Electromechanical system design-practice on designing haptic feedback PDF

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Complete description and practice on using Maxwell and FEM for designing haptic feedback...

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MAE 535: Design of Electromechanical Systems

Spring 2017

Design Optimization of a Semi-Active Haptic Feedback Device

Project Report Submitted by: Bal Govind (#200161457) Vinod Kumar Singla (#200149761) Naveen Sankar (#200160717)

MAE 535: Design of Electromechanical Systems

Spring 2017

Contents 1.

Problem Description and Magnetic Circuit Analysis (MCA) ............................................................................. 4

2.

Design Optimization ................................................................................................................................................. 6

3.

Validation .................................................................................................................................................................... 8

4.

Time response .......................................................................................................................................................... 11

Appendix ............................................................................................................................................................................ 12 Genetic Algorithm optimized design candidates: ................................................................................................... 12 Matlab Code: ................................................................................................................................................................. 12

MAE 535: Design of Electromechanical Systems

Spring 2017

List of Figures Figure 1. Concept schematic ............................................................................................................................................. 4 Figure 2. Simplified circuit for MCA ............................................................................................................................... 4 Figure 3. Spool & Cylinder ................................................................................................................................................ 5 Figure 4. FEMM Analysis (B in MRF = 0.6023 T) ....................................................................................................... 8 Figure 5. Solid model of spool, cylinder and coil .......................................................................................................... 9 Figure 6. Flux density variation in the MRF gap ........................................................................................................... 9 Figure 7. Flux density through mid-surface of cylindrical MRF fluid volume ...................................................... 10 Figure 8. Flux density through X-Y plane shows greater saturation near coil....................................................... 10 Figure 9. Simulink model for the device ....................................................................................................................... 11 Figure 10. Flux density (B) vs time ................................................................................................................................ 11 Figure 11. damping force vs time ................................................................................................................................... 11

List of Tables Table 1. Area & mean path length used to compute reluctance of segmented elements ....................................... 5 Table 2. Optimized design dimensions and specifications........................................................................................... 7 Table 3. Optimized design candidates ........................................................................................................................... 12

MAE 535: Design of Electromechanical Systems

Spring 2017

1. Problem Description and Magnetic Circuit Analysis (MCA) The design of the spool and cylinder is contingent on designer preferences and tradeoffs which are outlined below: •

The quantity of iron removed from the spool (to reduce weight) will affect the path of flux lines from the coil to the Magneto-Rheological Fluid (MRF) and baffle. As a later section on the Finite Element Analysis will show, if a relatively small quantity of iron is recovered to reduce the net weight of the device, the curvature of flux path-lines will be mostly unaffected. However, if a hole of relatively larger depth/ diameter is made in the spool, flux path increases sub-optimally.

•

The lengths of the spool and cylinder are decided based on the plausible travel of the lever in either direction. That is, for a lever of length, say, 12 inches with a travel of 4 inches in either direction and having a rod attached to the spool of 2 inches at the lever center, the cylinder length would be 6 inches. Note, these values are considered to limit overall footprint of the device. The dimensions will be further optimized to meet or exceed the performance specifications. Note, the inspiration behind 4-inch lever travel in either direction was taken from a typical mousepad which is about 8 inches in diameter.

Figure 1. Concept schematic •

To compute the reluctance of the magnetic circuit for analysis a simplified circuit (Figure 2) consisting several individual reluctances in series is considered. In addition, to resolve the reluctance of individual elements, the total volume is segmented as shown in Figure 3. Sections for which areas vary or are complex to compute, an estimate is made by taking average of areas of respective starting and ending sections. The areas and mean path length thus computed for each segment are shown in Table 1.

Figure 2. Simplified circuit for MCA

MAE 535: Design of Electromechanical Systems

Spring 2017

Figure 3. Spool & Cylinder

Table 1. Area & mean path length used to compute reluctance of segmented elements Segment

Area of cross section (Ax)

Mean Path length (Lx)

a

2𝜋(𝑟1 2 − 𝑟0 2 )

ℎ0

b c d

ℎ1

𝜋(𝑟1 2 − 𝑟0 2 + (𝑟1 + 𝑟0 )√(ℎ1 )2 + (𝑟1 − 𝑟0 )2 )

𝑟1 − 𝑟3

𝜋((𝑟1 + 𝑟0 )√(ℎ1 )2 + (𝑟1 − 𝑟0 )2 + (𝑟1 + 𝑟3 )√(ℎ1 )2 + (𝑟1 − 𝑟3 )2 )

