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ARCS Fermi ChopperRotor and Slit Package Assembly

Design and AnalysisFinal Report

Prepared byDesign Solutions, Inc.

Geneva, IL

May 25, 2004

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Introduction

This constitutes the final report on the design and analysis of the ARCS Fermi chopper for use in the Spallation Neutron Source (SNS) instruments. The goal of this work was to develop a design for the rotor and slit package assembly consistent with an initial scope of work. The final assembly should be designed for long life, i.e. it should be simple and the design should strive for a safety factor on tensile yield stress in all materials as high as possible. Initial design criteria are summarized below.

Science volume: 70 mm (2.76 in.) high65 mm (2.56 in.) wide100 mm (3.94 in.) long

Operating speed: 600 Hz (36,000 RPM)Surface area of rotor: 141 in2 (for cooling)Rotor emissivity: 0.8 (for cooling)Operating pressure range: 200 – 500 millitorrOperating energies: 100, 500, 700, 1000 meV

ISIS MAPS Chopper Model Development and Analysis

The ISIS MAPS high-speed chopper rotor and slit package assembly served as the initial design point and unofficial baseline for the ARCS Fermi chopper design. Although detailed drawings of the ISIS rotor are not available to us, enough information can be gleaned from reference drawings and other available information to construct a finite element model of the rotor and slit package assembly. Figures 1 and 2 illustrate the model of the ISIS chopper used in the analysis. The slit package consists of a central section made up of alternating aluminum grid plates (slits) and boron composite sheets (slats). The ISIS science volume is estimated to be 64 mm high, 60 mm wide, and 98 mm long, 17% smaller than the ARCS Fermi chopper science volume. Former plates define the curvature of the slit package assembly and serve as assembly aids during insertion into the rotor. Two dowel pins are inserted to lock the slit package assembly to the rotor.

Figure 1. ISIS MAPS chopper and slit package assembly – exploded view

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Figure 2. ISIS MAPS chopper and slit package assembly

Figure 3 shows the stresses and deflections resulting from the finite element analysis for the case in which only the rotational loads are considered, i.e. without a slit package assembly. The maximum stress in the rotor body for this case is 59,800 psi and the maximum radial deflection is 0.015 in. This figure shows the exaggerated deformed shape of the rotating structure and illustrates the reason that stress reduction in these structures is so difficult. The main loads in the structure are due to the structure itself, not the slit package assembly. The rotational force on the outer wall causes bending loads that are maximum at the inside corner of the slit package window. Adding material to strengthen and stiffen the corners adds mass, which further increases the resulting stresses. This is further exacerbated by the dowel-pin holes needed to secure the slit package in the rotor. Omitting the slit package load here and in the ARCS Fermi analysis makes the process of comparing different rotor geometries more straightforward.

Figure 3. ISIS MAPS chopper rotor stress and deflection plots – rotational load only

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The slit package load results from the rotational load acting on each individual slit package component at its effective radius. These forces act on the rotor at the slit package window sidewall and vary with the detailed makeup of the slit package assembly. Without details of the individual slit package components we can only estimate the slit package load. For this analysis the weight of the individual ARCS components were scaled by their respective sizes – the ISIS components are slightly smaller than their ARCS counterparts. The makeup, i.e. the sequence in which slits and slats are stacked to make up the slit package assembly, is that used in the ISIS Type 500F assembly, which has three aluminum slits for every absorbing slat. The outward force due to rotation, f, of any individual component is given by:

grWf

2 (1)

where: W = weight of the component = speed of rotationr = effective radius of rotationg = gravitational constant

The summation of all these forces from the slit package components as a function of radius is shown in figure 4. The center of the slit package assembly is zero in this figure. The sidewall is at 1.57 in. (40 mm). The total force acting on each sidewall is 21,000 lb. Acting over a surface are of 9.72 in2 (6,272 mm2) this results in an effective pressure of 2,150 psi. Figure 5 illustrates the finite element mesh with this uniform pressure load acting on the slit package window sidewall.

