An Integrated Approach towards Weight Estimation

An Integrated Approach towards Weight Estimation from CAD Model with Tolerances Sukrit Mittal, Abinash Kumar Swain, SN Sreenivas Rao Department of Mechanical and Industrial Engineering, IIT Roorkee Roorkee, Uttarakhand, 247667 [email protected] [email protected]

Aeronautical Development Agency Bangalore, India [email protected]

Abstract — This paper aims to involve the tolerance information of a part in estimating the weight of a part/product in nominal, Maximum Material Condition (MMC) and Least Material Condition (LMC). The proposition is to know the geometric variations in the design phase itself, so that the maximum weight of the final product or assembly can be controlled before the manufacturing begins. It expands to the development of a methodology enumerating various steps involved in calculating the weight of the final product. The research work proposed here is perhaps the first attempt in the literature to compute the MMC and LMC of the 3D CAD component. This development gets more interesting when it comes to aerospace industry where final weight of the machine is a major concern, as increase in weight leads to lesser fuel economy and poor performance. The solution inculcates principles of quality engineering. The proposed idea has been presented and further work has been identified. Keywords – Weight Estimation, Tolerance Analysis, Qualitative Analysis, Geometric Modelling.

1. INTRODUCTION In CAD drawing and 3D model, the designer uses nominal dimension of parts and assembly to communicate with the shop floor [1]. There are many problems in designing of a product and manufacturing it at industrial scale. One of the factors to this situation may be the differences in present capabilities of designing and manufacturing due to which the shape of the product cannot be produced exactly as designed [2]. Hence, the concept of tolerances plays a crucial role [3]. The computing power and algorithms developed allow us to design and analyze any product from a small pen to a gigantic ship but some variations come into picture when manufacturing is concerned. The standards of dimensioning and tolerancing form the foundation for the allowable variations [4]. There are many factors which are responsible for the variations in the available design and the corresponding component that the manufacturer produced. These factors can’t be removed but can be minimized with proper selection of tolerance band without sacrificing the quality of the components. The designer must prescribe certain range of variation that still guarantees fit, function and form to the actual

or manufactured part. Moreover, the designers (person responsible for quality check) will be able to see the expected variations in the manufactured product right at the time when the component is manufactured and take quick decisions to accept or reject the component. In aircraft industry, weight of the aircraft plays a major role in the performance of the aircraft. Moreover, a typical medium size aircraft contains millions of parts. For example, if each part contribute one gram extra weight to the total weight of the aircraft due to the manufacturing variation, it is 1000 kg. If we assume 20% of the component is responsible for this increase of the weight, it comes around 200 kg. For a fighter aircraft, the increment of 200 kg is a big number, which results in high energy consumption and losses during the flight [5]. Moreover most of the aircraft industry experiencing this weight increment at the assembly stage of the product, without knowing the cause. Due to these issues, weight estimation becomes a major concern in aircraft development [25] at the early stages of product development. It is crucial to know which parts are responsible out of million parts for this weight increment of the aircraft from the calculated nominal computed weight. These reasons motivate the development of algorithms and tools to automatically identify the maximum and minimum weights i.e., Maximum Material Condition (MMC) & Least Material Condition (LMC) within a specified tolerance band of a CAD component at the design stage. The first step of the process is the main design stage where different CAD software, analysis tools and optimization techniques are used to define, design and analyze the product. The dimensions considered are nominal dimensions, through which the weight of the product is estimated using some algorithm. But, the tolerances involved with various parts of the assembly tend to change the final weight. In reality, variations are inherited in the system when it comes to mass manufacturing. Thus, it becomes necessary to define associated tolerances with various parts of the product depending upon their usefulness [6]. The allocation of

plus/minus limits on dimensions started to appear in early 1900s, since then tolerance has been one of the most important considerations in product realization processes [8]. Taking these tolerances into account in the design phase itself can enhance the designing process. The designers will be able to see the expected variations in the manufactured product right at the time when the product is designed. Assembling the product virtually will make the designer able to visualize the expected weight increase & other changes and thus, necessary precautions can be inhibited in the design itself, so as to minimize the variations in the output product. At present, this visualization for changes and weight increment comes into picture after manufacturing during inspection (Refer to Fig. 1) when reverting back the whole process becomes difficult, especially the loss of money, material and time.

