Design for Manufacture. Machine and Process Capability

Transcription

1 Design for Manufacture Machine and Process Capability Design for manufacture (DfM) is anything that informs the designer about any aspect of the manufacture of the product that allows 'wise' decisions to be made." Introduction A design is not realised until it has been made. It is all very good producing a great design on paper but it won t become a product until some type of raw material is converted into a shape. In reality therein lies a problem uncertainties don t exist on paper but they do in real life. In theory a design on paper is perfect but when that design is realised and it is there before you, it is never perfect. Lengths can never be exact, angles are never fully vertical or horizontal, surfaces are never unblemished and perfectly flat. Whether a design is realised by hand or machine, it will contain errors. These are not really errors in the sense of something wrong but deviations from nominal. This is variability and is described by statistics. In order to cope with variability one can use things like tolerances and geometrical tolerances to define limits of features and thus to define manufacture. This goes part of the way to solving the problem but not all the way. One still has to make sure the process or machine one selects is capable of working to the tolerances the designer defines for correct function. This is described by the term machine and process capability. Thus, the fundamental question when selecting a process or machine is: is this process/machine capable of consistently producing parts within the tolerances specified? If the answer is yes one then must then decide what statistical control methodology is to be used to assess the process/machine and thereby to ensure adherence. If the answer is no, then either the process/machine needs to be changed or the required tolerances relaxed or 100% inspection used to eliminate out of range components. In order to use machine capability and answer the above question: is this process/machine capable of consistently producing parts within the tolerances specified? one must first determine what the machine &/or process is capable of. This requires some form of structured study and experimentation. Typically, a study will be as follows. Machine Capability Here the production machine under investigation is tested under controlled conditions to determine the normal variability. There must be no alterations to the machine variables or settings during the study since this would invalidate the outcomes. Any variations of factors external to the machine itself should be minimised, such as material or tooling. Indeed, prior studies should be undertaken to understand how any element within the machine system influences the machine - capability and uncertainty of the measuring equipment and tooling variability like wear and compensation. Process Capability Here the process under investigation is tested to determine the total variability and hence the process stability. The investigation needs to include all parts of the process system and chain people, inputs, machines, tooling, control and measuring equipment. It also needs 1 of 5

2 to take account of variability influences over periods of time relevant to the capability required such as the relevant working hours and industrial disturbances. Procedure for assessing the capability Based on the above, a procedure for assessing capability needs to be defined based on the variability sources which will influence the results. The factors to be considered normally fall under one or other of the following headings: Machine (e.g. degree of wear and choice of tooling); Measurement (e.g. resolution and spread of measuring instrument); Operator (e.g. how experienced and careful he/she is); Material (e.g. variations in surface smoothness and hardness); Environment (e.g. variations in temperature, humidity and voltage); Method (e.g. type of operation). The capability investigation steps are typically as follows. Here I will use an injection moulding machine as an example since this is a convenient system of inputs (plastic, temperature and flow): 1) Understand the part. Select the functional dimension/s or features of the part to be produced against which the capability is to be determined. In the context of a moulding process: is the injection moulded part to be assessed with respect to dimensions or angles or shrinkage or depressions or mould defects? 2) Understand the measuring system. Define the measurement methodology to be used to express the results of the study, then, what actual instruments are to be selected based on this methodology? Define and then undertake a study to determine the results. In the context of a moulding process: what measuring equipment and what measurement system or chain will have the acceptable variability in the context of that required? How does one assess or compensate for draft angles? How will the elastic deflection inherent with contacting plastic surfaces in measurement influence the results, how can such uncertainly be minimised? 3) Understand the raw material or incoming part quality. Define how the input quality of part or raw material influences the measurement outcomes. Define and then undertake a study to determine the results. In the context of a moulding process: what is the variability of the raw plastic granules, their consistency and the influence of things like humidity and cooling rate. 4) Understand the processing system. Determine the influence of the tooling &/or part location, machine rigidity, settings, automatic control, cycle time, vibrations or subsystem factors such as lubrication, coolant or temperature control. Define and then undertake a study to determine the results. In the context of a moulding process: what is the influence of the operating conditions of cycle time, production rate, heating and cooling times, the influence of single or multi- part dies. 5) Understand the operating procedure. Determine how the sequence of operating steps and their duration influence the measurement outcomes. Is there a difference between different operators or shift teams? Define and then undertake a study to determine the results. In the context of a moulding process: investigate timings to see how cycle times, flow rates and heating/cooling affect critical dimensions. 6) Conduct the variability study. When the influence of the above factors has been determined, a machine capability study can be undertaken knowing that one is only assessing the machine itself and not other factors. This study would involve such things 2 of 5

