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Economics of clinched joint compared to riveted joint and example of applying calculations to a volume product
Journal of Materials Processing Technology 172 (2006) 130–138
Economics of clinched joint compared to riveted joint and example of applying calculations to a volume product Juha Varis Department of Mechanical Engineering, Lappeenranta University of Technology, Lappeenranta, Finland Received 15 March 2004; received in revised form 7 July 2005; accepted 9 September 2005
Abstract Clinching is a mechanical joining method especially for sheet metal parts based on forming of joined materials, and no additional joining elements are needed. Remarkable benefits in the process can be shown particularly when joining pre-coated materials. The process was implemented for a mass production in a car manufacturing industry in 1980. Nowadays, a wide range of applications covers all sheet metal production industries. Another interesting mechanical joining method developed in 1990s is self-piercing riveting. This method is nowadays widely used for sheet metal joining, especially in car manufacturing industry where aluminium as a material for chassis is used. The process does not need any pre-working such as drilling or hole punching, joining takes less than a second of time, and no post-work is needed, either. Joining with and without additional elements differ significantly from each other on the basis of cost formation principles. In a technique without any additional element the unit and total costs decrease as the tool life increases. On the case of joining sheets with an additional element (e.g. self-piercing rivets), tooling costs can even be ignored, due to their minor significance. The total costs increase directly in proportion to the amount of joints. An economic comparison of the above-described mechanical joining methods is presented in this paper. Several points of view are discussed and mathematical calculations for, e.g. marginal costs are presented. The aim of the study is to present a general procedure for comparing joining costs of each method. © 2005 Elsevier B.V. All rights reserved. Keywords: Clinching; Self-pierce riveting; Economic; Costs; Sheet metal; Mechanical joining
1. Introduction 1.1. Joining of sheet metal Dozens of different methods exist to join metal plates less than 3 mm thick (sheet metal). In addition, there are several ways of grouping these techniques. The following table contains methods presented in MET Technical information 7/99, which is the most recent publication dealing widely with the topic in Finnish. The way of the presentation in Table 1 is simplified from the original source [1], which is based on many professional publications. Important for this article is the sub-classification of mechanical joints and it is presented more widely than other sub-classifications. In literature, there is also a distribution presented into loadbearing and fastening joints, where fastening joints mean joints which are not required to pass notable forces from one element to another, which, on the other hand, is the basic function of a load-bearing joint. Typically, different frames in blowers, cabi0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.09.009
nets, shelving and domestic appliances are load-bearing joints. Fastening joints hold parts together and in their position; applications are, for example, light fittings, trim panels and covering plates in domestic appliances. 1.2. The significance of an additional joining element in mechanical joints In general, mechanical joints may be manufactured with fewer costs if there is no need for any additional joining element. As far as mechanical joints are concerned, an additional joining element refers to all materials or extra components without which a joint cannot be made. Fasteners include, for example, rivets, nails, hooks, screws, nuts, battens and derivatives and combinations of the previous (cf. the list of processes above). Overall, the joint without an additional joining element can be quite profitable, because there are following direct expenses of making a joint with an additional joining element:
J. Varis / Journal of Materials Processing Technology 172 (2006) 130–138 Table 1 Welded joints
Mechanical joints
Resistance welding ... Fusion welding ... Brazed joints Soft soldering Hard soldering Arc soldering Glued joints
With additional joining element Nail joint Batten joint Screw joint Plate screw Bolt–nut Riveted joints Open-type Blind Self-piercing Without additional joining element Folded joint Tongue joint Clinched joint
• purchasing and storing the additional joining element; • handling and feeding devices of the additional joining element; • post-processing of the additional joining element packages (e.g. plastic strips); • positioning devices of the parts (in case holes in parts are to be done in advance). In addition to the previous, indirect costs are caused by additional work, which is due to: • handling the additional joining element; • fixing feeding malfunctions; • positioning the parts. Another perspective to consider is the need to open or disassemble the joint when using the product. None of the joining methods without an additional joining element can be opened or disassembled in a way that would allow it to be closed again. A clinch joint is opened by breaking it, e.g. by drilling. In this respect, many of the joints with an additional joining element are similar to the clinch joint, only joints with plate screws and screw–nut combinations may be opened and closed again without losing many of the features of the joint. The most difficult thing to consider at a general level is the strength of the joint and comparing different techniques with respect to the joint strength. What makes this significant is that the strength of a joint is an important dimensioning and designing variable in many cases. There are cases in which, at a general level, at least the same or even greater strength is reached in a joint without an additional joining element than in one with an additional joining element [2]. On the other hand, however, the situation might be completely opposite. Additional difficulties in the strength comparison include standard measures, e.g. which rivet size corresponds to the size of each joint without an additional joining element (e.g. clinching) [3]. Considering the matter at a general level is difficult also because of the lack of a universal way to calculate the strength of, e.g. a clinch joint. The means to determine the strength of a joint by calculations presented in literature [4–7] has proven to be case and material
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specific. Consequently, the exact strength of a joint can be found out only by destructive tests [8]. The break down mechanisms of different kind of joints differ from each other. Therefore, the strength value describing the greatest load-bearing capacity of the joint does not alone describe the joint behaviour as a whole. The best understanding is achieved only by comparing the displacement–force diagrams, in which the ductility of the joint under the influence of a force can be seen [3,9]. When executing strength comparisons, it is always necessary to remember, or in unclear cases to find out the desired level of strength to be achieved with the joint. It has earlier been presented that a joint only needs to carry the amount of load that it is subject to, no greater joint strength is required. The scale is very broad. The greatest joint strength does not lead to the greatest possible joint quality; a more comprehensive examining is needed and all joining methods exceeding the strength requirements should be taken under consideration. 1.3. The objective of the research This article is based on a research in which a Finnish machine shop compared different joining methods in manufacturing a large-volume and greatly demanding product. The research was carried out in order to find out alternatives for clinching that they had been using. After a technical selection of processes that could be applicable to the existing production line, the research was focused on comparing clinching and self-piercing riveting, with emphasis on economic aspects. The costs originating from replacing one process with another was not included in the calculations in order to keep the examination at a general level. The way of approaching the subject also underlines the differences between joining with and without an additional joining element. 2. Clinching Clinching is a mechanical joining process that is mainly intended for sheet metal (s < 3 mm), in which no additional joining element is used, but the joint is made by forming the plates locally, as presented in Fig. 1 [10]. The punch tool simply presses the plates inside a die forming a shape that locks the plates together. The first patent related to the subject was granted as early as 1897 [11], but the process was mainly adopted in the industry in the 1980s. The most remarkable step was when Mercedes-Benz introduced the process in the serial production of passenger car bodywork parts [12]. One year later the technique was introduced in an international machine tool exhibition (EMO) [13]. Nowadays, the process is widely used in different areas of plate product manufacturing and there are plenty of operational applications. Thinking of the equipment technique, clinching may be divided into three main components [3]: a pair of tools (punch and die) as described in Fig. 2a, a power unit (driving power pneumatics, hydraulics or a combination of those) and a Cframe, where the previous are attached to. There are two alternatives regarding to the part handling and the tool: the first is based on moving the tool and it is done by using so-called hand tongs (Fig. 2b), whereas in the second one the part is moved
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Fig. 1. The principle of clinching (TOX GmbH).