ℎ2 − ℎ1

𝜋(𝑟1 + 𝑟3 )(√(ℎ1 )2 + (𝑟1 − 𝑟3 )2 ) + √(ℎ2 )2 + (𝑟1 − 𝑟3 )2 ) 𝜋((𝑟1 + 𝑟3 )√(ℎ2 )2 + (𝑟1 − 𝑟3 )2 + 2𝑟1 ℎ2 )

e f

2𝜋(𝑟4 + 𝑟1 )ℎ2

2(𝑟4 − 𝑟1 )

2𝜋(𝑟6 2 − 𝑟5 2 )

ℎ0 + ℎ2

2𝜋(𝑟4 + 𝑟5 )ℎ2

g h

𝑟1 − 𝑟3

2(𝑟5 − 𝑟4 )

In addition to no fringing & saturation assumptions, assuming a fixed relative permeability of MRF (µrm = 4) and iron (µri = 5000) for magnetic circuit analysis (MCA), we can estimate the flux (Ф) and consequently the flux density (B) in the MRF. The equation for the magnetic circuit can then be written as: 𝑀𝑀𝐹 = 𝑁𝑖 = 𝑅Ф

𝑅 = 𝑅𝑎 + 𝑅𝑏 + 𝑅𝑐 + 𝑅𝑑 + 𝑅𝑒 + 𝑅𝑓 + 𝑅𝑔 + 𝑅ℎ

𝑁𝑖 = [

1 𝐿𝑏 𝐿𝑐 𝐿𝑑 𝐿𝑒 𝐿𝑓 𝐿ℎ 𝐿𝑎 𝐿𝑔 1 + + )+ + + + ( + ( )] Ф 𝜇0 𝜇𝑟𝑚 𝐴𝑎 𝐴𝑏 𝐴𝑐 𝐴𝑑 𝐴𝑒 𝐴𝑓 𝐴ℎ 𝜇0 𝜇𝑟𝑖 𝐴𝑔

The above equation is used to estimate flux density (B) for the optimized design in section 3 which is later validated with FEMM & Maxwell results. Note, non-linear B-H curves digitized from the project prompt figures and FEMM are used for the simulations.

MAE 535: Design of Electromechanical Systems

Spring 2017

2. Design Optimization There are several tradeoffs that exist between conflicting design requirements. Quantifying these tradeoffs is key to optimization problem setup. The objective function consists of damping force (Fd), total weight (M), input electrical energy (Ws), time constant (τ), flux density (B) and penalty function (p). A high penalty (p=1000) is added if the value of time constant exceeds 0.09 sec or if the damping force exceeds 110N. The limits are intentionally set lower than the allowed max limits to account for modelling uncertainties. To prevent flux saturation, maximum magnetic field density is restricted to 1.5 Tesla. The input electrical energy & total weight terms positive terms added to the objective function which penalize for increasing power utilization/weight. To ensure off state damping is less than 5 N, the gap is constrained to be always greater than 1.5mm. Different weighting factors are added to individual terms in the objective function to bring them around the same order of magnitude. Since, the objective function is highly non-linear, a robust heuristic search method - genetic algorithm (GA) - is used for optimization of design parameters. Based on an approximate overall cylinder width of 6 inches and spool width of 2 inches as determined by the maximum lever travel, the upper and lower limits are imposed on the individual design parameters. Notice the radii are constrained in such a way that they always result in a feasible design. Also, as explained in section 1, we have chosen 𝑟3 ≤ 𝑟1 and ℎ1 ≤ ℎ2 (since removal of more material contorts flux path lines and considerably increases the individual segment reluctances). The optimization problem in standard form is given below: 𝑀𝑖𝑛. 𝑜𝑏𝑗𝐹 = 𝑝 + 15𝑀 − 𝐹𝑑 + 𝑊𝑠 + 20 × 𝑚𝑎𝑥. [𝐵𝑚𝑎𝑥 − 1.5,0] Subject to: g1 (x): 𝑟2 - 𝑟1 ≤ 3 mm

g2(x): −𝑟2 +𝑟1 ≤ -0.5 mm g3 (x): 𝑟3 - 𝑟1 ≤ 0

g4 (x): −𝑟2 +𝑟4 ≤ 2 mm g5 (x): 𝑟2 - 𝑟4 ≤ -1 mm

g6 (x): −𝑟4 + 𝑟5 ≤ 3 mm

g7 (x): 𝑟4 - 𝑟5 ≤ -1.5 mm

g8(x): −𝑟5 + 𝑟6 ≤ 10 mm g9(x): 𝑟5 - 𝑟6 ≤ -2 mm

g10(x): ℎ1 - ℎ2 ≤ 0 With upper and lower bounds on design variables: 10 mm < 𝑟1 < 20 mm

