An Investigation on Speed Control of a Spindle Cluster Driven by Hydraulic Motor: Application to Metal Cutting Machines

Table 1

System parameters.

Symbol	Specifications of the (ATACOHS)
	Description	Source of Information	Unit	Value
	Motor displacement	Manufacturer data	m^3/rad	1210^−6
	Total fluid volume in pipes	Calculated	m^3	20.510^−5
	Hydraulic bulk modulus	Manufacturer data	N/m^2	1410^8
	Leakage coefficient of motor	Calculated experimentally	m^5/Ns	2.510^−11
	Stiffness of the V-belt	Calculated experimentally	N/m	20
	Radius of driven pulley	Manufacturer data	m	0.09
	Radius of drive pulley	Manufacturer data	m	0.09
	Inertia of load	Calculated	Nms^2/rad	4510^−3
	Inertia of motor	Calculated	Nms^2/rad	3.510^−3
	Tension on the belt	Calculated	N	-
	Input and output flow rate of the hydraulic motor	From experimental	m^3/s	-
	Supply pressure	From experimental	N/m^2	4910^5
	Current of proportional vales (maximum)	Manufacturer; data	mA	100
	Rotor speed	experimentally	rpm	-
	Working shaft speed	experimentally	rpm	-
	Valve flow gain	Manufacturer; data	(m^3/s)/mA	11.510^−3
	Rotation angle of rotor	Manufacturer data	rad	-
	Rotation angle of working shaft	Manufacturer data	rad	-
	Tachogenerat; or gain	Calculated; experimentally	V/rpm	0.0167
	Control voltage	Manufacturer data	vDC	0÷±10
	Valve control voltage	Manufacturer data	vDC	0÷±24
	equivalent viscous coefficient of motor	Calculated; experimentally	Nms/rad	29.510^−4
	Friction coefficient of working shaft	Calculated; experimentally	Nms/rad	0.118
	Load on working shaft	Calculated; experimentally	Nm	-