and the clinching is done by using a so-called standing machine. The car industry and other industries manufacturing large series of components are using a so-called multi-tool in which dozens of punches and dies join the parts simultaneously. An example of using a multi-tool is the hat rack of the Volvo S70 passenger car, in which approximately 70 tools join two deep drawn rack halves with a single press of the clinching machine. In applications like this it is possible to generate beneficial circumstances for the tools, e.g. by moving the tools precisely in the direction of their longitudinal axis, and due to the accurate planning of the tool control no torsion or twist occurs. The tool operating life in the Volvo application above is approximately 200,000 joints. The process includes a compressed air-operating tool cleaning nozzle for removing dirt, possibly coming out from plates, especially from the die. Clinching may also be robotized. The operating tool life is typically dozens of thousands of joints if the joining circumstances are optimal. The operating life estimates stated by the component manufacturers are generally 50,000–100,000 joints, which naturally depends on the materials joined. An even longer tool life is possible, as mentioned above. The longest operating life is achieved when joining mild steel types, e.g. so-called deep-drawing qualities. On the contrary, the circumstances when joining stainless steel are remarkably more demanding, especially due to work hardening and thus it is difficult to achieve numbers reaching hundreds of thousands of joints as described above. Yet, reaching the tool life of dozens of thousands of joints is common when joining stainless steel. The most common tool shapes are round and rectangular [14]. 3. Self-piercing riveting
Fig. 2. (a) Punch and die (BTM Scandinavia Ab) and (b) so-called hand tongs (B¨ollhoff GmbH).
Riveting with a self-piercing rivet is a joining method in which the riveting process does not require any premanufacturing of holes to the plates. As in clinching, during a process, which lasts approximately 1 s a rivet is pressed on plates that are set on one another. The joint type has to be a lap joint, as in clinching. The rivet forces its way to the junction and stays in a position where the upper surface of the rivet is at the same level as the surface of the upper plate penetrated into the plate. The formability of the bush-like rivet is used in the process in a way where, at the final stage of riveting, the counterpart of the riveting tool, i.e. the counter die (“Matrize” in Fig. 3), causes the upper surface of the rivet to spread. The transformed plates and the rivet lock each other and form a joint. In a correctly done joint no hole formation occurs during the process, provided that the length of the rivet was chosen correctly. The lower plate goes through a heavy formation, but remains unbroken and thereby
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Fig. 3. Cross-section of a self-piercing riveting joint. Stempel: a punch; F¨ugeteile: sheets; Matrize: a die; Halbhohlniete: a self-piercing rivet; Ausgestanztes material: deformed material (B¨ollhoff & Co. GmbH).
it is gas- and waterproof. There are half a dozen component manufacturers on the market, with basically similar appliances [1,3]. The process is suitable in joining sheet metal and fits both coated and uncoated materials. In Europe, the best-known largescale volume company applying the process is the German car manufacturer Audi AG, whose aluminium car bodies contain thousands of self-piercing rivets. For example, in the body manufacturing of their smallest model (Audi A2), 1800 pieces of self-piercing rivets are used. The process is also applied to the production of domestic appliances as well as to air-conditioning and construction industry products. Typical riveting devices are presented in Fig. 4(a and b). The driving power of the devices is most commonly pneumatic–hydraulics. The tools can reach a service life of 1,000,000 joints. The self-piercing riveting joint is usually stronger than a clinch joint of a similar size when joining steel sheets, especially if the rivet is made of stronger material than the sheets joined. The rivet material can be hardened steel, stainless steel or aluminium. Zinc-coated and baked rivets are manufactured, and for the most common types of coated sheet metal there are rivets in matching shades. When calculating the strength of the joint it is possible to use similar strength theory approaches as in calculating, for example, the strength of screw connections. In that case one needs to consider, among other things, the edge strength and the shear stability of both the sheets and the rivets. As stated already in connection with clinching, the most reliable strength can be found out with destructive tests. The strength values presented in literature should be considered with reservation, no matter what is the joining process in question, especially when it is not known if the value is an individual test result, an average value of test results, a characteristic value calculated from test results or some other value. 4. Case product As mentioned in the objective of this study, the joining process used in the company in focus is clinching without any additional joining element. In the following, the manufactured
Fig. 4. Self-piercing riveting devices: (a) manual device and (b) floor-type machine.
product and the present joining process with the equipment is presented to the extent necessary in this context. The subject of the research is a large-scale volume sheet metal product, in which two 9000 mm long parts are joined with 120 clinch joints. Sixty joints are made on each edge making the distance between the joints to 150 mm, which has been found out to
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Fig. 5. There are clinch joints at intervals of 150 mm in the product; the total length is 9000 mm.
