Chapter 1 Introduction
1.6 Problem-Solving
1.6.2 Part II
The 8 chapters in Part II explore applications of grinding. Part II covers grinding of conventional ductile materials, grinding of brittle-hard materials, grinding machine technology and rotary dress-ers, surface grinding, external cylindrical grinding, internal cylindrical grinding, centerless grinding, and ultrasonically assisted grinding. A particular emphasis is placed on developments in technology that can lead to improved part quality, higher productivity, and lower costs.
The authors draw on industrial and research experience, and give numerous references to scientific publications and trade brochures where appropriate. Readers will find the references to the various manufacturers of machine tools, auxiliary equipment, and abrasives a useful starting point for sourcing suppliers. The references to scientific publications provide an indication of the wide scope of research and development in this field around the world.
REFERENCES
Alden, G. I. 1914. “Operation of Grinding Wheels in Machine Grinding.” Trans. Am. Soc. Mech. Eng. 36, 451–460.
CIRP (International Institution for Production Engineering). 2005. Dictionary of Production Engineering II—Material Removal Processes, Springer, New York.
De Beers Industrial Diamond Division, 1983. “Abrasive Boron Nitride—The Family of Choice,” Cooley, B.A.
and Juchem, H.O., Diamond and CBN Grit Products, De Beers, UK.
DES (Jost) Report. 1966. “Lubrication (Tribology) Education and Research.” Her Majesty’s Stationery Office, London.
Guest, J. J. 1915. Grinding Machinery. Edward Arnold, London.
Marinescu, I. D., Rowe, W. B., Dimitrov, B., and Inasaki, I. 2004. Tribology of Abrasive Machining Processes.
William Andrew Publishing, Norwich, NY.
Rowe, W. B., Li, Y., Inasaki, I., and Malkin, S. 1994. “Applications of Artificial Intelligence in Grinding.”
Ann. Int. Inst. Prod. Eng. Res. Keynote Paper 43, 2, 521–532.
Rowe, W. B., Statham, C., Liverton, J., and Moruzzi, J. 1999. “An Open CNC Interface for Grinding Machines.”
Int. J. Manuf. Sci. Tech. 1, 1, 17–23.
Woodbury, R. S. 1959. History of the Grinding Machine. The Technology Press, MIT, Cambridge, MA.
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2 Grinding Parameters
2.1 INTRODUCTION
Grinding, in comparison to turning or milling, is often considered somewhat of a “black art” where wheel life and cycle times cannot be determined from standard tables and charts. Certainly precision grinding, being a finishing process with chip formation at submicron dimensions occurring by extru-sion created at cutting edges with extreme negative rake angles, is prone to process variability such as chatter, system instability, coolant inconsistency, etc. Nevertheless, with grinding equipment in a competent state of repair, performance can be controlled and predicted within an acceptable range.
Importantly, rules and guidelines are readily available to the end user to modify a process to allow for system changes. It is also essential to ensure surface quality of the parts produced. These objectives are balanced through an analysis of costs as described in subsequent chapters on economics and on centerless grinding. The importance of the grinding parameters presented below is to provide an understanding of how process adjustments change wheel performance, cycle time, and part quality.
Probably the best way for an end user to ensure a reliable and predictable process is to develop it with the machine tool builder, wheel maker, and other tooling suppliers at the time of the machine purchase using actual production parts. This then combines the best of the benefits from controlled laboratory testing with real components without production pressures, resulting in a baseline against which all future development work or process deterioration can be monitored.
The number of grinding parameters that an end user needs to understand is actually quite limited. The key factors are generally associated with either wheel life, cycle time, or part quality.
The purpose of this discussion is to define various parameters that relate to wheel life, cycle time, and part quality and to demonstrate how these parameters may be used to understand and improve the grinding process. In most cases, the author has avoided the derivations of the formulae, providing instead the final equation. Derivations and more detailed discussion can be found in publications such as Marinescu et al. [2004] or Malkin [1989].
