Material Mechanics, Properties and Strength Calculations: Cam Materials and Contact Stress

Cam Materials and Contact Stress

The strength demands on cams combine surface hardness with fatigue resistance under millions of stress repetitions.

Maximum Allowable Compressive Stress (Surface Endurance Limits)

Based on 100,000,000 cycles of pure rolling contact with a hardened steel roller:

Note the phosphate coating anomaly: SAE 4150 at 270–300 BHN drops from 188,000 psi to just 20,000 psi when phosphate-coated. Coatings can dramatically alter surface endurance behavior—a fact that catches many engineers off guard.

For stress repetitions significantly greater than 100,000,000 cycles, for appreciable misalignment, or where sliding occurs in addition to rolling, more conservative stress values must be used.

Hard-Facing Materials: Engineering Strength Onto Surfaces

Sometimes the base material provides structural strength while a different material provides surface strength. Hard facing applies wear-resistant alloys to surfaces by welding.

High-Speed Steel Hard Facing (RFe5 / EFe5)

• As-welded hardness: 55–60 Rc
• Annealed hardness: 30 Rc
• Hot hardness at 1100°F: 47 Rc (maintains strength at elevated temperature)
• Applications: Cutting tools, shear blades, forming dies, broaches
• Can withstand medium impact when tempered

Cobalt-Chromium Alloys

• Elastic limit (compression): 42,000 psi
• Yield strength (compression): 92,000 psi (0.01% offset), 150,000 psi (0.10% offset), 210,000 psi (0.20% offset)
• Oxidation-resistant up to 1800°F
• Excellent metal-to-metal wear resistance, resistant to galling

Copper-Base Alloy Hard Facing

Nickel-Chromium-Boron Alloys

These alloys retain hardness at elevated temperatures: NiCr-B rod deposits maintain 37 Rc at 1000°F after 3 minutes under load. Applications include seal rings, valves, screw conveyors, and cams.

Austenitic Manganese Steel Hard Facing (EFeMn)

• As-deposited hardness: 170–230 BHN
• Work-hardened hardness: 450–550 BHN
• Caution: Becomes brittle above 500–600°F—no useful hot hardness
• Outstanding for impact wear: low initial yield strength means compressive deformation rapidly raises strength until plastic flow ceases

Austenitic High-Chromium Iron (RFeCr-A / EFeCr-A)

• As-welded hardness: 51–62 Rc
• Excellent low-stress scratching abrasion resistance
• Dynamic compression stresses above 60,000 psi should be avoided
• Good oxidation resistance up to 1800°F
• Warning: Will withstand only light impact without cracking

Alloying Elements and Their Effect on Strength

Understanding what each alloying element does to strength is the key to selecting—and never again blindly substituting—materials.

The Alloying Element Guide

Nickel: Increases strength without seriously reducing ductility. Steels with 3.5% nickel are the toughest available, but they are more difficult to machine and show more distortion during heat treatment.

Chromium: Provides high hardness, improved wear resistance, and deeper hardening. When combined with proper heat treatment, chromium steels achieve excellent fatigue resistance.

Vanadium: Produces extremely fine-grained structure with high impact strength, but makes machining difficult.

Molybdenum: Increases strength without affecting ductility. For the same hardness, molybdenum steels are more ductile than any other alloy steels while maintaining nearly the same strength and superior toughness. Can be machined at higher hardness than other alloy steels.

Chrome-Nickel: Combines the ductility of nickel steels with the high strength, finer grain size, deep hardening, and wear resistance of chromium. More difficult to machine and heat treat than plain carbon steels.

Chrome-Vanadium: Tensile properties similar to chrome-nickel steels, but with increased hardening power, impact strength, and wear resistance from finer grain size.

Chrome-Molybdenum: Combines molybdenum's qualities with chromium's hardening depth and wear resistance. Very easily heat treated and machined—an important practical advantage.

Nickel-Molybdenum: Similar to chrome-molybdenum with reportedly greater toughness, but somewhat more difficult to machine.

Bearing Materials: Strength Under Sustained Load

The strength requirements for bearing materials differ fundamentally from structural components. Bearings must resist compressive loads, maintain dimensional stability under sustained pressure, and provide compatible sliding surfaces.

Babbitt Bearing Alloys (ASTM Standards)

Temperature sensitivity is critical: All babbitt alloys show dramatic strength loss at elevated temperature. ASTM Alloy 1, for example, drops from 4,400 psi yield at 68°F to just 2,650 psi at 212°F—a 40% reduction from a modest temperature increase.

