Clutches and Brakes | Design and Selection | William C. Orthwein | Tay

ABSTRACT

Conveniently gathering formulas, analytical methods, and graphs for the design and selection of a wide variety of brakes and clutches in the automotive, aircraft, farming, and manufacturing industries, Clutches and Brakes: Design and Selection, Second Edition simplifies calculations, acquaints engineers with an expansive range of application, and a

TABLE OF CONTENTS

chapter 1|4 pages

Friction Materials

chapter |2 pages

FIGURE 1 Display of brake lining fade test results. (Courtesy of Scan-Pac, Mequon, WI).

chapter |1 pages

FIGURE 2 Coefficient of friction versus sliding speed at an average pressures of 1.415 Mpa, or 205 psi (a), and 7.074 Mpa, or 1,026 psi (b), for the fillers as indicated; Open triangle: TiO ; filled triangle: ZrO; open

chapter |1 pages

square: glass; filled square: bronze; open circle: graphite; filled circle: MoS ; X: unfilled, half-filled

chapter |2 pages

FIGURE 3 Specific wear of PTFE as a function of sliding speed for.

chapter |2 pages

with a nominal coefficient of friction of 0.40. (Adapted from Reddaway Manufacturing Co., Inc., Newark, NJ.)

chapter |5 pages

FIGURE 6 Construction of brakes having sintered linings working against steel plates (upper) and having carbon linings working against carbon plates (lower). (Courtesy ASM Handbook, ASM International, Materials Park, OH.)

chapter 2|1 pages

Band Brakes

chapter |1 pages

FIGURE 1 Band brakes used in an automatic transmission system.

chapter |6 pages

FIGURE 2 Quantities and geometry used in the derivation of the band-brake design relations.

chapter |1 pages

FIGURE 4 (a) Lever-activated band brake; (b) backstop configuration with a= be ; (c) backstop with levers a

chapter |1 pages

FIGURE 5 Backstop.

chapter |5 pages

FIGURE 6 Positive discharge bucket conveyor cutaway and cross section. (Courtesy American Chain Association, Washington, DC.)

chapter 3|1 pages

Externally and Internally Pivoted Shoe Brakes

chapter |1 pages

FIGURE 1 Externally pivoted shoe brake. (Courtesy Automation & Process Technology Div., Ametek Paoli, PA.)

chapter |8 pages

FIGURE 2 Internal pivoted shoe brake. (Courtesy of Dyneer Mercury Products, Canton, Ohio.) FIGURE 3 Geometry involved in calculating moment M about pivot

chapter |11 pages

FIGURE 7 Design curves for Mf/(µMp) for φ1=10°. r/R ratios for the upper, external brake, curves are: 1—r/R=0.2; 2—r/R=0.4; 3—r/R=0.6; 4—r/R=0.8. r/R ratios for the lower, internal brake, curves are: 5—r/R=1.2; 6—r/R=1.4; 7—r/R=1.6; 8—r/R= 1.8.

chapter |1 pages

FIGURE 14 Primary pressure distributions.

chapter |1 pages

FIGURE 15 Primary pressure distributions. FIGURE 16 Secondary pressure distributions.

chapter |3 pages

FIGURE 17 Secondary pressure distributions.

chapter |2 pages

TABLE 3 Lining Pressure and Shoe Braking Torque Associated with Primary Shoe Pressure Given by Equation (4–12) (Unit Width Shoe)

chapter |1 pages

FIGURE 18 Electric drum brake activated by a cam attached to a magnet arm. (Courtesy of Warner Electric Brake & Clutch Co., South Beloit, IL.)

chapter |1 pages

FIGURE 19 Exploded view of the components of the electric brake shown in Figure 18. (Courtesy of Warner Electric Brake & Clutch Co., South Beloit, IL.)

chapter |1 pages

FIGURE 20 Electric drum brake activated by a cam and pin attached to the slightly rotating electromagnet. (Courtesy of Warner Electric Brake & Clutch Co., South Beloit, IL)

chapter |2 pages

FIGURE 21 Exploded view of the components of the electric brake shown in Figure 20. (Courtesy of Warner Electric Brake & Clutch Co., South Beloit, IL.)

