Datum B and C are assigned to the side surfaces of datum A and are given perpendicularity tolerances with respect to datum A. All geometrical tolerances on this part will refer to these datum A,B and/or C.

In figure 5, datum A (the most stable and easy to access surface on a part) on part 1 is the top surface of the part and is given a flatness tolerance, that is an unrelated tolerance (the family of form tolerance).

The transition temperature can be changed by manipulating the alloy’s composition. These alloys have a super elastic feature that can be used as a shock absorber for stone constructions, among other things.

Finally, the dimension and tolerance for the pulley (figure 10) are similar to the rotor part as both the pulley and rotor are cylindrical parts. Datum A is the internal (middle) cylinder of the pulley. Position tolerances are applied to control the axis of the big cylinder to be coaxes with the middle cylinder (datum A).

For the rotor (figure 10), the most stable feature for datum A is the main axis of the cylinder. Because, the rotor is cylindrical and does not have a large stable or flat surface. Geometric tolerances applied to the rotor are cylindricity to control the cylinder shape including the axis and position tolerances to control the axis of the middle cylinder.

Nickel alloys with chromium and molybdenum are added to increase creep rupture strength. Alloy 617, for example, has a composition of 20-24 percent chromium, 10-15 percent cobalt, and 8-10 percent molybdenum, with a minimum nickel concentration of 44.5 percent supplied under the brand names Inconel 617 and Nicole 617.

In figure 5 and 6, to tolerance pin and hole features, position tolerances are commonly used. The reason is that position tolerance also controls cylindricity of the pins and holes.

The results of the tolerance analyses with the two methods are $(70\pm 2.485) mm$ for the calculation based on worst-case method and $(70\pm 1.26) mm$ for the calculation based on statistical method.

Nickel-iron alloys are helpful in precise measurement equipment and thermostat rods because of their high dimensional stability. Other nickel-iron alloys with a higher nickel percentage are used in soft-magnetic applications such as transformers, inductors, and memory storage devices.

Alloy C-276 (N10276) is the most well-known of these corrosion-resistant alloys. They have a high resistance to reducing acids like hydrochloric and sulphuric acid. Several variations based on this composition have changed the Cr and Mo amounts and, in some cases, added Cu or W to increase corrosion resistance in more oxidizing or reducing environments. Alloy C-22 (N06022), Alloy 59 (N08059), Alloy C-2000 (UNS N06200), and Alloy 686 (N06686) are some of the alloys available.

The design and assembly of the belt tensioner are shown in figure 8. Meanwhile, figure 9 shows the different 2D projection views of the belt-tensioner assembly.

Figure 1 shows an illustration of the effect of mean-shift of the production process of a component. In this illustration, even if the process is under control (the process variations on both red and green situations are within $3\sigma$ tolerances), the produced component will be out of its tolerance.

How to dotolerance stackup analysis

In the early twentieth century, the discovery of ore resources in Russia and South Africa made large-scale nickel production viable. World War I and World War II soon followed, resulting in major increases in steel consumption and, as a result, nickels demand.

In this case we consider tolerance stack-up analysis in 2D, that is variation is considered in a planar plane and rotational variations are not considered.

The main goal of tolerance analysis is to check that the dimensions and tolerances of components are correct so that after the components are assembled, the assembled product can function as desired.

This smaller total variation implies that with statistical-based method, we can allocate higher values for the tolerance than with worst-case method. This higher tolerance values mean that the part can be manufactured and inspected at lower cost than the one with tighter tolerance.

Every part constituting an assembled product has tolerances assigned to the part’s features. These assigned tolerances cause variations on the key characteristics (KCs) of the assembled part. How can we know how much the variations on the KCs before manufacturing the parts?

This natural element is now used in various applications, making it one of the most important metals. Some of the nickel’s important uses are listed below:

There are four main parts constituting the assembly: base, support, rotor and pulley. The KC or the assembly key characteristic that should be controlled is the clearance between the pulley and the base so that there is no friction between the pulley and base during operation.

Nickel-molybdenum alloys are chemically resistant to strong acids and other reducers such as hydrochloric acid, hydrogen chloride, sulfuric acid, and phosphoric acid. An alloy, such as Alloy B-2, has a molybdenum concentration of 29-30% and a nickel concentration of 66-74 percent in its chemical makeup. Applications include pumps and valves, gaskets, pressure vessels, heat exchangers, and pipe work.

