CNC-CMM & Poisson Distribution - Coursework Example

?CNC-CMM & Poisson Distribution 513818 Development and Advances in CN-CMM A CMM or Coordinate Measuring Machine is a type of robot which is capable of moving along the three Cartesian coordinates. A probe attached to it feels the surface of the object along definite points thereby generating dimensions in x, y and z coordinates. This has specific uses in reverse engineering where a well designed model can be reverse engineered to ascertain its dimensions. This is ideal for manufacturing components where the technical backup to produce such a product may be lacking. However, in the field of quality and process control, this could be used to ascertain the number of defective parts or the number of components that are not in line with the required set of standard dimensions. (Spitz Steven Nadav, 1999) A whole set of comprehensive algorithms are used to generate program in the CNC or Computer Numerically Controlled machine so that that the CMM is completely automated and the dimensions obtained are exact after accounting all the tolerances. Source: www.mitutoyo.com, 2006, measuring surface profiles of cars The Inspection probing system Probes are usually classified as contact probes and non-contact probes. Contact probes generate dimensions by physically touching the work piece while non-contact probes do not require physical contact. (Spitz Steven Nadav, 1999) Hard probes are the most simple of probes; the accuracy of which depends on the skill of the operator. The probe is made to have contact with the component and the dimensions generated after compensating for probe diameter. These are used to measure distances between components and diameter and the angles at which bores are located in a work piece. (Genest David, 1999) Source: www.mitutoyo.com, 2006, Inspection probing system Touch trigger probes remove the manual part of scanning. An LED is used to generate a signal when the probe touches the surface of the work piece. An addition to this probe is the incorporation of piezo-sensors which mitigates the minor bending of the stylus when in contact with the work piece because the response is generated early. Similarly strain gauge sensors are capable of producing constant force on the stylus at any contact angle with the work piece. (Genest David, 1999) Source:www.mitutoyo.com, 2006,Stresses & displacement of an I beam of rail track Analog scanning probes are used to map surfaces of crankshafts and turbine blades. These are capable of continuously scanning large surfaces and generate analog output in the forms of contours and images. Irregular and complex shapes can be measured using this probe. This has two systems namely the open loop system and closed loop system. The open loop system senses the change is surface profile and adjusts itself automatically to retain contact with the surface. The open loop system on the other hand is driven along a predefined profile that is already present in the data base. It then generates an output regarding the degree of deviation of the measured profile from the standard piece. (Genest David, 1999) The non contact probes are the most effective way of generating data since contact between the probe and the work piece is done away with thereby reducing measuring errors. These laser probes direct a laser beam on the surface of the work piece. Its position is measured using the triangulation technique onto the probe receptor. Source:www.mitutoyo.com, 2006, Comparing actual and true surfaces Vision probe is another non contact probe which are give quite accurate results of small 2-D parts at very fast pace. This generates a number of measuring points on the image taken which are then compared to a standard work piece product. This gives us an inference about the deviations of the product from the ideal one. (Genest David, 1999) Communication standards The Dimensional Measuring Interface Standard (DMIS) improves the interaction between the computer aided systems like CAD/ CAM and the CMM machine to increase the efficiency and accuracy of the manufacturing process. It therefore provides the following advantages (i) Machines can also be utilized for multiple purposes and the principle of utilizing one type of machine for producing a specific component to reduce customer grievances is done away with. (ii) It also allows for greater flexibility of the CMM inspection software. This is a very important facet because identical parts of a machine are manufactured around the world at different plants. Having this portability of CMM inspection reduces cost. (Mills Keith, 1999) (iii) It never allows the CMM software to become outdated when revisions and up gradations would inevitably occur after every few years. (iv) CMM programmer deficiency that exists due to unavailability of qualified technicians can be mitigated using the DMIS as it allows better integration of CAD and CMM.