11 mm < 𝑟4 < 25 mm

5 mm < ℎ0 < 30 mm Where:

10.5 mm < 𝑟2 < 23 mm

12 mm < 𝑟5 < 27 mm

0 mm < ℎ1 < 22.5 mm

0 mm < 𝑟3 < 20 mm

14 mm < 𝑟6 < 37 mm

5 mm < ℎ2 < 22.5 mm

MAE 535: Design of Electromechanical Systems

Spring 2017

𝐹𝑑 (𝐵, 𝜈) = 𝜂𝜈

Damping force, Area between lands of the piston,

𝐴 = 2 × (2𝜋

𝑟4 +𝑟5 2

𝑊𝑠 = 𝑉𝑠 𝐼𝑠

Input electrical energy,

𝐴

𝑟5 −𝑟4

+ 𝜏𝑦 (𝐵)𝐴

ℎ2 )

𝑚𝑐 = 3𝜋(ℎ0 + 2ℎ2 )(𝑟6 2 − 𝑟5 2 )𝜌𝑖

Mass of the cylinder housing,

𝑚𝑠 = 𝜋[(ℎ0 + 2ℎ2 )(𝑟4 2 − 𝑟0 2 ) − 2ℎ1 (𝑟3 2 − 𝑟0 2 ) − ℎ0 (𝑟4 2 − 𝑟1 2 )]𝜌𝑖

Mass of the spool,

𝜋

Mass of the copper wire,

𝑚𝑤 =

Number of turns of copper wire,

𝑁𝑐 = ℎ0

Length of copper wire,

𝑙𝑤 = 2𝜋

4

𝑑𝑤 2 𝑙𝑤 𝜌𝑐

(𝑟2 −𝑟1 ) 𝑑𝑤 2

(𝑟1 +𝑟2 ) 2

𝑁𝑐

𝑀 = 𝑚𝑐 + 𝑚𝑠 + 𝑚𝑤

Total weight,

𝑁𝑐 2 𝑅𝑅𝑐

Time constant,

𝜏=

Reluctance of the circuit,

𝑅=

Wire resistance,

𝑅𝑐 =

Electrical resistivity of copper,

𝐿 1 ( 𝑎 𝜇0 𝜇𝑟𝑚 𝐴𝑎

+

4𝜌𝑒 𝑙𝑤 𝜋𝑑𝑤 2

𝐿𝑏 𝐴𝑏

+

𝐿𝑐 𝐴𝑐

𝐿

+ 𝐴𝑑 + 𝑑

𝐿𝑒 𝐴𝑒

𝐿𝑓

𝐿

+ 𝐴 + 𝐴ℎ ) + 𝑓

ℎ

𝐿𝑔 1 ( ) 𝜇0 𝜇𝑟𝑖 𝐴𝑔

𝜌𝑒 = 1.68 × 10−8 Ω. 𝑚

𝜌𝑖 = 7.87 × 103 𝑘𝑔/𝑚3

Density of iron,

𝜌𝑐 = 8.96 × 103 𝑘𝑔/𝑚3

Density of copper,

𝜇0 = 1.25663706 × 10−6 𝑚. 𝑘𝑔. 𝑠 −2 𝐴−2

Permeability of free space,

𝑉𝑠 = 12 𝑉

Supply Voltage,

The optimization algorithm is run 10 times and the results are tabulated for each run (see appendix). Since the optimized design candidates meet or exceed stated specifications, the design with lowest size/mass & objF value is selected as the final design. The final design dimensions are further rounded off to decrease the tolerance needed for machining and a non-significant variation in performance is observed. Table 2 shows the dimensions of the spool & cylinder for the optimized design and estimated specifications. Table 2. Optimized design dimensions and specifications Dimension (mm) Value