chapter |3 pages

Warner Electric Brake & Clutch Co., South Beloit, IL.)

chapter 4|1 pages

Linearly Acting External and Internal Drum Brakes

chapter |1 pages

FIGURE 1 Linearly acting, centrally pivoted shoe brake. (Courtesy of the Hindon Corp., Charleston, SC)

chapter |1 pages

FIGURE 2 Linearly acting, twin-shoe, internal drum brake with pneumatic activation (Girling Twinstop). (Reprinted with permission. ©1977 Society of Automotive Engineers, Inc.)

chapter |5 pages

FIGURE 3 Rim brakes with pneumatic activation (also used as rim clutches). (Courtesy of Eaton Corp., Airflex Division, Cleveland, Ohio.)

chapter |5 pages

FIGURE 6 Geometry used in the analysis of a linearly acting internal shoe drum brake.

chapter |3 pages

FIGURE 7 Curve 1: Distance h

chapter 5|1 pages

Dry and Wet Disk Brakes and Clutches

chapter |2 pages

FIGURE 1 Floating, or sliding, caliper disk brake. (Courtesy of Misco, Inc., North Mankato, MN.)

chapter |2 pages

FIGURE 2 Combination disk brake and disk clutch, both dry. (Courtesy of Minster Machine Co., Minster, OH.)

chapter |2 pages

FIGURE 4 Annular sector caliper disk brake. (Courtesy of Horton Manufacturing Co., Inc., Minneapolis, MN.)

chapter |1 pages

FIGURE 5 Caliper disk brake with circular pads, two pistons. (Courtesy of Misco, Inc., North Mankato, MN.)

chapter |3 pages

FIGURE 6 Typical caliper brake pad of sintered material for heavy aircraft brakes. (Note contour of the pad to place lining material toward the outer periphery of the disk.) (Courtesy Friction Products, Medina, OH.)

chapter |1 pages

FIGURE 7 Ventilated caliper disk brake. (Courtesy of Eaton Power

chapter |1 pages

Transmission Systems, Airflex Division, Cleveland, OH.)

chapter |3 pages

FIGURE 8 Approximate pad life as a function of the maximum disk pressure. (Courtesy of Twiflex Corp., Horseheads, NY.) FIGURE 9 Large calipers for disk brakes-model vs. referenced in Figure 8. (Courtesy of Twiflex Corp., Horseheads, NY.)

chapter |1 pages

FIGURE 11 Dry multiple-disk brake, pneumatically activated. (Courtesy of Wichita Clutch Co., Dana Corp.,

chapter |2 pages

Power Transmission Div., Toledo, OH.)

chapter |2 pages

FIGURE 13 Geometric relations between ρθr, and r . Arc length at

chapter |1 pages

inches acting on a disk 11.0 inches in diameter for p =300 psi.

chapter |4 pages

FIGURE 16 Caliper brake lining that is a sector of an annular ring.

chapter 6|1 pages

Cone Brakes and Clutches

chapter |5 pages

FIGURE 1 Cone brake and its geometry (partially worn lining).

chapter |1 pages

FIGURE 4 Design regions in the µ, α plane for cone clutches/brakes.

chapter |1 pages

FIGURE 5 Truck cone brake and rotor (drum). (From reference 1. Reprinted with permission, © 1978 Society of Automotive Engineers, Inc.)

chapter |2 pages

FIGURE 6 Cone brake on front-wheel-drive subcompact and the cone brake components. (From reference 1. Reprinted with permission, © Society of Automotive Engineers, Inc.)

chapter |8 pages

FIGURE 7 Cone geometry.

chapter 7|3 pages

Magnetic Particle, Hysteresis, and Eddy-Current Brakes and Clutches

chapter |3 pages

FIGURE 1 Representative hysteresis loops for (a) low-loss material and (b) high-loss material.

chapter |1 pages

FIGURE 4 Hysteresis brake with a 8-lb-ft capacity. (Courtesy of Magnetic Power Systems, Inc., Fenton, MO.)

chapter |1 pages

FIGURE 5 Magnetic particle clutch and brake combination. (Courtesy Simplatrol Dana Industrial, Webster, MA.)