( Mills Keith, 1999) (v) The DMIS offers a wide range of optical, touch and scanning probes that provides a complete comprehensive programming language which is independent of the method in which data is collected. 2. a. Sampling A sample is defined as the number of items that is taken out from a batch to ascertain the quality of the entire lot. Sampling inspection is a method to determine whether the entire batch should be accepted or rejected on the basis of the number of defective items obtained in the sample. (Grant E.L and R.S Leaverworth, 1998) For some areas of critical importance like parts of the satellite that are orbited into space require a 100% inspection of component parts. This is because of the highly precise nature of the exercise and the capital costs that could be incurred in the event of a failure. Similarly another area where 100% inspection is carried out in these times of terrorism is airport security. An area where 100% inspection is not possible is in assessing the nature of roads built over certain distance of land. The condom industry is another industry where it is impractical to measure the quality factor of each and every condom. (Khanna O.P and Sarup.A, 1998) Similarly machines producing nuts and bolts are qualified on the basis of a select sample of bolts passing the acceptance criteria. The exact nature of the item to be used in the service along with the additional cost that would be incurred to carry out 100% inspection is assessed before embarking on this exercise. It is also ascertained whether the use of sampling technique as opposed to 100% inspection would put the consumer at serious risk and a loss of goodwill to the manufacturer. Some of the advantages of sampling include (Khanna O.P and Sarup.A, 1998) (i) The time and money consumed is less. (ii) It increases the operating efficiency of the worker since continuous repeated checking would create boredom. (iii) Damage if any are restricted to the parts of the sample. (iv) Rejection of an entire batch on the basis of poor quality of a small sample motivates workers to improve the quality of work. b. Type I and Type II errors These errors are likely to occur during the examination of a batch of items for its quality. Type 1 error occurs when a good item is rejected as being defective. In industrial terms it is called ‘a false alarm’. Type II error is one in which a defective item is classified as a good product. This is called a ‘miss’ (Type I and II errors, 2000) True False Test reject H0 Type I error correct Decision accept H0 correct Type II error This can be represented in the form of a table where the ‘true’ items represent a product conforming to preset quality standards while ‘false’ represents items that are non-conformance. c. Sampling scheme and Poisson distribution A sample selected may not always be representative of the entire batch as the sample selected may all have good components while the rest of the batch is defective. The reverse is also true. It is therefore true that sampling involves a certain element of risk to the manufacturer and the purchaser which is plotted on the operating characteristics curve. (Steve H.K, 2003) Problem: Batch size n 50 items Accepted defectives a 3 items Percent of defectives p 10% Solution: Here P=0.1 n=50 a=d=3 The probability of the batch getting accepted is expresses as (Khanna O.P and Sarup.A, 1998) Plotting the operating characteristic curve for values of p ranging from 0 to 0.1 Y axis- Probability of batch getting accepted X axis- Percent defective From the graph it can be seen that the producers risk of having 2 percent defective goods rejected stands at (1-0.4) = 0.6 or 60 %. (Khanna O.P and Sarup.A, 1998) Again from the graph it can be seen that the purchasers risk of having 8 percent defective parts accepted stands at 0.2 or 20%. (Khanna O.P and Sarup.A, 1998) Reference List 1. Grant E.L and R.S Leaverworth, 1998, Statistical quality control, McGraw Hill 2. Mills Keith, 1999, Demystifying DMIS, Available at http://www.qualitydigest.com, [accessed on 5th April 2011] 3. Spitz Steven Nadav, 1999, Dimensional Inspection Planning for coordinate measuring machines, University of southern California. 4. Khanna O.P and Sarup.A, 1998, Industrial Engineering and Management, Dhanpat rai Publications. 5. Genest David, 1999, the Right Probe System Adds, Versatility to CMMs, Brown and Sharpe Manufacturing Company. 6. Type I and II errors, 2000, available at http://www.cliffsnotes.com, accessed on 5th April 2011] 7. Steve H.K, 2003, Studying the effect of the parameters of an attribute acceptance sampling plan on its operating characteristic curve: A visual approach, Journal of Statistics Education 8. Coordinate Measuring machines, 2006, Bulletin 1858, available at http://www.mitutoyo.com, [accessed on 5th April 2011] Read More