r1 13.6

r2 16.4

Specification Value

τ (s) 0.089

Specification Value

Ba (T) 1.49

r3 7.4

r4 17.4

r5 18.9

r6 23.3

h0 13.8

Fd (N) M (kg) lw (m) 108.15 0.79 58.26

Vs (V) 12

Is (A) 0.60

Ws(W) Nc 7.22 618

Bb (T) Bc (T) 1.33 1.17

Be (T) Bf (T) 0.858 0.70

Bd (T) 1.03

Bg (T) 0.598

h1 9.5

h2 12.7 Rc (Ω) 19.94

Bh (T) objF 1.49 -89.04

MAE 535: Design of Electromechanical Systems

Spring 2017

3. Validation To ensure accuracy of predicted magnetic field intensity (B) in the magnetorheological fluid (MRF) and performance specifications, both 2 dimensional (2D) and 3 dimensional (3D) finite element analysis (FEA) is done. Although a 2D FEA may seem redundant at first, but performing it is essential to establish confidence in the design before a 3D FEA is attempted as it is computationally expensive to conduct a 3D simulation. The relative permeability of MRF (µrm ) is set to 5 for the simulation as per the predicted magnetic field from MCA. The results from a 2D simulation performed in FEMM are shown in Figure 4. As it can be observed, the magnetic field in the MRF (0.6023 T) is within 3% of that predicted by magnetic circuit analysis (0.598 T).

Figure 4. FEMM Analysis (B in MRF = 0.6023 T)

The 3-D magneto-static analysis is then performed with an objective of finding the effective magnetic flux density in the region encompassed by the magnetorheological fluid. The geometry modelled in Ansys Maxwell 15.0 is shown in Figure 5. It is formed by the revolution of the individual component crosssections, which are parameterized. The excitation is defined at the cross-section of the coil in a circumferential direction. The dimensions of the computational domain (‘Region’) exceed that of the device by 250 per cent in all axes to account for effects of fringing. Properties of the non-linear behavior of the MRF and pure iron are tabulated and incorporated into the B-H curves in the materials’ database. The convergence criteria is a uniform 0.5 percent of energy residuals for the cases considered. This is achieved in about 15 iterative passes with progressively increasing tetrahedral grid size.

MAE 535: Design of Electromechanical Systems

Spring 2017

Figure 5. Solid model of spool, cylinder and coil

We particularly investigated the variance of flux through the radial gap filled by the baffle between the spool and the cylinder. As shown in Figure 6, the flux density shows small variation along the radial distance in the MRF between the r4 and r5.

Figure 6. Flux density variation in the MRF gap

MAE 535: Design of Electromechanical Systems

Spring 2017

Further shown in contour plots of Figures 7 & 8, fringing occurs along the edges of the radial conduction paths. There is sharp rise in flux density at the interface of the MRF and the ferromagnetic cylinder. Objectively, the non-linear B-H relationship causes the gradient in magnetic field, the mean of which corroborates the results of magnetic circuit analysis and 2-D FEMM analysis.

Figure 7. Flux density through mid-surface of cylindrical MRF fluid volume

Figure 8. Flux density through X-Y plane shows greater saturation near coil

MAE 535: Design of Electromechanical Systems

Spring 2017

4. Time response To analyze the variation of damping force as supply voltage (Vs = 6 (1+ sin(t))) is varied from 0 to 12 V sinusoidally with time, a Simulink model (Figure 9) is created. As it can be observed from Figures 10 & 11, there is a one to one correlation between variations in supply voltage and the associated damping force/gap flux density.

Figure 9. Simulink model for the device

Figure 10. Flux density (B) vs time

Figure 11. damping force vs time

MAE 535: Design of Electromechanical Systems

Spring 2017

Appendix Genetic Algorithm optimized design candidates: Table 3. Optimized design candidates DV r1 r2 r3 r4 r5 r6 h0 h1 h2 objF