3 6 Sigma as machine number; operation number and description; tooling numbers and machine settings. The results from the above tests are then compared to the tolerance required using a assumed distribution of six standard-deviations (6 sigma), assuming normal probability. This 6-sigma value means that % of the potential values are covered or 3.4 parts per million are in error. Statistical Analysis Before one can assess the capability, the specification limits required for satisfactory function need to be defined. The specification limits define the range of acceptable values of Upper Specification Limit () Lower Specification Limit () Figure 1 6σ distribution within the Upper & Lower Specification Limits a feature within which it will function correctly. For example, assume the diameter of a piston with its associated tolerance is φ80mm h6. The h6 tolerance for a size of 80 is 0um and -19um. Thus, for the piston, this means specification limits of φ80.000mm and φ79.981mm. The φ80.000mm is the upper specification limit () and the φ79.981mm is the lower specification limit (). The difference between the and the is the specification range or tolerance. The and allow the capability to be determined. The simplest and most straightforward indicator of capability is the Process Capability Index (Cp) or its equivalent, the Machine Capability Index (Cm). It is defined as the ratio of the specification range to the process range; using +/- 3σ limits, where σ (sigma) is the standard deviation. This is often described as six-sigma quality. We can express this index as: Cp (or Cm) = ( - )/6σ This ratio expresses the proportion of the range of the distribution falls within the specification limits. This assumes that the mean is centred and the distribution is normal, see figure 1. If the capability index (either Cm or Cp) is 1.0, then a six-sigma distribution equals the specification range (the tolerance) and thus, % of the output of the process will be just within the specification limits (since we used six-sigma) and the process is said to be "just capable". If the index is less than unity then a process is incapable and indeed unreliable because part of the distribution will fall outside the tolerance. Alternatively, if the index is say 2.5, the distribution spread fits 2½ times into the tolerance width. The higher the value of Cp (or Cm), the better. Note that sometimes the inverse of Cp is used as an index and this is termed Cr, (Cr = 1/Cp). Figure 1 shows a 6-Sigma distribution within specification limits where. Of interest is that prior to 1980, the quality of US manufacturing processes was generally Cp = 0.67 (Bhote, 1988). This means that much of US manufacturing was incapable and therefore the quality was unreliable. In contrast, in the early 1980 s, Japanese industry had adopted a standard of Cp=1.33. A comparison of these two values underlines why the Japanese were so successful at this period. However, many high-tech companies 3 of 5

4 3 Sigma Tool wear drift Figure 2 The drift of a 6σ distribution due to (say) tool wear over time. mean Figure 3 An off-set 6-Sigma distribution. Cpk = 0.0 consider even this to be too low. For example, at this time, Minolta used 2.0 as their minimum (Bhote, 1988). However, as useful as Cp (or Cm) is, it does not tell the whole story. What is important is where the distribution falls within the specification limits. Taking machining as an example, it may be that the wearing process of a tool causes a component diameter to increase. Although the distribution may not change the whole distribution will drift towards the upper specification limit (). Assuming the tool continues to wear, a point will be reached where one tail of the 6σ distribution matches the. If the drift continues further and the distribution tail goes past the, the process will start to produce scrap even more scrap components than the 6σ 3.4 parts per million. Drift can be seen as the movement of the mean of the distribution and thus, the assessment of the relationship of the distribution to the and is based on the mean. This is expressed by the indices Cpk (or Cmk) where X is the distribution mean, see figure 3. The Cpk index describes the process capability corrected for position. It is not much use having a high Cp index if the process setting is way off centre in relation to the middle of the tolerance range. Cpk = Cpkl = (Mean - )/3σ Cpk = 1.5 Cpk = 1.0 Cp = 2.0 Cpk = 2.0 OR Cpk = Cpku = ( - Mean)/3σ Figure 4 Various values of Cp and Cpk. or expressing these two equations in one: Cpk = ( nearest specification limit - X )/3σ These two equations will yield two results, one for each of the relationships to the and the. If these two values are identical, the distribution is centred. If these values are not equal and the distribution is symmetrical, then the distribution mean has drifted towards either the or the. Figure 4 shows specification limits and various values of Cp (or Cm) and Cpk (or Cmk). Control limits Control limits are important to machine or process control because they set the limits of the process and alert the system when the behaviour changes. They are not the same as the specification limits which are the functional limits for acceptable performance. Control 4 of 5

5 limits are used along with the distribution mean on a control chart to control the process and provide alerts caused by drift or sudden changes in the process. Specification limits are used to determine, through actual measurements of a component, whether the component is acceptable for function. In quality control parlance, specification limits are concerned with the voice of the customer and control limits are concerned with the voice of the process. The aim of the control chart is to provide the control limits, on a time basis, within which the process is monitored. The aim is to keep the distribution centre appropriately close to the target value. This target value is usually mid-way between the two control limits. The ideal is when the mean of the distribution coincides with the mid-point of the control limits. The control graph is typically a time-based graph plotting the mean against time. Often this is called an X-bar graph where the X-bar means mean. Sample groups of results enable the mean to be determined. How many readings constitute a sample is beyond the scope of this hand-out and is the subject of more detailed statistical definitions, however, typically a sample group would be 3, 4 or 5 sequential readings. When the Cpk value exceeds unity (see figures 3 and 4) some action must be undertaken or the 6σ principle will be sacrificed. Just letting things drift until Cpk = 1 and then acting is somewhat of a panic reaction. More usually, one would want to exert finer control such that the mean is kept closer to the mid-point and a shift in the mean of something like tolerance +15% is preferable. References Bhote KR. World Class Quality Design of Experiments Made Easier. American Management Association Esawi AMK & Ashby MF, Cost-based ranking for manufacturing process selection, Procs 2nd Int Conf Integrated Design & Manufacture in Mechanical Engineering (IDMME 98), Compiegne, France, May 27-29, Vol 4, pp , Open University, 2009, Unit: T172-2, Manufacturing : < accessed: March of 5