# Grinding Parameters

**DOI:**https://doi.org/10.1007/978-3-642-35950-7_6424-4

## Synonyms

## Definition

For grinding processes the actuated variables (e.g., cutting speed, feed velocity) and the system variables (e.g., grinding tool properties) have to be distinguished from the grinding parameters. The grinding parameters depend on the actuated and system variables and allow a good correlation to the process forces, process temperatures, surface roughness, and grinding tool wear. The most important grinding parameters, that are described here, are the material removal rate Q_{w}, the material removal rate per unit active grinding wheel width Q′_{w}, the geometrical contact length l_{g}, the kinematic contact length l_{k}, the equivalent chip thickness h_{eq}, and the medium single-grain chip thickness h_{cu}.

## Theory and Application

### Introduction

The grinding process is a geometrically undefined cutting process due to the undefined number and geometry of cutting edges interacting with the workpiece. The load on the workpiece as well as the load on the grinding wheel is a result of the programmed actuated variables, the cutting tool properties, and the workpiece properties. Due to the complex interrelationships in the grinding process, the parameters have been defined to describe the process behavior. These parameters are described in the following entry (see also standard ISO 3002–5 1989).

### Process Parameters

_{c}, the feed velocity v

_{f}, the depth of cut a

_{e}, and the width of cut a

_{p}(see Fig. 1, see also Denkena and Tönshoff 2011). The cutting speed is in general equal to the circumferential speed of the grinding wheel. The feed velocity is oriented in feed direction. The feed direction in grinding processes can be oriented in tangential or axial to the grinding wheel. For this reason, the tangential feed velocity v

_{ft}and the axial feed velocity v

_{fa}have been defined. In cylindrical grinding, the feed velocity can also be oriented radial to the grinding wheel. In this case, the radial feed velocity v

_{fr}is defined. Depending on the grinding process, also the workpiece can have an actuating velocity which is not in every case equal to the feed direction. This velocity is then called the workpiece velocity v

_{w}. The depth of cut a

_{e}is the engagement of the grinding wheel in radial direction, while the width of cut a

_{p}is the engagement of the grinding wheel in axial direction. For this reason, the depth of cut a

_{e}is also known as the working engagement, and the width of cut a

_{p}is known as back engagement (Fig. 2).

Further parameters relevant for grinding processes are the width of the grinding wheel b_{s}, the width of the workpiece b_{w}, and the diameter of the grinding wheel d_{s} as well as for cylindrical grinding the diameter of the workpiece d_{w}.

### Productivity

_{w}(Saljé 1991). The material removal rate is a result of the process actuated values working engagement a

_{e}, feed velocity v

_{f}, and back engagement a

_{p}and can be calculated for peripheral grinding by (see Fig. 1)

In general, the material removal rate can be calculated by the actuating cross section A_{w}, which is the cross section between tool and workpiece orthogonal to the feed direction. A general overview on the process parameters and the calculation of the material removal rate for these processes is given in Fig. 1.

_{w}:

### Geometrical and Kinematic Engagement Conditions

_{con}which can be determined by the geometrical contact length l

_{g}and the back engagement a

_{p}. The geometrical contact length l

_{g}is shown in Fig. 1 and depends on the grinding wheel radius r

_{s}and the working engagement a

_{e}:

_{k}considers the feed and cutting speed for ideal even surfaces. It can be calculated by (see Fig. 3).

(+ down grinding, − up grinding)

while the parameter q is the speed ratio v_{c}/v_{ft}.

_{w}has to be the same as the material volume which is removed per time unit by the cutting speed and the engagement of the single grains. The produced volume flow is known as the internal material removal rate Q

_{wi}. According to Kurrein (1927) the internal material removal rate can be calculated by

_{eq}is the equivalent chip thickness which can then be calculated by (Fig. 4)

Kurrein also defined the external material removal rate Q_{wa}, which can be calculated equal to the material removal rate Q_{w} (Kurrein 1927).

_{c}. The equivalent chip thickness is a mathematical value and is not equal to the removed material per grain (Denkena and Tönshoff 2011). For the determination of the medium single-grain chip thickness, the number of grains in the contact zone N

_{A}has to be known (Reichenbach et al. 1956). The number of grains in the contact zone N

_{A}depends on the grain size and the grain concentration. For the same grain concentration, an increased grain size results to a decreased number of grains in the contact zone. When N

_{A}is determined by counting the grains via a view on the grinding wheel surface, the following presumptions have to be considered:

Every grain is cutting actively.

Every grain has the same protrusion height.

Elastic and plastic deformations are not considered.

The path overlap is not considered.

Lambda is a factor that describes the shape of the grains.

The number of active grains in the contact area N_{A} depends on the geometric contact area as well as the grain size and the grain concentration in the grinding wheel. This means that the medium chip thickness per grain depends on the grinding wheel properties as well as the actuated values. The medium grain chip thickness can be increased by increasing the feed rate, the working engagement, the grain size, and the grinding wheel radius or by decreasing the cutting speed and the grain concentration in the grinding wheel. Several results show that the values contact length as well as medium grain chip thickness show a good correlation to the process results tool wear and workpiece properties (Brinksmeier 1991; Lierse 1998). An increasing contact length leads to higher temperatures in the contact zone and though to a higher tendency toward grinding burn. A higher medium grain chip thickness leads to a higher mechanical load on the grains and though to a higher tendency toward grain breakout and to higher wear rate. Furthermore, a higher medium grain chip thickness results in a higher workpiece roughness. With this knowledge, the grinding process can be optimized regarding tool wear, workpiece properties, and productivity.

## Cross-References

## References

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