Tin babbitt (80–90% tin with 3–8% copper and 4–14% antimony) follows a clear rule: increasing copper or antimony produces increased hardness and tensile strength with decreased ductility.

Quick-Reference Decision Framework

When selecting materials based on strength requirements, use this decision hierarchy:

Step 1: Identify the primary loading mode

• Predominantly tensile → prioritize yield strength and elongation
• Predominantly compressive → consider gray or white cast iron
• Cyclic/fatigue → prioritize endurance limit and impact strength
• Impact/shock → prioritize elongation and impact toughness

Step 2: Identify the operating environment

• Elevated temperature → check hot hardness and creep properties
• Corrosive → select appropriate alloy grades (CF-8, CF-8M, etc.)
• Wear-intensive → consider surface hardening or hard facing

Step 3: Match the manufacturing process

• High volume → die casting alloys (Al, Zn, Mg, Cu base)
• Complex shapes, moderate volume → sand casting (iron, steel)
• Maximum strength → wrought or forged alloy steel
• Surface strength only → hard-facing deposits

Step 4: Verify the strength-ductility trade-off

• High strength + low ductility = brittle, sudden failure risk
• Moderate strength + high ductility = forgiving, progressive failure with warning
• Match to consequences of failure

Step 5: Apply appropriate factors of safety

• Static loads, ductile materials: 1.5–2.0 on yield
• Fatigue loads: use endurance limit with appropriate life factors
• Impact loads: apply application factors (1.0–2.8 depending on severity)
• Human safety applications: never less than code requirements

Your Next Step

The difference between the practitioner before the crane collapse and the practitioner after it wasn't knowledge—it was respect for the consequences of getting material strength wrong.

Every number in this guide represents a physical reality. Tensile strength is the force required to tear atoms apart. Yield strength is the boundary between reversible deformation and permanent damage. Elongation is the warning distance between "fine" and "fractured."

Here's your challenge: Take the next material specification you write or review, and check it against the five-property minimum from Principle 1. Does it specify only tensile strength? Does it account for the actual loading conditions? Does it include the appropriate safety factors?

If the answer to any of those questions is "no," you now have the reference tables and formulas to fix it.

The material doesn't care about your budget constraints, your delivery schedule, or your procurement manager's opinion. It will fail exactly when the applied stress exceeds its capacity—and not one cycle later.

Build that truth into every specification, and you'll never have to explain why a crane fell.

This guide draws from ASTM, ANSI/ASME, AGMA, AISC, and ASME Boiler Code standards. All specifications referenced are for educational purposes—always verify current editions of applicable codes for design work.

Every Formula You Need to Master Manufacturing Processes

How One Miscalculation Destroyed a $40,000 Production Run — and the Mathematics That Could Have Prevented It

A stamping press screams through 100 strokes per minute. Sheet steel feeds into the die. Blanks cascade into bins. Everything looks perfect—until quality control pulls the first sample from the second shift.

The drawn shells are splitting at the base. Every single one.

the practitioner Holloway, a tooling engineer at a mid-sized automotive parts supplier, stares at the wreckage. Two thousand shells, scrap. The line is down. The customer is calling.

The root cause? Someone calculated the blank diameter using the wrong formula—ignoring the thickness reduction during drawing. The blank was oversized by 0.3 inches. That fraction translated into excessive tensile stress at the punch nose, and the metal tore apart.

This is what happens when you skip the math.

Manufacturing processes aren't just physical operations—they're mathematical operations performed on metal. Every punch, bend, draw, cast, and spark follows precise formulas that determine success or failure. Miss a variable, round the wrong number, or choose the wrong equation for your conditions, and you don't just make a bad part—you destroy tooling, waste material, and shut down production.

This guide is the complete mathematical reference for manufacturing processes. Every formula. Every variable. Every decision framework. Whether you're calculating punching forces, bending allowances, blank diameters, EDM parameters, or casting shrinkage—it's here.

Bookmark this page. You'll need it.

Punching and Blanking: The Force Calculations That Save Dies

The Core Formula for Punching Force

Every hole punched through sheet metal requires a specific force. Underestimate it, and your punch shatters. Overestimate it, and you're wasting press capacity that could be running production.