These alloys are also prized for their high-temperature creep and rupture properties. These alloys are typically 30-35 percent nickel, 19-23 percent chrome, and a minimum of 39.5 percent iron. Due to their high iron concentration, these alloys have been categorized as stainless steel.

Nickel is classified as a transition metal. Because of its slow oxidation rate at normal temperatures, it is hard, malleable, and corrosion-resistant. It’s also magnetic at ambient temperature and has a high melting point.

Every part constituting an assembled product has tolerances assigned to the part’s features. These assigned tolerances cause variations on the key characteristics (KCs) of the assembled part.

The nominal value of the KC (the clearance between the pulley and base) can be calculated by summing all the nominal values ($X_{n}$) for every feature (points) in the tolerance chain. The nominal value of the KC is:

To perform the tolerance stack-up analysis, we need to define the tolerance chain of the part. Figure 3 shows the KC and tolerance chain of the part in figure 2. Tolerance chain describes the propagation of accumulated tolerances from point A to point B.

The metal was dubbed kupfernickel, ‘the devil’s copper,’ by fifteenth-century German miners who believed they could extract copper from nickel ores in Saxony. Due to their futile attempts to extract copper from the ore and likely due to the health effects caused by the ore’s high arsenic content.

Nickel is a strong, shiny, silvery-white metal common in our daily lives, appearing in everything from television remote batteries to stainless steel kitchen sinks. Although many nickel alloys, including stainless steel, are safe to work with, additional care must be taken to protect the safety of people working with some other nickel compounds, including metallic nickel, because they have been linked to cancer.

Corrosion resistance, high-temperature strength, and electrical resistance are desirable properties of nickel-chromium alloys. NiCr 70/30, for example, has a melting point of 1380oC and an electrical resistivity of 1.18-m. Nikrothal 70, Resistohm 70, and X30H70. Nickel-chromium alloys are heating elements in toasters and other electrical resistance warmers.

Statistical-based analysis is a tolerance analysis method that sum-of-squares all values of allocated tolerances. This method assumes some degree of confidences on the estimated sum-of-squares total variations ($2\sigma$ is 95% confidence).

Table 3 shows the results of the 2D tolerance stack-up analysis based on worst-case method and table 3 shows the results of the analysis based on statistical method. As can be observed from table 3 and 4, beside assembly shift, other variations occur and are caused by bonus tolerances.

Fibrosis, lung cancer, and other diseases are more common in these employees. When high nickel concentrations accumulate in the air, soil, food, or water supply, humans are in danger of poisoning.

This book is a humble effort to map well-known and proven principles and rules from various disciplines, such as management, organization decision theory, leadership, strategy, finance and marketing, into a single practical research guide that applies to all disciplines.

Shape retention and shape memory qualities are seen in nickel-titanium alloys. By making a shape out of this alloy at a higher temperature and then deforming it from that produced shape at a lower temperature, the alloy will remember its original shape and reform it when heated to this so-called transition temperature.

In this example, an assembly consisting of two parts is used. The assembly use not only “+/-” tolerance, but also geometric tolerance (GD&T).

Sulfides containing nickel, copper, and iron are found in Canadian ores. Pentlandite (Ni, Fe)9S8  is the most important nickel mineral, followed by pyrrhotite (FeS to Fe7S8), in which some of the iron is replaced by nickel. The primary copper mineral in these ores is chalcopyrite (CuFeS2) and cubanite (CuFe2S3).

The datum B and C on the support is used as the references of the hole position to insert the rotor part. Other geometrical tolerances on the support are profile tolerances to control the surface profile of the surfaces.

In addition, We also recommend books “Deep Work: Rules for Focused Success in a Distracted World” about how to do work that give big results by Cal Newport.

Figure 7 shows the tolerance chain of the two parts’ assembly. The KC is the vertical distance between point A and point B and also shown in figure 7. In figure 7, we can observe there are many variation sources related to the centre of the pins and holes that are the assembly features.

The nominal dimension and tolerances (both “+/- ” and GD&T) of the parts are shown in figure 10. In figure 10, for the base, there are three datums: A, B and C. Datum A (selected due to the surface is the most stable and easy to access) is the main reference and has a flatness tolerance of $0.01 mm$, that is the tightest tolerance due to datum A is the main reference for all geometric tolerances on the base.

But remember, there will be a small probability that the KC will be not met after assembly because there is a change that some defective parts pass the inspection.

