Accurate prediction of tool life enables a manufacturer to precisely plan metalworking processes according to tool wear, and thereby control costs while avoiding downtimes due to unexpected tool behaviour or unacceptable workpiece quality. By Patrick de Vos, Corporate Technical Education Manager, Seco Tools.

In a metal cutting operation, a tool deforms workpiece material and causes it to shear away in the form of chips. The deformation process requires a significant amount of force, and the tool endures a variety of mechanical, thermal, chemical and tribological loads. Over a period of time, these loads eventually cause the tool to wear to the point that it must be replaced.

Accordingly, for more than a century, scientists and engineers have created and tested mathematical models that factor in the forces upon a tool to provide estimates of expected tool life. Many of these models focus on a specific tool’s performance in a certain material and operation, and simple formulas and repetitive testing produce valid tool wear projections. However, generalised models that can be applied across a wide range of workpiece materials and tools are more useful in industrial applications. Because these models take into account a variety of tool wear factors, their mathematical complexity increases in accordance with the number of factors considered – the more factors, the more complex the calculation.

While simple tool life equations can be solved via handwritten mathematics and manual calculation, today’s computer-executed analysis is necessary to solve equations of complex models in an amount of time that is practical within a production environment. Digital calculations are very reliable, but manufacturers should maintain a critical attitude towards the results, especially when machining advanced workpiece materials and employing extreme machining parameters. Overall, progress in tool life model development has brought academic theory and practical application into close alignment.

The Archard model

Modelling of wear processes is not limited to metal cutting applications. In the 1950s, British engineer John F Archard developed an empirical model for the rate of abrasive wear between sliding surfaces based on deformation of the asperity, or roughness, of the surfaces.

His equation is: Q= KWL / H.

Here, Q is the wear rate, K is a constant wear coefficient, W is the total normal load, L is the sliding distance of the surfaces, and H is the hardness of the softer of the two surfaces. The model basically states that the volume of material removed due to abrasive wear is proportional to friction forces.

However, the Archard model does not describe tool wear phenomena, but rather predicts the progression rate of wear over time. The model includes the influences of the speed with which the two surfaces interfere with each other, mechanical load, surface strength, material properties and wear coefficient.

Nonetheless, it should be noted that the Archard model was not developed for application at the high speeds common in metalworking, and it does not include the effect of temperature on the wear processes. Both surface strength and wear coefficient will change in response to the 900 deg. Celsius temperatures generated in metal cutting. As result, the Archard model alone does not sufficiently describe tool life in metal cutting.

The Taylor model

In the early 1900s American engineer FW Taylor developed a tool life model that included factors relevant to metal cutting. Taylor observed that increasing depth of cut had minimal effect on tool life. Increasing feed rate had somewhat more effect, while higher cutting speeds influenced tool life the most. This prompted Taylor to develop a model focused on the effect of varying cutting speeds. The equation for Taylor’s basic model is vC * Tm = CT, where vC is cutting speed, T is tool life, and m and CT are constants with CT representing the cutting speed that would result in a tool life of one minute.

Taylor also observed that tool wear typically accelerates at the beginning of an operation, settles into a steady but slower rise in a second phase, and finally enters a third and final phase of rapid wear until the end of tool life. He designed his model to represent the length of time between phases two and three.

As a result, Taylor’s model does not apply at lower cutting speeds in which workpiece material adheres to and builds up on the cutting edge, affecting the quality of the cut and damaging the tool. Also outside the model’s scope are cutting speeds high enough to promote chemical wear. The low- and high-speed wear modes share the characteristics of unpredictability – wear resulting from adhesive or chemical mechanisms can occur either quickly or slowly. The Taylor model is based on the second phase of tool life, namely steady and predictable abrasive wear.

The original Taylor model concentrates on the effects of cutting speed and is valid if depth of cut and feed do not change. After depth of cut and feed are established, speed is manipulated to modify tool life.

Further experiments led to development of an extended Taylor tool life model equation that included more variables and consequently was more complex. The equation also includes a variable that accounts for the rake angle of the tool, as well as constants for various workpiece materials. Despite the additional factors, this model is most accurate when changing one cutting condition at a time. Altering several conditions simultaneously can produce inconsistent results.

Also, the original Taylor model was unable to fully account for the geometric relationship of the cutting tool to the workpiece. A cutting edge can be engaged in a workpiece in an orthogonal orientation (perpendicular to the direction of feed), or obliquely (at a rake angle relative to the feed direction). And, a cutting edge is considered “free” if its corners are not involved in cutting and “non-free” when the tool’s corner is engaged in the workpiece. Free orthogonal or free oblique cuts are rarely present in modern metal cutting, so their relevance is limited. Taylor’s extended equation added a variable for cutting edge rake angle, but no allowance was made for corner engagement of the tool.

