22-Mec-A4 Design and Manufacture of Machine Elements · December 2013

Question 4 of 8: "Snap-through" when blanking a hard steel plate

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. National Examination, 07-Mec-A4 Design and Manufacture of Machine Elements, December 2013 — 3 hours, open book, any non-communicating calculator permitted. Eight questions on six pages, divided into Part A (manufacturing processes, Q1–Q4) and Part B (machine-element design, Q5–Q8). The rubric asks for three questions from Part A and two from Part B, five questions constituting a complete paper, all of equal value (20 % each). All eight questions are solved here.

Reference texts.

Kalpakjian & Schmid, Manufacturing Engineering and Technology, 7th ed. — sand casting and casting defects (Ch. 10–12), adhesive bonding and joint design (Ch. 32), fusion welding and weld defects (Ch. 30–31), sheet-metal shearing and blanking (Ch. 16).
Budynas & Nisbett, Shigley's Mechanical Engineering Design, 10th/11th ed. — eccentrically loaded shear joints (Ch. 8–9), combined stresses and stress transformation (Ch. 3), statically indeterminate shafts and deflection (Ch. 4), brakes and clutches (Ch. 16).
Hibbeler, Mechanics of Materials, 10th ed. — transverse shear (\(VQ/Ib\)), combined loading and Mohr's circle (Ch. 7–9).
Faires, Design of Machine Elements, 4th ed. — double-block (double-shoe) brakes, self-energizing geometry, equal-wear proportioning.
ASM Handbook Vol. 15 Casting and Vol. 6 Welding, Brazing and Soldering — hot-spot/shrinkage defects; hydrogen-induced cold cracking and preheat practice (see also CSA W59 and CSA W47.1 for Canadian fabrication practice).

Check: Part B is figure-driven. Every dimension used below was read from the printed figures. Two readings are stated explicitly in Given so a grader can substitute a different interpretation without redoing the method: (i) in Figure A the low rivet is taken as lying on the same vertical centreline as the third rivet of the top row (75 + 75 = 150 mm from the left-hand rivet); (ii) in Figure D the dimension \(a\) is the horizontal spacing, measured along the operating lever, between the pin taking the upper shoe link and the pin taking the lower shoe link, with the 10 in operating arm measured from the lower-link pin.

Question 4: "Snap-through" when blanking a hard steel plate (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Explanation — snap-through (reverse-load, break-through shock)

The bang is not the punch hitting the plate; it happens at the end of the cut, and it is a release of stored elastic energy. During shearing, the punch first deforms the sheet plastically (rollover), then penetrates it, and cracks initiate at the punch and die edges. In a ductile sheet those cracks propagate slowly, the penetration before fracture is a large fraction of the thickness, and the punch force falls off gradually as the burnished band grows. In a hard, low-ductility steel the penetration before fracture is small — often only 10–20 % of the thickness — so the force climbs to a very high peak and then the crack from the punch edge runs across the remaining ligament almost instantaneously.

At the instant of that peak load, the whole machine — the press frame, the crankshaft, the connecting rod, the bolster, the die shoe and the tooling — is elastically strained, and it is storing energy \(U = \tfrac{1}{2}\,F_{\max}^2/k_{\text{press}}\), where \(k_{\text{press}}\) is the effective stiffness of the machine and die stack. When fracture completes, the resisting force collapses to essentially zero in a fraction of a millisecond. There is now nothing to hold the strained frame back, so it springs forward, the moving members overshoot, the clearances in the crank and gib joints reverse, and the load momentarily goes negative — the "reverse load". The frame then rings at its natural frequency. The audible bang is that impulse radiated as sound; the same impulse is what fatigues press frames and tie rods, chips punch edges and loosens die fasteners.

Figure 4.1 — Left: the force–stroke traces. The hard plate gives a tall, narrow peak followed by instantaneous unloading, which is the snap. Right: grinding shear onto the punch face converts the simultaneous cut into a progressive one.

(b) Minimising it, without changing the material

Every effective remedy does one of two things: it lowers the peak force \(F_{\max}\), or it makes the unloading gradual instead of instantaneous. In rough order of effectiveness and cost:

Grind shear (an angle) onto the punch or die face. This is the standard answer. Instead of the whole cutting perimeter engaging simultaneously, the cut starts at one point and progresses around the profile. The total work \(\int F\,ds\) is unchanged, but it is spread over a longer stroke, so \(F_{\max}\) falls by anything from 30 % to 60 % and the force decays smoothly rather than collapsing. A shear height of about one to one-and-a-half sheet thicknesses is usual. Put the shear on the die when the blank is the product (so the blank stays flat) and on the punch when the slug is scrap.
Stagger the punches in a multi-punch or progressive tool by stepping their lengths in increments of about the sheet thickness, so no two punches break through at the same instant. This is the same idea applied at the tool-layout level.
Optimise the die clearance. A clearance that is too small forces secondary shear and drives the force up; too large increases rollover and burr. Setting the clearance correctly for the grade and thickness (typically of the order of 6–12 % of the thickness per side for hard steel, from the tool-design tables) minimises both the peak force and the fracture energy.
Fit snap-through dampers. Modern mechanical presses offer hydraulic shock-absorbing die cushions or nitrogen "anti-snap-through" cylinders that absorb the released frame energy. Retrofitting these, or adding a hydraulic overload protector, is the fix when the tooling cannot be re-ground.
Reduce the press speed and, if the press is oversized for the job, move the work to a press whose capacity and stiffness are better matched — a very stiff frame stores less energy at a given force, and a slower stroke reduces the dynamic overshoot. Keeping the tooling sharp also matters: a dull punch raises \(F_{\max}\) and worsens the snap.

Two things a candidate should not propose: annealing or substituting the sheet (explicitly ruled out by the question), and simply moving to a larger press without shear or dampers, which raises the stored energy and usually makes the bang worse.

Topic. Shearing/blanking mechanics, punch force–stroke behaviour, and press snap-through.

Key relations. Blanking force \(F = 0.7\,UTS \times t \times L\) (perimeter \(L\), thickness \(t\)); shearing work \(W = \int F\,ds \approx K\,F_{\max}\,t\); elastic energy stored in the press \(U = \tfrac12 F_{\max}^2/k_{\text{press}}\); shear height on the punch \(\approx (1\!-\!1.5)\,t\); typical die clearance a few per cent of \(t\) per side, larger for harder material.

Why this works. The severity of the snap is governed by how fast the load disappears, not by how large it was. A hard sheet fractures after very little penetration, so the load drops from its maximum to zero in a very short stroke and the press frame — which is nothing but a very stiff spring holding \( \tfrac12 F_{\max}^2/k\) of energy — is released as if a rope had been cut. Grinding shear onto the tool forces the perimeter to be cut sequentially, which both lowers \(F_{\max}\) (less perimeter engaged at any instant, so less stored energy for the same job) and stretches the unloading over many milliseconds so the release becomes a push rather than an impact. Dampers attack the same term from the other end by giving the released energy somewhere to go.

Common pitfall. Believing that shear on the punch reduces the work done and therefore the press capacity in energy terms — it does not; it redistributes the same work over a longer stroke, so the flywheel energy requirement is essentially unchanged while the peak force falls. A second pitfall is putting the shear on the punch when the blank (not the slug) is the product, which distorts the part.

Source. Kalpakjian & Schmid, Manufacturing Engineering and Technology, 7th ed., Ch. 16 (sheet-metal shearing: punch force, clearance, shear angle on punches and dies, snap-through and press selection).

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