ISIS MAPS Slit Package AssemblyCumulative Force Due to Rotation vs. Slit Package Radius

0

5000

10000

15000

20000

25000

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Radius (in)

Cum

ulat

ive

forc

e (l

b) Slit package end plate

Figure 4. ISIS MAPS estimated cumulative slit package sidewall load

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Figure 5. ISIS MAPS chopper rotor with pressure-loaded sidewall

Finally, figure 6 shows the stress and deflection results from the analysis with this additional sidewall load. From these figures, the maximum stress in the rotor due to rotation and the slit package load is 83,500 psi and the maximum radial deflection is 0.024 inches.

Figure 6. ISIS MAPS chopper rotor stress and deflection plots – rotational load plus 2150 psi slit package load

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Von Mises stresses are generally used when comparing the state of stress in a structure with the yield strength of the material. In the ISIS MAPS chopper case, the rotor material is believed to be a 7000-series aluminum alloy for which the published yield strength is on the order of 55,000 psi [1]. Given that to be the case, the ISIS MAPS rotor almost certainly operates with stresses above the yield strength of the material. In spite of the fact that it appears to be operating reliably, we have opted to look for a solution with lower operating stresses for the ARCS Fermi chopper rotor – significantly lower if possible.

ARCS Fermi Chopper Rotor Design Development

In spite of the apparent high stresses in the ISIS rotor, that same basic shape served as the initial design point for the ARCS Fermi chopper. We elected to use a rotor with sufficient diameter to completely enclose the slit package and sufficient height to meet the surface area requirement listed above. There are several slit package variants to consider, but their overall layouts are similar. Figure 7 shows a typical partial slit package stack-up and figure 8 shows the top view of the slit package assembly used to initially size the slit package window and rotor. The 2 mm thick minimum former plate thickness was chosen as a compromise between low weight, needed to minimize the slit package rotational load, and structural integrity, needed in the slit package assembly and insertion processes.

Figure 7. ARCS Fermi chopper – partial slit package stack

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Figure 8. ARCS Fermi chopper initial slit package outline – top view (dimensions are in mm)

The drive shaft interface was given by the drive manufacturer and is shown in figure 9.

Figure 9. ARCS Fermi chopper drive shaft interface

The resulting initial rotor is shown in figure 10. The overall height is 7.5 in. and the diameter is 6 in. The slit package window is 2.81 in. (71.43 mm) wide by 2.76 in. (70 mm) high to accommodate the slit package shown in figure 8. The material is 7175-T74 or similar suitable 7000 series aluminum alloy.

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Figure 10. ARCS Fermi chopper – initial rotor configuration

Figure 11 shows the stresses and deflections resulting from the finite element analysis for the case in which only the rotational loads are considered, i.e. without a slit package assembly. The maximum stress in the rotor body for this case is 76,000 psi and the maximum radial deflection is 0.013 in. The published tensile ultimate strength for this alloy is 64,000 psi and the tensile yield strength is 52,000 psi so clearly something has to be done to reduce this peak stress value as well as to allow for the additional load induced by the slit package [1].

Figure 11. ARCS Fermi chopper initial rotor stress and deflection plots – rotational load only

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Reducing the operating stresses and deflections from this starting point is an iterative process. The first step in this process was to remove material in the center of the rotor body. This was done as shown in figure 12. The cut is made so that the minimum depth through the slit package window is just equal to the 100 mm depth of the slit package (see figure 8).

Figure 12. ARCS Fermi chopper – interim rotor configuration

The resulting stresses and deflections for this case are shown in figure 13. The maximum stress in the rotor body for this case is 60,000 psi and the maximum radial deflection is 0.010 in.

Figure 13. ARCS Fermi chopper interim rotor stress and deflection plots – rotational load only

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The development work done in arriving at the design shown in figure 12 made it clear that –because the main load is due to the rotor material itself – removing material in the center of the rotor was necessary to reduce the rotational stresses.