2.1.1 WHEEL LIFE
The statement that a process can be controlled “within an acceptable range” requires some definition.
A recent study by Hitchiner and McSpadden (2005) investigated the process variability of various vitrified cubic boron nitride (CBN) processes as part of a larger program to develop improved wheel technology. They showed that under “ideal” conditions repeatability of wheel life within ±15% or better could be achieved. However, variability associated with just wheel grade from one wheel to another (±1% porosity), all within the standard limits of a commercial specification, made the process less repeatable and increased the variability to ±25%. In the field, for example, in a high-production internal-grinding operation with 20 machines, the average monthly wheel life was tightly maintained within ±5%. However, these average values obscured an actual individual wheel life variability of
±100%! Of these, wheels with very low or zero life were associated with setup problems while the large variability at the high end of wheel life was associated with machine-to-machine variables such as coolant pressure, spindle condition, or gauging errors. A process apparently in control based on monthly usage numbers was actually quite the opposite (Figure 2.1 and Figure 2.2).
Wheel makers and machine tool builders are usually in the best position to make predictions as to wheel performance. Predictions are based on either laboratory tests or past experience on comparable applications. Laboratory tests tend to reproduce ideal conditions but can make little
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10 Handbook of Machining with Grinding Wheels
allowance for a deficiency in fixturing or coolant, etc. In fact, the author witnessed a situation where the laboratory results and the actual field wheel life differed by a factor of 40. The loss of wheel life in the field was caused by vibration from poor part clamping and wheel bond erosion from excessively high coolant pressure. Laboratory data were able to inform the end user that there was a major problem and provide evidence to search for the solution.
2.1.2 REDRESS LIFE
In practice, the end user seeks to reduce cycle time for part production as a route to reducing costs and increasing production throughput. The number of parts produced per dress is critical for economic production [Rowe, Ebbrell, and Morgan 2004]. For parts produced in large batches, redress life can be given as the number of parts per dress . If redress has to take place for every part produced, the cost of grinding is greatly increased. Long redress life depends on having the correct grinding wheel for the grinding conditions and also on the dressing process. Dressing parameters are discussed further in the chapter on dressing.
2.1.3 CYCLE TIME
Cycle time is usually defined as the average total time to grind a part. For a batch of parts produced in a total time , the cycle time is
FIGURE 2.1 Monthly average wheel life values for high-production internal grinding operation.
FIGURE 2.2 Individual wheel life values over same period as Figure 2.1.
100.000
50.000
0
Monthly wheel life average values
Wheel life
nd
nb tb
t t
c n
b
b
=
150.000
100.000
Wheel life
50.000
0
Individual wheel life values by month DK4115_C002.fm Page 10 Thursday, November 9, 2006 5:14 PM
Grinding Parameters 11 The cycle time, therefore, depends on the dressing time, as well as the grinding time, and the loading and unloading time.
2.2 PROCESS PARAMETERS
2.2.1 UNCUT CHIP THICKNESS OR GRAIN PENETRATION DEPTH
The starting point for any discussion on grinding parameters is “uncut chip thickness,” , as this provides the basis for predictions of roughness, power, and wear [Shaw 1996]. Uncut chip calculations are typically based on representations of the material removed in the grind process as a long, slender, triangular shape with a mean thickness, . However, a more practical way of looking at this parameter is to think of as representing the depth of abrasive grit penetration into the work material. In fact, this parameter is often termed the grain penetration depth. The magnitude of may be calculated from the various standard parameters for grinding and the surface morphology of the wheel.
where = wheel speed, = work speed, = depth of cut, = equivalent wheel diameter, C= active grit density, and r= grit cutting point shape factor.
Other useful measures of grain penetration include equivalent chip thickness . However, equivalent chip thickness takes no account of the spacing of the grains in the wheel surface.