be the most suitable when taking into account both the tightness and the strength requirements of the product. The total of joint spots in one consignment is as many as 200,000 joints. The materials of the sheets joined are on the punch side Alz DX51D AZ 150, nominal thickness 1.0 mm and ultimate strength 500 MPa, and on the die side Alz DX52D AZ 150, nominal thickness 1.0 mm and ultimate strength 420 MPa. During transportation and assembly some bending load is directed onto the product and during usage, in addition to the bending load caused by the own mass of the product, only a small amount of dynamic load, the relevance of which for a single joint spot is calculated to be only about 5 N. The size (diameter) of the clinch joint used in the manufacturing of the product is 6 mm measured from the side of the die. The joint is made onto the edge of two roll formed sheets (Fig. 5) so that there is only a small amount of space around the tool. On the punch side the joint is made into a groove 14 mm wide. The diameter of the punch is 4.2 mm. 4.1. Clinching device In order to make clinch joints on two opposite sides of the product at the same time, there is double clinching equipment in the frame of the device. C-framed tools are attached onto a block that automatically travels along linear guides. A logic control monitors the operations of the system which is capable of making all the joints in the product unattended. It is possible to install self-piercing riveting equipment and accessories into the frame without a need for major modifications in the construction. 4.2. Problems discovered in clinching Problems in the durability of clinching tools were discovered when manufacturing the product. The tools withstood a making of only about 4000–5000 joints. Usually, the tool broke down so that the punch snapped from the base of the tip element. Even worse, in finished products there appeared to be joints that opened out. In some places dozens of joints had broken down and therefore, the operational features of the product had
been deteriorated remarkably. The breakage took place soon after implementation, from which one may presume that the first damages were caused as early as during installation or even during transportation. A significant point is that the continuous use during several years has not produced any joint breakages, so the fatigue durability is not the primary focus [15,16]. Analyzing and repairing the problems is discussed in an article on the quality control of clinch joints and an example of applying it to a large-scale volume product in Ohutlevymagazine 2/2003 (Puristusliitoksen laadunvalvonta ja esimerkki sen soveltamisesta er¨aa¨ seen volyymituotteeseen in Finnish), pp. 36–45. Speculative results attained by developing the process are briefly presented in the following. The service life of the tools has multiplied after changes made to the system. Even when starting up the production, 19,000 joints have been made with one pair of tools before the punch breaks. The principal guarantee of succeeding has been the socalled floating tool structure with which the tool finds its way into a natural position in relation to the sheets to be joined [15]. A thin layer of cutting oil is sprayed onto the junction just before joining in order to reduce friction between the tools and the sheets. The significance of the lubrication only is not studied in this research. International literature supports the view according to which the service life of the tools may be extended by lubricating the surfaces before joining. 5. Cost comparison 5.1. Significance of tool service life to unit costs As presented above, a typical clinching tool service life for the material type in question is 50,000–100,000 joints. Knowing that in joining without an additional joining element the joint unit cost decreases when the tool service life increases and the average price of a pair of clinching tools (punch and die), observing all the different component manufacturers, is D 500, it is possible to calculate the clinch joint unit cost according to Eq. (1). Since the operating principles of the equipment compared are similar, no other costs originating from the use are taken into account in the calculations for sake of clarity. The other costs can result from pressurized air, maintenance, service and electricity. Let us examine five different alternatives for a clinching tool service life as follows: The unit cost of a joint =
the price of a pair of tools tool operating life
(1)
(a) typical tool life 50,000 joints, unit cost = D 500/50,000 joints = 1 cent; (b) typical tool life 100,000 joints leads to a unit cost of 0.5 cents; (c) the tool life, resulting from problems in joining as stated above, has at its best only been 5000 joints, which leads to a unit cost of 10 cents; (d) after some changes in the construction, with one pair of tools, a tool life of 19,000 joints is reached, which leads to a unit cost of 2.6 cents;
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(d) service life 19,000 joints ⇒ 200,000 joints at 2.6 cents = D 5200/batch; (e) service life 200,000 joints ⇒ 200,000 joints at 0.25 cents = D 500/batch. 5.2. Unit cost of self-piercing riveting
Fig. 6. The dependency of a clinch joint unit cost on tool service life (cents/piece).
(e) the optimal tool life would be the total need of a manufacturing batch, or 200,000 joints, in which case the unit cost would be 0.25 cents. It can be seen that the lowest unit cost is 40 times smaller than the greatest unit cost. The dependency of the clinch joint unit cost as a function of the tool service life is presented in Fig. 6; the limiting points in the diagram are 5000 and 200,000 joints/a pair of tools, which were used in the previous calculations. The amount of joints to be made in one production batch of the product in question is 200,000 pieces. Thus the cost of one manufacturing batch can be calculated by multiplying the total amount of joints by the cost of one joint (Eq. (2)). Batchspecific costs for the five different service lives mentioned above are calculated in the following: Joining costs for a manufacturing batch = the size of the batch × unit cost of a joint
(2)
(a) service life 50,000 joints ⇒ 200,000 joints at 1 cent = D 2000/manufacturing batch; (b) service life 100,000 joints ⇒ 200,000 joints at 0.5 cents = D 1000/batch; (c) service life 5000 joints ⇒ 200,000 joints at 10 cents = D 20,000/batch;
In the calculations, the service life of a self-piercing riveting tool is assumed to be 1,000,000 joints and the price to be D 500. The price of a self-piercing rivet is 1.5 cents a piece at the price level of the year 2003, but when purchased in greater lots the volume discount is 40%, which is taken into account in the calculations. Consequently, the final price of a rivet is 0.9 cents a piece. The costs of joining techniques with additional joining elements consist of both tool costs and additional joining element costs. As regards to tool costs, a unit cost can be calculated by dividing the tool price by the amount of joints, which is in this case D 500/1,000,000 joints, which makes the unit cost only 0.05 cents a joint. In a joint with an additional joining element the total cost impact is directly proportional to the amount of joints, as presented in Fig. 7. The manufacturing batch of the product in question requires 200,000 joints, in which case it is relevant to examine the comparable total cost that can be calculated according to the unit price of a rivet; 200,000 joints × 0.9 cents/a self-piercing rivet = D 1800/manufacturing batch. 5.3. Comparing cost effects The basic difference between joining techniques with and without an additional joining element when examining batchspecific costs is clearly presented in Fig. 7. In other words, the more joints with one pair of clinching tools can be made, the smaller is the total cost of joining. Considering joining techniques with an additional joining element, tooling costs are not that significant in self-piercing riveting, so the main costs are due to the additional joining element. That is why the costs of a product resulting from joining technology are final already at the designing stage when the amount of joints is decided. The costs in manufacturing can basically be affected only by making sure that the tools are used correctly. This can also be generally applied to other joining techniques with and without an additional joining element if we take into account the technology issues discussed above. In Fig. 7, the Y-axis is limited to D 5000 for practical reasons. In the X-axis, both the tool service life in clinching and the required amount of rivets in self-piercing riveting are presented. 5.4. Determining minimum service life for clinching tools The total cost of a manufacturing batch of self-piercing riveting was previously calculated as D 1800. From Eqs. (1) and (2), we can derive Eq. (3), from which can be calculated the required
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Fig. 7. Costs of a manufacturing batch according to the clinching tool service life and the amount of rivets in self-piercing riveting.
service life of a clinching tool, with which the total cost is the mentioned as it is in self-piercing riveting.
D 1800
The tool service life =
size of a batch × price of a tool pair , joining cost of a manufacturing batch (3)
where the answer is (200,000 joints × D 500)/D 1800 = 55,555 joints. The validity of the magnitude can also be seen with the help of arrows (a1 and a2) drawn in Fig. 7. Therefore, the 55,555 joints we got as the answer is a limit value. Clinching tools that last longer make clinching a more profitable process than self-piercing riveting as it comes to the joining costs. The situation can also be the opposite. As stated earlier, by changing the construction of the device the service life of clinching tools has been raised from 5000 to 19,000, which is still far from the limit value calculated. When comparing the total costs, clinching is almost three times more expensive with the service life achieved, which can be calculated as follows: D 5200/D 1800 = 2.89. Also, this can approximately be seen in Fig. 7 (arrow b). As presented earlier, the typical tool service life for the material type in question is 50,000–100,000 joints. The minimum service life calculation presented earlier puts in this respect more pressure on trying to reach the limit of 50,000 joints. With the means presented above, the service life of clinching tools has already been lengthened in this particular case. Discussing the subject at a general level is not easy; aiming at lengthening the service life leads to case-specific examinations and measures. If a clinching tool lasts for 100,000 joints, the total cost of a manufacturing batch would be D 1000 as calculated above, in which case self-piercing riveting would be a 1.8 times more expensive process (D 1800/D 1000). If the target level of 200,000 joints with one pair of tools was reached, the cost difference between the processes would be 3.6 times in favor of clinching.
