calibrated, and graduations were engraved at a 90° interval

• 2. Proper fixture maintenance and machine maintenance schedule were established, and regular checks were included in the check lists

• 3. After every 12,000 components, the grinding shoes need to be replaced

• 4. Coolant recirculation pressure was set at a value of around 15 kg of force

After incorporating the above actions in the manufacturing control plan, the sameprocedure can be horizontally deployed for solving of pragmatic problems of similarnature.

Conclusion

SPC studies were found to be useful for eliminating the special cause of errors,streamlining the process, and making the process a capable manufacturing process byimproving the C_p and C_pk values of the key quality characteristic under study. Thecause-and-effect diagram formed an important scientific tool for enlisting thecauses behind the poor performance of the process. On adapting the DMAIC approach,the estimated standard deviation ‘σ’ of the thrust facethickness is reduced from 0.408 to 0.048, while the process performance capabilityindex C_pk is enhanced from 0.12 to 1.37.

The C_p/C_pk values after performing the few iterations of data collection weregreater than 1.33, and hence the process was declared as a capable process. Afterperforming the root cause analysis, the major root cause, confirmed by the one-wayANOVA technique, was the improper setting of the tool wear compensation knobfollowed by the replacement of worn-out fixture rest pads for the thrust facegrinding KPC. Hence, the one-way ANOVA technique was employed successfully foridentification of the root cause liable for the low process capability.