The evolution of the design ultimately resulted in the rotor shown in figure 14. When compared to figure 12, material has been removed from two cavities on either side of the slit package window. The rib between them serves to reduce the radial deflection of the bottom of the cavities. The radial holes around the top and bottom perimeters are used to insert balance weights after final assembly has been completed.

Figure 14. ARCS Fermi chopper – near final rotor configuration

The resulting stresses and deflections for this case are shown in figure 15. The maximum stress in the rotor body for this case is 42,300 psi and the maximum radial deflection is 0.008 in.

Effect of the sidewall load

As discussed in the ISIS MAPS development and analysis section, all the analyses so far have only included the rotational loads, i.e. not the loads on the rotor due to the slit package itself. The final design analysis must include the effects of the sidewall load induced by the rotation of the slit package assembly. For this analysis, the heaviest slit is assumed, i.e. the 700 meV assembly. It consists of an alternating pattern of a single composite slat followed by two aluminum slits. The total stack-up contains 44 slats and 86 slits. As shown in figure 8, the end plates or formers are aluminum plates, 2 mm thick at their thinnest points. Figure 16 is a plot of the cumulative contribution of each slit and slat summed from the center. The contribution of each component is determined using equation (1) above.

The total is 17,000 lb. This is the force exerted by the outermost former plates on each of the two slit window sidewalls. Over a sidewall surface area of 70,000 mm2 or 10.85 in2, this is equivalent to an applied pressure of 1500 psi on each sidewall.

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Figure 15. ARCS Fermi chopper near final rotor stress and deflection plots – rotational load only

700 meV Slit Package AssemblyCumulative Force Due to Rotation vs. Slit Package Radius

02000400060008000

1000012000140001600018000

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Radius (in)

Cum

ulat

ive

forc

e (lb

)

Slit package end or former plate

Figure 16. ARCS Fermi chopper – Slit package induced sidewall load

Figure 17 shows the resulting stresses and deflections for this case. The maximum stress in the rotor body for this case is 66,800 psi and the maximum radial deflection is 0.013 in. This represents an increase in stress of over 50% compared to the case with no sidewall load. Figures 18 and 19 show the rotor and slit packages structures for this “near final” design.

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Figure 17. ARCS Fermi chopper near final rotor stress and deflection plots –rotational load + 1500 psi sidewall load

Figure 18. ARCS Fermi chopper and slit package assembly – near final design – exploded view

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Figure 19. ARCS Fermi chopper and slit package assembly – near final design

Perforating the formers in this design using the same pattern as the windows in the aluminum slits inside the slit package assemblies reduces the sidewall load to 1300 psi. The corresponding analysis results are shown in figure 20.

Figure 20. ARCS Fermi chopper near final rotor stress and deflection plots –rotational load + 1300 psi sidewall load

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Final Design

As mentioned earlier, the design development described above resulted in the “near final” rotor configuration. Work on the slit package assembly, particularly the assembly techniques developed to fabricate it has led to a change in the former plate thickness. Rather than the nominal 2 mm thick formers shown in figure 8, the proposed thickness is now 6.4 mm at mid-length. The increased thickness provides material at the ends of the slit package assembly for machining features on the assembly tooling. This configuration is shown in figure 21. The increased slit package width is detrimental to the design in two ways. First, it requires an increase in the slit package window width, which increases the radius of the rotating structure and the resulting rotational stresses. Second it exacerbates the sidewall load due to the formers themselves because of their increased thickness. To minimize this second effect, the formers are perforated like the aluminum slits like those in figure 7. This reduces their weight to nearly that of the thinner formers shown in figures 8, 18, and 19. The resulting sidewall load is essentially identical to the case with the thinner formers, i.e. 1500 psi. For comparison, using the 6.4 mm thick formers without perforations, results in an equivalent sidewall load of 2500 psi, over half of which is due to the formers.