examples. Then there is discussion on validation and applications of the system followed by the conclusion with the scope of further development. 2. PRIOR WORK Tolerance computation involves the methods to analyze the tolerances for the worst case scenario (MMC & LMC conditions) or estimation of statistical deviation from the designed product. This topic has been reviewed in [7,8,9]. A significant part of tolerance modelling is the representation of tolerances appropriately, so that variation in the tolerances can be obtained and processed effectively. The worst case scenario models the tolerances, such that the variation should be at bound point of dimensions [9,10]. The statistical approaches towards analyzing the tolerances obtain the orientation and size of tolerances from the models and also consider their distribution over the geometry, such that there is a statistical distribution model corresponding to each tolerance & dimension [12,13,14,15]. Though, the further computation part still remains very complicated. In professional works, the data obtained for tolerance specification is the nominal dimensional data (default product geometry). This data can be easily extracted from a CAD modeler using different algorithms, though only few researches report a truly effective CAD integration. The tolerance data should involve detailed part design which should be known in early design stage [16,17]. This is a key point in the proposed method which aims to compute the results from different geometries possible within the specified tolerance (acceptance) limits. Several techniques can be employed for tolerance dimensioning and analysis at the design stage, but mostly cover the statistical analysis in real time computation.

Fig 1: Role of tolerances in manufacturing The objective of tolerance analysis is to check the extent and nature of the variation of an analyzed dimension or geometric feature of interest [9]. The processing of a 3D model for such analysis consists of a two phases. First one is analysis of the design and the possible associated tolerances with different dimensions in the design, so as to give the output in terms of minimum and maximum weight and dimensions of the CAD models, which will correspond to the LMC and MMC condition for the designed product. Secondly, to give the variation of expected weight between the minimum and the maximum weight. This will make the user able to relate between the design variations and the manufacturing variations, and thus the improvements can be incorporated in the design itself. “The quality should be inculcated in the design, itself.” This paper is organized as follows. The next section enumerates the prior work done in weight estimation. Then there is an overview followed by the implementation details and a few

Statistical approach have been very familiar and interesting when it comes to tolerance analysis. The prior part in this approach is easy and for the secondary part, several techniques have been developed for tolerance allocation and computation based on root square method (RSS) [18] and optimization of tolerances [19,20,21]. However, the conventional statistical techniques tend to employ the normal distribution as the primary base which fails to predict the assembly of parts with non-normal distributions. Tsai and Quo proposed a novel method based on statistical moments [15]. They also identified that it is too pessimistic to consider worst case analysis models as it assumes that the dimensions of all components can occur at their extremes simultaneously. With the advancement of computers and CAD/CAM techniques in 1970s, the tolerance and related issues have continuously drawn attention of many researchers due to which large number of articles have been published over these years [8]. When it comes to qualitative approach in industrial applications, statistical variations related to tolerances and dimensions became a major concern and took to another new

level. There have been some recent studies that propose new methods of modelling tolerances and applications that have raised interest. A representative work that describes a systematic solution for tolerance computation inculcating geometric characteristics on both statistical and worst case models [22]. Beaucaire et al. [23] defines an approach towards predicting quality for the designer by tolerance analysis. Qureshi et al. [13] proposed a mathematical formulation of the tolerance analysis integrating quantifier so that a single description of the geometrical requirement can be obtained. There has been massive research, when it comes to statistical tolerance analysis and worst case model estimation which utters its need in the present times. Several techniques have been developed which use the tolerance data, alignment, dimensions, distributions and other model & knowledge based information to estimate the required output. Most of the techniques developed either tend to discuss the worst case analysis or statistical techniques. 3D geometrical variation is a key component in product realization which has not been developed as extensively as work has been done in statistical analysis and worst case estimation (bound points). 3. OVERVIEW Primarily, our approach refers to the analyses of toleranced dimensions of two types namely (i) linear and (ii) radial. The linear dimension is allocated between two fixed points or lines (parallel), but generally along with an edge whereas the radial dimension is allocated to any curve present in the 3D space defining location of proper center associated with it. The method aims to parse through the STEP file (AP214) of the CAD model which contains all the relevant information regarding the model. The program extracts the coordinates of vertices, endpoints of edges, center of different arcs and the nominal dimensions from the STEP file. The tolerance information is available separately. To limit the computations to a certain level, the system takes discrete values of a dimension in the tolerance range defined in the model and enumerate all the possible combinations of the dimensions which are possible within the acceptance limit of the part or product. For each possible combination, the system generates a unique geometry according to the interpretation method designed which processes the dimensional information to transform nominal (default) geometry into the geometry corresponding to that combination. The user can also prioritize the dimensions by setting a preference order of different dimensions of the model. Its effect on the computation is explained later in the article. Taking the combinations one by one, a physical geometry is generated (different from the default geometry) which will be subjected to a volume computation algorithm (preferably by box counting) and saves the volume data acquired. By multiplying from the density (which will be constant for a single part), the weight of the component can be obtained. The acquired possible weights will be subjected to a sort in ascending order which will