The Taylor model has shortcomings when viewed in hindsight from today’s level of metal cutting technology and complexity. However, over its long history the Taylor model has been an excellent basis for tool life predictions and under certain conditions still provides valid tool life data.

Role of chip thickness

As engineers developed and studied tool life models, it became clear that the generated chip thickness is closely related to tool life. Chip thickness is a function of depth of cut and feed measured perpendicular to the cutting edge and in the plane perpendicular to the direction of cutting. If the cutting edge angle is 90 degrees (0 degrees lead angle in the US), depth of cut and chip width are the same, and feed and chip thickness are as well.

The extent that the tool’s corner is engaged in the workpiece adds another variable to determination of chip thickness. A way to account for the involvement of a tool’s nose radius was developed by Swedish engineer Ragnar Woxén in the early 1960s. He provided a formula for equivalent chip thickness in turning operations that calculates theoretical chip thickness along the tool nose. The result essentially straightens out the nose radius and enables the chip area to be described with a rectangle. Use of that description enables a model to reflect the engagement of the tool’s rounded nose.

The Colding model

A tool life model developed by Swedish professor Bertil Colding in the late 1950s describes the relationship between tool life, cutting speed and the equivalent chip thickness as well as incorporates additional factors in the cutting process. These factors include tool material and geometry, temperature and workpiece machinability. This model and the complex equation related to it enables accurate evaluation of the effect of combined changes in multiple cutting conditions.

Colding recognised that changing the equivalent chip thickness (feed rate) changes the relationship between cutting speed and tool life. If equivalent chip thickness increases, cutting speed must be lowered to maintain the same tool life. The more that chip thickness increases, the greater the impact of changing cutting speeds.

On the other hand, if the equivalent chip thickness decreases, tool life increases and the effect of higher cutter speeds decreases as well. Many combinations of feed, depth of cut, lead angle and nose radius can produce the same equivalent chip thickness value. And if a constant equivalent chip thickness is maintained at constant cutting speed, tool life will remain constant as well, despite variations in depth of cut, feed and lead angle.

The Colding model reflects the relationship of changing equivalent chip thickness to tool life and cutting speed when machining within the steady abrasive wear conditions of the Taylor model. However, it also takes into account other wear factors. Estimates derived from these factors are of minimal importance when machining routine materials such as steels that produce steady abrasive wear. However, the model’s projections outside the Taylor range become crucial when working with materials such as superalloys and titanium that have a tendency to strain harden. That is because at low equivalent chip thicknesses, the tool cuts through strain-hardened material, raising cutting temperatures and requiring lower cutting speeds to reduce temperature and maintain tool life.

However, through a portion of the cutting range a combination of greater chip thickness and higher cutting speed, or more productive cutting conditions, will result in longer tool life. When the concept of increasing two cutting parameters and increasing metal removal rate at the same time was introduced in the 1960s and 1970s, it was a breakthrough idea and contrary to then-current experience and intuition.

The development of models that include multiple factors in the metal cutting process, such as the Colding model, in combination with concepts of the Taylor and Archard models, has served to bring theory and reality in line with each other.

Practical application of increasingly complex tool life models requires computer-executed analysis of the multiple factors they employ. Simple models dedicated to a certain tool, workpiece material and cutting conditions can be calculated manually in a short time. The basic Taylor model can provide results relatively quickly when calculated manually, for instance.

Nonetheless, even the extended Taylor model can require extensive time to calculate by hand, and manual calculation of factors in the Colding equation is impractical in a production environment. To take full advantage of these advanced models’ predictive abilities, manufacturers should utilise computerised calculation programs. These programs can resolve complex equations in seconds or less and provide useful machining guidance. However, the electronic calculation aids do not remove a machinist’s responsibility to think critically and compare the results with common sense and experience gained in practical work on the shop floor.

In the end, tool life modelling is not a purely academic pursuit; it exists to enable manufacturers to increase productivity and control costs. The key considerations in manufacturing are how long it will take and how expensive it will be to produce a certain number of acceptable workpieces. It is important to know how long a tool can cut accurately and productively before replacement is necessary. Process reliability and controlling the cost of tools and downtime depend on accurate predictions of tool life. The models also enable processes to be altered to maximise speed, quality or reliability. The further development of cutting tool life models will continue to enable manufacturers to fine-tune their processes and meet their production goals.