2.2.2 WHEEL SPEED
Wheel speed, , is given in either meters/second (m/s) or surface feet per minute (sfpm). To convert the former to the latter, use a rule of thumb multiplication factor of approximately 200 (or 196.85 to be precise).
2.2.3 WORK SPEED
Work speed, , is a term most typically applied to cylindrical grinding; equivalent terms for surface grinding are either traverse speed or table speed.
2.2.4 DEPTH OF CUT
Depth of cut, , is the depth of work material removed per revolution or table pass.
2.2.5 EQUIVALENT WHEEL DIAMETER
Equivalent wheel diameter, , is a parameter that takes into account the conformity of the wheel and the workpiece in cylindrical grinding and gives the equivalent wheel diameter for the same contact length in a surface grinding application (i.e., as ). The plus sign is for external cylindrical grinding, while the negative sign is for internal cylindrical grinding.
= workpiece part diameter
= wheel diameter
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12 Handbook of Machining with Grinding Wheels
2.2.6 ACTIVE GRIT DENSITY
Active grit density, C, is the number of active cutting points per unit area on the wheel surface.
2.2.7 GRIT SHAPE FACTOR
Grit shape factor, r, is the ratio of chip width to chip thickness. In most discussions of precision grinding, the product C⋅r is considered as a single factor that can be somewhat affected by dress conditions; but under stable grinding conditions, that is, with a fixed or limited range of dress conditions, can be considered as a constant for a given wheel specification.
There are several key parameters that research has shown to be directly dependent on :
2.2.8 FORCE PER GRIT
Grit retention is directly related to the forces experienced by the grit and these forces increase with uncut chip thickness. It can be seen that for a constant stock removal rate ( ) forces are lower at large depth of cut and low table speed. Hence, a softer grade might be used for creep feed rather than for reciprocated surface grinding. A softer grade has a better self-sharpening action and reduces grinding forces.
Wheel wear can accelerate as a wheel diameter gets smaller and force/grit increases.
2.2.9 SPECIFIC GRINDING ENERGY
Specific grinding energy, (or u in older publications), is the energy that must be expended to remove a unit volume of workpiece material. The units are usually J/mm3 or in.lb/in.3; conversion from metric to English requires a multiplication factor of 1.45 × 105. Analysis of the energy to create chips leads to the following relationship between and :
where n= 1 for precision grinding. The relationship is logical insofar as it takes more energy to make smaller chips, but is valid only so long as chip formation is the dominant source. In general terms, for precision grinding of hardened steel, the surface roughness will follow a trend rather like that shown in Figure 2.3 as a function of specific energy (see below).
Hahn [1962] and Malkin [1989] show that in many cases, especially in fine grinding or low metal removal rates, significant energy is consumed by rubbing and ploughing. Under these cir-cumstances specific energy, , varies with removal rate, , as illustrated in Figure 2.3.
2.2.10 SPECIFIC REMOVAL RATE
Specific removal rate, or , is defined as the metal removal rate of the workpiece per unit width of wheel contact, . The units are either mm3/mm/s or in.3/in./min. To convert from the former to the latter requires a rule of thumb multiplication factor of approximately 0.1 (or 0.1075 to be precise).
For very low values of Q′, rubbing and ploughing dominate, but as Q′ increases so does the proportion of energy consumed in chip formation. More to the point, the energy consumed by rubbing and ploughing remains constant, thereby becoming a smaller proportion of the total energy
hcu
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Grinding Parameters 13
consumed as stock removal rates increase. Precision grinding for the steels illustrated in Figure 2.4 gives specific energy values of 60–30 J/mm3, of which about 20 J/mm3 is associated with chip formation.
Chip formation dominates in high removal-rate precision applications such as camlobe grinding or peel grinding with vitrified CBN or rough grinding with plated CBN. Under these circumstances
is a good predictor of performance.
2.2.11 GRINDING POWER
Grinding power, P, can be estimated from the specific grinding energy, , using the equation
where is the width of grind.