give the results as the maximum and minimum weights for product. In addition, the system plots this data with the number of occurrences to obtain a bell-shaped curve (normal distribution). The designed model and the actual product will fall somewhere in between the extremities defined after the sorting of weights. The maximum weight will correspond to a unique geometry which will be representing the physical shape of the product in the worst case scenario. This opens the scope for the quality engineer to predict the actual manufacturing scenario in the design phase itself. The basic layout takes the idea of virtual manufacturing of the product (with pre-assigned tolerances). The results from the inspection of manufactured population is then stacked up to give specified results such as weight in MMC, LMC, the statistical distribution and large amount of other parameters that can be deduced using these basic design parameters. The proposed algorithm/solution considers the analysis of a single part, whereas in real scenario, the product consists of assemblies involving multiple parts ranging from a few to millions. To analyze the weights at that stage, each part can be processed individually, and from the weight data, the limits, mean value and standard deviation can be acquired. This data can be stacked up to formulate similar parameters at the subassembly and full-assembly level which opens a new scope of work taking this part analysis to assembly level. 4. IMPLEMENTATION DETAILS This section refers to the journey from the thought process to the algorithm development. Currently, the algorithm is in development stage, but the methodology has been identified and theoretical base is included to validate the optimality of the solution. The steps involved in the processing are shown in Figure 2 which is further discussed in detail later in this section. 4.1 Extraction & stacking of data After the parsing, i.e., the co-ordinates of vertices, edge information is extracted and stored in two different structures Struct1 & Struct2 respectively. In Struct2, the data addressing a particular edge will be grouped together containing the following information. • Edge number • Nominal length • Endpoints (endpoint1 & endpoint2) • Tolerances (upper & lower limit) The edge number is the priority number as mentioned in the framework. The system will ask for manual input, in case of

disagreement, the numbers will be assigned randomly and accordingly the information will be processed.

1. Input: The CAD file and the tolerance information. 2. Extract the coordinate, edge and tolerance information. 3. Ask the user to input variable ‘y’. 4. Calculate and enlist the various possible combinations. 5. for each combination : model the virtual geometry. 6. for each virtual geometry : compute the volume 7. for each geometry: Calculate the weight = (Volume) X (Input Density). 8. Sort the different Weight values in ascending order. 9. Pick the first, last and mean value after sorting. 10. Plot the normal distribution curve for the given problem. Fig 2: Steps for algorithm

• Taking this new geometry as input, follow the same procedure for edge number 2 and so on till the last edge is modified. • The volume computing algorithm is applied to the geometry obtained after this procedure and the volume obtained is stored in another structure say Struct3 with the corresponding combination number. 4.3 Sorting and getting required results The volumes (or weights) acquired above are subjected to bubble sort algorithm for increasing order. From here, the minimum and maximum weights are obtained from the first value and last value of the sorting results. From the numbering of combinations, the geometry corresponding to the maximum weight (MMC) and minimum weight (LMC) can be obtained covering Steps 8 & 9 as mentioned in Fig 2. More over the system will store these two geometries separately, so that they can be viewed whenever required. They can also be used to compare it to the designed geometry and identifying whether such geometry will be acceptable or not, or say whether they should tighten their bands of tolerances. In simple words, the outputs can be used for verification and validation of the designed geometry. 4.4 Qualitative Analysis

4.2 Computing the combinations This part refers to steps 3 to 7 mentioned in Steps for algorithm in Fig 2. Let’s say ‘n’ is the number of edges whose information is stored in Struct2. Another variable ‘y’ is asked from the user as manual input which correspond to the number of discrete points that will be taken corresponding to a particular dimension in between its tolerance limits. By simple probability theory, the number of combinations will be (yn). More is the value of y, more is the computing power required. A list of all the combinations is prepared with each combination containing the information regarding every dimension in the order of their priority number. Let’s say, the system is computing for ith combination. The steps involved in the geometrical modelling are: •

Taking initial geometry as default nominal.