The precise formula for circular holes:

$$F = \frac{\pi \times D \times S \times T}{2000}$$

Where:

• $F$ = Force required (tons)
• $D$ = Diameter of the hole (inches)
• $S$ = Shearing strength of the material (lb/in²)
• $T$ = Thickness of the stock (inches)
• 2000 = Conversion factor (pounds per ton)

The Quick Approximation Method

For production floor calculations where you need a fast answer, use this simplified formula:

$$F = D \times T \times K$$

Where $K$ is a material factor:

The result gives force directly in tons.

Example: Punch a 2-inch diameter hole through ¼-inch steel:

$$F = 2 \times 0.25 \times 80 = 40 \text{ tons}$$

Non-Circular Holes: The Perimeter Method

When the hole isn't round, you replace the diameter $D$ with one-third of the hole perimeter:

$$F = \frac{P}{3} \times T \times K$$

Where $P$ = total perimeter of the hole.

Example: Punch a 1-inch square hole in ¼-inch steel:

• Perimeter = 4 inches
• Equivalent diameter = 4 ÷ 3 = 1.333 inches

$$F = 1.333 \times 0.25 \times 80 = 26.67 \text{ tons}$$

Example: Punch a 1 × 2 inch rectangular hole in ¼-inch brass:

• Perimeter = 6 inches
• Equivalent diameter = 6 ÷ 3 = 2 inches

$$F = 2 \times 0.25 \times 65 = 32.5 \text{ tons}$$

Approximate Tensile Strengths for Punching Calculations

When you substitute tensile strength for shearing strength (to build in a safety margin), use these values:

Pro Tip: Always use tensile strength rather than shearing strength for press selection. This ensures your equipment has adequate reserve capacity and accounts for material variability, dull tooling, and misalignment.

Clearance: The Hidden Variable That Changes Everything

Clearance is the gap between the punch and die on one side only. It's not the total difference between punch and die diameters—a misconception that has ruined countless dies.

$$\text{Clearance (one side)} = \text{Die radius} - \text{Punch radius}$$

Standard clearance formulas:

Where clearance is applied:

• Blanking (part = blank): Die is made to finished size; punch is made smaller (clearance subtracted from punch)
• Perforating (part = sheet with hole): Punch is made to finished hole size; die is made larger (clearance added to die)

How Clearance Affects Punching Pressure

This is the relationship most engineers overlook. Clearance doesn't just affect edge quality—it directly changes the force you need:

Reducing clearance increases required pressure. Tighter isn't always better—it costs energy and accelerates tool wear.

Sheet Metal Bending: The Formulas That Prevent Short Parts

Why Bending Math Matters

the practitioner Ramasamy, a fabrication engineer, once received a rush order for 500 enclosure panels with three 90-degree bends each. Her operator cut the blanks based on the inside dimensions of the finished part—no bend allowance. Every single panel came out short by almost half an inch. The material was specialty stainless steel, already cut to length. No time to reorder.

The lesson cost the shop two days and the price of 500 blanks.

Bending calculations exist because metal doesn't bend at a sharp mathematical line—it stretches along a neutral axis that shifts depending on the material, thickness, and bend radius. You must account for the length of stock consumed by each bend.

The Three Master Bending Formulas

These formulas, developed from extensive experiments by the an electrical manufacturer, calculate $L$ = the length of straight stock consumed by a 90-degree bend:

Formula 1 — Soft Brass and Soft Copper:

$$L = (0.55 \times T) + (1.57 \times R)$$

Formula 2 — Half-Hard Copper and Brass, Soft Steel, and Aluminum:

$$L = (0.64 \times T) + (1.57 \times R)$$

Formula 3 — Bronze, Hard Copper, Cold-Rolled Steel, and Spring Steel:

$$L = (0.71 \times T) + (1.57 \times R)$$

Where:

• $L$ = Length of straight stock required for the bend (inches)
• $T$ = Thickness of material (inches)
• $R$ = Inside radius of the bend (inches)

Key Insight: Notice that the radius coefficient (1.57) is identical across all three formulas—it's essentially $\frac{\pi}{2}$, the arc length of a quarter circle at unit radius. The only variable that changes between materials is the thickness multiplier (0.55, 0.64, or 0.71), which accounts for how much the neutral axis shifts outward in harder materials.