FIGURE 2.3 Example of the relationship between surface roughness and specific grinding energy for a fixed Q′.
FIGURE 2.4 Examples of specific grinding energy U′ trends versus stock removal rate Q′. 2
1.5
Surface finish (µm Ra)
1
0.5
0 20 40 60
Specific grinding energy U’ (J/mm3)
80 100
ec∝h1cu
ec
P= ⋅ ′ ⋅ec Q bw bw
Vitrified CBN/chilled cast iron high speed camlobe grinding
Alox/hardened carbon steel general precision grind
Plated CBN/soft steel high speed roughing
0 0 20 40 60 80
Specific grinding energy U’ (J/mm3)
100 120
50 100 150
Stock removal rate Q’ (mm3/mm/s) DK4115_C002.fm Page 13 Thursday, November 9, 2006 5:14 PM
14 Handbook of Machining with Grinding Wheels
2.2.12 TANGENTIAL GRINDING FORCE
Tangential grinding force, Ft, may then be calculated from
2.2.13 NORMAL GRINDING FORCE
Normal grinding force, Fn, is related to the tangential grinding force by the coefficient of grinding, a parameter defined in a similar way to friction coefficient.
2.2.14 COEFFICIENTOF GRINDING
Coefficient of grinding is µ, where
The value for µ can vary from as little as 0.2 for low stock removal applications for grinding hard steels and ceramics to as high as 0.8 in very high stock removal applications such as peel grinding, or grinding soft steels or gray cast iron. Coolant can also have a major impact on the value as a result of the hydrodynamic pressure created by high wheel speeds. The effect is particularly noticeable with high-viscosity straight oils. Typical precision-grinding applications on steels have values of µ in the range of 0.25–0.5.
Since tangential force can be readily calculated from power but not from normal force, knowledge of µ is particularly useful to calculate required system stiffness, work holding requirements, chuck stiffness, etc. Figure 2.5 plots general values for µ as a function of material classes and hardness. For most precision production grinding processes with hardened steel or cast iron it can be seen that µ tends to a value of about 0.3. Note, however, that these numbers are for flat profile wheels in a straight plunge mode. If a profile is added to a wheel or the angle of approach is changed from 90°, then allowance must be made for increased normal forces and for side forces.
FIGURE 2.5 µ(Ft/Fn) for major material types in precision grinding.
F P DK4115_C002.fm Page 14 Thursday, November 9, 2006 5:14 PM
Grinding Parameters 15
2.2.15 SURFACE ROUGHNESS
Surface roughness, not surprisingly, is closely related to uncut chip thickness.
2.2.16 RT ROUGHNESS
Rt roughness is the SI parameter for maximum surface roughness, the maximum difference between peak height and valley depth within the sampling length. As a first approximation, Rt is independent of depth of cut but is dependent on , , , and . The relationship between surface roughness and specific grinding energy can also be readily obtained by direct substitution.
Rt is but one of several measures of surface roughness. Two other common roughness standards are Ra roughness and Rz roughness.
2.2.17 RA ROUGHNESS
Ra roughness is the arithmetic average of all profile ordinates from a mean line within a sampling length after filtering out form deviations.
2.2.18 RZ ROUGHNESS
Rz roughness is the arithmetic average of maximum peak-to-valley readings over five adjacent individual samplings lengths. Rt and Rz values are much larger than Ra roughness values for mea-surements from the same surface.
Two other parameters related to surfaces, especially those used for rubbing contact, are defined as follows:
2.2.19 MATERIAL OR BEARING RATIO
Material or bearing ratio, tp, is the proportion of bearing surface at a depth p below the highest peak.
2.2.20 PEAK COUNT
Peak count, Pc, is the number of local peaks that project through a given band height. tp is less for grinding than for other operations such as honing, although it can be improved to some extent by a two-stage rough-and-finish grind with wheels of very different grit size. Pc can be controlled somewhat by adjusting dress parameters.