chapter |2 pages

FIGURE 6 Schematic of a magnetic brake/clutch to display its operation. (a) Magnetic particle clutch. (b) Input shaft “R” and output shaft “N” are positioned within the electromagnetic coil. Magnetic particles lay loosely between input and output components. No current is applied to the coil. No torque is transmitted. (c) Here maximum current energizes the coil. The clutch now operates at 100% of clutch rating. Full transmission of torque occurs. Depending on coil current, any level between 0 and 100% torque transmission is possible. (Courtesy Magnetic Power Systems, Inc., Fenton, MO.)

chapter |1 pages

FIGURE 7 Magnetic lines of force linking the outer member (OM) and the inner member (IM). (Courtesy of Sperry Electro Components, Durham, NC.)

chapter |1 pages

FIGURE 8 (a) Torque current curve for a particular brake; (b) torque voltage curve for a series of magnetic particle brakes. (Courtesy of Sperry Electro Components, Durham, NC, and Simplatrol Dana Industrial, Webster, MA.)

chapter |1 pages

FIGURE 9 Torque-slip speed curves for dry friction and magnetic particle brakes (also clutches).

chapter |1 pages

FIGURE 10 Hysteresis clutch with cutout section showing the OM (which also forms the outer shell), the IM, and the electromagnetic coil. (Courtesy of Magnetrol Inc., Buffalo, NY.)

chapter |2 pages

FIGURE 11 Schematic of (a) a hysteresis brake and (b) a hysteresis clutch. The E-shaped cross section represents the cross section of the OM and its inner post (the outer shell in Figure 10). (Courtesy of Magnetrol, Inc., Buffalo, NY.)

chapter |2 pages

inner post. (Courtesy of Magnetrol, Inc., Buffalo, NY.) FIGURE 13 Torque (also termed slip torque) differential speed (or slip speed) for hysteresis brakes of different capacity. The dashed line shows the effect of increased cooling. (Courtesy of General Electro-Mechanical Corp., Buffalo, NY.)

chapter |2 pages

. FIGURE 14 Torque versus differential speed (a) and torque versus control current (b) for a particular hysteresis brake. Torque differential speed curve shown corresponds to approximately 30 mA of control current through a 1900-Ω coil. (Courtesy of General Electro Mechanical Corp., Buffalo, NY.)

chapter |1 pages

FIGURE 15 Eddy-current loops induced in the IM by the changing H field in an eddy-current brake.

chapter |1 pages

FIGURE 16 Combined torque rotational speed curve and torque excitation curves for eddy-current brakes. (Courtesy of Eaton Power Transmission Systems, Industrial Drives Operations, Kenosha, WI.)

chapter |1 pages

FIGURE 17 Air-cooled eddy-current brakes with torque capacities from 5 to 1740 Ib-ft and power dissipation from 0.75 to 100 hp. (Courtesy of Eaton Power Transmission Systems, Industrial Drives Operations, Kenosha, WI.)

chapter |3 pages

FIGURE 18 Combination hysteresis/eddy-current brake/clutch. (Courtesy of Simpatrol Dana Industrial, Webster, MA.)

chapter 8|3 pages

Acceleration Time and Heat Dissipation Calculations

chapter |5 pages

FIGURE 1 Brake and gear train schematic. Moments of inertia I

chapter |1 pages

FIGURE 2 Dynamic torque as a function of the speed difference, or slip speed, between input and output shafts. (Courtesy of Warner Electric Brake & Clutch Co., South Beloit, IL.)

chapter |4 pages

FIGURE 3 Schematic conveyor systems where viscous damping is due to (a) the process itself or (b) a retarder to aid in stopping.

chapter |3 pages

FIGURE 5 Conveyor belt schematic.

chapter |3 pages

FIGURE 7 Schematic of motor, clutch, gear train, and kiln.

chapter |1 pages

element relative to the stationary element.) (Courtesy of Warner Electric Brake & Clutch Co., South Beloit, IL.)

chapter |1 pages

FIGURE 9 Schematic of motor, gear train, and drum for a typical crane. A retarder, if used, may be added at either end of the motor shaft.

chapter |4 pages

FIGURE 10 Sketch of a hoist showing the wire rope extension beyond the drum.