Bending Angles Other Than 90 Degrees

For any angle other than 90°, first calculate $L$ using the appropriate formula above, then adjust:

$$L_{\text{actual}} = L \times \frac{\text{Angle of Bend}}{90}$$

Critical distinction: The "angle of bend" is the angle through which the material has actually been bent, not necessarily the angle shown on the drawing.

How to interpret drawing angles:

Worked Example: Multi-Bend Part in Soft Steel

Problem: Find the total length of a part with a 180° bend and a 60° bend. Material: soft steel, thickness $T$ = 0.125 inches.

• Bend 1 radius $R$ = 0.375 in. (180° bend)
• Bend 2 radius $R$ = 0.625 in. (60° bend)

For the 180° bend:

$$L_1 = \left[(0.64 \times 0.125) + (1.57 \times 0.375)\right] \times \frac{180}{90}$$ $$L_1 = [0.080 + 0.589] \times 2.0 = 1.338 \text{ inches}$$

For the 60° bend:

$$L_2 = \left[(0.64 \times 0.125) + (1.57 \times 0.625)\right] \times \frac{60}{90}$$ $$L_2 = [0.080 + 0.981] \times 0.667 = 0.707 \text{ inches}$$

Total length = Straight sections + $L_1$ + $L_2$ = 3.5 + 1.338 + 0.707 = 5.545 inches

The Deduction Method for Square Bends

For production shop work on counters, bank fittings, and general fixtures, an alternative method works from outside dimensions and subtracts a deduction:

For V-die formed bends:

$$X = 1.67 \times B \times G$$

For draw-bench formed bends:

$$X = 1.33 \times B \times G$$

Where:

• $X$ = Total amount to deduct from the sum of outside dimensions
• $B$ = Number of bends
• $G$ = Decimal equivalent of the stock gauge thickness

Quick Reference: Deductions for V-Die Square Bends

Quick Reference: Deductions for Draw-Bench Square Bends

Example: A strip with two bends, outside dimensions 2 + 1½ + 2 inches, stock thickness 0.125 in., formed in a V-die:

• Sum of outside dimensions = 5.5 inches
• Deduction (from table, 11 gauge, 2 bends) = 0.416 inches
• Blank length = 5.5 − 0.416 = 5.084 inches

Drawn Shell Mathematics: From Flat Blank to Three-Dimensional Part

The Blank Diameter Problem

This is where the practitioner Holloway's production run failed. The blank diameter for a drawn cylindrical shell must account for every square inch of surface area that will exist in the finished three-dimensional part. Get it wrong by even a small amount, and you either can't fill the die or you tear the metal.

Formula 1: Sharp-Cornered Shells (Thin Stock, No Thickness Reduction)

$$D = \sqrt{d^2 + 4dh}$$

Where:

• $D$ = Diameter of the flat blank
• $d$ = Diameter of the finished shell
• $h$ = Height of the finished shell

Example: Shell diameter = 1.5 inches, height = 2 inches:

$$D = \sqrt{1.5^2 + (4 \times 1.5 \times 2)} = \sqrt{2.25 + 12.0} = \sqrt{14.25} = 3.78 \text{ inches}$$

Formula 2: Round-Cornered Shells

When the bottom radius $r$ doesn't exceed ¼ of the shell height:

$$D = \sqrt{d^2 + 4dh} - r$$

Simply subtract the corner radius from the sharp-corner result.

Formula 3: When Thickness Changes During Drawing

Heavy stock drawn to thinner walls changes the area relationship. Use the mean height method:

$$M = \frac{h \times t}{T}$$

Where:

• $M$ = Mean height (use this instead of actual height in the blank diameter formula)
• $h$ = Actual height of drawn shell
• $t$ = Thickness of drawn shell (after drawing)
• $T$ = Thickness of stock before drawing

Example: Shell 2 inches in diameter, 3.75 inches high. Original stock = 0.050 in., drawn thickness = 0.040 in.:

$$M = \frac{3.75 \times 0.040}{0.050} = 3.0 \text{ inches}$$

Now use $M = 3.0$ instead of $h = 3.75$ in the blank diameter table or formula. The blank diameter for a 2-inch diameter shell at 3 inches height = 5.29 inches.

Warning: This formula is accurate unless the thickness reduction exceeds about one-fifth of the original thickness. Greater reductions will produce blanks slightly too large—but this error is conservative since drawn shell edges are typically trimmed.