the amount of joints made in the product, the profitability of self-piercing riveting offers a possibility for that. If we study again the clinching too l service life of 19.000 joints, the difference in total costs is 2.89-fold. It means that when calculating with Eq. (2), the amount of joints can also be increased up to 2.89 times larger, which means 577,777 rivet joints. In that case, there would be rivets in the product at intervals of about 50 mm. As stated in the introduction, in many cases a joint with a rivet is stronger than a joint made only of the base material, so in practice, this is important only if the tightness of the construction needs to be increased. However, the opposite situation occurs when clinching tool service life of over 55,555 joints is achieved, for example, 100,000 or 200,000 joints as already earlier presented as examples. With a clinching tool service life of 100,000 joints, to reach the same total costs calculated with Eq. (2), only 111,111 rivets can be used, which is 56% of the amount planned. With this amount of rivets the distance between joints increases to be 1.8 times longer, i.e. 270 mm, which is not structurally possible. The service life of 200,000 doubles the value. Let us consider the total costs but with relative values. In that case, with Eqs. (1) and (2) and in Fig. 7 it can approximately be seen that with a joint amount of 111,111 pieces the total costs in both clinching and self-piercing riveting are equal. So-called normalized total costs are graphically presented in Fig. 8, where the amount of rivets and the clinching tool service life are on the X-axis, as pointed out earlier. The relative difference of the joining techniques in the total costs can be seen on the Y-axis.
5.5. Varying the amount of rivets As stated earlier, as long as the clinching tool service life is less than 55,555 joints, self-piercing riveting is a more profitable process considering the total costs for the 200,000-joint series studied. We could also argue that if there is a need to increase
Fig. 8. The comparative total costs of clinched joints and self-piercing riveted joints as a function of the clinching tool service life and the amount of selfpiercing rivets.
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Fig. 9. The line rising upwards presents the effect of increasing the clinching tool service life in the total cost savings achieved when compared to self-piercing riveting. Also, the increase in savings (as percentage units) and the proportional need for increasing the service life between the points of examination are presented in the figure.
The limit value of 111,111 joints is equivalent to the value 1 on a comparative scale, which therefore means that the total costs are equal in both processes. If the clinching tool service life falls short of the limit value, it is possible to use more rivets in a joint with equal total costs than in clinching (the number is n-fold) according to the diagram and the relative value indicated by the Y-axis. The part of the diagram that exceeds the limit value (111,111 pieces) shows how much less there are rivets to be used with equal total costs compared to the amount of clinched joints.
interval. Correspondingly, the amount of cost savings achieved is low, which is depicted with a line symbolized by squares in Fig. 9 and presented as percentage units in the third column from the left in the table next to the figure. The line symbolized by triangles in Fig. 9 and the column on the right-hand side in the table present the relative need to increase the tool service life between the points of examination. It can be stated that considering the total costs, the savings required for a proportional tool service life increase is reached at no examination interval.
5.6. The cost resonance of increasing the clinching tool service life
6. Conclusions
The increase in total cost savings compared to self-piercing riveting, if it is possible to lengthen the clinching tool service life, is presented with a line symbolized by rhombi in Fig. 9. The amount of 55,555 joints that was calculated above and with which the total costs are equal, is used as the lowest limit. The examination ends at the service life of 200,000 joints. The second column from the left in the table next to the figure presents cumulative savings in numerical values when the chosen interval of examination is 10,000 joints. It can be noted that a maximum of 72% of cost savings in the total joining costs can be reached. The area of examination is very broad when evaluating the issue from the viewpoint of increasing the tool service life. The change from one end to the other would mean that the tool service life would need to be increased by 3.6-fold. The shape of the graph is explained by the division of the examination period into 15 sectors, when the relative increase in service life remains small between the blocks at the upper end of the examination
Joining with and without an additional joining element differ significantly from each other on the basis of cost formation principles. In a technique without an additional joining element the unit costs decrease as the tool service life increases, and also the total costs decrease. On the contrary, the additional joining element unit costs in the technique with an additional joining element are constant and tooling costs in self-piercing riveting can even be ignored in this example due to their minor significance. Total costs increase directly in proportion to the amount of joints in techniques using an additional joining element. The durability of clinching tools depends on the materials joined. Although different materials can be joined with same tools, the most reliable reference data is attained when it is possible to examine a large production run within which the tool service life runs out. In such a case, it has been possible to minimize the influence of other so-called external factors in the tool service life. By comparing the two processes, we can determine the minimum value for the service life of clinching tools, with equal
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total costs for one manufacturing batch. The number is a limit value, and going under or exceeding it leads to reducing or increasing the price competitiveness of the clinching technology. We have also presented a way to calculate, with the aid of the limit value, possibilities to increase the amount of rivets in joints without losing the advantage in price competition against clinching. This article introduces a possibility to calculate and analyze the cost effects of joining techniques with and without an additional joining element in product manufacturing. The points presented may be considered as a general model of analysis that can also be applied to other processes than the ones presented here by using the correct numerical values for each technique. The model also serves in estimating the sensitivity of the cost effects of a single process, a situation that can rise, for example, when optimizing portions of the most profitable additional joining element offered for large production runs. It is important to note that the means of examination presented in the article are only one part of the investment cost estimations. As stated in the beginning, for example, the proportion of investments in equipment needed or their significance has not been taken into account at all since the objective was a clear and easily applied exposition. References
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[1] Ohutlevyjen liitt¨aminen (Joining of Sheet Metals), MET Tekninen tiedotus 7/99, Metalliteollisuuden Kustannus Oy, Helsinki, 1999, p. 6, ISBN 951-817-705-8, ISSN 0788-0987 (in Finnish). [2] B. Nilsson, E. Sagstr¨om, Handbok f¨or Stuknitning (Handbook for Clinching), No. 1, Fakta rapport: Bearbetning och fogning av plat, Sveriges Verkstadsindustrier, Stockholm, 1995, p. 87 (in Swedish). [3] J. Varis, Kuumasinkityn lujan rakenneter¨aksen puristusliitt¨aminen (Clinching of Zinc-Coated High Strength Structural Steel), Research
[15]
[16]
Report, No. 27, Lappeenranta University of Technology, Department of Mechanical Engineering, Lappeenranta, 1998, p. 122 (in Finnish). R.F. Pedreschi, B.P. Sinha, The potential of pre-joining in cold-formed steel structures, Construction Building Mater. 10 (4) (1996) 243–250. R.F. Pedreschi, B.P. Sinha, R. Davies, Advanced connection techniques for cold-formed steel structures, J. Struct. Eng. 123 (2) (1997) 138–144. R. Davies, R. Pedreschi, B.P. Sinha, The shear behaviour of pressjoining in cold-formed steel structures, Thin-Walled Struct. 25 (3) (1996) 153–170. L. Budde, U. Klasfauseweh, Analysen der Beanspruchungen durchsetzgef¨ugter Strukturen, B¨ander Bleche Rohre 33 (5) (1992) 46–48 (in German). J. Lepist¨o, J. Varis, TOX® -puristusliitoksen simulointi elementtimenetelm¨aa¨ k¨aytt¨aen (FE-Simulation of a TOX® Clinching Method), Ter¨asrakenteiden tutkimus-ja kehitysp¨aiv¨at, Espoo, January 18–19, 2000, p. 8 (in Finnish). J. Varis, A novel procedure for establishing clinching parameters for high strength steel sheet, Dissertation, Acta Universitatis Lappeenrantaensis 105, Lappeenranta University of Technology, Finland, 2000, p. 84, ISBN 951-764-490-6, ISSN 1456-4491. H.P. Liebig, J. Bober, R. Beyer, Connecting Sheet Metal by Press Joining, vol. 25, no. 9, B¨ander Bleche Rohre, 1984, p. 7 (reprint: VogelVerlag, W¨urzburg). Deutsches Reichspatent DRP-No. 98517, 1897 (in German). D. Zeitmann, Stand der industriellen Anwendung des Durchsetzf¨ugens und der Stanzniettechnik bei Mercedes-Benz, Innovative F¨ugetechniken f¨ur Leichtbaukonstruktionen, Paderborn, November 7–8, 1996, pp. 79–85 (in German). T. Facklam, H.P. Liebig, Schutzleiterverbindung in Druckf¨ugetechnik, Sonderdruck aus etz, Bd.109 H.24, 1988, pp. 1126–1130 (in German). O. Hahn, L. Budde, Analyse und systematische Einteilung umformtechnischer F¨ugeverfahren ohne Hilfsf¨ugeteil, Blech Rohre Profile 37 (1) (1990) 29–32 (in German). J. Varis, Puristusliitoksen laadunvalvonta ja esimerkki sen soveltamisesta er¨aa¨ seen volyymituotteeseen, Ohutlevy 2/2003, Teknologiainfo Teknova Oy, Forssa, 2003, pp. 36–45, ISSN 1239-4122 (in Finnish). J. Varis, The meaning of follow-up on a long term clinching process, in: JOIN’03 Conference, Lappeenranta University of Technology, Lappeenranta, Finland, May 21–22, 2003, p. 11.