The resulting final design rotor and slit package are shown in figures 22 and 23. The overall height remains at 7.5 in. and the maximum diameter at 6 in. For comparison with earlier results, the stresses and deflections due to the rotational load only are shown in figure 24. The maximum stress in the rotor body for this case is 45,600 psi – up from 42,300 for the case with the 2 mm thick former plates – and the maximum radial deflection is 0.009 in The added sidewall load due to the slit package are shown in figure 25. The maximum stress in the rotor body for this case is 71,400 psi – up from 66,800 for the case with the 2 mm thick former plates – and the maximum radial deflection is 0.015 in.

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Figure 21. ARCS Fermi initial slit package outline – top view (dimensions are in mm)

Figure 22. ARCS Fermi chopper and slit package assembly – final design – exploded view

Figure 23. ARCS Fermi chopper and slit package assembly – final design

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Figure 24. ARCS Fermi chopper near final rotor stress and deflection plots – rotational load only

Figure 25. ARCS Fermi chopper near final rotor stress and deflection plots –rotational load + 1500 psi sidewall load

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Conclusions and Summary

The design development of the ARCS Fermi chopper has been challenging and has resulted in an exhaustive set of analysis options, iterations, and results. Referring back to the introduction to this report, the development has led to a design, which satisfies the original design goals. The rotor houses a series of slit package assemblies, which satisfy the science volume requirements rotating at 600 Hz. The surface area available for cooling is 152.5 in2 and the emissivity is controllable through the selection of surface finish and surface treatment. The table below represents an attempt to summarize all the analysis cases described in this report. All except case 10 have corresponding stress and deflection plots shown in the above figures.

Summary table of stress and deflection resultsCase no. Description eq max (psi) r max (in)

1 ISIS MAPS – rotational load only 59,800 0.0152 ISIS MAPS – rotational + slit package loads 83,500 0.0243 ARCS Fermi baseline cylindrical geometry –

rotational load only76,000 0.013

4 ARCS Fermi interim rotor configuration –rotational load only

60,000 0.010

5 ARCS Fermi near final rotor configuration –rotational load only

42,300 0.008

6 ARCS Fermi near final rotor configuration –rotational load + 1500 psi sidewall load (2 mm thick solid aluminum formers)

66,800 0.013

7 ARCS Fermi near final rotor configuration –rotational load + 1300 psi sidewall load (2 mm thick perforated formers)

63,500 0.012

8 ARCS Fermi final rotor configuration – rotational load only

45,600 0.009

9 ARCS Fermi near final rotor configuration –rotational load only + 1500 psi sidewall load (6.4 mm thick perforated formers)

71,400 0.015

10 ARCS Fermi near final rotor configuration –rotational load only + 2500 psi sidewall load (6.4 mm thick solid aluminum formers)

88,800 0.019

The potential rotor alloys are all 7000 series aluminum. The final choice will be determined primarily by availability and strength. Yield strengths exceeding 70,000 psi are rare with most alloys advertised in the mid 50,000 to low 60,000 psi range. Nearly all of the cases presented here that include the sidewall load due to the slit package exceed these values. The possible exception being case 7 which has the thin 2 mm thick formers, perforated like the aluminum slits in the slit package assembly. To ensure a greatest margin of safety – all other slit package parameters being constant – the weight of the former plates must be kept to a minimum. For reference, using no formers at all, with the 700 meV slit package, results in a sidewall load of 1175 psi and a corresponding peak stress of 61,400 psi. This represents the lowest possible stress for this rotor design and a safety factor of approximately one depending on the specific alloy. For a greater margin, a reduction in either the science volume or rotating speed would be required.

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The preferred volume reduction would be first by reducing the width, currently 65 mm, then the length, currently 100 mm.

Designing structures at or near the yield strength isn’t necessarily a recipe for failure, but does make it difficult to predict their performance and long-term reliability. The ISIS MAPS chopper rotor described at the beginning of this report is proof that such structures can work and can be reliable for long periods of time.

References

1. Military Handbook - MIL-HDBK-5H: Metallic Materials and Elements for Aerospace Vehicle Structures, U.S. Department of Defense (public release), December 1998.