chapter |1 pages

FIGURE 11 (a) Torque (N-m) as a function of shoe subtended angle for a drum diameter of 200 mm. (b) Torque (N-m) as a function of disk or drum diameter d (mm) (1) a linearly acting drum brake, (2) an annular disk brake, (3) a band brake, (4) a caliper brake.

chapter |2 pages

FIGURE 12 Magnetic particle brake dynamometer. (Courtesy of Sperry Electro Components, Durham, NC.)

chapter |1 pages

FIGURE 13 Representative torque-slip speed curve for hysteresis brake showing the effect of improved cooling. (Courtesy of General Electro-Mechanical Corp., Buffalo, NY.) FIGURE 14 Typical slip watts-rpm curve for a magnetic particle clutch for various means of cooling. A force air; W, circulated water; otherwise, radiation and convection to ambient

chapter |1 pages

air. (Courtesy of Magnetic Power Systems, Inc., Fenton, MO.)

chapter |3 pages

FIGURE 15 (a) Schematic of a tension-control drawing process; (b) the corresponding diagram of the forces acting on the web; (c) draw and tension motors used in braking.

chapter |1 pages

FIGURE 17 Torque-speed curve for the load. FIGURE 18 Typical eddy-current clutch curves c, d, and e in (a), which may be used to drive the load in (b). In (a) the slip speed is represented by ω ,

chapter |1 pages

FIGURE 19 Load torque-speed and clutch torque-slip speed curves used to find minimum slip speed for load levels 1, 2, and 3 based on 100% coil excitation.

chapter |1 pages

FIGURE 20 Graphical relation between the motor operating speed, the minimum eddy-current clutch slip speed, and the load curve. Less than 100% coil excitation curves are dashed.

chapter |1 pages

FIGURE 21 Coil current and slip speed combinations that permit more than one torque-slip speed combination for some coil excitation values. FIGURE 22 Increased slip speeds to obtain unique coil current values for each point on the torque-speed curve

chapter |6 pages

for the load when using an eddy-current clutch.

chapter 9|1 pages

Centrifugal, One-Way, and Detent Clutches

chapter |3 pages

FIGURE 1 Centrifugal clutch. (Courtesy Dana Corp., Inc., Toledo, OH.)

chapter |1 pages

FIGURE 2 (a) Variation of pressure (kPa) with β for λ=0.2, 0.4, 0.6, and 0.8 for curves 1, 2, 3, and 4, respectively. (b) Variation of width (cm) with β for λ=0.2, 0.4, 0.6, and 0.8 for curves 1, 2, 3, and 4, respectively. (c) Variation of pressure (kPa) with λ for β=0.2, 0.4, 0.6, and 0.8, respectively. (d) Variation of contact speed (rpm) with λ for β=0.2, 0.4, 0.6, and 0.8 for curves 1, 2, 3, and 4, respectively.

chapter |2 pages

FIGURE 3 (a) Sector cross section. (b) Curve 1: pressure P (kPa) vs. β; Curve 2: initial contact speed n (rpm) vs. β. (c) Sector width w (cm) vs. β.

chapter |3 pages

FIGURE 4 Spring clutch and its components. (Courtesy Warner Electric Brake & Clutch Co., South Beloit, IL.)

chapter |1 pages

FIGURE 5 Typical roller clutch configurations. (a) Outer cam type of roller one-way clutch diagram. (b) Caged roller type of clutch diagram

chapter |6 pages

(hook-type cam). (c) Loose roller type of clutch diagram (leg-type cam). (d) Inner can type of roller one-way clutch diagram. (Reprinted with permission; © 1984 Society of Automotive Engineers, Inc.)

chapter |1 pages

FIGURE 8 Overrunning sprag clutch. (Courtesy Dana Corp., Inc., Toledo, OH.)

chapter |3 pages

FIGURE 9 Conventional sprag and a sector of its inner and outer races.

chapter |1 pages

FIGURE 11 Conventional sprags with their retaining springs and cages. (a) Typical single-cage one-way clutch diagram. (b) Typical full-complement

chapter |3 pages

sprag one-way clutch diagram. (c) Typical double-cage sprag one-way clutch diagram. (d) Sprag one-way clutch diagram. (Reprinted with permission; © 1984 Society of Automotive Engineers, Inc.)