Economics of clinched joint compared to riveted joint and example of applying calculations to a volume product Juha Varis Department of Mechanical Engineering, Lappeenranta University of Technology, Lappeenranta, Finland Received 15 March 2004; received in revised form 7 July 2005; accepted 9 September 2005
Abstract Clinching is a mechanical joining method especially for sheet metal parts based on forming of joined materials, and no additional joining elements are needed. Remarkable benefits in the process can be shown particularly when joining pre-coated materials. The process was implemented for a mass production in a car manufacturing industry in 1980. Nowadays, a wide range of applications covers all sheet metal production industries. Another interesting mechanical joining method developed in 1990s is self-piercing riveting. This method is nowadays widely used for sheet metal joining, especially in car manufacturing industry where aluminium as a material for chassis is used. The process does not need any pre-working such as drilling or hole punching, joining takes less than a second of time, and no post-work is needed, either. Joining with and without additional elements differ significantly from each other on the basis of cost formation principles. In a technique without any additional element the unit and total costs decrease as the tool life increases. On the case of joining sheets with an additional element (e.g. self-piercing rivets), tooling costs can even be ignored, due to their minor significance. The total costs increase directly in proportion to the amount of joints. An economic comparison of the above-described mechanical joining methods is presented in this paper. Several points of view are discussed and mathematical calculations for, e.g. marginal costs are presented. The aim of the study is to present a general procedure for comparing joining costs of each method. © 2005 Elsevier B.V. All rights reserved. Keywords: Clinching; Self-pierce riveting; Economic; Costs; Sheet metal; Mechanical joining
1. Introduction 1.1. Joining of sheet metal Dozens of different methods exist to join metal plates less than 3 mm thick (sheet metal). In addition, there are several ways of grouping these techniques. The following table contains methods presented in MET Technical information 7/99, which is the most recent publication dealing widely with the topic in Finnish. The way of the presentation in Table 1 is simplified from the original source [1], which is based on many professional publications. Important for this article is the sub-classification of mechanical joints and it is presented more widely than other sub-classifications. In literature, there is also a distribution presented into loadbearing and fastening joints, where fastening joints mean joints which are not required to pass notable forces from one element to another, which, on the other hand, is the basic function of a load-bearing joint. Typically, different frames in blowers, cabi0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.09.009
nets, shelving and domestic appliances are load-bearing joints. Fastening joints hold parts together and in their position; applications are, for example, light fittings, trim panels and covering plates in domestic appliances. 1.2. The significance of an additional joining element in mechanical joints In general, mechanical joints may be manufactured with fewer costs if there is no need for any additional joining element. As far as mechanical joints are concerned, an additional joining element refers to all materials or extra components without which a joint cannot be made. Fasteners include, for example, rivets, nails, hooks, screws, nuts, battens and derivatives and combinations of the previous (cf. the list of processes above). Overall, the joint without an additional joining element can be quite profitable, because there are following direct expenses of making a joint with an additional joining element:
J. Varis / Journal of Materials Processing Technology 172 (2006) 130–138 Table 1 Welded joints
Mechanical joints
Resistance welding ... Fusion welding ... Brazed joints Soft soldering Hard soldering Arc soldering Glued joints
With additional joining element Nail joint Batten joint Screw joint Plate screw Bolt–nut Riveted joints Open-type Blind Self-piercing Without additional joining element Folded joint Tongue joint Clinched joint
• purchasing and storing the additional joining element; • handling and feeding devices of the additional joining element; • post-processing of the additional joining element packages (e.g. plastic strips); • positioning devices of the parts (in case holes in parts are to be done in advance). In addition to the previous, indirect costs are caused by additional work, which is due to: • handling the additional joining element; • fixing feeding malfunctions; • positioning the parts. Another perspective to consider is the need to open or disassemble the joint when using the product. None of the joining methods without an additional joining element can be opened or disassembled in a way that would allow it to be closed again. A clinch joint is opened by breaking it, e.g. by drilling. In this respect, many of the joints with an additional joining element are similar to the clinch joint, only joints with plate screws and screw–nut combinations may be opened and closed again without losing many of the features of the joint. The most difficult thing to consider at a general level is the strength of the joint and comparing different techniques with respect to the joint strength. What makes this significant is that the strength of a joint is an important dimensioning and designing variable in many cases. There are cases in which, at a general level, at least the same or even greater strength is reached in a joint without an additional joining element than in one with an additional joining element [2]. On the other hand, however, the situation might be completely opposite. Additional difficulties in the strength comparison include standard measures, e.g. which rivet size corresponds to the size of each joint without an additional joining element (e.g. clinching) [3]. Considering the matter at a general level is difficult also because of the lack of a universal way to calculate the strength of, e.g. a clinch joint. The means to determine the strength of a joint by calculations presented in literature [4–7] has proven to be case and material
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specific. Consequently, the exact strength of a joint can be found out only by destructive tests [8]. The break down mechanisms of different kind of joints differ from each other. Therefore, the strength value describing the greatest load-bearing capacity of the joint does not alone describe the joint behaviour as a whole. The best understanding is achieved only by comparing the displacement–force diagrams, in which the ductility of the joint under the influence of a force can be seen [3,9]. When executing strength comparisons, it is always necessary to remember, or in unclear cases to find out the desired level of strength to be achieved with the joint. It has earlier been presented that a joint only needs to carry the amount of load that it is subject to, no greater joint strength is required. The scale is very broad. The greatest joint strength does not lead to the greatest possible joint quality; a more comprehensive examining is needed and all joining methods exceeding the strength requirements should be taken under consideration. 