2.2.21 COMPARISON OF ROUGHNESS CLASSES
Comparison of various international surface roughness systems is given in Table 2.1.
2.2.22 FACTORS THAT AFFECT ROUGHNESS MEASUREMENTS
Relative values between different roughness systems will vary by up to 20% depending on the metal-cutting process by which they were generated. Even when considering just grinding, the abrasive type can alter the ratio of Rz to Ra, CBN often giving a higher ratio to alumina. This
R h
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16 Handbook of Machining with Grinding Wheels
difference also shows up cosmetically when looking visually at surfaces ground with alumina or CBN. When changing from lapping to fine grinding, the change in appearance of the finish can be dramatic, changing from a matt-pitted surface to a shiny but scratched surface, both of which have comparable surface roughness values. The type of grinding process will also affect the appearance in terms of the grind line pattern. For example, in face grinding of a shoulder using, for example, a 2A2 or 6A2 wheel, the grind gives a cross-hatch appearance as in Figure 2.6(a). In angle approach grinding, the face is produced with line contact and the lines are concentric with the journal diameter as in Figure 2.6(b).
2.2.23 ROUGHNESS SPECIFICATIONS ON DRAWINGS
Common roughness specifications (marks) on part drawings are shown in Figure 2.7. This gives both the current standard practice, especially in Europe, and the older machining marks still seen
TABLE 2.1
Guideline Comparisons of International Surface Finish Systems
Ra Rt Rz RMS CLA PVA
FIGURE 2.6 Comparison of grind pattern from (a) face and (b) angle approach line contact grinding.
Cross-hatch grind pattern from a face grind operation, e.g., shoulder
kiss or double disc grind
Concentric rings grind pattern from a plunge or angle approach shoulder
grind with line contact
(a) (b)
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Grinding Parameters 17
especially on Japanese drawings. One (∇) or two (∇) marks are indicative of a turning or milling operation, but three (∇) or four (∇) marks are indicative of the requirement to grind or even lap.
Two other force-related factors are of particular interest to end users with low stiffness systems such as internal grinding. The first is stock removal parameter Λ.
2.2.24 STOCK REMOVAL PARAMETER
Λ is defined as the ratio between stock removal rate and normal force:
Λ is an indicator of the sharpness of the wheel, but is limited by the fact that it must be defined for each wheel speed and removal rate. The second factor is decay constant τ.
2.2.25 DECAY CONSTANT τ
When the infeed reaches its final feed point, the grinding force F will change with time t as the system relaxes according to the equation
Ft and power are directly related; therefore τ can be determined from a log plot of the decay in power during spark-out. After 3τ virtually all grinding has ceased, preventing any improvement in part tolerance, while roughness, as shown above, will not improve further. Consequently, spark-out times in internal grinding should be limited to no more than 3τ.
2.2.26 G-RATIO
G-ratio is used as the primary measure of wheel wear. This is defined as G-ratio = Volume of material ground per unit wheel width
Volume of wheel worn per unit wheel width FIGURE 2.7 Print markings for surface finish.
Symbol for machining
Surface designated
Machining marks approximate values (common on Japanese prints)
Other designated roughness values
∇ ∇
∇ ∇ ∇
∇ ∇ ∇ ∇
∇ 25 Ra (µm) 3.2 Ra (µm) 0.8 Ra (µm)
≤0.16 Ra (µm)
Machining process Ground
0.25 Roughness Ra (µm)
R2 1.6 Part print finish markings
Λ = ′Q Fn
F=F e0 −t/τ
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18 Handbook of Machining with Grinding Wheels G-ratio is dimensionless with values that can vary from <1 for some soft alox creep feed vitrified wheels
18 Handbook of Machining with Grinding Wheels G-ratio is dimensionless with values that can vary from <1 for some soft alox creep feed vitrified wheels