Where $ Tol_{i}$ is the $i$-the tolerance in equal-bilateralformat ($\pm Tol_{i}$) and $k$ is a safety factor to take into account variances from components supplied from other companies. In general, $k=1.5$ if components are supplied from other companies. If all components are made in-house, $k$ can be set to 1 (meaning the variations of components can be controlled because the components are made in-house).

Tolerance allocation and tolerance stack-up analysis always come “hand-in-hand” and cannot be separated each other. Tolerance stack-up analysis and tolerance allocation are iterative processes that are carried out until the desired KC of an assembly is satisfied based on given geometrical and dimensional tolerances (GD&T) on parts.

The detailed dimensions and tolerances of the two parts are shown in figure 5 and 6. It is worth to note that in figure 5 and 6 there are datums. These datums are the requirements of using GD&T, especially to tolerance related features.

Nickel-Copper Alloys are nickel-base alloys with a substantial alloying element of copper (Cu) of 29-33 percent. Mono-phase solid solution of copper and nickel. Heat-treatable nickel-copper alloys with 3% aluminum (Al) and 0.6 percent titanium (Ti) as additional alloying elements can be enhanced by precipitation hardening.

Table 1 shows the analysis based on worst-case method. The direction of tolerance propagations that are relevant is only in horisontal direction. From table 1, the results of the total variation based on worst-case method is that the distance variation between point A and B is $5.325mm$ and the nominal distance is $50.33mm$.

Tolerance stackup analysis Excel

The tolerance chain is shown as red arrows and is flowing through the features affecting the KC. The determination of this tolerance chain is half-science and half-art. Because, very often, there are several ways in defining the tolerance chain of an assembly.

Table 5 shows the detailed calculation of the mean ($X_{n}$) and variation ($T_{x}$) for each point on the tolerance chain in figure 11. In table 5, the mean and variation value for each point on the chain are presented. Note that the tolerance format is in equal-bilateral format.

The nickel carbonyl gas decomposes on the surface of pre-heated nickel pellets that circulate through a heat chamber until they reach the necessary size. This procedure can be used to make nickel powder at greater temperatures.

It is worth to note that, in general, with additional geometric tolerances, the total variation will be higher than in the case where only “+/-” tolerancing is used. The reason is that with geometric tolerance, the source of tolerance values is more than only use “+/-” tolerances.

Toleranceloopexample

If too much nickel enters the human body, it has negative consequences like many other metals on the planet. For starters, inhaling certain nickel compounds while mining can cause miners to develop life-threatening allergies.

However, the separation method for these ores is significantly less expensive than for lateritic ores like those found in New Caledonia. Furthermore, nickel sulfides frequently contain impurities of other precious elements that can be extracted economically.

Belt-tensioners are commonly found on various applications, such as timing-belt systems in car engines, chain tensioners in bicycles and conveyor belts in factories. The main components of a belt-tensioner are pulleys to bear the belts so that tensions can be applied to the belts.

A systematic approach on tolerance stack-up analysis is necessary to reduce the number of iteration processes to determine correct tolerance values on part’s features.

Tolerance stack-up analysis is unique because this analysis is half-science and half-art (depends on how we determine a tolerance chain)

The other geometric tolerances on base are profile tolerance and position tolerance. The position tolerance controls the accuracy of the holes as the features to assemble other parts to the base.

Most metals, including copper, chromium, iron, and molybdenum, will easily alloy with nickel. The addition of nickel to other metals changes the properties of the alloy, which can be utilized to achieve desirable attributes like improved corrosion or oxidation resistance, increased high-temperature performance, or reduced coefficients of thermal expansion.

Since the analysis is 2D, we only consider variation in horizontal and vertical directions. Specifically for this case, only variation chains in vertical direction are relevant since the clearance (KC) is in vertical direction.

The tolerance chain of the belt-tensioner is shown in figure 11. In figure 11, the KC is clearance or gap between the pulley and base, as being mentioned above, and is shown as green arrow in figure 11.

The distance between the pulleys and the base on the tensioner should be maintained. Because, the pulley should not touch the base when the tensioner is in operation.

In figure 2, the tolerance is shown in two formats: unequal bilateral (figure 2 left) and equal bilateral (figure 2 right) formats. Both worst-case and statistical-based analyses require tolerances to be in equal bilateral format.

Nickel-chromium-iron alloys combine these elements to generate alloys that resist oxidation and high-temperature corrosion. Alloy 800, also known as Incoloy 800, Ferrochronin 800, Nickelvac 800, and Nicrofer 3220, is used in furnace components such as petrochemical furnace cracker tubes and as a sheathing material for electrical heating elements.