• Consider the edge numbered as 1 and compute its length in this geometry, say L1. • Compare it with the dimension stored in the first place in ith combination (L2) and compute the difference. • Keeping the mid-point and alignment of the edge as same, shift the endpoint1 & endpoint2 such that they are displaced equally and the distance between them becomes L2. • Fix these two coordinates, i.e., they will not change during processing of this combination.

When we plot the discrete data of weights with bands of number of occurrences and join them by a smooth curve, a bellshaped curve is obtained (normal distribution). This curve is analyzed to obtain the extreme data, probability of the product to be acceptable and standard deviation from the mean value. Here comes the effect of the discrete values (y). More the number of combinations, more the values of weights acquired, thus smoother is the curve obtained. Also, the mean value may come out to be more accurate than the one with lesser combinations, but the difference won’t be much. Hence, we can optimize the minimum value of ‘y’ required for providing the best results. This curve can further be analyzed for acceptability, defects and quality standards. 4.5 Results & Examples a. Let’s take an example of a cuboid with nominal dimensions defined as [3mm X 4mm X 5mm] with 10% of uncertainty in every dimension as shown in figure 3.

Fig 3: Nominal geometry of cuboid Extraction of coordinate and edge information as shown in figure 4:

Fig 5: Few cases out of possible combinations

Fig 4: Determining coordinates and edges There are three dimensions, i.e., n=3. If we input the value y=3, the number of combinations will be 27 (3 3) while the algorithm will take the nominal value, maximum limit and minimum limit. Some of the virtual geometries out of the 27 combinations are shown in Figure 5 which is a point of concern in product realization.

The nominal value of the volume is 60 mm3. The volumes obtained from all the combinations are analyzed to get the max. value as 79.86 mm3, min. value as 43.74 mm3 and the mean value (of all values) as µ=60 mm3 which coincides with the one with the value obtained from the nominal dimensions validating the results. Out of the geometries shown in Fig 5, the first one corresponds to the nominal dimensions while the last one corresponds to the max. volume (MMC condition) which allows you to visualize the variations. Coming to the qualitative analysis, the standard deviation obtained from the volume data obtained above is σ=8.51 mm3. The upper limit corresponds to (µ+2.33*σ), while the lower limit corresponds to (µ-1.91*σ). The normal distribution curve for given case is shown in the graph below.

One of the critical observations from the above graph can be that the mean value does not lie in the middle of upper and lower limits. Thus, the proposed algorithm gives the worst case analysis results as well as statistical analysis results. b. Let’s take another example involving cylindrical faces, say a hollow cylinder with considerable wall thickness with given dimensions and 5% of uncertainty in each dimension as shown in Fig 6. Di = 6 mm; Do = 10 mm; H = 8 mm

Fig 6: Nominal geometry of hollow cylinder Again, the number of dimensions involved in computation are three, i.e., n = 3. Taking y = 3, the number of combinations comes out to be 27. In case of nominal dimensions, the volume comes out to be 402.124 mm3. From all the 27 values obtained, the min. volume is 344.6 mm3 while the maximum value 465.51 mm3. Again, it can be seen that the mean value doesn’t lie exactly at the center of upper limit and lower limit as the arithmetic mean of the upper and lower limit is 405.55 mm3. It also suggests that only the worst case estimation is not enough to design a manufacturing process, statistical deviation also plays a significant role which cannot be neglected. 5. DISCUSSION The overall idea is towards development of a system that can process the information obtained from CAD geometry to produce the weight values and worst case results. In the year 2000, Morse (Cornell University) proposed a methodology to process tolerance data for assembly purposes, but it was limited one – dimensional computation [24]. From 1970s, lot of research has been done in tolerance allocation and processing.

