Grinding power and torque requirement

One of the first steps that have to be taken in the design procedure of the cylindrical grinding machine is the calculation of power required for a certain metal removal rate.

This has to be determined to choose the right motor for driving the spindle. Grinding data are seldom available in handbooks, which usually recommend a small range of depth, and work speeds at constant grinding wheel speed.

The determination of the amount of the available spindle power that can be utilized for chip removal under no chatter conditions at any given spindle speed is of great signifi-cant. The objective of this section is to predict the dynamic behavior of the spindle and multiple natural frequencies.

The grinding specific energy can be chosen according to the requirements for a specific grinding scenario. The movement of the grinding wheel is designed in such a way that provides grinding capability for cylindrical surfaces and planes perpendicular to the center line of the workpiece.

Grinding wheels vary enormously in design based on the application they are used. A grinding wheel is bonded and designed according to the particular process requirement.

A general-purpose wheel will give greatly inferior removal rates and economics com-pared to an optimized and appropriate wheel for the particular product. However, wheel selection and optimization can be critical for large-scale production in aerospace and automotive industry. A larger diameter of the grinding wheel results in a longer wheel life, and moreover it eases the problem coupled with small diameters at high speeds which raise the risk of grinding wheel explosion.

The grinding wheel used in the presented test rig has a thickness of 25𝑚𝑚, hole size of 51 𝑚𝑚 and the outer diameter of 200𝑚𝑚 with electro bonded aluminum oxide in ce-ramic bonding and hardness grade of M. Based on the dimension of the grinding wheel and the workpiece the power and speed requirement is initially calculated for a direct drive.

Recommended grinding parameters are summarized in Table 2.1, and 2.2 for optimal selection of the grinding wheel, and workpiece speed, depth of cut, grit size, and specif-ic material removal rate.

In the tables below parameter 𝑞 denotes the fraction of the circumferential velocity of the grinding wheel to the workpiece, 𝑢_𝑤 is the circumferential speed of the workpiece in 𝑚/𝑚𝑖𝑛, and finally 𝑢_𝑠 is the circumferential speed of the grinding wheel in 𝑚/𝑠. The width of the grinding wheel is represented by 𝑏 in 𝑚𝑚. Parameter 𝑎 shows the depth of cut in 𝜇𝑚 and 𝑠 states the longitudinal feed of the workpiece in 𝑚𝑚/𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛.

Table 2.1 Standard values for grinding [6]

Grinding Steel, soft

III Surface grinding with the wheel circumference IV Surface grinding with the grinding face

Table 2.2 Depth of cut and feeds in grinding [6]

Grinding method Rough grinding cut Finish grinding

Depth of cut 𝑎 (µm) 20 … 50 2,5 …10

Longitudinal feed 𝑠 (mm/rev) (2/3 … 4/5)·b (1/4 … 1/2)·b

The recommended grinding wheel speed normally has a range between

Based on the fraction value 𝑞 and the maximum grinding wheel circumferential speed of 25 𝑚/𝑠 the workpiece circumferential speed is determined as

𝑢_𝑤 = 12 𝑚/𝑚𝑖𝑛 (2.2) 5 20

4 

 b

s mm/rev (2.3)

The grinding force for an external cylindrical grinding scenario with hard steel based on the values of the Tables 2.1, and 2.2 and the determined values is calculated as follow-ing in 𝑚𝑚. The maximum depth of cut of 50 µ𝑚 is chosen in the calculation of the cutting force to estimate the force for rough grinding case. By taking this value as the maxi-mum depth of cut the resulting maximaxi-mum power can be determined as

9

Where P_m is the maximum power, 𝜂 demonstrates the efficiency of the grinding spindle including the transmission element (belt). The standard transmission factor used for the belt driven spindle is 0.8. For the rotational speed of the grinding wheel we have

1000 2387

The driving motor torque at 100% load is calculated as follow

The motor that has been chosen to run the spindle is a K21 R 63 G2 three phase motor with squirrel cage rotor from VEM Company. The speed variation of the motor is car-ried out using a MI1 Vacon variable frequency drive.

The variable frequency drive alternating current is fed to the motor at a frequency and voltage required to produce the desired motor speed, and a 50 𝐻𝑧 frequency produces 100% of the motor speed.

2.1.1 Power transmission

A belt-driven Spindle is quite similar in design to a conventional direct driven spindle, with some noticeable differences. A typical belt driven spindle assembly consists of the spindle shaft, held with a bearing support system. The mechanism that provides the force to run the grinding spindle is usually externally mounted. This means the power and rotation are supplied to this spindle by an external motor. The motor is mounted adjacent to the spindle, and the torque is transmitted to the spindle shaft by means of a cogged or v-belt. The power, torque and speed of the spindle will therefore depend upon the characteristics of the driving motor, and the belt ratio used between the motor and the spindle. The application of belt drive for the spindle makes it possible to have pow-er, torque and speeds which are dependent upon the driving motor final specifications that can be modified based on the application by choosing a different motor or belt ra-tio. In this case high power and torques are possible to be applied since the driving mo-tor is mounted externally to the spindle shaft. Therefore, it is often possible to use a very large motor for running the spindle. However, the application of belt driven spindle limits the maximum speed since it generates excessive vibration.

A v-belt drive is a non-synchronous drive that offers a very smooth rotating action with minimum vibration, and is suited for applications such as grinding or finish, and boring.

A v-belt type drive for the spindle is designed to drive the grinding wheel. The driving pulley (SPZ 60) has an outer diameter of 60 𝑚𝑚 and the driven pulley (SPZ 562) on the spindle has an outer diameter of 110 𝑚𝑚 and with taper lock bushing on the shaft. So the transmission ratio of the belt drive is 0.545. Based on the maximum output speed of the motor 3100 𝑟𝑝𝑚 the spindle can achieve the speeds up to 1690 𝑟𝑝𝑚, which results in maximum circumferential speed of about 18 𝑚/𝑠 for the grinding wheel.

The center distance between pulleys is 𝑐 = 100 𝑚𝑚. For the calculation of the contact angles we have

) 2.4619

arcsin( 2