Formula 4: Volume-Based Method for Heavy Reductions

$$D = \sqrt{a^2 + \frac{(a^2 - b^2) \times h}{t}}$$

Where:

• $a$ = Outside diameter of the shell
• $b$ = Inside diameter of the shell
• $t$ = Thickness of shell at bottom
• $h$ = Depth of the shell

Formula 5: Weight-Based Method for Irregular Shapes

$$D = 1.1284 \sqrt{\frac{W}{w \times t}}$$

Where:

• $W$ = Weight of the shell
• $w$ = Weight of the metal per cubic inch
• $t$ = Thickness of the shell

Depth and Diameter Reductions: The Drawing Sequence

A shell can only be drawn so deep in a single operation. Exceed the limits and the metal tears. Here are the governing rules:

Rule 1: The depth of the first draw should never exceed the diameter of the shell.

Rule 2: The first shell diameter should equal approximately 60% of the blank diameter.

Rule 3: Subsequent diameter reductions depend on stock thickness:

Example: A 3-inch diameter shell in 1/16" stock after the first draw can be reduced by 20% on the next draw:

$$3.0 \times (1 - 0.20) = 2.4 \text{ inches}$$

Then 20% again: $2.4 \times 0.80 = 1.92$ inches, and so on.

Critical Note: These figures assume the shell is annealed after the first draw and at least between every two subsequent operations. Without annealing, the work-hardened metal will crack.

Ironing Limits

When drawing thins the wall (ironing), the amount per operation is limited:

• Standard operations: 0.002 to 0.004 inch per side
• Final draw (for good finish): Not more than 0.001 inch per side

Drawing Rectangular Shapes

Corner radius limits the achievable depth:

Electrical Discharge Machining (EDM): The Spark-Gap Mathematics

The Duty Cycle Equation

$$\text{Duty Cycle (\%)} = \frac{\text{On Time}}{\text{On Time} + \text{Off Time}} \times 100$$

A typical cycle might last 100 µs total: 40 µs on, 60 µs off = 40% duty cycle.

How Cycle Parameters Affect Performance

This table reveals the precise mathematical relationships between EDM control settings and outcomes:

Key relationships revealed by the data:

• Halving on time and off time (row 1 → row 2): Doubles frequency, slightly reduces MRR, but 2.5× increase in electrode wear while improving finish from 400 to 300 µin. Ra
• Reducing off time only (row 1 → row 3): Doubles frequency, 15× improvement in MRR (0.08 → 1.2), dramatically reduces wear, but slightly rougher finish
• Halving peak current (row 1 → row 4): Same frequency and duty cycle, 3.5× improvement in MRR, same wear rate, improved finish

Metal Removal Rates in the supplied reference electrode-positive polarity on high-carbon steel

Power Selection Rule of Thumb

$$\text{Amps} = \text{Electrode Area (in}^2\text{)} \times 50 \text{ to } 65$$

Example: A ½-inch square electrode:

$$0.5 \times 0.5 \times 50 = 12.5 \text{ amps}$$

Electrode Wear Classification

Electrode and Workpiece Material Compatibility

This is your decision matrix for electrode selection:

Workpiece Material Properties for EDM

Decision Rule: The melting points and specific gravities of the electrode and workpiece should preferably be similar for optimal performance. This is why copper (melting at 1,980°F) pairs well with aluminum (1,220°F) and steel (2,500°F), while graphite (sublimating at 6,330°F) resists thermal damage better for roughing operations.

Wire EDM Specifications

• Heat-Affected Zone (HAZ): With proper on/off time adjustment, depth can be held below 1 micron (0.00004 in.)
• Arc gap control: Power source maintains preset arc gap within 0.1 micron (0.000004 in.) of programmed position
• EDM drilling: Can drill a 0.04-inch diameter hole through 4-inch thick steel in approximately 3 minutes
• Practical hole size limits: Minimum ~0.012 in. (due to overcut and electrode rigidity); Maximum ~0.12 in. (for standard EDM drilling)

Casting Mathematics: From Molten Metal to Finished Part

Estimating Casting Weight from Pattern Weight

When no finished casting exists, you can estimate weight from the pattern using multiplication factors:

Example: A white-pine pattern weighs 4 pounds. Estimated cast-iron casting weight:

$$4 \times 16.00 = 64 \text{ pounds}$$

For cored castings: Fill the core-boxes with dry sand, then multiply the sand weight by:

Subtract the result from the solid casting weight to get the cored casting weight.