x1 13.41 15.32 13.36 16.50 18.01 22.43 20.57 12.72 12.74 -88.30

x2 13.27 15.21 4.32 16.21 17.71 22.11 20.31 4.71 12.91 -86.26

x3 15.47 17.96 9.78 19.12 20.69 24.94 14.89 4.43 14.30 -86.56

x4 13.59 16.42 7.40 17.43 18.93 23.28 13.79 9.47 12.68 -89.05

x5 13.59 16.34 6.16 17.42 18.92 23.27 14.15 5.37 12.67 -88.72

x6 13.48 15.63 13.48 16.63 18.13 22.57 18.23 12.79 12.79 -89.09

x7 13.55 15.83 13.55 16.95 18.46 22.87 17.24 12.67 12.67 -89.56

x8 13.59 16.27 3.57 17.27 18.77 23.15 14.55 5.71 12.78 -88.47

x9 13.59 16.30 11.04 17.34 18.84 23.20 14.40 12.25 12.64 -89.65

x10 13.44 15.81 3.90 16.81 18.31 22.69 16.57 5.65 12.81 -87.66

Matlab Code: % MAE 535 Design of Electromechanical Systems - Course Project % Optimization for semi-haptic feedback device design % Optimization_master.m Vinod Kumar Singla 4/20/2017 clear all;clc;close all; lb = [10;10.5;0;11;12;14;5;0;5]; % lower bounds on individual design variables ub = [20;23;20;25;27;37;30;22.5;22.5]; % upper bounds on individual design variables opts = gaoptimset('PlotFcn',{@gaplotbestf,@gaplotstopping},'Generations',2000,'TolFun',1e-8); fitnessfcn = @objF; nvars = 9; nonlcon = []; Aeq = []; beq = []; A = [-1 1 0 0 0 0 0 0 0;1 -1 0 0 0 0 0 0 0;-1 0 1 0 0 0 0 0 0;... 0 -1 0 1 0 0 0 0 0;0 1 0 -1 0 0 0 0 0;0 0 0 -1 1 0 0 0 0;... 0 0 0 1 -1 0 0 0 0;0 0 0 0 -1 1 0 0 0;0 0 0 0 1 -1 0 0 0;... 0 0 0 0 0 0 0 1 -1]; b = [3;-0.5;0;2;-1;3;-1.5;10;-2;0]; [x,fval,exitflag,output] = ga(fitnessfcn,nvars,A,b,Aeq,beq,lb,ub,nonlcon,opts) % MAE 535 Design of Electromechanical Systems - Course Project % Optimization for semi-haptic feedback device design % objF.m Vinod Kumar Singla 4/20/2017 function f = objF(x) %Note: x = [r1, r2, r3, r4, r5, r6, h0, h1, h2] r1 = 1e-3*x(1); r2 = 1e-3*x(2); r3 = 1e-3*x(3); r4 = 1e-3*x(4); r5 = 1e-3*x(5); r6 = 1e-3*x(6); h0 = 1e-3*x(7); h1 = 1e-3*x(8); h2 = 1e-3*x(9); % Data needed r0 = 1e-3; % inner bore dia, m

MAE 535: Design of Electromechanical Systems

Spring 2017

rho_i = 7.87*10^3; % iron density, Kg/m^3 rho_c = 8.96*10^3; % copper density, Kg/m^3 dw = 25*1e-5; % copper wire dia, m mu_0 = 1.25663706*1e-6; % Permeability of free space , m*kg*s^-2*A^-2 mu_ri = 5000; % Relative Permeability of iron, dimensionless mu_rf = 4; % Relative Permeability of mrf, dimensionless Nc = h0*(r2-r1)/dw^2; % Number of wire turns, dimensionless Lw = 2*pi*Nc*(r1+r2)/2; % Wire length, m Aw = pi*dw^2/4; % cross sectional area of wire, m^2 rhoe = 1.68*10^-8; % electrical resistivity of copper (ohm-m) %yeta = 250; % dynamic viscosity of mrf, Pa-s, for v = 1 m/s Rw = rhoe*Lw/Aw; % total wire resistance, ohms Vs = 12; % Supply voltage, volts Is = Vs/Rw; % current in the coil, amps As = pi*(r4+r5)*h2*2; % area b/w lands of piston & cylinder wall, m^2 penalty = 0; % Will be increased for exceeding a certain preset # of turns % mass calculation mc = 3*pi*(r6^2-r5^2)*(h0+2*h2)*rho_i; % Cylinder mass, Kg, assuming cylinder length to be 3 times to that of spool ms = pi*((2*h2+h0)*(r4^2- r0^2)-2*h1*(r3^2-r0^2)-h0*(r4^2-r1^2))*rho_i;%Spool mass, Kg mw = (pi/4)*dw^2*Lw*rho_c; % coil mass, Kg M = mc+ms+mw; % Total mass of spool, cylinder and coil, Kg % Magnetic circuit analysis (MCA) for calculating B in mrf Aa = 2*pi*(r1^2-r0^2); La = h0; Ab = pi*(r1^2-r0^2+(r1+r0)*sq...