CNC Router Feeds and Speeds Calculator with Tool Deflection

For a flat end mill, $v_f=f_z z n$ and $v_c=\pi D n$ with explicit unit conversions. Removal rate is $Q=a_p a_e v_f$ and net cutting power is $P_c=u_c Q$. These are the Sandvik milling relationships (attached metric sheet H79, page 1). Drive input is $P_c/\eta$, torque is $P_c/\omega$, and equivalent average tangential force is $P_c/v_c$.

Let $r=a_e/D$ and $\beta=\cos^{-1}(1-2r)$. From circular engagement geometry, a tooth's chip thickness is $h(\theta)=f_z\sin\theta$ over $0\leq\theta\leq\beta$. Thus $q=\sin(\min(\beta,90^\circ))$ and $h_{\max}=q f_z$. Compensation uses $f_z=h_{\mathrm{base}}/q$; otherwise $f_z=h_{\mathrm{base}}$. Above half engagement, $q=1$. Sandvik gives the equivalent straight-edge relation; BZT publishes rounded check factors.

The following force-envelope construction is derived here, not a published peak-force correlation. Convert $u_c$ to $k_c$ in N/mm². For constant $k_c$, $F_{t,\mathrm{tooth}}=k_c a_p h_{\max}$. A straight-flute cross-section has at most $N=\lceil z\beta/(2\pi)\rceil$ teeth engaged. The resultant lateral force is bounded within this ideal model by $F_{\mathrm{env}}=N F_{t,\mathrm{tooth}}\sqrt{1+r_F^2}$. This assumes all tooth-force magnitudes simultaneously reach their individual maxima and add without cancellation. Actual peak force can exceed this ideal bound when the cutting-energy model is inaccurate. A known lateral load can replace it.

Use $D_{\mathrm{eq}}=k_dD$, $I=\pi D_{\mathrm{eq}}^4/64$, and the Euler–Bernoulli tip-load result $\delta=F L^3/(3EI)$. Integrating $EI y''=F(L-x)$ with zero root displacement and slope gives $y(x)=Fx^2(3L-x)/(6EI)$, used for the drawn shape. Mitsubishi's end-milling lesson motivates the equivalent-diameter model and its 0.7–0.8 diameter ratio. Applying the entire lateral load at the tip is conservative relative to that same load distributed nearer the clamp. The stickout sweep keeps force, diameter and modulus fixed.

A sharp, flat end mill follows a straight path with constant axial and radial engagement. Tooth spacing is uniform and feed per tooth is small compared with diameter. The animation shows conventional milling; reversing the engagement direction changes the chip history but not these maximum-thickness, removal and power results.

Specific cutting energy and the radial/tangential force ratio are user inputs, held constant. The force ratio default of 0.3 is an illustrative assumption. The default energy of 0.88 J/mm³ corresponds to KEYENCE's A7075 example value at 0.1 mm/tooth, not all aluminum alloys or router materials. Available spindle power means continuous shaft output at the selected RPM.

The cutter is an elastic, uniform equivalent cylinder perfectly clamped at its root. The entered equivalent diameter models bending stiffness; 0.75 is illustrative. Everloy's KD05 modulus supports the 600 GPa default, but cutter grades differ. The deflection allowance and machine limits are user-selected. No failure strength or safety factor is implied.

Use for screening and sensitivity studies of straight peripheral or slot milling. Require ordered machine RPM limits and a spindle speed inside that range in either speed mode. Also require 0 < radial width ≤ diameter, axial depth ≤ unsupported stickout, ordered chip-load bounds, and a baseline load inside that range. Check the current cutter data for material, diameter, depth, speed, lubrication and chip evacuation; the range does not track geometry automatically.

Very low engagement amplifies both feed and sensitivity to runout. A warning appears below 2% engagement with compensation. The small-feed approximation is flagged above feed per tooth / diameter = 0.1. These are modeling screens, not toolmaker limits.

The bending model omits shear deformation, stepped shanks, holder/spindle/machine compliance, wear, runout, vibration and regenerative chatter. A warning flags stickout below 2 diameters and displacement above 2% of stickout. Passing a static deflection or power allowance does not establish a stable or safe machining process. Use measured force or stiffness for critical accuracy work.

KEYENCE's worked power value includes division by efficiency and is therefore checked against modeled drive input power, not net shaft cutting power. ShopBot's page 6 contains a diameter typo; the reference uses the consistent dimensions on page 7. The animation is illustrative slow motion; view scales are separate and the displayed bending magnification is capped to keep the sketch readable.