1.3. The objective of the research This article is based on a research in which a Finnish machine shop compared different joining methods in manufacturing a large-volume and greatly demanding product. The research was carried out in order to find out alternatives for clinching that they had been using. After a technical selection of processes that could be applicable to the existing production line, the research was focused on comparing clinching and self-piercing riveting, with emphasis on economic aspects. The costs originating from replacing one process with another was not included in the calculations in order to keep the examination at a general level. The way of approaching the subject also underlines the differences between joining with and without an additional joining element. 2. Clinching Clinching is a mechanical joining process that is mainly intended for sheet metal (s < 3 mm), in which no additional joining element is used, but the joint is made by forming the plates locally, as presented in Fig. 1 [10]. The punch tool simply presses the plates inside a die forming a shape that locks the plates together. The first patent related to the subject was granted as early as 1897 [11], but the process was mainly adopted in the industry in the 1980s. The most remarkable step was when Mercedes-Benz introduced the process in the serial production of passenger car bodywork parts [12]. One year later the technique was introduced in an international machine tool exhibition (EMO) [13]. Nowadays, the process is widely used in different areas of plate product manufacturing and there are plenty of operational applications. Thinking of the equipment technique, clinching may be divided into three main components [3]: a pair of tools (punch and die) as described in Fig. 2a, a power unit (driving power pneumatics, hydraulics or a combination of those) and a Cframe, where the previous are attached to. There are two alternatives regarding to the part handling and the tool: the first is based on moving the tool and it is done by using so-called hand tongs (Fig. 2b), whereas in the second one the part is moved
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Fig. 1. The principle of clinching (TOX GmbH).
and the clinching is done by using a so-called standing machine. The car industry and other industries manufacturing large series of components are using a so-called multi-tool in which dozens of punches and dies join the parts simultaneously. An example of using a multi-tool is the hat rack of the Volvo S70 passenger car, in which approximately 70 tools join two deep drawn rack halves with a single press of the clinching machine. In applications like this it is possible to generate beneficial circumstances for the tools, e.g. by moving the tools precisely in the direction of their longitudinal axis, and due to the accurate planning of the tool control no torsion or twist occurs. The tool operating life in the Volvo application above is approximately 200,000 joints. The process includes a compressed air-operating tool cleaning nozzle for removing dirt, possibly coming out from plates, especially from the die. Clinching may also be robotized. The operating tool life is typically dozens of thousands of joints if the joining circumstances are optimal. The operating life estimates stated by the component manufacturers are generally 50,000–100,000 joints, which naturally depends on the materials joined. An even longer tool life is possible, as mentioned above. The longest operating life is achieved when joining mild steel types, e.g. so-called deep-drawing qualities. On the contrary, the circumstances when joining stainless steel are remarkably more demanding, especially due to work hardening and thus it is difficult to achieve numbers reaching hundreds of thousands of joints as described above. Yet, reaching the tool life of dozens of thousands of joints is common when joining stainless steel. The most common tool shapes are round and rectangular [14]. 3. Self-piercing riveting
Fig. 2. (a) Punch and die (BTM Scandinavia Ab) and (b) so-called hand tongs (B¨ollhoff GmbH).
Riveting with a self-piercing rivet is a joining method in which the riveting process does not require any premanufacturing of holes to the plates. As in clinching, during a process, which lasts approximately 1 s a rivet is pressed on plates that are set on one another. The joint type has to be a lap joint, as in clinching. The rivet forces its way to the junction and stays in a position where the upper surface of the rivet is at the same level as the surface of the upper plate penetrated into the plate. The formability of the bush-like rivet is used in the process in a way where, at the final stage of riveting, the counterpart of the riveting tool, i.e. the counter die (“Matrize” in Fig. 3), causes the upper surface of the rivet to spread. The transformed plates and the rivet lock each other and form a joint. In a correctly done joint no hole formation occurs during the process, provided that the length of the rivet was chosen correctly. The lower plate goes through a heavy formation, but remains unbroken and thereby
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Fig. 3. Cross-section of a self-piercing riveting joint. Stempel: a punch; F¨ugeteile: sheets; Matrize: a die; Halbhohlniete: a self-piercing rivet; Ausgestanztes material: deformed material (B¨ollhoff & Co. GmbH).
it is gas- and waterproof. There are half a dozen component manufacturers on the market, with basically similar appliances [1,3]. The process is suitable in joining sheet metal and fits both coated and uncoated materials. In Europe, the best-known largescale volume company applying the process is the German car manufacturer Audi AG, whose aluminium car bodies contain thousands of self-piercing rivets. For example, in the body manufacturing of their smallest model (Audi A2), 1800 pieces of self-piercing rivets are used. The process is also applied to the production of domestic appliances as well as to air-conditioning and construction industry products. Typical riveting devices are presented in Fig. 4(a and b). The driving power of the devices is most commonly pneumatic–hydraulics. The tools can reach a service life of 1,000,000 joints. The self-piercing riveting joint is usually stronger than a clinch joint of a similar size when joining steel sheets, especially if the rivet is made of stronger material than the sheets joined. The rivet material can be hardened steel, stainless steel or aluminium. Zinc-coated and baked rivets are manufactured, and for the most common types of coated sheet metal there are rivets in matching shades. When calculating the strength of the joint it is possible to use similar strength theory approaches as in calculating, for example, the strength of screw connections. In that case one needs to consider, among other things, the edge strength and the shear stability of both the sheets and the rivets. As stated already in connection with clinching, the most reliable strength can be found out with destructive tests. The strength values presented in literature should be considered with reservation, no matter what is the joining process in question, especially when it is not known if the value is an individual test result, an average value of test results, a characteristic value calculated from test results or some other value. 4. Case product As mentioned in the objective of this study, the joining process used in the company in focus is clinching without any additional joining element. In the following, the manufactured
Fig. 4. Self-piercing riveting devices: (a) manual device and (b) floor-type machine.
product and the present joining process with the equipment is presented to the extent necessary in this context. The subject of the research is a large-scale volume sheet metal product, in which two 9000 mm long parts are joined with 120 clinch joints. Sixty joints are made on each edge making the distance between the joints to 150 mm, which has been found out to
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Fig. 5. There are clinch joints at intervals of 150 mm in the product; the total length is 9000 mm.