Tolerancestack-up loop diagram

Tolerance stack-up analysis is a method used to evaluate the cumulative effect of tolerances allocated on the features of components and to assure that the cumulative effect is acceptable to guarantee the functionality of a product after assembly processes.

A belt-tensioner assembly is presented in this example. The belt-tensioner has a function to provide force so that the tension level of a belt can be maintained.

As can be seen in table 5, the nominal values ($X_{n}$) for all geometrical tolerances (at point A, D,F,G, I,J,K,L,M,N) are always zero. Because, in perfect condition, all geometrical variations should be zero.

Nickel is recovered principally from the nickel sulfides pentlandite, pyrrhotite, and millerite, containing approximately 1% nickel, and the iron-bearing lateritic ores limonite and garnierite, which contain around 4% nickel.

Nickel-iron alloys are used in applications where a low thermal expansion rate is desirable. The coefficient of thermal expansion of Invar is about a tenth of that of carbon steel.

Note that with this statistical-based method, we do not need to inspect all parts to be within their tolerances. Instead, we can sample parts from a batch production and inspect them.

By performing tolerance stack-up analysis, important questions regarding the assembly process and the final KC of a product can be answered before manufacturing, for examples:

The experience of design and manufacturing engineers play an important role on the first determination of tolerance values. Because, the value of tolerances are directly related to how difficult a part can be made and how much the cost to make the part.

Tolerance stack-up analysis cannot be separated with tolerance allocation. Because both tolerance analysis and allocation are an iterative process that is performed until the variation on the final KC below a threshold.

For the support (figure 10), the most stable surface for datum A is the bottom surface of the support with flatness tolerance of $0.01 mm$. The other datums are datum B and C that have perpendicularity tolerances with respect to datum A.

Meanwhile, table 2 shows the analysis based on statistical method. From table 2, the total variation calculated by statistical-based method is $2.82mm$ with the same nominal dimension of $50.33mm$.

Worst-case analysis is a tolerance analysis method that adds all maximum values of allocated tolerances. Worst-case analysis is formulated as:

With the capability of estimating the final variation, design correction and improvement can be done at early design stages and can significantly save product development costs.

For this analysis, the total variation is calculated by root-sum-squared all the $T_{x}$. The safety factor in this analysis is 1.5 considering some parts are made from other manufacturers.

There is also some gold, silver, and the six platinum-group metals, and their recovery is crucial. Cobalt, selenium, tellurium, and sulfur can all be extracted from ores.

These bonus tolerances are obtained because the hole and pin features deviates from the maximum material condition (MMC) of the holes and pins.

As explained before, with statistical-based method, the total variation is smaller than that calculated from worst-case method. In this case, the total variation calculated by using statistical-based method is 47% lower than that of worst-case method.

In 1751, Baron Axel Fredrik Cronstedt isolated pure nickel for the first time, but it had been known for a long time. Chinese texts from circa 1500BC mention ‘white copper,’ which was almost certainly a nickel-silver alloy.

Nickel matte and nickel oxide can be made from sulfide ores by froth flotation, hydrometallurgical, or magnetic methods. The Sherritt-Gordon Treat is routinely used to process further these intermediate products, which typically contain 40-70 percent nickel.

Tolerance stackcalculation

We sell tutorials (containing PDF files, MATLAB scripts and CAD files) about 3D tolerance stack-up analysis based on statistical method (Monte-Carlo/MC Simulation).

If you want more details and interesting 3D tolerance stack up analysis, we sell tutorials (containing PDF files, MATLAB scripts and CAD files) about 3D tolerance stack-up analysis based on statistical method (Monte-Carlo/MC Simulation). You can purchase from the given link.

Despite being the fifth most prevalent element on (and in) our planet, pure nickel reacts with oxygen and is thus rarely found on the surface. Nickel is particularly stable when combined with iron, which explains its presence in iron-bearing ores and its practical use in stainless steel production.

Tolerance stack-up analysis is a powerful method to estimate the final variation on the key characteristic (KC) of an assembly before manufacturing.

Different names refer to the same tolerance stack-up analysis, such as: tolerance analysis, tolerance-chain analysis, variation stack-up analysis and assembly-chain analysis.

Because of their high iron content, lateritic ores are frequently smelted using pro-metallic techniques. Because lateritic ores have high moisture content (35-40%), they must be dried in a rotary kiln furnace. It generates nickel oxide, which is reduced in electric furnaces at temperatures ranging from (1360 0C -1610 0C and volatilized to produce Class I nickel metal and nickel sulfate.