chapter |1 pages

FIGURE 13 Throw-in sprag configuration and spring. (a) Regular engagement. (b) Centrifugal throw-in engagement.

chapter |2 pages

FIGURE 14 Sprag and race geometry: r =radius of inner race; r=radius of

chapter |3 pages

rotation and the strut angle. (Courtesy Dana Corp., Toledo, OH.) FIGURE 16 Relative overrun speed envelope showing representative variation between models. (Courtesy Dana Corp., Toledo, OH.)

chapter |3 pages

FIGURE 18 Forces acting on a single wedge tooth. (Courtesy Horton Mfg. Co., Minneapolis, MN, and Machine Design, Penton Press, Cleveland, OH.) FIGURE 19 Overload release clutch using clutch plates and wedge-shaped release cam. (Courtesy of Carlyle Johnson Machine Co., Manchester, CT.)

chapter |2 pages

FIGURE 21 Detent positions for an indexing ball and detent overload clutch.

chapter |1 pages

FIGURE 22 Torque limiting clutch. From the Carlyle Johnson Machine Co., Bolton, CT, Web page on the Thomas Register Web site.

chapter |5 pages

FIGURE 23 Torque as a function of the adjustable gap for the models noted. From the Carlyle Johnson Machine Co., Bolton, CT, Web page on the Thomas Register Web site.

chapter 10|3 pages

Friction Drives with Clutch Capability

chapter |2 pages

for all curves; curve 1, ξ=0.3; curve 2, ξ=0.6; curve 3, ξ=0.8.

chapter |5 pages

FIGURE 4 Upper drawing: enlarged sketch of sliding motor mount for a belt drive. Lower drawing: linkage geometry.

chapter |7 pages

FIGURE 7 Friction drive.

chapter |2 pages

FIGURE 11 Plots of the radius of curvature ρ as a function of distance z from the apex of cones having the included half-angle θ shown. The units of ρ are the units of z.

chapter |3 pages

FIGURE 12 Intersection curves of contacting cones with a plane perpendicular to the contact line in terms of the coordinates in Figure 10. Upper curve, z=3 in., =55° (driver); lower curve, z= 6 in., =35° (driven).

chapter |3 pages

FIGURE 14 Variation of the ratio of the weight to belt tension, W/T, with the ratio ξ=b/a. Upper pair: top curve, θ=20°, =15°; bottom curve, θ=30°, =15°. Lower pair: top curve, θ=20°, =20°; bottom curve, θ=30°, =20°.

chapter |1 pages

α=14°, and β=20° for all curves. γ=1000 on the largest-amplitude curve, γ=500 on the intermediate curve, and γ=200 on the smallest-amplitude curve.

chapter |4 pages

FIGURE 17 Intersection curves of a driver and a driven cone with a plane at the z-values listed. Graph (a): upper curve, z= 4.25 in., =50°; lower curve, z= 6.00 in., =40°. Graph (b): upper curve, z= 6.20 in., =45°; lower curve z= 5 8304 in =45°.

chapter 11|1 pages

Fluid Clutches and Brakes

chapter |1 pages

FIGURE 1 Cross section of a semitoroidal impeller and runner and their enclosure, or housing. (Courtesy TRI Transmission & Bearing Corp., Lionville, PA.)

chapter |3 pages

FIGURE 2 Runner and shaft in a fixture used for dynamic balancing. Not all of the balancing equipment is shown. (Courtesy TRI Transmission & Bearing Corp., Lionville, PA.)

chapter |6 pages

motor and a belt drive using the sheave that is a part of the right-hand side of the housing, shown in cross section. (Courtesy Fluid Drive Engineering Co., Inc., Burlingame, CA.) FIGURE 6 Clutch/brake torque/speed curve for the unit shown in Figure 5. (Courtesy Fluid Drive Engineering Co., Inc., Burlingame, CA.)

chapter |3 pages

magnetorheological brake. (© 2003 Lord Corporation. All rights reserved.) FIGURE 11 Typical torque in newton-meters vs. electric current in amps. It should not be used for specifications. (© 2002 Lord Corporation. All rights reserved. Lord Corp., Materials Division, Cary, NC.)

