The phrase "tolerance stack" usually refers to a geometric problem: when multiple components are assembled, the dimensional variation in each part accumulates in ways that can push the assembly outside specification. That is a well-understood design problem with established statistical analysis tools.
There is a parallel problem in process parameter space that does not have an equally well-known name, but it causes similar kinds of frustration. When you adjust one machining parameter, you have also adjusted the effective operating conditions for every other parameter in the system. The parameters are not independent. Optimizing them sequentially, one at a time, produces results that are locally optimal but not globally optimal. Understanding why requires looking at the specific coupling mechanisms.
The Feed Rate Example: One Change, Four Effects
Take feed rate as a representative case. Increasing feed rate on a turning operation affects at minimum: material removal rate (directly, obviously); chip geometry and chip breaking behavior; cutting forces at the tool-workpiece interface; heat generation in the cutting zone; and surface roughness through the kinematic relationship between feed, nose radius, and the curvature of the tool path.
Each of those effects then propagates. Higher cutting forces increase tool deflection, which directly affects dimensional accuracy: if the tool deflects 8 microns under load, you cannot hold a 10 micron bilateral tolerance without accounting for that deflection in your setup. Higher heat generation affects tool wear rate, which means the same feed rate that is optimal at the beginning of a tool life cycle may produce unacceptable surface roughness at 80% of tool life. Worse chip breaking behavior affects surface finish through chip re-cutting and may also affect coolant effectiveness by altering the chip evacuation dynamics.
None of this is news to experienced process engineers. The problem is not that the interactions are unknown. The problem is that they are addressed sequentially in practice: adjust feed rate, observe the dominant effect, adjust the most immediate problem, observe again. This one-at-a-time approach is rational given limited production time, but it misses the fact that the interaction terms in the parameter response surface often have larger effects than the main effects. You can optimize feed rate and depth of cut independently until both are locally good, and still be sitting well below the joint optimum because their interaction is antagonistic in the regime you happened to explore.
Spindle Speed and Its Coupling Partners
Spindle speed is the parameter most often adjusted first in trouble-shooting, and it has the most coupling partners. At the resonance frequencies of the workpiece-fixture system, increases in spindle speed produce chatter regardless of feed rate, depth of cut, or coolant conditions. But the resonance frequencies are not fixed: they depend on the stiffness of the workholding, which depends on clamping force, which changes as the part is machined (material removed alters the local stiffness distribution). A spindle speed that avoids chatter during roughing may excite resonances during finishing passes on the same part.
The coupling between spindle speed and surface finish is nonlinear. Below a material-dependent threshold speed, built-up edge formation on the cutting tool degrades surface finish in a way that is insensitive to feed rate adjustments. Above that threshold, the dominant surface finish driver shifts to feed rate and nose radius. The threshold speed depends on the workpiece material, the cutting tool material and coating, and the coolant conditions. A parameter sheet that recommends a fixed spindle speed range for a material class is glossing over this transition behavior.
The practical consequence: a shop that has found workable spindle speeds for 6061 aluminum does not automatically have workable spindle speeds for 7075 aluminum with the same feed rate. The material properties are different enough that the built-up edge threshold moves. Running the 7075 job at the 6061 parameters produces a surface finish problem that looks like a feed rate problem but is actually a spindle speed problem, and the one-at-a-time diagnostic process may chase it in the wrong direction for several iteration cycles.
Coolant as a System Variable, Not a Fixed Input
Coolant conditions are often treated as fixed background variables rather than as parameters in the optimization problem. This is understandable because coolant flow rates and concentrations are harder to vary systematically in a production environment than spindle speed or feed rate. But treating coolant as fixed while optimizing other parameters can produce results that are suboptimal in ways that are not apparent until conditions change.
Coolant concentration affects cutting zone temperature, chip evacuation, and tool wear rate. It couples most strongly to spindle speed (via the thermal effects at the tool-workpiece interface) and to depth of cut (via its effect on chip evacuation in deep cuts or blind bores). A feed rate and spindle speed combination that holds tolerance with 8% coolant concentration may not hold tolerance with the same combination at 5% concentration after a concentration drift event. If the optimization was done with coolant as a fixed variable, the process has an unmodeled sensitivity that only shows up when the coolant supply changes.
This is not a hypothetical scenario. Coolant concentration drift is a common production variability source, and it is one of the reasons that processes that held tolerance during qualification sometimes exhibit unexpected drift in production without any obvious parameter change.
Why Sequential Optimization Fails to Find the Joint Optimum
The mathematical structure of sequential parameter optimization is a coordinate descent on the process response surface: fix all parameters at current values, optimize one, fix it at the new value, move to the next. Coordinate descent converges to the true optimum only when the response surface is separable: when the optimal value of each parameter is independent of all others. For most precision machining operations, the response surface is not separable. It contains interaction terms that make the optimal value of feed rate a function of spindle speed and depth of cut simultaneously.
In those cases, coordinate descent can converge to a local optimum that is noticeably worse than the global optimum. The shop runs a stable process at a set of parameters that satisfy the spec. The process improvement opportunity exists but is invisible because the optimization method used was not capable of finding it.
This is where joint search methods, including Bayesian optimization over the full parameter space, have a structural advantage. The search evaluates combinations of parameters simultaneously. It can discover that a combination of (feed rate A, spindle speed B) is superior to the neighborhood of the individually optimized (feed rate A', spindle speed B') because it captures a favorable interaction term that neither individual optimization step would find.
The Practical Implication for Process Engineering
The takeaway here is not that sequential parameter adjustment is wrong and must be abandoned. For experienced engineers working on familiar material-geometry combinations, sequential adjustment with good intuition about the relevant interactions often produces near-optimal results faster than a formal joint search. The intuition is a compressed representation of the interaction structure, built through years of observing which adjustments help and which cause secondary problems.
The takeaway is that sequential adjustment with good intuition does not generalize. When the engineer leaves, when the material spec changes, when the geometry is novel, or when the tolerance requirement tightens to the point where interaction effects matter, the approach breaks down. The knowledge embedded in the intuition is not accessible without the person who carries it.
Building a systematic record of joint parameter observations, including the ones that did not work and the ones that worked under specific conditions, is what makes the interaction structure explicit enough to transfer. That is the data problem that needs to be solved before the optimization problem can be solved at scale.