Nickel-Copper Alloys have excellent acid and alkali corrosion resistance, high mechanical strength, good flexibility, and a low coefficient of thermal expansion. The alloys have low machinability. Chemical processing equipment, valve stems, springs, pumps, shafts, fittings, heat exchangers, screw machine products, and marine equipment use nickel-copper alloys.

Industrial furnace components, gas turbines, nitric acid catalyst grid supports, and fossil fuel production facilities require these alloys.

Based on this method, the total variation is calculated by summing all the absolute values of $T_{x}$. Based on this method, all manufactured parts (base, support, pulley and rotor) should be inspected to assure that all parts are in tolerance.

From figure 11, the tolerance chain is A—B—C—D—E—F—G—H—I—J—K—L—M—N—O. B,C,E,H are nominal dimensions so that their variations are zero. A,D,F,G,I,J,K,L,M,N,O are due to tolerances both dimensional and geometrical tolerances so that the mean value is zero.

Tolerance stackupexamplePDF

However, with GD&T, the tolerancing of the part is better than only using “+/-“ tolerances. Because, with GD&T, the representation of the parts and assembly considers the real conditions of the manufacturing process of the parts so that the results of the tolerance analysis will be significantly more accurate than the analysis that only considers “+/-” tolerance (you may read this post for more explanations).

In this post, we will discuss two types of real-time processing applied to global navigation satellite system (GNSS) signal processing. In addition, we will discuss a circular buffering system for real-time applications with equal data rate of input and output.

Nickel is extremely strong and corrosion-resistant, making it ideal for reinforcing metal alloys. It’s also ductile and malleable, which means its numerous alloys may be formed into wire, rods, tubes, and sheets.

In this example, both tolerance analysis and allocation will be presented. The 2D tolerance analyses of the parts constituting the belt-tensioner assembly use both worst-case and statistical-based methods.

In figure 6, datum A (again, the most stable and easy to access surface on a part) on part 2 is the bottom surface of the part and is also given a flatness tolerance. And, similar to part 1, the other datum B and C are assigned to the side surfaces of datum A.

The smaller the tolerance value, the tighter the tolerance, and then the higher the production and inspection cost, and otherwise.

The Mond (or Carbonyl) Process is most popular and efficient technique for treating nickel sulfide is the Mond (or Carbonyl) Process. The sulfide is treated with hydrogen and fed into a volatilization kiln in this procedure. At around 60 0C, it reacts with carbon monoxide to generate nickel carbonyl gas.

James Riley gave a talk to the Iron and Steel Institute of Great Britain in 1889 about how nickel may be used to improve traditional steel. Riley’s talk sparked interest in nickel’s good alloying qualities, and it also corresponded with the discovery of huge nickel reserves in New Caledonia and Canada.

The nickel separation process is largely dependent on the ore type. Nickel sulfides, such as those found in the Canadian Shield and Siberia, are typically found deep below, making extraction difficult and costly.

Laterites are ore that forms due to peridotite weathering with a minor fraction of nickel. In subtropical climates, weathering eliminates most of the host rock, but the contained nickel dissolves and percolates downstream, potentially reaching a high concentration to make mining profitable.

It is important to note that datum A on both part 1 and 2 has the smallest (tightest) tolerance values compare to other tolerances. The reason is that datum A is the main reference of other datums and tolerances and should be manufactured with the highest accuracy compared to other features on part 1 and 2.

Nickel, with the symbol Ni and the atomic number 28, is a chemical element. Nickel is a silvery-white, brilliant metallic element that occurs naturally. It is the sixth most prevalent element on the planet and is abundant in the crust and core. Nickel, like iron, is a common element in meteorites and is also found in trace amounts in plants, animals, and oceans.

In this example, the slot feature of a component made by a milling process is analysed. Figure 2 shows the dimensions and tolerances of the features on the component. The KC is the distance between the two slots.

Multilateration is a position determination method that is locating an object by accurately computing the distance between the object and three or more other objects (e.g., transmitter or laser tracker) with known positions. This method is also known as hyperbolic position determination.

This post will explain the method used to analyse tolerance/variation stack-ups in 2D. Examples are given to give a clear understanding on how to perform 2D tolerance stack-up analysis on parts.

Figure 4 shows the two parts used in this example. The assembly features are the two pins and holes of the parts. These pins and holes are the features that join the two parts.