chapter 12|3 pages

Antilock Braking Systems

chapter |2 pages

snow build-up in front of the tire as its rotation slows to zero.

chapter |1 pages

FIGURE 4 Flywheel and valve positions for the Lucas Girling SCS during panic braking.

chapter |1 pages

FIGURE 5 Flywheel and valve positions for the Lucas Girling SCS during return to normal braking.

chapter |4 pages

FIGURE 6 Graph of x/s as a function of t/τ from equation 12–1.

chapter |1 pages

decision limits α, and α, and brake

chapter |2 pages

FIGURE 9 Wheel reference angular velocity ω based upon accelerator data, optimum slip limits ω and ω, angular

chapter |1 pages

FIGURE 10 Single-axis accelerometer capable of measuring acceleration from ±20g to ±500g, depending upon the model, which may be attached to the vehicle. (Courtesy GS Sensors, Ephrata, PA.)

chapter |7 pages

FIGURE 11 Plan view of accelerometer locations in a vehicle. Accelerometers a and a record

chapter 13|3 pages

Brake Vibration

chapter |1 pages

FIGURE 2 Vibration mode of a yoke-type disk brake at 10 kHz. (Reprinted with permission; © 1984 Society of Automotive Engineers, Inc.)

chapter |1 pages

FIGURE 3 Vibration of a first-type disk brake at kHz. (Reprinted with permission; © 1984 Society of Automotive Engineers, Inc.)

chapter |1 pages

FIGURE 4 Reconstruction of a double-pulsed hologram of a squealing yoke-type caliper exposed at a noise

chapter |1 pages

level of 120 dB at 2.5 kHz along with its frequency spectrum. (Reprinted with permission; © 1984 Society of Automotive Engineers, Inc.)

chapter |1 pages

FIGURE 5 Vibration mode of a squealing yoke-type caliper exposed at 120 dB at 3.1 kHz along with its frequency spectrum. Reconstruction of

chapter |3 pages

a double-pulsed hologram. (Reprinted with permission; © 1984 Society of Automotive Engineers, Inc.) FIGURE 6 Relation between contour lines in an interference hologram and the displacement perpendicular to the plane of the interference pattern.

chapter |1 pages

FIGURE 9 Backplate modes at 1888 Hz for a 180×30 mm drum brake. Noisy configuration. (Reprinted with permission, © 1984 Society of Automotive Engineers, Inc.)

chapter |1 pages

FIGURE 10 Backplate modes at 1771 Hz after backplate modification for a 180×30 mm drum brake. Quiet configuration. (Reprinted with permission; © 1984 Society of Automotive Engineers, Inc.)

chapter |1 pages

FIGURE 11 Backplate modified by adding stiffening ridges and a central raised portion, which reduced squeal by 6.5 dB at low frequency (820–990 Hz) and 4.8 dB at high frequency (1681–1888 Hz). FIGURE 12 Squeal histogram for a vehicle test on a chassis dynomometer.

chapter |2 pages

FIGURE 13 The natural, or resonant, frequencies of each component of the automotive disk brake tested.

chapter |1 pages

FIGURE 14 Sketch of a caliper and disk showing the spring and dashpot associated with each of the masses involved.

chapter |1 pages

FIGURE 15 (a) Variation of squeal index α. with variation in the friction coefficient; (b) assumed dependence of the friction coefficient µ on the relative, or slip, velocity.

chapter |1 pages

FIGURE 16 Sketch of the caliper and disk brake assembly. FIGURE 17 Dependence of the squeal index on the torque member stiffness.

chapter |1 pages

FIGURE 18 Examples of calculated mode shapes of the disk.

chapter |1 pages

FIGURE 19 Examples of mode shapes for the brake pad. FIGURE 21 Examples of mode shapes for the torque member of the caliper. (a) and (b) Modal analysis (left); FEM (right).

chapter |2 pages

FIGURE 22 Photograph and cross section of a ThermoQuiet brake pad. (Courtesy Wagner Brake Products, Federal-Mogul Corp., Southfield, MI.)

chapter 14|6 pages

Engineering Standards for Clutches and Brakes