be the most suitable when taking into account both the tightness and the strength requirements of the product. The total of joint spots in one consignment is as many as 200,000 joints. The materials of the sheets joined are on the punch side Alz DX51D AZ 150, nominal thickness 1.0 mm and ultimate strength 500 MPa, and on the die side Alz DX52D AZ 150, nominal thickness 1.0 mm and ultimate strength 420 MPa. During transportation and assembly some bending load is directed onto the product and during usage, in addition to the bending load caused by the own mass of the product, only a small amount of dynamic load, the relevance of which for a single joint spot is calculated to be only about 5 N. The size (diameter) of the clinch joint used in the manufacturing of the product is 6 mm measured from the side of the die. The joint is made onto the edge of two roll formed sheets (Fig. 5) so that there is only a small amount of space around the tool. On the punch side the joint is made into a groove 14 mm wide. The diameter of the punch is 4.2 mm. 4.1. Clinching device In order to make clinch joints on two opposite sides of the product at the same time, there is double clinching equipment in the frame of the device. C-framed tools are attached onto a block that automatically travels along linear guides. A logic control monitors the operations of the system which is capable of making all the joints in the product unattended. It is possible to install self-piercing riveting equipment and accessories into the frame without a need for major modifications in the construction. 4.2. Problems discovered in clinching Problems in the durability of clinching tools were discovered when manufacturing the product. The tools withstood a making of only about 4000–5000 joints. Usually, the tool broke down so that the punch snapped from the base of the tip element. Even worse, in finished products there appeared to be joints that opened out. In some places dozens of joints had broken down and therefore, the operational features of the product had
been deteriorated remarkably. The breakage took place soon after implementation, from which one may presume that the first damages were caused as early as during installation or even during transportation. A significant point is that the continuous use during several years has not produced any joint breakages, so the fatigue durability is not the primary focus [15,16]. Analyzing and repairing the problems is discussed in an article on the quality control of clinch joints and an example of applying it to a large-scale volume product in Ohutlevymagazine 2/2003 (Puristusliitoksen laadunvalvonta ja esimerkki sen soveltamisesta er¨aa¨ seen volyymituotteeseen in Finnish), pp. 36–45. Speculative results attained by developing the process are briefly presented in the following. The service life of the tools has multiplied after changes made to the system. Even when starting up the production, 19,000 joints have been made with one pair of tools before the punch breaks. The principal guarantee of succeeding has been the socalled floating tool structure with which the tool finds its way into a natural position in relation to the sheets to be joined [15]. A thin layer of cutting oil is sprayed onto the junction just before joining in order to reduce friction between the tools and the sheets. The significance of the lubrication only is not studied in this research. International literature supports the view according to which the service life of the tools may be extended by lubricating the surfaces before joining. 5. Cost comparison 5.1. Significance of tool service life to unit costs As presented above, a typical clinching tool service life for the material type in question is 50,000–100,000 joints. Knowing that in joining without an additional joining element the joint unit cost decreases when the tool service life increases and the average price of a pair of clinching tools (punch and die), observing all the different component manufacturers, is D 500, it is possible to calculate the clinch joint unit cost according to Eq. (1). Since the operating principles of the equipment compared are similar, no other costs originating from the use are taken into account in the calculations for sake of clarity. The other costs can result from pressurized air, maintenance, service and electricity. Let us examine five different alternatives for a clinching tool service life as follows: The unit cost of a joint =
the price of a pair of tools tool operating life
(1)
(a) typical tool life 50,000 joints, unit cost = D 500/50,000 joints = 1 cent; (b) typical tool life 100,000 joints leads to a unit cost of 0.5 cents; (c) the tool life, resulting from problems in joining as stated above, has at its best only been 5000 joints, which leads to a unit cost of 10 cents; (d) after some changes in the construction, with one pair of tools, a tool life of 19,000 joints is reached, which leads to a unit cost of 2.6 cents;
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(d) service life 19,000 joints ⇒ 200,000 joints at 2.6 cents = D 5200/batch; (e) service life 200,000 joints ⇒ 200,000 joints at 0.25 cents = D 500/batch. 5.2. Unit cost of self-piercing riveting
Fig. 6. The dependency of a clinch joint unit cost on tool service life (cents/piece).
(e) the optimal tool life would be the total need of a manufacturing batch, or 200,000 joints, in which case the unit cost would be 0.25 cents. It can be seen that the lowest unit cost is 40 times smaller than the greatest unit cost. The dependency of the clinch joint unit cost as a function of the tool service life is presented in Fig. 6; the limiting points in the diagram are 5000 and 200,000 joints/a pair of tools, which were used in the previous calculations. The amount of joints to be made in one production batch of the product in question is 200,000 pieces. Thus the cost of one manufacturing batch can be calculated by multiplying the total amount of joints by the cost of one joint (Eq. (2)). Batchspecific costs for the five different service lives mentioned above are calculated in the following: Joining costs for a manufacturing batch = the size of the batch × unit cost of a joint
(2)
(a) service life 50,000 joints ⇒ 200,000 joints at 1 cent = D 2000/manufacturing batch; (b) service life 100,000 joints ⇒ 200,000 joints at 0.5 cents = D 1000/batch; (c) service life 5000 joints ⇒ 200,000 joints at 10 cents = D 20,000/batch;
In the calculations, the service life of a self-piercing riveting tool is assumed to be 1,000,000 joints and the price to be D 500. The price of a self-piercing rivet is 1.5 cents a piece at the price level of the year 2003, but when purchased in greater lots the volume discount is 40%, which is taken into account in the calculations. Consequently, the final price of a rivet is 0.9 cents a piece. The costs of joining techniques with additional joining elements consist of both tool costs and additional joining element costs. As regards to tool costs, a unit cost can be calculated by dividing the tool price by the amount of joints, which is in this case D 500/1,000,000 joints, which makes the unit cost only 0.05 cents a joint. In a joint with an additional joining element the total cost impact is directly proportional to the amount of joints, as presented in Fig. 7. The manufacturing batch of the product in question requires 200,000 joints, in which case it is relevant to examine the comparable total cost that can be calculated according to the unit price of a rivet; 200,000 joints × 0.9 cents/a self-piercing rivet = D 1800/manufacturing batch. 5.3. Comparing cost effects The basic difference between joining techniques with and without an additional joining element when examining batchspecific costs is clearly presented in Fig. 7. In other words, the more joints with one pair of clinching tools can be made, the smaller is the total cost of joining. Considering joining techniques with an additional joining element, tooling costs are not that significant in self-piercing riveting, so the main costs are due to the additional joining element. That is why the costs of a product resulting from joining technology are final already at the designing stage when the amount of joints is decided. The costs in manufacturing can basically be affected only by making sure that the tools are used correctly. This can also be generally applied to other joining techniques with and without an additional joining element if we take into account the technology issues discussed above. In Fig. 7, the Y-axis is limited to D 5000 for practical reasons. In the X-axis, both the tool service life in clinching and the required amount of rivets in self-piercing riveting are presented. 5.4. Determining minimum service life for clinching tools The total cost of a manufacturing batch of self-piercing riveting was previously calculated as D 1800. From Eqs. (1) and (2), we can derive Eq. (3), from which can be calculated the required
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Fig. 7. Costs of a manufacturing batch according to the clinching tool service life and the amount of rivets in self-piercing riveting.
service life of a clinching tool, with which the total cost is the mentioned as it is in self-piercing riveting.