Statistical analysis has been a topic of great interest as discussed in the literature section. The idea is roughly a simplistic approach towards basic geometric modifications and compiling the results together to produce certain object oriented results. Aiming towards developing a platform for weight estimation, the idea is motivated from the fundamentals of quality management. Suppose, there is a manufacturing unit for a particular type of threaded bolt. There are always inherent variations in any manufacturing system due to which the actual output shows some variation from the desired output. This variation may be big or small. The variance of the output depends upon the manufacturing process and the quality standards inculcated that defines the acceptance of the product when its variation from the desired output is in between certain specified limits. The proposed methodology tries to inculcate these principles in weight estimation. The tolerance modelling, in our case, refers to assigning tolerances within which the product will be accepted. In case of any violations with these limits, the part is rejected. The problem statement that stood as a barrier was the manufactured product weighed more than expected from CAD model analysis. It’s easy to control and find out the scope of improvement by manual analysis when the final product has up to twenty parts. After that, it becomes a reason for high cost and labor involvement to analyze, say 40-50 parts beyond which it is almost impossible. The proposed method aims to resolve this issue targeting several aspects in the analysis, say geometrical analysis and qualitative analysis. By principles of quality management, the probability of variation on either side of the mean value is equal, i.e., the probability of existence of geometry corresponding to each combination is equal. This means creating all the combinations actually corresponds to a large sample of the manufactured population. It is analogous to estimating the results in the design stage that were at first being observed after the manufacturing has begun. Population estimation has been an integral part of mechanical design and manufacturing under the parenthesis of quality engineering from a very long time. But, it has ever been limited numerical data when it comes to estimation, say weight, volume, cost, and many other parameters required for defining the sustainability of the product. For the first time, there is an approach that involves the geometrical changes in the product. At the end of the analysis, the system produces the virtual geometry showing the worst case product. It opens a whole new level of qualitative analysis and estimations when it comes to real time manufacturing in the design stage itself. 6. APPLICATIONS 6.1 Weight estimation It is a methodology that aims to calculate the weight of the final part/product by virtually creating the population, computing their weight using existing algorithms and take its

mean. Let’s take an example of aircraft industry [25]. Thousands of parts are there in one aircraft, due to which weight estimation is required in various phases of design stage [26]. Analysis using statistical and analytical approaches is being done in almost every industry. Our method holds the potential to estimate the weight with similar accuracy to the one who is actually manufacturing and measuring the weight. Simultaneously, it returns the geometry in worst case analysis which has its own importance. 6.2 Quality checks & benchmarking The conformity of parts being manufactured is verified by means of tolerance specifications for manufacturing [27]. As discussed earlier, the proposed method tries to inculcate quality characteristics in the design itself. The computed data can be used to design the quality checks required during the manufacturing in order to control the final output quality of the product. Moreover, these results can be used to create benchmarks for the requirements of the final output. Using multiple iterations, one can predict the minimum quality requirements for different parts of the assemblies. 6.3 Robotic systems In the era of automation and machine learning, a key point of consideration is the ability of the robot to sense an object. Most of the work in robotic manipulation assumes that parts do not have shape variations [10]. Our approach can be a benefit in field of robotics where the sensing experience of any system can be manipulated under some restrictions (known as tolerances). Orienting devices such as bowl feeders frequently fail due to the variations in different parts, especially when they’re supplied by the manufacturers. 7. CONCLUSION This paper discussed a new methodology for tolerance computation and worst case estimation using geometric approach rather than regular statistical approach. The geometric approach not only gives the numerical result, as weight in MMC condition, it also analyses and builds the virtual geometry corresponding to that weight. Our approach considers part by part analysis of every possible configuration including the variations in the model due to manufacturing tolerances. The system can also return possible geometries corresponding to a particular weight that can be used to view the geometry as per the MMC and LMC condition. The implementation of the algorithm is under progress which considers regular geometries. Besides, the development of a more rigorous algorithm for complex geometries, involving some free form surfaces is also in progress. Further, as discussed earlier, the solution proposes a new approach towards worst case estimation which opens a whole new area of research. The solution can be extended from individual parts to full scale assemblies. The way of computing/building geometries from initial configuration and

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