D 1800
The tool service life =
size of a batch × price of a tool pair , joining cost of a manufacturing batch (3)
where the answer is (200,000 joints × D 500)/D 1800 = 55,555 joints. The validity of the magnitude can also be seen with the help of arrows (a1 and a2) drawn in Fig. 7. Therefore, the 55,555 joints we got as the answer is a limit value. Clinching tools that last longer make clinching a more profitable process than self-piercing riveting as it comes to the joining costs. The situation can also be the opposite. As stated earlier, by changing the construction of the device the service life of clinching tools has been raised from 5000 to 19,000, which is still far from the limit value calculated. When comparing the total costs, clinching is almost three times more expensive with the service life achieved, which can be calculated as follows: D 5200/D 1800 = 2.89. Also, this can approximately be seen in Fig. 7 (arrow b). As presented earlier, the typical tool service life for the material type in question is 50,000–100,000 joints. The minimum service life calculation presented earlier puts in this respect more pressure on trying to reach the limit of 50,000 joints. With the means presented above, the service life of clinching tools has already been lengthened in this particular case. Discussing the subject at a general level is not easy; aiming at lengthening the service life leads to case-specific examinations and measures. If a clinching tool lasts for 100,000 joints, the total cost of a manufacturing batch would be D 1000 as calculated above, in which case self-piercing riveting would be a 1.8 times more expensive process (D 1800/D 1000). If the target level of 200,000 joints with one pair of tools was reached, the cost difference between the processes would be 3.6 times in favor of clinching.
the amount of joints made in the product, the profitability of self-piercing riveting offers a possibility for that. If we study again the clinching too l service life of 19.000 joints, the difference in total costs is 2.89-fold. It means that when calculating with Eq. (2), the amount of joints can also be increased up to 2.89 times larger, which means 577,777 rivet joints. In that case, there would be rivets in the product at intervals of about 50 mm. As stated in the introduction, in many cases a joint with a rivet is stronger than a joint made only of the base material, so in practice, this is important only if the tightness of the construction needs to be increased. However, the opposite situation occurs when clinching tool service life of over 55,555 joints is achieved, for example, 100,000 or 200,000 joints as already earlier presented as examples. With a clinching tool service life of 100,000 joints, to reach the same total costs calculated with Eq. (2), only 111,111 rivets can be used, which is 56% of the amount planned. With this amount of rivets the distance between joints increases to be 1.8 times longer, i.e. 270 mm, which is not structurally possible. The service life of 200,000 doubles the value. Let us consider the total costs but with relative values. In that case, with Eqs. (1) and (2) and in Fig. 7 it can approximately be seen that with a joint amount of 111,111 pieces the total costs in both clinching and self-piercing riveting are equal. So-called normalized total costs are graphically presented in Fig. 8, where the amount of rivets and the clinching tool service life are on the X-axis, as pointed out earlier. The relative difference of the joining techniques in the total costs can be seen on the Y-axis.
5.5. Varying the amount of rivets As stated earlier, as long as the clinching tool service life is less than 55,555 joints, self-piercing riveting is a more profitable process considering the total costs for the 200,000-joint series studied. We could also argue that if there is a need to increase
Fig. 8. The comparative total costs of clinched joints and self-piercing riveted joints as a function of the clinching tool service life and the amount of selfpiercing rivets.
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Fig. 9. The line rising upwards presents the effect of increasing the clinching tool service life in the total cost savings achieved when compared to self-piercing riveting. Also, the increase in savings (as percentage units) and the proportional need for increasing the service life between the points of examination are presented in the figure.
The limit value of 111,111 joints is equivalent to the value 1 on a comparative scale, which therefore means that the total costs are equal in both processes. If the clinching tool service life falls short of the limit value, it is possible to use more rivets in a joint with equal total costs than in clinching (the number is n-fold) according to the diagram and the relative value indicated by the Y-axis. The part of the diagram that exceeds the limit value (111,111 pieces) shows how much less there are rivets to be used with equal total costs compared to the amount of clinched joints.
interval. Correspondingly, the amount of cost savings achieved is low, which is depicted with a line symbolized by squares in Fig. 9 and presented as percentage units in the third column from the left in the table next to the figure. The line symbolized by triangles in Fig. 9 and the column on the right-hand side in the table present the relative need to increase the tool service life between the points of examination. It can be stated that considering the total costs, the savings required for a proportional tool service life increase is reached at no examination interval.
5.6. The cost resonance of increasing the clinching tool service life
6. Conclusions
The increase in total cost savings compared to self-piercing riveting, if it is possible to lengthen the clinching tool service life, is presented with a line symbolized by rhombi in Fig. 9. The amount of 55,555 joints that was calculated above and with which the total costs are equal, is used as the lowest limit. The examination ends at the service life of 200,000 joints. The second column from the left in the table next to the figure presents cumulative savings in numerical values when the chosen interval of examination is 10,000 joints. It can be noted that a maximum of 72% of cost savings in the total joining costs can be reached. The area of examination is very broad when evaluating the issue from the viewpoint of increasing the tool service life. The change from one end to the other would mean that the tool service life would need to be increased by 3.6-fold. The shape of the graph is explained by the division of the examination period into 15 sectors, when the relative increase in service life remains small between the blocks at the upper end of the examination
Joining with and without an additional joining element differ significantly from each other on the basis of cost formation principles. In a technique without an additional joining element the unit costs decrease as the tool service life increases, and also the total costs decrease. On the contrary, the additional joining element unit costs in the technique with an additional joining element are constant and tooling costs in self-piercing riveting can even be ignored in this example due to their minor significance. Total costs increase directly in proportion to the amount of joints in techniques using an additional joining element. The durability of clinching tools depends on the materials joined. Although different materials can be joined with same tools, the most reliable reference data is attained when it is possible to examine a large production run within which the tool service life runs out. In such a case, it has been possible to minimize the influence of other so-called external factors in the tool service life. By comparing the two processes, we can determine the minimum value for the service life of clinching tools, with equal
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total costs for one manufacturing batch. The number is a limit value, and going under or exceeding it leads to reducing or increasing the price competitiveness of the clinching technology. We have also presented a way to calculate, with the aid of the limit value, possibilities to increase the amount of rivets in joints without losing the advantage in price competition against clinching. This article introduces a possibility to calculate and analyze the cost effects of joining techniques with and without an additional joining element in product manufacturing. The points presented may be considered as a general model of analysis that can also be applied to other processes than the ones presented here by using the correct numerical values for each technique. The model also serves in estimating the sensitivity of the cost effects of a single process, a situation that can rise, for example, when optimizing portions of the most profitable additional joining element offered for large production runs. It is important to note that the means of examination presented in the article are only one part of the investment cost estimations. As stated in the beginning, for example, the proportion of investments in equipment needed or their significance has not been taken into account at all since the objective was a clear and easily applied exposition. References
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